Keywords: Escherichia coli, Cybergenetics, Microfluidics, Control theory, Machine learning, Synthetic biology, Systems biology, Image analysis

Recent progresses in microfluidics, synthetic biology, and microscopy automation now make it possible to control gene expression externally and in real time. Among the challenges facing the field of external real-time control of gene expression is the control of intricate, multistable gene regulation networks as well as the control of several target genes at the same time. To advance the domain in this direction we studied the controllability of a simple bistable twogenes network, the so-called genetic toggle switch, in the vicinity of its unstable equilibrium point for extended periods of time.

Throughout this document, we present the development of a custom control platform for external control of gene expression at the single-cell level as well as a bacterial cellular chassis and a library of toggle switch genetic circuits for us to control. We use the platform to drive and maintain our genetic system in its region of unstability with both closed-loop and open-loop strategies. Not only do we demonstrate that in silico control platforms can control genetic systems in out-of-equilibrium states, we also notably maintain a population of cells in their unstable area with open-loop periodic stimulations. These results suggest the possible emergence of different regimes of stability in gene regulation networks submitted to fluctuating environments, and can potential insights in the study of cellular decision making.

We also introduce a new approach for microscopy image analysis which exploits information hidden in several focal planes around the specimen instead of using only a single-plane image. The objective of this method is to automatically label different parts of an image with machine learning techniques inspired by hyperspectral imaging. The method is then shown to facilitate segmentation and be easily adaptable to various different organisms.

I would like to thank all the interns who worked with me throughout this PhD. First of all, Agnes Köhler, Melanie Kirch, Catherine Eisenhauer and Jean-Baptiste Caron worked with me in close collaboration on the genetic control project presented here, and I benefitted greatly from their fresh views on the project. I would also like to thank Pierre Ivanovitch who worked with me on the image analysis method presented in this thesis and accomplished a formidable amount of work. I also collaborated with Rémi Sieskind, Amaury Monmeyran and Théo Maire who worked on a number of exciting side-projects.

I would of course like to thank all the members of the team and of the entire laboratory Matière et Systèmes Complexes for their help and all the fruitful exchanges we had, but also for the wonderful atmosphere in which I did my PhD. I would like to thank specifically Jannis Uhlendorf, Clément Vulin and Xavier Duportet for being excellent teachers, Zacchari Ben Meriem, Chiara Fracassi, Adrien Hallou, Fabien Furfaro, Max Piffoux and Marguerite Benony for their stimulating collaboration on a number of side-projects, and finally other members of the laboratory Artémis Llamosi, Zoran Marinković, Raphaël Ponthieu, Sara Bonavia, Adrien Marck and David Pereira for their support, both scientific and personal. Also a special thank you to Stéphane Pinhal and Antoine Decrulles who, while not being part of the lab, helped me get started with molecular biology and gave me excellent advice. I greatly benefitted from the help, skills, and knowledge of technicians and engineers in the department, Carine Vias, Arnaud Grados, Laurent Réa, Matthieu Receveur, and Stéphan Suffit. Thank you also to Kévin Lhoste and Vladimir Hermand at the hackerspace and fab-lab l'Openlab. I am very grateful for the exchange and collaborations I could have with other permanent researchers in the laboratory, namely Gaëlle Charron, Benoit Sorre and Jean-Marc di Meglio.

xi

Re sume

Les progrès récents de la microfluidique, la biologie synthétique, la microscopie automatisée rendent aujourd'hui possible le contrôle externe de l'expression des gènes en temps réel. Parmi les défis que devra relever le domaine du contrôle externe et temps-réel de l'expression des gènes se trouve la possibilité de contrôler des réseaux de régulation génique aux dynamiques complexes et multi-stables, et le contrôle de multiple gènes en parallèle. Pour faire avancer le domaine dans cette direction nous avons étudié la contrôlabilité d'un réseau bistable composé de deux gènes, appelé genetic toggle switch, ou bascule génétique, autour de son point d'équilibre instable sur de longues périodes.

Dans ce document, nous présentons la mise en place d'une plateforme de contrôle externe de l'expression des gènes en cellule unique, ainsi que le développement d'un châssis cellulaire bactérien et d'une librairie de circuits de bascules génétique à contrôler. Le travail de développement technologique est présenté dans un premier temps : Une nouvelle implémentation en parallèle du système de microfluidique connu sous le nom de "mother machine' y est présenté ainsi que le développement d'une solution de mélange d'inducteurs chimiques basée sur des valves interconnectées commandées en modulation de largeur d'impulsion sont présenté ainsi que des tests de validation. Le développement technique de l'automatisation de la plateforme de microscopie-microfluidique, notamment informatique, ainsi qu'une brève présentation de la stratégie d'analyse d'image en temps réel impliquée, sont discutés. La construction d'une librairie de toggle switch bistables basés sur la double répression LacI-TetR et différents par leurs force de liaison ribosomales est également détaillée ainsi qu'un nombre d'innovations techniques, nécessaires à cette fin, de la technique de clonage "MoClo'. Enfin, la caractérisation du système ainsi que le développement d'un modèle quantitatif, à la fois déterministe et stochastique, sont présentés afin de pouvoir à la fois estimer la position du point d'équilibre instable de notre toggle switch, et prédire la faisabilité de notre objectif de contrôler le toggle switch génétique autour de son point d'équilibre instable.

xii Une fois opérationnelle, nous utilisons la plateforme pour diriger et maintenir notre système génétique dans sa région d'instabilité avec des techniques de stabilisation à la fois en boucle ouverte et en boucle fermée. Dans un premier temps, une seule cellule est contrôlée et est entraînée vers le point d'équilibre instable du toggle switch, grâce à l'utilisation d'un contrôleur proportionnel-intégral. En augmentant le gain proportionnel de ce contrôleur nous observons que le reste de la population peut être entraînée. Dans le cas extrême d'un contrôleur bang-bang, cas limite du contrôleur proportionnel-intégral où le gain est infini, toute la population est entraînée avec la cellule effectivement contrôlée. Nous démontrons donc non seulement que les plateformes de contrôle in silico peuvent être utilisées pour contrôler un système génétique dans un état hors-équilibre, nous démontrons aussi la possibilité de maintenir une population de cellules dans leurs région d'instabilité à l'aide de stimulation dynamiques en boucle fermée. En étudiant la dynamique sous-jacente de ce phénomène populationnel grâce aux modèles théoriques développés et calibrés sur nos données, nous suggérons la possibilité d'un phénomène de stabilisation dynamique semblable au phénomène du pendule de Kapitza. Cette étude indique, lorsque les cellules sont soumises à des stimulations périodiques de fortes concentrations d'inducteurs, un changement dans le régime de stabilité du système et transforme la zone instable du toggle switch en attracteur global. Nous démontrons ensuite expérimentalement ce phénomène et l'observons pour une gamme de stimulations périodiques. Ces résultats suggèrent l'émergence de régimes de stabilité différents dans des réseaux de régulation génique lorsqu'ils sont soumis à des environnements fluctuants, et peuvent fournir de nouvelles perspectives dans l'étude de la prise de décision cellulaire. Notamment, de telles fluctuations périodiques sont observées dans des circuits de différentiations de précurseurs neuronaux en amont d'une prise décision cellulaire.

Enfin nous présentons aussi une nouvelle approche pour l'analyse d'images de microscopie qui exploite l'information cachée dans plusieurs plans focaux autour du spécimen au lieu d'utiliser seulement un seul plan focal. En effet, lorsque plusieurs images de microscopie sont acquises, pour un même objet, dans plusieurs plan focaux différents, l'intensité d'un même pixel va varier de façon différente selon la nature de l'objet présent sur ce pixel, pour des raisons de propriétés liées à la matière de l'objet ainsi qu'à sa forme et à la diffraction qu'elle entraîne. Par conséquent, cette « signature » de l'objet observé permet de l'identifier. Il s'agît donc d'un problème de classification, et nous utilisons des techniques classiques d'apprentissage machine, les machines à support de vecteurs, pour classifier ces signatures en fonction de la nature de l'objet observé. Nous démontrons la possibilité d'ainsi identifier dans des images de microscopie différentes cellules, comme la bactérie E. coli, la levure S. cerevisiae, ou des cellules cancéreuse humaines de type HeLa. Nous pouvons aussi identifier les sous-parties de ces cellules comme le cytoplasme ou la membrane, mais aussi identifier des structures de microfluidique ou des contaminants. La méthode facilite ensuite la segmentation de l'image et peut être facilement adaptée à différents organismes.

Mots-clés : Escherichia coli, Cybergénétique, Microfluidique, Automatique, Apprentissage machine, Biologie synthétique, Biologie des systèmes, Analyse d'images. ): It is generally accepted that the tensions in the many muscles implied in any movement, to grasp a pencil for example, are updated throughout the entire process according to sensory inputs (e.g. vision, touch, and proprioception) and advanced control algorithms taking place at all levels of the nervous system. Similarly, in physiology, following the seminal paper by Grodins [START_REF] Grodins | Respiratory Responses to CO2 Inhalation. A Theoretical Study of a Nonlinear Biological Regulator[END_REF] on the subject, the study of body homeostasis including thermoregulation, blood pressure, blood pH, and the levels of calcium, potassium, sodium and glucose in the blood were all studied from the angle of control theory [START_REF] Milhorn | Application of Control Theory to Physiological Systems[END_REF].

Foreword

Table of Contents

The discovery of DNA, and more importantly, the identification of genetic regulation mechanisms in 1961 [START_REF] Jacob | Genetic regulatory mechanisms in the Synthesis of proteins[END_REF] opened the way to the study of the inner workings of cells themselves. Refinements in protein sensing technology and in quantitative biology over the years unveiled the staggering complexity of the genetic-proteomic circuitry. Gene networks have since become one of the main subjects of study of systems biology, and the seminal works of Alon, [START_REF] Barkai | Robustness in simple biochemical networks[END_REF][START_REF] Alon | Robustness in bacterial chemotaxis[END_REF] in the late 1990s first suggested and demonstrated that adaptation to constant stimuli by the bacterial chemotaxis system is a robust property of the network and not a result of fine-tuning of biochemical parameters. In the following years, control theoreticians looked into the interplay between network topologies and the robustness of their responses. A review on the subject can be found in [START_REF] Stelling | Robustness of Cellular Functions[END_REF]).

The early 2000s also saw the appearance of another related field: synthetic biology. Synthetic biology stems from the progress made in genetic manipulation tools in the late 1980s and 1990s (most notably in cloning techniques, PCR and DNA sequencing) and systems biology. It aims at integrating an exogenous genetic network in the cell that not only can provide the genetic information for synthesizing new proteins, as is routinely done in traditional genetic manipulations, but also incorporates a function or program encoded into the genetic material to respond to certain external or internal stimuli or to increase the robustness of the desired process. Potential applications include drug production and smart drug delivery, biofuel synthesis, bioremediation, biosensing, and waste processing [START_REF] Collins | Synthetic biology: applications come of age[END_REF][START_REF] Cameron | A brief history of synthetic biology[END_REF]. Because synthetic biology draws a significant part of its goals from computer science and electrical engineering, control theory was rapidly incorporated into the fundamental concepts that drove its development. The difficulty of designing synthetic genetic modules to assemble into more elaborate systems became rapidly apparent, and soon engineered circuit modules involved feedback loops to increase robustness and reliability. For a detailed description of the co-evolution of synthetic biology and control theory see (Del Vecchio et al. 2016).

Unfortunately the processing subtleties that can be involved in modern control algorithms can hardly ever be incorporated into genetic circuitry, and a new theoretical framework for in vivo internal stochastic control algorithms must be formulated to reach the long-term objectives of synthetic biology. But looking at the history of control theory, the trend over the post-war era has been to externalize the control process out of the electromechanical realm into the more computation-indulgent digital one. Key technological advances that made this shift possible were the development of reliable, precise, digital sensors on one hand, and efficient and Foreword powerful electromechanical actuators on the other, with of course the exponentially increasing computational power of modern microprocessors. In the years to come, the expansion of in vivo external real-time control to new applications will be fostered by: a) renewed interest in fluorescent probe design following the recent breakthrough of super-resolution imaging; b) the actuation capacity provided by the sophistication of optogenetics over the last decade; and c) continued innovation in microfluidics both for observation and actuation through chemicals delivery.

Externalizing Control

Inducible promoters are now routinely used in systems and synthetic biology to understand and construct genetic regulatory networks. Because of the stochasticity of gene expression and its limited measurability in cells, such uses have long remained limited to short term, full induction of populations of cells. Fine-tuning of in vivo protein levels in bacteria remains a challenge.

Before using drug-responsive promoters like the lac or tet systems (Lutz & Bujard 1997) to induce gene expression in living cells, the first technique to study the action of a gene in an organism was complete gene knockout. Not only is it a demanding task, but the process is not reversible, not quantitative, and one cannot observe the effect of the gene's removal on the rest of the genetic network dynamically. A step towards quantifiable and dynamic studies of gene expression was made with the introduction of phage promoters in the cells, such as P L of phage lambda [START_REF] Elvin | Modified bacteriophage lambda promoter vectors for overproduction of proteins in Escherichia coli[END_REF] or the RNA polymerase and promoter of T7 phages [START_REF] Studier | Use of bacteriophage T7 RNA polymerase to direct selective high-level expression of cloned genes[END_REF]. Again, those techniques are not convenient and hardly quantitative: it required heavy cloning procedures where all the phage transcription machinery had to be expressed by the cell, and the induction level of the promoters could not be fine-tuned over time, as the P L promoter is activated by temperature shifts and T7 promoter activation necessitates the introduction of the T7 RNA polymerase in the cell via phage infection. Finally, during the 1990s, a lot of effort was put into the development and characterization of inducible promoters that could be quantitatively tuned, induced over wide ranges of expression, and would be orthogonal to most of the cells' natural repressors [START_REF] Guzman | Tight regulation, modulation, and high-level expression by vectors containing the arabinose PBAD promoter[END_REF][START_REF] Skerra | Use of the tetracycline promoter for the tightly regulated production of a murine antibody fragment in Escherichia coli[END_REF]. The most widely used systems are the lac and tet promoter-repressor couples (Lutz & Bujard 1997). These inducible systems opened the way for quantitative studies of gene regulatory networks and later, synthetic biology. However, although these newer inducible promoters allow for a more finely graded induction of gene expression levels than the original on/off phage-based systems, and refinements based on self-regulating feedback loops make this resolution even finer [START_REF] Nevozhay | Negative autoregulation linearizes the dose-response and suppresses the heterogeneity of gene expression[END_REF]Rosenfeld et al. 2002), induced gene expression is still unpredictable, heterogeneous, and shows significant fluctuations in time.

Foreword 2 Scientific problem: Long-term and real-time control of a bistable genetic system in single-cell bacteria

The main objective of my PhD was to develop a single cell control platform to study the feasibility of control in single cell Escherichia Coli bacteria, and specifically control of a bistable gene circuit, the toggle switch. It implied studying and integrating together the different domains that are necessary for a functional control platform: actuation through synthetic biology and microfluidics, sensing through microscopy and image analysis, and control theory.

The genetic toggle switch consists in two genes mutually repressing each other, and features two stable states in which either of the two genes is expressed and completely represses the other. A third, unstable, equilibrium point in which the two genes expression levels are such that their equivalent repression strengths are balanced is predicted by deterministic models of the system. However in practice the cells are always in either of the two stable states and can sometimes switch between the two due to random fluctuations. My objective was to maintain Escherichia coli cells harboring this circuit in their unstable area by dynamically changing their environment.

This genetic toggle switch control problem bears several similarities with the benchmark control problem of the inverted pendulum and allowed me to investigate the potential offered by external control theory on single-cell control. The genetic toggle switch is also a fundamental topology in core natural gene regulatory networks as well as one of the foundational results of synthetic biology and as such is frequently used in complex synthetic circuitry when bistability, memory or binary signal processing is desired. Hence, studying the dynamics of the toggle switch, especially in its unstable area, where it is rarely observed, was also one of the goals of this thesis. Combining a hands-on approach made possible by external cell control with a theoretical study of its dynamics made it possible to study the behavior of a multistable gene regulatory network out of equilibrium, as it is perturbed by time-varying perturbations that modify its phase portrait, thus allowing us to further the study of multistable genetic systems and raise new questions about their implications in stochastic cell fate determination, commitment and its reversibility, and the extent of dynamic or periodic stimulations in natural gene networks.

Approach

To make single-cell control of a multistable genetic system possible, I started by designing a control platform for single-cell bacteria. I developed several microfluidic chips to contain Escherichia coli cells and be able to both observe single cells for extended durations, and programmatically and rapidly change their environment. I also worked on image analysis to extract long-term single cell fluorescence levels, and experimented with state-of-the-art segmentation algorithms before developing my own image segmentation algorithm. I also developed a modular set of programs to integrate the different software parts of the control platform together and completely automate all hardware elements.

Foreword

In parallel I developed Escherichia coli strains to minimize interferences between the host cell and the lac and tet systems I used to control gene expression. I iterated on the chassis strains while trying to control simple transcription units. I developed a library of 36 dual-reporter LacI-TetR toggle switches, and picked the best of them to conduct characterization experiments to identify the parameters of a model inspired by other works in the literature. I used both deterministic and stochastic simulations based on this model to assess its controllability and study different control strategies and implementations.

Once platform development, biological implementation, and theoretical study reached maturity, I performed control experiments under various control strategies. The knowledge garnered from these successful control experiments on the behavior of toggle switch in its unstable area allowed me to identify a family of open-loop dynamic stimulations that would invert the stability map of the system.

Contributions

The first, practical, contribution of this thesis is the development of a platform combining hardware and software elements from different disciplines, to achieve long-term tracking, real-time actuation, and external control on single-cell bacteria. This platform combines microfluidics, microscopy automation, image analysis, and control. The platform offers the possibility to control the expression level of a specific gene with minor genetic manipulations and minimal knowledge of the underlying process. It is also highly modular: the implementation of the control platform consists of different processes that communicate with each other, so that parts of the control loop, like image analysis or control strategy computation, can be modified independently and adapted to different situations, and also be distributed over several machines if more computational power is needed. We believe this platform, in combination with other works in the field, will open the way to a new level of precision in the study of gene regulatory networks dynamics.

Because the platform allows for single-cell measurements, we were able to use it on an in vivo stochastic bistable system: the genetic toggle switch. The genetic toggle switch can be viewed as the genetic equivalent to the benchmark problem in control theory that is the inverted pendulum problem. Multistable systems are widespread in all dynamical systems and their control and controllability has always been an important subject of study. Multistability can be undesirable: it can force discretization of responses, with a limited number of accessible states linked to the attractors of the system, when one might want to investigate its intermediate, graded responses. But it can also be advantageous in systems where mutuallyexclusive tasks are attached to specific states of the systems, like in differentiation. In all cases, controlling multistable systems is a generally more difficult problem than controlling linear or non-linear monostable systems. It is an important milestone in any control implementation, and demonstrates the potential of our control framework.

Beyond the simple demonstration of the potential of control theory, multistability plays a central role in the genetic circuitry of all organisms, and is a core element of any advanced Foreword synthetic biology circuit. The toggle switch in particular is present in many gene regulatory networks involved in cellular decision making, and has been used in a number of synthetic circuits where strong bistable filtering of genetic information was necessary (see State of the Art for a detailed analysis). The ability to control multistable systems opens the way to high precision setting of cellular state, even allowing for the study of intermediate states out of equilibrium before the system is fully committed. We also demonstrate the possibility of stabilizing the system in areas that are inaccessible with traditional induction techniques, thus expanding the area of investigation on gene regulatory networks. In particular, it allowed us to investigate the dynamics of the toggle switch in the vicinity of its unstable steady-state.

Another contribution of this thesis is multiple inputs-multiple outputs (MIMO) gene control. MIMO systems are also a common subject of study in control theory, since most systems consist in intricate, multivariate interactions, where more than one input knob can help better steer the system, and one might want to control more than one of its outputs. The genetic toggle switch is a perfect example of a non-streamlined genetic circuit where MIMO control is necessary. In a more general sense, MIMO control of gene expression should improve the performance of GRNs (Gene Regulatory Network) control.

This work is also the first theoretical and experimental study of dynamic stabilization in an externally-driven gene regulatory network. The study of cellular response to dynamic stimulations is still in its infancy, with studies of time-varying concentrations of morphogens inputs on embryo development and patterning booming in the late 2000s and early 2010s (see [START_REF] Kutejova | Temporal dynamics of patterning by morphogen gradients[END_REF]Sorre et al. 2014 for discussions of those results). The results presented here illustrate the importance of out-of-equilibrium study of gene regulatory networks dynamics, which can lead to unexpected results, even from well-documented network topologies. The model developed to study the dynamic response of the toggle switch to external stimuli gave valuable insights into how multistable systems react to dynamic stimulations and as such can be used to further study the behavior of this fundamental network.

One of the tools I developed, Stack-based image analysis, can be used beyond the scope of single-cell bacteria segmentation, and can be transparently applied to other organisms without any software modifications. This method proposes the use of machine learning methods on zstacks of images above and below focus to identify regions of the images for cell segmentation. Cell segmentation is one of the core difficulties of single-cell control, and although recent developments in the field of Convolutional Neural Networks (CNN) are promising, no cell segmentation algorithm has given satisfactory results for online, long-term cell tracking yet. The use of high-dimension information hidden in Z-stacks combined with traditional segmentation algorithms and newer deep learning techniques can lead to fast advances in online image analysis of microscopy images, with possible further developments in 3D segmentation.

Finally, all the tools I developed, especially the control platform, will be released in opensource and open-hardware formats, and my data will be made available, following a movement in modern science of transparency and exchange that I believe will be beneficial to science in general and to the field of external control in particular.

Outline

My thesis document is organized as follows:

Chapter 1 will present the state of the Art, detailing both the recent development of external real-time control of gene expression, and the central role of double negative feedback loops, or toggle switches, in both natural and synthetic gene regulatory networks.

In chapter 2, I present the main techniques and implementation choices for controlling the genetic toggle switch. I discuss the development of Escherichia coli chassis strains to circumvent problems caused by cellular processes interfering with the control inputs. I report the various constructs I developed for obtaining a bistable switch and the changes in implementation that occurred throughout my work. I also present the implementation of the control platform, with various obstacles and solutions for microfluidic chip fabrication, inputs delivery, image analysis, cell containment and experiment automation. I close this chapter by discussing the modeling of the toggle switch and its simulation, both deterministic and stochastic, as well as the control implementation choices and the parameters identification approach.

In chapter 3, I present the main results of this thesis, both numerical and experimental, and present their implications on our understanding of the toggle switch dynamics and on genetic multistability in general.

In chapter 4, I present a novel image analysis and cell segmentation algorithm inspired by hyperspectral imaging. The results extend well beyond bacteria cell segmentation and holds great promises for online cell segmentation, and can be combined with other techniques in cell segmentation, especially recently developed deep neural network for cell segmentation.

Chapter 5 concludes this thesis.

The Appendix present additional data and development made during this thesis.

Foreword

Chapter I

State of the art

Genetic networks as dynamical systems.

As the study of biological systems becomes increasingly quantitative, ecosystems, organisms and genetic circuits are studied more and more with tools from dynamical systems theory. This evolution was the result of improved measurement techniques over several decades. In the dynamic study of gene regulation networks, the shift occurred throughout the 1990s and led first to the establishment of the field of systems biology (Alon 2007;Kitano 2002), and then to the field of synthetic biology (Benner and Sismour 2005;Endy 2005). Although the two fields are connected and mutually benefit from one another, the former favors a top-down approach to the question and focuses on large-view studies of gene networks made of smaller, finer detailed subunits (or systems), while the latter, synthetic biology, favors a bottom-up approach in which hands-on studies of minimal synthetic genetic networks are used to gain understanding on gene expression by mimicking nature (Di Ventura et al. 2006). The quality of the dynamical data acquired on the evolution of genetic circuits increased thanks to developments in several fields I the 1980s and 1990s. First of all, as discussed in the introduction of this thesis, the development of new genetic manipulation techniques [START_REF] Sambrook | Molecular cloning : a la oratory anual 2nd ed[END_REF], inducible genetic systems (Lutz and Bujard 1997) and intracellular fluorescent probes (Shaner, Steinbach, and Tsien 2005) in this period made the assembly, steering and observation of such systems possible. But the study of the dynamics of those systems was still rudimentary, and biological microfluidics, in combination with automated timelapse microscopy, was developed subsequently to facilitate the study of gene regulation networks in time and at the single cell level. Microfluidic chips are microfabricated devices in which low volumes of fluids are moved, mixed, separated or otherwise processed to miniaturize procedures with applications in various domains of physics, chemistry and biology. Microfluidic rapidly became a key element in the study of the dynamics of synthetic gene regulation networks because it could be used both to trap cells and hence monitor their fluorescence over many generations, possibly at the single cell level, but also because it could be used to change the environment of the cells dynamically (Bennett and Hasty 2009). With this type of setup, inducible synthetic systems could be steered and observed in real time, and the study of their dynamic response to time-varying perturbations was used to gain a deeper understanding of the temporal mechanics of genetic systems. (Bennett et al. 2008;Hersen et al. 2008;Mettetal et al. 2008) are seminal studies that used microfluidic devices to create temporal changes in the growth medium to study dynamic biological phenomena. In (Bennett et al. 2008;Hersen et al. 2008) the authors used periodic osmotic shocks to study the frequency response of the High Osmolarity Glycerol pathway in yeast and used those results to identify the mechanisms of the cellular response to shocks at different timescales. In (Bennett et al. 2008) the authors also studied the frequency response in yeast to periodic changes in the external carbon source by using a microfluidic platform. The galactose utilization network is shown to filter out fast fluctuations in the nutrients source, but to slowly adapt to long-term evolutions. In this paper the interplay between mathematical modeling, dynamic experiments and biology is elegantly illustrated by the discovery of a previouslyunknown post-transcriptional regulation loop in the network because of a discrepancy between the model-predicted dynamics of the system and experimental data.

function. Secondly, even though the different studies differ in their cell culture apparatus, measurement method and actuation, the feedback loop is implemented in silico and the level of refinement of the feedback function is much higher than any possible internal implementation of genetic regulation. Finally, those different studies achieve levels of control of their respective systems that open-loop stimulation based on models and predictions could not have achieved. The first one (Toettcher et al. 2011b) to be published focused on controlling a signaling pathway by first driving fluorescence recruitment at the membrane of HeLa cells, and then using the method to recruit the PI 3-kinase responsible for the synthesis of phosphatidylinositol-3-phosphate (PIP3) at the membrane and thus control the location of those lipids. The PI 3-kinase is attached to the Phy-PIF optogenetic2 system (Toettcher et al. 2011a) for actuation and the production level and location of the lipids are monitored through an engineered fluorescent proxy: PHAkt-Cerulean, which binds to the produced lipids (see . Recruitment and fluorescence levels are monitored via epifluorescence microscopy. Optogenetic membrane recruitment is activated by shining light on cells observed. Because of the dynamics of the different systems involved, the time resolution of their acquisitions is in the order of seconds, and their experiments typically last about 10 minutes. Because of this short timescale and the optogenetic actuation, the study did not require a complex cell culture and input delivery platform and the experiments were performed in liquid cultures on a microscope. A proportional-integral controller connects the observation and actuation in silico. Proportional-integral (PI) controllers are controllers that correct an error between a measured output of the system of interest and a target level by changing the input to the system both proportionally, i.e. by a quantity that is proportional to the current error, and integrally, i.e. by a quantity that is proportional to the integral of the error over time. Several procedures exist to fine-tune PI controllers to minimize oscillations and overshooting (Åström and Hägglund 2006), but they all apply to linear systems. For the class of nonlinear systems we are interested in here, those techniques can be used as a starting point but their results usually need to be refined empirically. The authors show that not only are they able to control membrane recruitment and the synthesis of PIP3 with a PI controller, at setpoint levels and in time-varying profiles, they also reduce cell-to-cell variability in recruitment resulting from non-uniform expression of the optogenetic system. In the second study [START_REF] Milias-Argeitis | In silico feedback for in vivo regulation of a gene expression circuit[END_REF], the authors use a control platform to drive the expression of a synthetic system (see Figure 2-4a) in a population of Saccharomyces cerevisiae cells. The expression of a fluorescent protein downstream of an another Phy-PiFbased optogenetic system (Tyszkiewicz and Muir 2008) is controlled around a setpoint by using pulses of light in a batch culture of yeast cells. In liquid batch apparatuses, cells grow in suspension in a liquid media, under constant shaking and temperature control. However since the cells are growing in large volumes in a flask, the sensing must be done on a sample of the cell culture because the traditional instruments used for fluorescence measurement are not adapted for in situ use in large volumes of cell culture. Here the state of the cells is measured periodically by flow cytometry and used by the control algorithm. A model-predictive control approach is chosen to implement the feedback loop between measurement and actuation. In model predictive control, or MPC, a dynamic model of the system is used to predict how the process will react to series of possible inputs, and the best course of action is applied until the next acquisition. This type of approach thus requires a priori knowledge about the system to control, but typically yields better results than PI controllers. A state estimation algorithm is also used in combination with the model-predictive controller to estimate the state of the nonobservable variables that are used by the model-predictive controller. The authors demonstrate the possibility to control the gene expression level at various levels of expression for several hours, and also the possibility to drive the system after different random perturbations to the state of the cells.

Finally, in (Uhlendorf et al. 2012) the authors use the natural high osmolarity glycerol (HOG) pathway in Saccharomyces cerevisiae to control gene expression downstream of it (see Figure 2-4c). The HOG pathway is a phosphorylation cascade, and one of the genes that are activated downstream of it is STL1 (Rep et al. 2000). The authors used its native promoter to drive the expression of a fluorescent protein by submitting the cells to pulses of high-osmolarity media.

The level of the fluorescent protein is observed in real time and at the single-cell level by time-lapse microscopy and automated image analysis, and the cells are grown in a microfluidic chip in which the osmolarity of the growth media flown through the chip can be changed in real time. In microfluidic chips the problem of cell sampling and measurement is greatly simplified, and the same population of cells, or even single cells, can be followed over extended periods of time. Again a model-predictive control approach is chosen to numerically close the loop. The authors use their platform to perform setpoint control experiments and also to force the cells fluorescence to follow time-varying profiles for up to 17 hours. They demonstrate that pre-computed open-loop dynamic stimulation cannot control the system as accurately. The microfluidic and time-lapse components of the platform allowed for both population and single-cell control. The individual cells were segmented through a circular Hough transformation. The authors use their platform to demonstrate the feasibility of control at the single cell level, but they also use the single-cell data acquired study the effect of population and single-cell control on noise levels.

Together, these studies demonstrate that real-time control can be used to robustly drive intracellular processes in real-time, dynamically limit the effects of gene expression stochasticity, or counter the effects of endogenous feedback loops. Different types of intracellular processes are controlled, in different organisms and with different actuation and sensing method, demonstrating the versatility of external control of gene expression.

use galactose and glucose to turn on or off the expression of the GAL1 promoter to control the fluorescence level of GFP. On top of the previously-used control algorithms, the authors propose zero average dynamics control. Zero average dynamics (ZAD) is a type of slidingmode control algorithm. It produced results comparable to model-predictive control. In [START_REF] Fracassi | Automatic Control of Gene Expression in Mammalian Cells[END_REF] the same team developed a microfluidic platform for long term control of gene expression in mammalian cells. A fluorescent protein under a synthetic tetracyclineinducible system is controlled over extended periods of time (up to 58 hours).

In [START_REF] Melendez | Real-time optogenetic control of intracellular protein concentration in microbial cell cultures[END_REF]) the authors use an approach similar to [START_REF] Milias-Argeitis | In silico feedback for in vivo regulation of a gene expression circuit[END_REF] but improve the automation of the platform and add a turbidostat to the cell culture apparatus, i.e. they control the density of cells in the flask. They also use a bang-bang control approach: It is similar to the PI control approach, but does not apply intermediary inputs to the system it tries to control. Instead the system is fully activated or inhibited when it is respectively below or above its objective. With this setup the authors are able to drive protein expression for up to 45 hours.

Finally, in [START_REF] Milias-Argeitis | Automated optogenetic feedback control for precise and robust regulation of gene expression and cell growth[END_REF]) the authors expand on the approach described in [START_REF] Milias-Argeitis | In silico feedback for in vivo regulation of a gene expression circuit[END_REF]) and develop a similar platform for bacteria. Additional effort is put on the automation of the platform and the authors can precisely control gene expression but are also able to control the growth rate of the cells by actuating on the vital synthesis of methionine (see Figure 2-4d). The sensing of the population density is done by optical density directly in the flask and the growth rate is derived from it. This result demonstrates the possibility offered by in silico control of gene expression to manipulate fundamental functions with minimal modifications to the cell.

All of these improvements on the principle of in silico control platforms show on one hand how much potential the field has. Control theory is a broad discipline and all the knowledge gathered over the decades of existence of the field can be used to drive the development of those control platforms. On the other hand, it also shows how recent this field is. So far, all applications of the approach remain limited to proofs of concepts on the feasibility of the method on new toy systems or organisms or on the comparison of performance between different control strategies. Although the ultimate goal is to use control to induce precise intracellular perturbations to study the response of the rest of the cell, the field is still being explored. The knowledge necessary to apply this methodology to biological question still needs to be acquired and open questions on the potential of the field remain. During this PhD I worked on the question of external control of multistability in bacteria, by studying stabilization of a bistable genetic system in its unstable area.

Closely related to the dynamical study of gene expression, recent advances in iterative experiment design [START_REF] Ruess | Iterative experiment design guides the characterization of a light-V-Conclusion inducible gene expression circuit[END_REF]) could be combined with control platforms to further automate the study of intracellular processes: Instead of having the experimenter run control experiments and then decide on what perturbations to run next, the data could be analyzed onthe-fly by iterative experiment design algorithms which would, as a higher-level layer, dictate control profiles to the control platform to maximize the quantity of information acquired, thus completely automating the process.

Apart from the dynamic study of genetic systems, external control of gene expression could also be applied to other domains of study. Being able to drive intracellular processes of interest can also of course find applications in biotechnology. In this domain, external feedback control has already been suggested to improve productivity, robustness and batchto-batch reproducibility [START_REF] Polizzi | Genetically-encoded biosensors for monitoring cellular stress in bioprocessing[END_REF]. In [START_REF] Milias-Argeitis | Automated optogenetic feedback control for precise and robust regulation of gene expression and cell growth[END_REF]) the authors already discuss the scalability of their approach to industrial bioreactors. Although some of the studies presented here were performed in batch cultures [START_REF] Melendez | Real-time optogenetic control of intracellular protein concentration in microbial cell cultures[END_REF][START_REF] Milias-Argeitis | In silico feedback for in vivo regulation of a gene expression circuit[END_REF], 2016) of yeast or bacteria and are therefore closer in their implementation to bioreactors, scaling up the size of the batch culture raises a number of issues, one of them being the difficulty to stimulate cells with optogenetic tools in the dense, opaque molasses that can typically be found this kind of apparatus.

portion of chains of optimal length exist in the colony. This constitutes a prime example of cellular decision making and bet-hedging3 in bacteria driven by a toggle switch.

The genetic toggle switch in synthetic biology

Gardner and Collins published the first synthetic genetic toggle switch in bacteria [START_REF] Gardner | Construction of a genetic toggle switch in Escherichia coli[END_REF]. They implemented two versions, a temperature-IPTG sensitive one, and the aTC-IPTG sensitive toggle switch I worked on in my thesis. They show that after the toggle has been induced into one state or another, it remains in that state until the opposite inducer is added to the growth medium. It is worth noting that only one of the two branches is monitored directly with a fluorescent reporter. Later implementations will use a reporter on both branches to monitor the state of the system, making model fitting and parameters identification more difficult. The system was soon adapted to mammalian cells with an antibiotic-regulated switch that showed bistability even after encapsulation and implantation in mice (Kramer et al. 2004). The toggle switch was then given its pivotal role in synthetic biology as a building block by being interfaced with other synthetic and endogenous elements to drive biosensing, biofilm formation, cell-density-dependent gene activation (Kobayashi et al. 2004), improvement of metabolic biosynthetic productivity of biofuels (Anesiadis, Cluett, and Mahadevan 2008), or to monitor changes in the mammalian gut environment (Kotula et al. 2014). Advances in modeling and prediction of synthetic circuits behavior eventually led to automated design of toggle switches in silico and accurate prediction of their stability (Chen et al. 2012;Ellis, Wang, and Collins 2009). The study by Chen and colleagues in 2012 constitutes, to my knowledge, the only example of a dual-reporter toggle switch in the literature, however the authors did not use it to fit a dynamic model of the toggle switch.

The toggle switch has since gone through major implementation modifications. A major change in bistability implementation in synthetic circuits occurred in the 2000s when (Ham et al. 2006) designed a recombinase switch which, while not exactly equivalent to a toggle switch in its topology, leads to strong bistability and low leakage. It does not rely on transcription factors to inhibit the expression of a gene, but instead uses invertases that will flip a promoter's orientation to stably turn two gene's expression fully on or off. The principle can even be generalized to an n-states switch by using orthogonal invertases since the number of possible states evolves exponentially with the number of recombinases (Ham et al. 2008). This type of system has been used in synthetic biology since then as an advanced, robust and reversible memory module (Bonnet, Subsoontorn, and Endy 2012) and to perform computational tasks within the cells (Moon et al. 2011;Yang et al. 2014). However such systems have an all-or-none nature to them and are not well-suited to the control problem we are interested in. Another exotic implementation of the genetic toggle switch is based on RNA interference in mammalian cells (Deans, Cantor, and Collins 2007), which allows for specific gene targeting and is used to control various biological processes.

But the most important change in gene regulatory network design and construction in the last few years was brought by the recent revolutions in transcriptional regulator design with the stochastic cell fate determination in naïve cells. They develop a deterministic coupled ODE model with nested Hill functions to account for the double repression in the inducer-TFpromoter interaction. They fit experimental results and use it to predict the stability of their designs. They also then run stochastic simulations of their model to study stochastic cell fate determination. This study is of particular interest for this work since it is the only one that has been fitted to real data. I use the model and parameters in this study as a starting point for my own model (See Chapter 2).

Theoretical control of the toggle switch

External control of genetic systems is still in its infancy, and although no experimental attempts have been made so far to control a genetic toggle switch externally, there are a few theoretical studies on the subject. I the first theoretical studies on controllability and control of the genetic toggle switch (Farcot and Gouzé 2007a, 2007b, 2008) the authors report a piecewise affine differential model of the toggle switch and make it follow a transition graph between the different regions of their model by inferring piecewise constant feedback control laws. Another study on the subject of toggle switch control can be found in (Wang et al. 2016). A control framework for nonlinear differential models is developed for controlling multistable networks, including an "enhanced" version of the genetic toggle switch. Their control framework is based on bifurcation analysis and focuses on control and controllability of the system from one attractor, or stable state, to another. A small discussion of the possibly beneficial effects of noise on controllability is also included, where the authors argue that an appropriate amount of noise can help destabilize attractors that would otherwise be too strong for the control strategy to successfully drive the system around.

We can also cite the series of papers by Sootla and colleagues (Sootla et al. 2013;Sootla, Oyarzún, et al. 2016;Sootla, Mauroy, and Goncalves 2016) where the authors focus on robust switching pulse strategies between the two stable states of a LacI-TetR toggle switch. Their proposed solutions are based on either reinforcement learning, which they conclude can be impractical due to the large amount of measurement data it necessitates, or on monotone systems theory, which relies on a model but is robust to parametric uncertainty. They go on to identify the so-called "switching separatrix" in the space of the two parameters of the input pulses (duration and intensity) and, interestingly, use their framework to investigate forced oscillations in a generalized eight species repressilator. They do not however investigate periodic switching between the states of the toggle switch or the out-of-equilibrium behavior of their eight species model.

Two focus on the specific question of controlling the genetic toggle switch towards its unstable equilibrium point or towards the unstable area. In the first one the authors use a piecewise affine model to describe the toggle switch and use the piecewise constant control framework previously described to drive the system towards the unstable steady state (Chaves and Gouzé 2011). They suggest approximate solutions to drive the system in the neighborhood of the state, or by passing through an unstable state cyclically. The second paper (Mohajerin Esfahani, Milias-argeitis, and Chatterjee 2013) uses the toggle switch system as an example to demonstrate the possibilities offered by the recently developed stochastic motion planning framework (Mohajerin Esfahani, Chatterjee, and Lygeros 2015) or external cell control. The authors develop a stochastic differential equation model of the toggle switch by deriving the Langevin equation of the system, and then infer optimal input policies that maximize the probability of staying in the neighborhood of the deterministic unstable equilibrium point. They also investigate the possibility of controlling the toggle switch with only one input inducer and observe a dramatic decrease in performance.

In this thesis we will explore the possibility to control externally the bistable genetic toggle switch around its unstable equilibrium point. This thesis provides the first control results on bacteria at the single-cell level. New tools are created for this particular task, and others are improved, thus expanding the domains of applicability of in silico cybergenetics. The toggle switch is a fundamental topology encountered in both synthetic and natural gene regulation networks, and being able to control toggle switches and to maintain them in their unstable area opens the door to the study of intricate multi-stable networks, but it also opens a new range of possible usage for this topology in synthetic genetic circuits. In this thesis we demonstrate for example that it is possible to "reset" a population of toggle-switch-bearing bacteria by stabilizing them in the unstable area and then releasing the stabilization to let them separate in the two basins of attraction. It is also a difficult control problem, which would have required tedious trial-and-errors to implement in vivo, and solving it demonstrates the possibility offered by single-cell external control approaches. Finally, observing the dynamics of the genetic toggle switch in the vicinity of its unstable equilibrium point helped us expand the knowledge on its dynamics. Ga d e , Ti oth S., Cha les R. Ca to , a d Ja es J. Colli s.

. Co st u tio of a Ge eti Toggle S it h i Es he i hia Coli. Nature 403(6767):339-42.

Ham, Timothy S., Sung K. Lee, Ja D. Keasli g, a d Ada P. A ki .

. Desig a d Construction of a Double Inversion Recombination Switch for Heritable Sequential Ge eti Me o edited Rose a Jea e Redfield. PLoS ONE 3(7):e2815.

Ham, Timothy S., Sung Kuk Lee, Jay D. Keasli g, a d Ada P. A ki .

. Yao, Gua g, Tae Ju Lee, Seii hi Mo i, Joseph R. Nevi s, a d Li g ho g You.

A Tightl Regulated Inducible Expression System Utilizing Thefim Inversion Recombination

. A Bistable Rb-E F S it h U de lies the Rest i tio Poi t. Nature Cell Biology 10(4):476-82.

Chapter II Observing and actuating on trapped bacterial cells

Table of Contents

Introduction

The development of an external single-cell control platform involves a number of different methods and scientific fields: genetic engineering, signal processing, microfabrication, microscopy, electrical engineering, control theory, and programming were all required to achieve real-time control of gene expression in bacteria. Specifically, the possibility of controlling gene expression through an in silico feedback loop at the single cell level was made possible by recent developments in time-lapse microscopy, cell segmentation, and microfluidics, but a number of open problems still remain to be solved by the experimenter for each different application. The necessity of automated and on-line imaging, data analysis and actuation required by real-time control increased the difficulty of creating such a platform. In this chapter, I discuss the obstacles I had to cope with and the implementation choices I made.

The first section focuses on the biological aspects of my work. I start by describing how I modified the host cell strains to prevent endogenous cellular processes from interfering with the synthetic toggle switch. Then, I review the different iterations for the design of the toggle switch itself. The design and construction methods were chosen to maximize the chances that at least one designed circuit would be bistable. I finish the section by describing the characteristics of the selected circuit.

In the second section, I discuss the hardware and software choices that were made to develop the platform. In order to control a multistable system and be able to accurately measure its state, I needed to be able to track single cells for extended periods of time and to extract their level of fluorescence periodically, which necessitated a microfluidic-based platform rather than a batch-culture type of platform. The platform described in this section is comprised of: a custom-made microfluidic chip for long-term tracking of bacteria as well as automated chemical actuation; an entirely automated epifluorescence microscope; various pieces of software to link the different interfaces together, extract data, and run the control algorithms; and finally a custom-made electronic valve actuator for precise, real-time modification of the chemical environment of the cells.

Finally, the last section of this chapter details the mathematical model derived from a simplified chemical description of our toggle switch, and the simulation algorithms that were used to study the feasibility of real-time control of the toggle switch. The control algorithms used to control toggle switches in real-time (namely the PI and bang-bang strategies) are also discussed. The last part of the section describes the procedure for parameters identification that was applied to characterization data.

Chassis development

The cellular chassis1 is an integral part of the platform, as the genome of the organism needs to be modified in such a way that the toggle switch can be implemented, observed, and controlled. In the case of this toggle switch based on the action of the tet and lac repression systems, some cellular mechanisms, described in the following paragraphs, can interfere with the action of the inducible promoters and impede the controllability of the system, and had to be removed. Furthermore, E. coli possess flagella and can usually swim around in their growth media, which presents a problem for long-term observation and tracking in the microfluidic device. In Figure 2-1, a hierarchical representation of the main strains presented in this study is given. After several rounds of experimental characterization, the final chassis strain, bPH_127, is selected as the best host for synthetic circuits to control.

As a starting point for my chassis, I used the JW1907 strain from the Keio collection [START_REF] Baba | Construction of Escherichia coli K-12 in-frame, single-gene knockout mutants: the Keio collection[END_REF]). The Keio mutants collection features all possible E. coli K-12 BW25113 strains with all non-lethal single-gene knockouts in the genome. In JW1907 the fliA gene is knocked out. fliA encodes for the specialized flagellar sigma factor σ28 (McCarter 2006; [START_REF] Wilkinson | Regulation of flagellum number by FliA and FlgM and role in biofilm formation by Rhodobacter sphaeroides[END_REF][START_REF] Ikebe | Structure and expression of the fliA operon of Salmonella typhimurium[END_REF][START_REF] Dailey | Mutants in disulfide bond formation that disrupt flagellar assembly in Escherichia coli[END_REF], and is traditionally removed to prevent the cells from swimming around in microfluidic chips. Keio strains feature a resistance cassette, which I removed to obtain the first chassis strain bPH_103.

From this strain, I developed the strain bPH_104 by deleting the lacY gene. Gene lacY expresses a lactose permease that is responsible for bi-stability in the lac operon [START_REF] Santillán | Origin of bistability in the lac Operon[END_REF][START_REF] Ozbudak | Multistability in the lactose utilization network of Escherichia coli[END_REF]). The expression of LacY is activated when lactose (or analogues such as Isopropyl β-D-1-thiogalactopyranoside2 ) is present in the growth media, and this increase in expression of the permease causes more lactose to be transported into the cytoplasm, further increasing permease expression (see strain BW25113 in Figure 2-2). This type of self-activating network makes the expression of genes downstream of the promoter bistable: LacY would interfere with our constructions based on the lac promoter and with lactose/IPTG induction. I removed the lacY gene using standard P1 phage transductions [START_REF] Miller | A short course in bacterial genetics: a laboratory manual and handbook for Escherichia coli and related bacteria[END_REF]. Interestingly, once the LacY permease is removed, lactose or its equivalent IPTG can still diffuse through the membrane, although at much lower rates [START_REF] Marbach | Lac operon induction in Escherichia coli: Systematic comparison of IPTG and TMG induction and influence of the transacetylase LacA[END_REF]). Thus we could drive the internal concentration of inducer but without the bistable effects of the lac operon.

Finally, I implemented a variant of this strain by integrating the regulator genes tetR and lacI in tandem to the chromosomes of bPH_104 to produce two more strains, bPH_121 and bPH_122, respectively. The constitutive expression of TetR and LacI allowed me to control the expression of any gene placed under a lac or tet promoter. The cassette containing lacI and tetR was transferred from the E.coli strain DH5αZ1 (Lutz & Bujard 1997), again by standard P1 phage transduction [START_REF] Miller | A short course in bacterial genetics: a laboratory manual and handbook for Escherichia coli and related bacteria[END_REF]). I did not remove the antibiotic resistance cassette used for selection, therefore the bPH_121 and bPH_122 strains are spectinomycin resistant. These two strains are the chassis strains I used to conduct my first series of control experiments and gather knowledge on the different systems I was working with.

Early in my exploratory experiments I observed adaptation to anhydrotetracycline (aTC) induction of the tet system, i.e. the response of the tet system to successive inductions would weaken over time. aTC is part of the tetracylines family of antibiotics and it is the inducer of choice for the tet induction system in bacteria because it is less toxic to cells than tetracycline itself or its readily-available variants [START_REF] Rasmussen | Molecular basis of tetracycline action: identification of analogs whose primary target is not the bacterial ribosome[END_REF]. The tet induction system is derived from the Tn10 operon system, which is activated in presence of tetracycline and expresses an efflux pump for evacuating tetracyclines out of the cytoplasm. The original wildtype BW25113 strain does not have the tetA gene responsible for the expression of the tetracyclines-specialized pump. However, it is suspected that Escherichia coli uses another efflux pump for adapting to high concentrations of tetracycline: the acriflavine pump encoded by the acrA and acrB genes [START_REF] Ma | Genes acrA and acrB encode a stress-induced efflux system of Escherichia coli[END_REF][START_REF] Zgurskaya | AcrA is a highly asymmetric protein capable of spanning the periplasm[END_REF][START_REF] Le | Protein expression enhancement in efflux-deleted mutant bacteria[END_REF], which are present in the genome of BW25113. No clear connection has been identified between the tetracyclines and the two genes, but it would not be surprising that the expression of AcrA and AcrB is directly or indirectly activated by tetracyclines levels, thus leading to slowly decreasing activation of the tet promoter's expression by aTC. See strain BW25113 in Figure 2-2 for a visual representation of the mechanism.

In order to make control of gene expression with the tet system possible for extended periods of time, I designed another strain in which the acrA and acrB genes were deleted. To do this, I removed the two genes, which are next to each other, in a one-step deletion from the "wildtype" BW25113 genome. Then I transferred the double deletion through P1 phage transduction into strain bPH_104 to obtain strain bPH_127, as is the classical procedure to avoid off-target mutations. Double acrAB deletion was performed by a modified Wanner chromosomal deletion/integration protocol [START_REF] Datsenko | One-step inactivation of chromosomal genes in Escherichia coli K-12 using PCR products[END_REF]. This protocol uses lambda-red homologous recombination to replace the target genes in the chromosome with a selection cassette. Because the technique requires short homology regions flanking the acrAB genes, I could easily obtain them via oligo annealing. I transferred the regions into standard modular cloning (MoClo) plasmids3 to rapidly construct the replacement cassettes and to offer the possibility of fast chromosomal integration of MoClo circuits. Once the acrA and acrB genes were removed, we observed a higher sensitivity to light, especially during fluorescence imaging, and antibiotics, as well as a lower growth rate in presence of antibiotics. It is believed that the acriflavine pump that those two genes encode for is actually a multi-drug efflux pump transporting a wide range of toxic elements out of the cell [START_REF] Zgurskaya | AcrA is a highly asymmetric protein capable of spanning the periplasm[END_REF]. However, the absence of this efflux pump may lead to the accumulation of other toxic chemicals, leading to the hypersusceptible phenotype observed in the new bPH_127 strain.

Because this strain was going to be transformed with toggle switch plasmids in order to control them, I constructed it from the bPH_104 strain instead of bPH_122. This way the strain did not express LacI and TetR constitutively, which would interfere with the functioning of the toggle switch.

To summarize, the final chassis strain bPH_127 is a quadruple mutant of Escherichia coli K12 BW25113 strain with genes fliA, lacY, acrA and acrB knocked out. The cells do not selfpropel, their response to IPTG or other lactose derivatives is not bistable and they do not flush out tetracyclines.

Now that it has been developed, the chassis strains I developed and present here can be used for controlling other systems as they are adapted to the control framework. A list of the strains I developed during my PhD can be found in appendix A.

LacI-TetR toggle switch

I chose to develop a toggle switch based on the lac and tet systems, both because these systems have been extensively used and studied in synthetic biology, and because inducer chemicals can be delivered into the growth media to the expression downstream of each system. To be able to observe the state of the toggle switch in real time, I also ensured that two different fluorescent reporter proteins would be co-expressed with the toggle switch. I chose to combine LacI with the mKate2 fluorescent protein and TetR with the mEGFP protein. The two opposite parts of the toggle switch consisting of, on one hand, the tet promoter (pTet), the lacI gene and the mKate2 fluorescent protein, and, on the other hand, the lac promoter (pLac), the tetR gene and the mEGFP fluorescent protein, are referred to as "branches" here. Also, in order to maximize the chances of having at least one bistable toggle switch, I constructed a library of circuits with different expression strengths for the two branches. I eventually picked the circuit in the library that seemed the most promising, circuit 2.31 (see appendix A).

The final toggle switch design is illustrated in Figure 2-3. This 2.31 plasmid was eventually transformed into bPH_142 strain and used to perform the control experiments described in the next chapter. In the rest of the section I will present the design choices that were made to construct this circuit, the protocols I used and developed to construct the library and some of the problems I ran into.

Modular Cloning (MoClo) and toxicity issue

To build a bistable toggle switch it is important that both TetR and LacI are expressed in proportions such that their mutual repressive strengths are comparable. Also, tagging both genes with a different fluorescent protein allows for the monitoring of the state of the toggle switch by microscopy. Thus, developed a library of toggle switch circuits to ensure I would obtain at least one bistable toggle switch with appropriate properties (dynamics, bistability, symmetry). I took advantage of recent technical progresses in the field of molecular cloning and developed a few techniques of my own to accelerate the process.

It also allows an easy combinatorial assembly: because parts are standardized, several assembly pots can be easily set up with a single variation between them (e.g a different 5'UTR, various promoters…), and each would produce a different transcription unit. Golden Gate / MoClo even offers the possibility of assembling families of construct variants in one pot [START_REF] Engler | Golden gate shuffling: A one-pot DNA shuffling method based on type ils restriction enzymes[END_REF], although the task of screening for the better constructs then becomes the bottleneck [START_REF] Engler | Golden gate shuffling: A one-pot DNA shuffling method based on type ils restriction enzymes[END_REF][START_REF] Engler | Generation of Families of Construct Variants Using Golden Gate Shuffling[END_REF]. See Figure 2-4 for a description of the MoClo protocol as well as illustrations and appendix A for a list of the MoClo vectors used and developed in this thesis.

To summarize, the Modular Cloning technique offers a number of valuable advantages for circuit library assembly, and I used this method to assemble my library of toggle switches. To maximize the chances of obtaining a bistable switch, a simple solution was to design and implement circuits with a wide range of protein translation rates. These different circuits would only differ in their ribosome binding sites, so the only part that would change in my assemblies would be the 5'UTR parts of each branch ("U" part of MoClo assemblies). Once I transferred the ribosome binding site (RBS) libraries to the MoClo Level 0 plasmids (pL0-U), the possibility to rapidly produce all the variants of each branch used in the circuits greatly sped up the process. It would also permit rapid reconstruction of the branches if necessary, since I could re-use the same parts. With the knowledge gathered on the branches during this work on the toggle switch to model circuit behavior, I can also construct new circuits with those same branches without much effort or time.

I had to cope with several complications during the assembly of the toggle switches. At the transcriptional unit level, the promoter or RBS region of the level 1 transcriptional units were mutated. The fact that these specific parts of the branches were mutated suggested that the proteins expressed from the plasmids caused significant burden to cells. This intuition was also supported by the fact that the pUC replicon [START_REF] Yanisch-Perron | Improved M13 phage cloning vectors and host strains: nucleotide sequences of the M13mp18 and pUC19 vectors[END_REF] used in the backbone plasmids of the MoClo system create a high number of plasmid copies, from 500 to 700 copies per cell [START_REF] Lin-Chao | High copy number of the pUC plasmid results from a Rom/Rop-suppressible point mutation in RNA II[END_REF].

Todecrease the burden caused to cells, I developed a library of MoClo backbone plasmids based on low copy origins of replication (see Figure 2-5A). I mainly used the ACYC family of plasmids, which are based on a p15A replicon [START_REF] Chang | Construction and characterization of amplifiable multicopy DNA cloning vehicles derived from the P15A cryptic miniplasmid[END_REF] producing about 10-12 plasmids per cell [START_REF] Sambrook | Molecular cloning : a la oratory anual 2nd ed[END_REF], and a chloramphenicol resistance gene for selection. I also developed MoClo variants from the CDF plasmids family, based on the CloDF13 replicon [START_REF] Veltkamp | Replication and gene functions of the bacteriocinogenic plasmid CloDF13[END_REF]) which produces about 20 to 40 copies per cell [START_REF] Sambrook | Molecular cloning : a la oratory anual 2nd ed[END_REF], and with either Kanamycin or Spectinomycin resistance genes (see appendix A for a list of all the low-copy MoClo plasmids). The use of these novel backbone plasmids does not change the procedure for Modular Cloning, except for differing antibiotics used at the selection step.

more than two parts at once. In the MoClo version of this Golden gate technique, the overhangs are standardized so that they always ligate in a specific order. The MoClo procedure illustrated in this panel is level 0 promoter integration into the library, i.e. the introduction of a new promoter into a level 0 pL0-P backbone. The bpiI restriction enzyme is used for level 0 assemblies. B) Level 1 assembly. In level 1 assembly a transcription unit is created from level 0 parts on level 0 plasmids (pL0). In this study the level 0 plasmids that will be used are promoters (pL0-P), RBSs (pL0-U), coding sequences (pL0-SC), and terminators (pL0-T). These 4 elements constitute the basic parts of transcription units in bacteria. In this illustration 4 of those parts are assembled together and into a level 1 backbone plasmid (pL1) to form a transcription unit. The bsaI restriction enzyme is used for level 1 assembly. C) Level 2 assembly. In level 2 assembly, transcription units from previous level 1 assemblies are ligated together and into a level 2 backbone to form a genetic circuit. Level 2 assembly is performed with bpiI restriction enzymes.

This change in the copy number of plasmids per cell solved the mutation problem for almost all variants of the toggle switch branches. An interesting outcome is that although the copy numbers of plasmids in each cell with this new library were between 10 and 70 times lower than the original MoClo plasmids, the plasmid yields out of the plasmid preparation steps that were performed at the end of each MoClo step were only 2 to 5 times lower than the typical yields with pUC origins. This result illustrates a tradeoff between yield and the burden on the amplifying cells. Higher copy plasmids may not always be the best choice for MoClo, and for plasmid preparation in general, especially in the case of Golden Gate cloning, which does not require high concentrations of plasmids. A remarkable result of the original MoClo paper is that the authors are able to seemingly easily construct 11 different transcription units and assemble them into a 33 kb plasmid, without burden problems. It is important to note however that the circuits developed are to be expressed in plants, with plant promoters and plant virus RBSs used in the transcription units. So, even though the plasmid preparations are performed in bacteria at each MoClo step, the encoded proteins are not expressed, and the burden is therefore much lower.

Unfortunately, in a few cases I still had problems assembling the plasmids, even with low copy plasmids. I did not know whether expression burden during plasmid preparation was the problem or if it was happening earlier, during DNA assembly. To circumvent the issue without having to pinpoint the source of the problem, I incorporated a new part into my library of RBSs in MoClo level 0 format (see Figure 2-5B and parts 32 and 33 in appendix A). This part consists of type IIS identification sites instead of an actual RBS sequence: this way, non-functional transcription units can be constructed and assembled into circuits, and the real RBSs can be incorporated into the circuit at the last moment (see Figure 2-5C). This solved several problems: firstly, there was no protein expression burden from the level 1 plasmids during plasmid preparation of the toggle switch branches, in which the lac and tet promoters are completely unrepressed. Secondly, the assembly of multiple parts at once, although an advantage of the MoClo technique, is of course less efficient than a one part-one backbone assembly with the same procedure. Therefore, the fact that RBS integration was done at the end of the whole assembly, with only one part inserted at a time, would compensate the ligation difficulties that could be associated to that specific part. Finally, even though this method required one extra step to start from single parts to obtain a final working switch, once I got the version of the toggle switch circuit with the "wildcard" restriction-site parts inserted where the RBSs should be, it took only one extra step to produce a new, different toggle switch. With this circuit now, inserting completely new RBSs only requires one robust and efficient golden gate step. Or two in the case of a "double-wildcard" toggle switch.

Operons are omnipresent in bacteria and are its main method of transcriptional coupling in cases where different proteins must be expressed at comparable levels. RNA polymerases transcribe the coding sequences of all genes in an operon on a single strand of messenger RNA, and ribosomes translate it into proteins from the same strand. Although coupling can be even stronger with fusion protein designs, an operon induces a strong correlation between fluorescence intensity and transcription factor concentration in the cell since most of intrinsic noise seems to happen at the transcription level [START_REF] Ozbudak | Regulation of noise in the expression of a single gene[END_REF].

In an operon, the ribosomes read each coding sequence and release the unfolded protein strand at the end of each CDS when they reach a stop codon. Normal ribosome behavior when they reach a stop codon is to unbind from the RNA strand. However, two mechanisms exist in operons to ensure that the ribosome continues translating after each gene. The first, more common one is the presence of another ribosome binding site in the intercistronic region [START_REF] Maizels | E. coli lactose operon ribosome binding site[END_REF][START_REF] Schaefer | Ribosome-binding sites and RNA-processing sites in the transcript of the Escherichia coli unc operon[END_REF]). This allows for different translation rates between the different CDS in the case of operons where proteins need to be expressed in non-equal stoichiometry but still have linear co-expression levels. In those cases ribosomes that just unbound the previous coding sequence immediately rebinds the next ribosomal binding site and continues translation, but other ribosomes can also bind to the second coding sequence directly. A second, more complex mechanism induces translational coupling and coexpression in a 1:1 stoichiometry. In this mechanism, the stop codon of the first CDS is next to, or sometimes overlaps with, the start codon of the next coding sequence, and the end of the CDS of the first gene features a statistically weak Shine-Delgarno sequence4 [START_REF] Oppenheim | Translational coupling during expression of the tryptophan operon of Escherichia coli[END_REF][START_REF] Torgov | Efficiency and frequency of translational coupling between the bacteriophage T4 clamp loader genes[END_REF][START_REF] Govantes | Mechanism of translational coupling in the nifLA operon of Klebsiella pneumoniae[END_REF].

I developed both types of operon by PCR amplification and re-assembly into a MoClo pL0-SC plasmid similar to that of fusion proteins described in section 2.5. I only developed the versions where the fluorescent reporter genes were placed after the tetR and lacI genes, so that I could infer whether co-expression of both proteins in the operon was happening from simple fluorescence measurements. I then assembled these new CDS level 0 parts into level 1 transcription units for the branches of my toggle switch (see appendix A, level 1 TUs 1.40 to 1.51). I could not get the overlapping stop-start codon strategy to work, and continued working with only the multiple RBS operon designs.

Fusion protein branches design

Before designing operon-based toggle switches, I tried to design fusion proteins to observe the state of the toggle switch. I designed circuits with the LacI and TetR transcription factors fused to the monomeric fluorescent proteins mKate2 (red fluorescent protein) and mEGFP (green fluorescent protein). I initially went through the trouble of making fusion proteins because measuring their associated fluorescence would give me the state of the toggle switch directly, whereas other methods such as co-expression, in an operon or another transcription unit under the same promoter, would not have a 1:1 transcription factor to fluorescent report ratio, as the co-expressed protein levels would be subject to independent noise and independent degradation times.

There are examples in the literature of fusions between the TetR and LacI proteins with fluorescent reporters (Rosenfeld et al. 2002;[START_REF] Webb | Bipolar localization of the replication origin regions of chromosomes in vegetative and sporulating cells of B. subtilis[END_REF][START_REF] Dewar | Tension between two kinetochores suf ces for their bi-orientation on the mitotic spindle[END_REF][START_REF] Marshall | Interphase chromosomes undergo constrained diffusional motion in living cells[END_REF][START_REF] Kato | Chromatin of endoreduplicated pavement cells has greater range of movement than that of diploid guard cells in Arabidopsis thaliana[END_REF]. For TetR-GFP fusions it has been demonstrated that the TetR transcription factor keeps its DNA-binding property, represses expression downstream of the tet promoter, and is still inhibited by tetracyclines (Rosenfeld et al. 2002). The LacI-FP fusions, on the other hand, were proven to bind the DNA domains, but the expression downstream of the lac promoter as well as the effect of lactose equivalents have not been reported in the literature. Due to the tetrameric nature of both LacI and TetR binding to DNA, it was unclear whether DNA binding of fusion proteins could take place, but the aforementioned studies proved otherwise. The question of IPTG-LacI binding was still open.

I developed the fusion proteins, each with the fluorescent reporter on either the N-terminus or the C-terminus of the transcription factor protein, to obtain the following assemblies: LacI::mKate2, mKate2::LacI, TetR::mEGFP and mEGFP::TetR. I amplified the coding sequences by PCR and inserted type IIS enzymes restriction site at the 5' and 3' tail ends of the amplicons to introduce a standard flexible Serine-Glycine protein linker [START_REF] Chen | Fusion protein linkers: property, design and functionality[END_REF] between the two coding sequences (see appendix A). I then transferred them back into standard pL0-SC MoClo vectors to be able to use them in my assemblies. Unfortunately Level 1 cloning was problematic for most of the branches, and I would sometimes get mutations in the linker region in addition to the more usual mutations in the RBS and promoter regions. I did not assemble them into toggle switches right away, but instead assembled them into simpler one-gene-one-feedback circuits (see circuits 2.4 and 2.5) to rapidly find out whether the circuits would respond to inducer inputs and to see if I was able to measure the fluorescence levels.

Although the cells were fluorescent, large foci would appear in the cells indicating toxicity, as well as a remarkable increase in photosensitivity resulting in cell death during the first few hours of time-lapse experiments, and those cells that did not die right away would often elongate or stop growing altogether. This could be a sign of misfolding of the transcription factors, leading to toxic aggregates. It seems however that not all of the transcription factors would misfold, since, in survivor cells, the levels of each fluorescence level could be swayed with IPTG or aTC induction. Still, it became rapidly evident that the catastrophic cellular death rate during observation would make it almost impossible to try to control individual cells on any practical time horizon. for input delivery. Finally, I wrote software for microscope control, basic image analysis, control and communication with the valves controller, thus closing the loop and allowing for cellular control.

Microfluidics

I had the opportunity to access a clean room facility at Paris-Diderot University where I could experiment with lithography and microfabrication techniques, and design my own wafers for microfluidic devices. Our team has a history of developing its own microfluidic wafers for S. cerevisiae (Uhlendorf et al. 2012;[START_REF] Vulin | A quantitative approach to microbial population growth using tailored cylindrical yeast colonies[END_REF]Llamosi et al. 2016) and I took advantage of the expertise in the team to develop my own devices for bacteria.

Molded PDMS devices

The dominant approach for making microfluidic devices is based on soft lithography and PDMS molding. A silicium wafer is covered in a layer of epoxy-based resin of known thickness. The resin is insulated to obtain a desired pattern on the wafer. The insulation techniques used in this thesis are described in the following two sections. Once the desired pattern has been drawn, the so-called master wafer is used as a reusable negative for replicamolding of the pattern with Polydimethylsiloxane.

Polydimethylsiloxane (PDMS) is a transparent silicon that is a viscous fluid in its monomeric form, and an elastic solid when homopolymerized. Liquid PDMS supplemented with a curing agent to catalyze polymerization is poured onto the wafer mold. The liquid PDMS will perfectly follow the mold's shape and then cure into its solid polymerized form. To form a working microfluidic device, the solidified silicon is peeled off the master wafer and stuck onto a glass slide. The glass slide floors the circuit and the device can then be used to load cells, flow media and various chemical, and the chambers and channels can be observed through the glass slide on a microscope. Transmitted light can be shone through the device since PDMS is transparent.

Microfluidic wafers fabrication methods

Various methods exist for developing microfluidics devices for in vivo cell cultures and observation, such as wafer engraving, 3D printing, or CNC milling. The most common technique is so-called "soft' lithography, in which layers of epoxy-based resins are insulated locally to create patterns on a silicium wafer. This method is described in this section and was used to develop the microfluidic devices presented here.

Photolithography

The most common way of designing microfluidic devices is by coating a wafer with an epoxy-based resin, the SU-8 resin developed in the 1980s by IBM, and then illuminating this resin with high intensity UV light. The light goes through a custom made negative mask and only the desired parts are exposed to the high-energy photons. The resin is photosensitive and will solidify when exposed to high-energy particles. A solvent bath will dissolve all parts that were not exposed to the UV light, and only the exposed part will remain. Coating of the wafer is performed with a spin coater, and rotational speed is adjusted to obtain precise layer thickness. Several variants of the resin exist, of different viscosities, to allow for a wide range of possible layer thickness (from about 500nm to 100μm). Several objects of different heights can be obtained on the same device by sequentially applying different layers of SU-8 and insulating them with UV light one by one through patterned chrome masks (see step 2a in Figure 3-1). A review of the type of devices that can be obtained with this procedure is given in [START_REF] Ng | Components for integrated poly(dimethylsiloxane) microfluidic systems[END_REF].

Although photolithography is a relatively simple and fast process, it is limited in its resolution by the diffraction of light on the insulation mask. Details under 5 µm start getting difficult to obtain and require the use of vacuum chambers and optical filters. The closer the dimensions get to the wavelength of UV light, the more imprecise the details get.

Electron-Beam lithography

For smaller details, typically around 1 micron or less, I had to use electron-beam lithography, or EBL: Since using a lithography mask causes diffraction that limits the resolution of the insulation, the solution is to direct the high-energy particles beam directly towards the wafer and scan it through the parts to be polymerized. However, mechanical orientation of the beam is very imprecise, and a light beam cannot be bent easily towards a specific location on the wafer. Electron trajectories, on the other hand, can be very precisely oriented with an electromagnetic field, as is routinely done in a scanning electron microscope. In practice, electron-beam lithography actually uses slightly modified scanning electron microscopes to guide an electron beam over a resin layer, following an insulation path predetermined numerically by the experimenter (see step 2b in Figure 3-1). Similarly to photolithography, the high-energy electrons create Lewis acids in the resin and catalyze the homopolymerization reaction.

EBL allows for nanometer-precise details, and since no physical mask is used, the variety of shapes, sizes, details and structures of the microfluidic circuits obtained is not limited by the price and delays linked to the manufacturing of a photolithography mask. It cannot be used on thick layers of resin however, since electrons scatter in matter as they lose energy penetrating into SU-8. Increasing the energy of the electrons allows for deeper penetration, but the penetration depth increases only logarithmically with the electrons' energy [START_REF] Suñé | Electron beam lithography for Nanofabrication[END_REF]). The working surface on our apparatus is also limited to, at best, 1mm. One can insulate several working surfaces, but the details may not be perfectly aligned from one working area to the next since the displacement between scanning surfaces is performed mechanically.

Although this method has been used extensively in other domains of micro-and nanofabrication [START_REF] Tseng | Electron beam lithography in nanoscale fabrication: Recent development[END_REF][START_REF] Suñé | Electron beam lithography for Nanofabrication[END_REF], and has been demonstrated to be a versatile microand nano-fabrication method in SU8 resin [START_REF] Kudryashov | Grey scale structures formation in SU-8 with e-beam and UV[END_REF], its usage in microfluidic devices fabrication is still anecdotal [START_REF] Mali | Facile fabrication of microfluidic systems using electron beam lithography[END_REF]). I started working on this technique after discussing my light diffraction problems with quantum physicists at the clean room who used this method routinely on other resins. Although the production of a complete device with EBL and photolithography is more tedious than with photolithography only, iterations on the EBL part of the designs can occur at a much faster time scale because the technique does not require the edition of a new insulation mask after each modification to the desired pattern. I them. Two methods exist: 1) let cells grow everywhere in the microfluidic chip. The cells end up colonizing the chambers and at this point the cells in the flow channel are flushed away. This method has various limitations: first of all, it requires setting up the experiment a long time in advance to let the cells grow into the chambers. The second problem is that flushing will not be 100% efficient, and some cells will remain in the channel flow after flushing and grow in the flow channel. 2) Centrifuge cells into the chambers. I designed a microfluidic chip centrifugation arm that can be used with a spin coater to ease cell loading. Once the cells were loaded I would set up the chip in the input delivery and flow apparatus and on the microscope for single cell observation.

Early device designs: Population chambers

I based my first wafers on the device developed by Jannis Uhlendorf in our team for his control platform for yeast (Uhlendorf et al. 2012). I adapted it to get the right height for the chambers to make sure that my bacteria would not grow in several layers in the chambers or be able to move at all once in there, but of course the chambers also had to be high enough to allow the cells to enter in the first place. I found that the optimal height for the growth chambers was 0.7µm. Because the chambers were wide compared to their height of 0.7µm, the ceiling of the chambers would often collapse.

Surface passivation, clogging, and flushing

Bacteria tend to grow everywhere in microfluidic devices, both on PDMS and glass. This can cause several problems: First of all the accumulation of cells in the channels just outside of the growth chambers can exert pressure on the cells inside the chambers and have an impact on their growth rate. Secondly, the number of cells growing in the delivery channels would keep on increasing, possibly up to a point where nutrients and input chemicals are segregated or consumed by those cells, hindering the controllability of the cells inside the growth chambers. Finally, bacteria tend to aggregate and form biofilms, and an uncontrolled growth in the main flow channel would rapidly lead to clogging of the channel, possibly with biofilms forming in the entire apparatus.

I have faced all the above scenarios, both in mother machine devices and in monolayer devices, and the necessity of good control of bacterial growth outside of the dedicated chambers rapidly became evident. Surface passivation was a first step to help reduce the spread of bacteria in main channel. I started using bovine serum albumine (BSA) with the population device described in section 3.1.4, and the results were promising. I followed the same procedure with the mother machine device but two problems arose: first of all, BSA is a fragile and somewhat expensive protein. Its passivation effect degrades with time and new stocks must be prepared periodically. It also degrades throughout the experiment and after 12 to 16 hours bacteria start growing in the channels again. The second, more inconvenient problem was that cell loading in the mother machine chambers was harder after BSA passivation. Whether it was caused by accumulation of BSA in the chambers, a higher fluid viscosity or other effects is unknown, but I had to passivate the surface after cell loading, which was both more complicated and less efficient since some cells were already stuck to the surfaces of the device.

I switched to a cheaper and more robust alternative with Pluronic F-127. Surface passivation with pluronic prior to cell loading did not pose the same problem as BSA. Pluronic is a cheaper and more stable molecule, so not only was storage not a problem, I could also mix Pluronic into the growth media that would later be flown through the microfluidic device and autoclave it, which meant that surfaces would not be depleted of Pluronic over time.

To further reduce cell growth outside of the dedicated chambers I would also periodically flush them by running the peristaltic pump at full speed for a short period of time (usually for 30 seconds every 30 minutes). The custom program interfacing with the pump would also communicate with the acquisition session, to ensure that the pump was not flushed during acquisitions: With the pump running at full speed, the minor change in pressure in the chip would suffice to slightly distort the shape of the chambers, thus reducing the performance of the autofocus, drift correction, and image analysis. See section 0 for more details.

Input delivery

Characterizing the library of putative toggle switches and carrying out PI control experiments required the possibility of injecting variable levels of the two inducers in the microfluidic chip, so I had to develop some sort of mixing apparatus. While a variety of microfluidic mixers exist in the literature [START_REF] Lee | Microfluidic Mixing: A Review[END_REF], none of them was suited to our approach. Passive mixers introduce delays in the time between mixing and delivery or require complex microfabrication techniques, and active methods require even more complex assembly methods, sometimes alongside the integration of bulky and obstructive hardware close to the chip. Moreover, those systems require some form of pressure control system, which is itself a costly and finicky piece of equipment.

In our implementation of microfluidic mixing, we assumed that the process of delivery through the microfluidic tubing and channels via peristaltic pumping, and the diffusion through the cellular membrane, acts as a low pass filter for chemical signals between the environment and the cytoplasm, and therefore would tend to average out fast oscillatory changes in the environment. Such an assumption makes it possible to use pulse-width modulation in our drug delivery method. To get a certain "sensed" concentration of inducers for the cell, we switch between three inputs: one with a high concentration of IPTG (1mM), one with a high concentration of aTC (100ng/mL), and one without inducers for dilution. For a certain concentration of inducer, the duty cycle is adapted and diffusion in the tubing and the device and through the membrane does the rest (see Figure 345). To ensure that the average concentration sent to the cells was the one indicated by our choice of duty cycle, we calibrated the duty-cycle to concentration ratio by running the valve controller for extended periods of time at different duty-cycle values and measured volume depletion. We then used this 3-way PWM valves setup to mix solutions of fluoresceine and rhodamine and measured fluorescence levels in a microfluidic chip to double check our result and also to verify that cells received a mixed level of both inducers (see .

To be able to alternate fast enough between media and also to resist high flow rates and high pressures, we used valves from the Lee Company. These valves operate on 12 V and can draw up to 100 mA. For those reasons they could not be operated with a simple Arduino and a power adaptation circuit was necessary, especially to drive more than one valve. We designed a custom arduino-based circuit board to host all electronic components and act as an interface between the computer and the solenoid valves. The board can drive up to 36 different valves.

To optimize space, adaptability and ease of use, the card is built around an Arduino nano board that drives two MCP23017 chips5 over i2c serial, which themselves drive power MOSFETs that drive the valves. The entire design and code for Matlab and the Arduino Nano can be found on github 6 . I have since developed new, more compact implementations of this board to drive up to 40 solenoid valves for other projects that can be found on the same page.

Reference crosses

In the next section (3.2) I am going to present some of the image analysis and data extraction algorithms I used to monitor cells fluorescence. But an important step prior to that is the optimization of the acquired images. The image analysis is greatly simplified if the images are of good quality and their acquisition conditions are consistent with eachother. Good focussing is an important aspect of this process. A microscope does not stay in focus on the observed specimen over time if its position is not corrected periodically. Images are acquired automatically and in real time, without user supervision and usually at several different positions on the chip. All these issues further complicate the task of acquiring good quality, consistent data.

Autofocussing is a non-trivial problem in time-lapse microscopy, and online image analysis requires a precise and robust autofocus for optimal quality data. A number of autofocussing algorithms exist, and can be separated in two groups: hardware based autofocus and imagebased autofocus. The hardware based ones measure the distance between the objective and the specimen observed, usually using laser triangulation, and try to maintain this distance constant. Although this approach is usually more robust, it does not measure image properties directly, and uses the proxy of the measured distance instead. Unfortunately, the measure can drift over time, especially in the case of immersion oil objective. The changes in focus are usually small, but in the case of bacteria, minor variations in focus can have dramatic effects on the quality of the extracted data. The second approach measures some property of the images acquired (usually average image gradient) and tries to minimize or maximize it.

Although this can produce satisfactory results, the robustness of such a method is often inadequate for time-lapse microscopy of live cells. Because the cells are growing in the field of view, the measured properties of the image change over time, which can lead to focus drift microfluidic devices or even different organisms. We have used it to perform robust real-time segmentation of our cells on this platform, but not on closed loop experiments. This algorithm has been designed in my last year of PhD and has evolved continuously during that time period. To keep data consistent between experiments as well as to avoid the delays that a full integration into the platform might cause, we decided not to use it in our control experiments.

Prior to the development of this technique however, we developed several cell segmentation techniques. The first, most robust one, simply extracts the fluorescence from the end of the mother machine chamber. This simple method was used for online image analysis for fluorescence extraction because it would perform robustly throughout the experiment. Other methods were also developed for a posteriori image analysis.

Robust algorithm for online measurement of fluorescence levels

Cell segmentation is performed a posteriori because it usually requires tinkering and often trials-and-errors to work robustly on an entire dataset, and its performance can vary from one dataset to another to another. Most cell segmentation approaches still require a significant amount of manual corrections by the user to reach satisfactory tracking performance. Because of this, traditional segmentation approaches based on morphology or active contours could not be used on online experiments. A much simpler image analysis technique was used for the majority of the toggle switch analysis.

In time-lapse acquisitions of the mother machine device, the mother cells at the end of the mother machine chambers stay in the same position in the image throughout the entire experiment. Bacteria reproduce by dividing in the middle, so some part of the image always included a significant portion of the mother cell. The algorithm used for online image analysis simply extracts the mean fluorescence from that part of the image. At the beginning of the experiment, the user selects the chambers to observe throughout the experiment and draws a rectangular region of interest (ROI) of 20 by 10 pixels where the mother cell is. During the time-lapse acquisition, lateral drift is corrected, and the fluorescence in GFP and RFP is measured and sent to the control algorithm.

Image gradient and ellipsis fitting on mother machine images

With the mother machine microfluidic device, the segmentation problem was greatly simplified, and the algorithm described above was sufficient to extract fluorescence levels for the mother cells, but could not identify daughter cells and extract their fluorescence. Here I describe a simple segmentation algorithm to identify single cells in the chambers and measure their fluorescence.

Identifying growth chambers is a simple task, since they are well separated and of known size and shape. With the chambers identified, the complexity of segmenting cells in each chamber decreased significantly. The cells cannot grow side-by-side, which is a major problem for morphology or active contour methods (see Figure 3-10 and chapter 4), and also grow in a well-aligned strand of cells. One of the disadvantages of the narrow chambers though is the proximity of the cells borders with the chamber walls, which can interfere with morphology operations such as range filtering or with active contour methods.

I developed a custom segmentation program that circumvents the problem of the PDMS walls and identifies the separations between cells robustly. To avoid dealing with the walls altogether, only the image gradient along the chambers axis was considered and not the 2D image gradient commonly used for edge detection. In combination with morphology operations and thresholding the identification of cells separation would be easily and robustly obtained throughout an entire image sequence. Ellipses were then fitted to the identified cell regions to identify elliptic ROIs for fluorescence extraction. Although ellipses are not the best model for describing the shape of Escherichia coli bacteria, the minimal number of their parameters allowed for fast and robust identification with known algorithm. More complex descriptions of the shape of the cells would have taken more time to fit and be more prone to errors. Moreover, it became rapidly apparent that even in the simplified setting of the mother machine, considerable user oversight was still necessary for the segmentation to run smoothly in online experiments.

The main problem emerged from the fact that between experiments lighting and focusing conditions are never exactly the same. Even throughout an experiment and even with state-ofthe art autofocussing, focus might drift slightly over time. Aging cells also present visible differences from young cells. All those changes require fine-tuning of the few parameters of the algorithm before each experiment, with the hope that the images will not change too much throughout the experiment. So even though the algorithm I developed can segment an entire time-lapse automatically with almost no segmentation errors a posteriori, it could not be used for online segmentation since in this case the optimal segmentation parameters must be guessed prior to the experiment.

active contour or feature extraction techniques like the generalized Hough transform, sometimes in combination with a model of the expected cell shape and various cost minimization schemes. I tried most of the available cell segmentation programs I could find in the literature [START_REF] Kamentsky | Improved structure, function and compatibility for CellProfiler: modular high-throughput image analysis software[END_REF][START_REF] Chowdhury | Cell segmentation by multi-resolution analysis and maximum likelihood estimation (MAMLE)[END_REF][START_REF] Hilsenbeck | Software tools for single-cell tracking and quantification of cellular and molecular properties[END_REF][START_REF] Wang | Image segmentation and dynamic lineage analysis in single-cell fluorescence microscopy[END_REF][START_REF] Young | Measuring single-cell gene expression dynamics in bacteria using fluorescence time-lapse microscopy[END_REF][START_REF] Delgado-Gonzalo | Spline-based framework for interactive segmentation in biomedical imaging[END_REF][START_REF] Huth | TimeLapseAnalyzer: Multi-target analysis for live-cell imaging and timelapse microscopy[END_REF][START_REF] Klein | TLM-Tracker: software for cell segmentation, tracking and lineage analysis in time-lapse microscopy movies[END_REF][START_REF] Hand | Automated tracking of migrating cells in phase-contrast video microscopy sequences using image registration[END_REF]. Unfortunately, although they can perform well for offline cell segmentation, and near perfectly with a user's supervision, none of them gave satisfactory results for online segmentation and tracking.

The core problem with those methods is that they rely on a long sequence of minor operations that, though efficient and relatively robust when taken separately, amass into a complex segmentation procedure with a lot of independent tuning parameters. Each sequence in the whole operation is optimized by the user to give the best results for a reduced collection of images, and then the algorithm is applied to entire time-lapse sequences. Unfortunately the optimization of the parameters of a list of operations by the user is a very rigid approach, which doesn't generalize well to new situations and is especially detrimental to online segmentation. The thresholds, structuring elements sizes or other parameters will not be optimal for all images or even all cells in a single image, leading to segmentation inaccuracies, and accumulating tracking errors. The user/developer can try to set up rules for the program to adapt and tune its parameters to different situations, but very quickly the algorithm turns into an ever-increasing collection of exceptions and caveats and special cases, and it ends up being even less applicable to other experiments. See Figure 3-10 for an illustration of the problems faced by those algorithms.

Experiments automation

Experiment automation, although not as obviously demanding as other technical components of the real time control platform, required a substantial amount of work. While numerous microscope management software exist, few allow interfacing with custom programs. We also wanted to be able to implement complex image acquisition routines, and this dictated our implementation of our own acquisition engine from low-level microscope management function. Following the same logic, we developed the other parts in the control loop in a modular structure: Each part of the algorithm would consist of objects with standardized inputs and outputs to make the replacement of any algorithm in the loop seamless, such as a switch between control strategies (e.g. PI, Bang-bang) or between image analysis algorithms.

To make the entire experimental automation robust we also divided the automation into four main independent blocks: 1) Microscope management, 2) image analysis, 3) control algorithms, and 4) microfluidic actuator supervision. These four blocks were implemented in Matlab and run separately in four different Matlab sessions that would communicate through TCP/IP. Beyond making the software more robust because the four blocks work independently and asynchronously, it also facilitates parallelization or even distribution of the entire control feedback loop over different machines: i.e. to run the image analysis or control strategy block on a separate machine for computational reasons.

All traditional microscopy brands implement their own in-house version of microscopy platform control software. However, our application requires some interfacing with the microscope software, and the microscopy brands develop closed, proprietary software that will not interface with all other brands. To access this level of flexibility we used the opensource microscope management suite Micromanager [START_REF] Edelstein | Advanced methods of microscope control using μManager software[END_REF].

Micromanager is an open-source, cross-platform desktop application, to control a wide variety of motorized microscopes, scientific cameras, stages, illuminators, and other microscope accessories. It supports a wide range of microscopy hardware and can also be interfaced with custom hardware, with native support for Arduino-based devices. Although it features a graphical user interface and scripting abilities, the standalone version of Micromanager was not flexible enough for our usage and could not easily be interfaced with our Matlab analysis functions. But a convenient feature of the program is the possibility to access the Core API of Micromanager, as well as some of its graphical functions, through Matlab. We developed a functional Graphical User Interface to control our microscope via Matlab, and at the same time implemented an advanced time-lapse acquisition engine, with easy interfacing with our custom scripts. It gave us the liberty to call our homemade Matlab scripts in the middle of microscopy acquisitions, and to send information to other Matlab sessions easily. We also implemented custom scripts for autofocussing or lateral drift stabilization.

The other three modules of experiment automation are mainly servers that communicate with each other to close the feedback loop. Each one of them would instantiate object implementations of the image analysis, control and actuators supervision algorithms and forward it the data received. The inputs and outputs of the object methods are standardized so that different algorithms can be used without requiring any re-writing of the main structure of the code. For example, the image analysis algorithm described in chapter 2 was integrated to the platform with little effort once the algorithm implementation was standardized.

Although still a work in progress, this general code architecture and corresponding user interfaces are proposed as a generic implementation of any gene expression control platform, in which different core algorithms can be used interchangeably on a variety of hardware equipment. All source code as well as documentation can be found on our github page for the project 7 .

With the platform assembled and automated, the cell chassis constructed and toggle switch circuits assembled, I could start to acquire characterization data and, with the knowledge gathered from it, develop a mathematical model of my system to simulate control in silico and study its response to dynamic perturbations.

Modeling

To understand the dynamics of our system and analyze the results of the control experiments on genetic toggle switches, we developed an in silico model of toggle switch behavior. The mathematical model of the system was fitted to experimental data and used to study theoretically the controllability of the toggle switch with various control strategies. It was then used to analyze the behavior of the toggle switch after surprising control experiments results and helped us understand its response to dynamic perturbations. We developed both deterministic and stochastic simulation approaches to study the effects of noisy gene expression on control performance.

Although models of the toggle switch exist in the literature, none of them have been fitted to data, except for the one described in Wu et al. (2013). But, their LacI-TetR toggle switch was implemented in Saccharomyces cerevisiae, and based on a completely different family of promoters. I used their study of the genetic toggle switch as a starting point for developing a model of the toggle switch. The model is presented here in its final version.

The reaction network of the genetic toggle switch and our modeling choices are described in the following paragraphs. Any gene regulatory network cannot be entirely independent from its host cell, and of course some of the modeling choices are going to appear as oversimplifications of the intricate network surrounding even this simple 2-gene synthetic circuit. Nonetheless, we believe they are sufficient to understand the main dynamics of the toggle switch and study its response to dynamic perturbations and control. We could have reduced the complexity of our model even further, as in early studies of the toggle switch [START_REF] Gardner | Construction of a genetic toggle switch in Escherichia coli[END_REF][START_REF] Cherry | How to make a Biological Switch[END_REF], but we are especially interested in the dynamics of our system, and those early models do not account for the inertial nature of the evolution of our toggle switch state, which is a key element in the evaluation of the performance of the different possible control approaches.

The reaction network

In this section I present a model of the pseudo-reactions describing the functioning of the genetic toggle switch that was used as a basis for developing our model.

LacI-DNA and LacI-IPTG interactions

The lac repressor LacI forms a tetramer of four identical subunits that normally binds tightly to the promoter. However, the repressor can also be only partially bound and not fully inhibit the expression of the genes downstream of the promoter. When IPTG binds to LacI, the protein changes shape and no longer can bind to the DNA. A detailed description of the DNA-LacI-IPTG interactions can be found in [START_REF] Lewis | Crystal structure of the lactose operon repressor and its complexes with DNA and inducer[END_REF]. A list of the corresponding interactions is then8 :

With and describing the dimeric and tetrameric versions of LacI respectively, while and represent the repressed states of the LacI tetramer and lac promoter respectively.

TetR-DNA and TetR-aTC interactions

In a similar fashion, TetR dimers assemble to bind to DNA. Although they do not twist DNA into a loop, the TetR family of repressors strongly binds to DNA through a Helix-Turn-Helix motif. Access to DNA is thus blocked for RNA polymerase binding. However, the TetR protein features a cavity in which tetracyclines can bind. In the presence of tetracyclines the TetR protein changes conformation and can no longer bind DNA. It is not clear whether two dimers can bind a tet operator. For a detailed description of those interactions see [START_REF] Ramos | The TetR Family of Transcriptional Repressors[END_REF]. The list of interactions is 9 : With describing the dimeric state of TetR. and representing the repressed states of the TetR dimer and tet promoter respectively.

Transcription and translation

Transcription happens downstream of the unrepressed promoters, and proteins are then translated from the transcribed mRNAs. We do not consider here leaky expression connected to partial binding of the repressor to the toggle switch and consider that a bound dimeric/tetrameric repressor completely represses the expression of the promoter. coefficients, which are not fixed to 4 as a strict mechanistic interpretation would have it, and are given a wide fitting range instead. 9 Again, monomer binding to DNA and aTC is not represented. Monomer interaction as well as the potential double binding of TetR dimers to DNA is taken into account in the non-preset hill coefficient in the fitting section.

Dilution and degradation

Finally we model the decrease in protein and mRNA levels caused by growth dilution and degradation. In the case of protein dilution we do not model cell volume specifically, we model it instead as a normal degradation reaction for simplicity:

With the symbol representing nothing, or null.

ODE model

To reduce the dimensionality of our model and to reduce the number of parameters involved we model the binding-unbinding event using Hill functions. With this assumption, the ODE model was narrowed down to a 5-dimensional set of coupled ODEs:

Transcription ⁄ ⁄
The transcription rate consists in two main terms: The "basal rate" describing leaky expression from completely repressed promoters, and the modulated expression rate describing the expression from the proportion of unrepressed promoters consisting in two nested Hill functions. The rate of unrepressed transcription is represented by the parameters, and the and terms represent respectively the half occupation level and Hill coefficient for each of the binding-unbinding mechanisms. This structure causes the rate of transcription of each mRNA species to be a decreasing function of the opposing free protein, and the fraction of the free protein is also a decreasing Hill function of the associated inducer.

The degradation of the two mRNAs is a simple linear function. The LacI and TetR variables in the model represent all forms of the repressors, monomers, dimers and tetramers, with and without bound inducers.

Translation

Here the degradation of LacI and TetR is a linear function of the protein. But because it is generally accepted that decrease in protein concentration is mostly due to dilution [START_REF] Larance | Global subcellular characterization of protein degradation using quantitative proteomics[END_REF], the degradation rate is the same for both proteins.

IPTG delay

We observed significant delay in the action of IPTG molecules, which we connected to the removal of the LacY permease that transported it through the membrane (see section 2.1). We added a first order equation for a simplified model of diffusion through the membrane with a constant diffusion term . To keep the model simple, diffusion time of aTC through the membrane was considered negligible. The and variables are input signals provided by the experimenter or the control algorithm.

Matlab code implementing those equations can be found on our modeling github repository 10 .

Because the mRNA dynamics and the protein dynamics evolve different timescales, we used a stiff ODE solver (ode23s in Matlab) to integrate the equations in between changes in the driving and variables. In in silico control experiements, the control algorithm is ran outside of the model evaluation algorithm for the sake of implementation simplicity and modularity. Therefore our general implementation considers the ODE set to be a switched nonlinear system and features a custom solver for such systems built around the ode23s solver11 .

Gillespie's stochastic simulation algorithm

Because noise can greatly affect the quality of control, I also developed a stochastic model based on the pseudo-reactions described in section 4.112 . This interpretation is based on a continuous-time Markov chain model of the process and can be solved using Gillespie's Stochastic Simulation Algorithm (SSA) [START_REF] Gillespie | Exact stochastic simulation of coupled chemical reactions[END_REF]. The Gillespie algorithm is an exact simulation of the stochastic behavior of a process. However, because it was designed to simulate random encounters between relevant molecules due to Brownian motion, it requires simulating every single reaction between two or less molecules/complexes. In our case, we kept the assumption on the Hill functions done in the ODE model of the reactions network for two reasons. Firstly, parameters were fitted to the Hill-based ODE model, and it would not have been possible to deconstruct the model back into equations where all binding and unbinding events are simulated. Even if a deconstructed model had been fitted to the characterization data, some of the parameters could not have been identified because of current limits on protein data resolution, and to my knowledge state-of-the-art in vivo proteins levels measurement is still a long way from reaching the necessary precision level. The second reason is that binding-unbinding events happen orders of magnitude more often than other events, which led us to the Hill functions in the first place, and simulating those events with Gillespie's SSA would severely increase computational time. Applying this approximation to the SSA in the case of chemical kinetic systems with disparate rates is a common workaround to this issue, and in most cases does not have a major impact on the simulated levels of noise [START_REF] Rao | Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm[END_REF]. The pseudo-reactions modeled by our SSA implementation and their propensities are described in Table 4.3-1. The implementation of the stochastic model can be found in our github repository 13 IPTG diffusion was considered deterministic and the IPTG concentration dynamics were integrated outside of the SSA function through Matlab's ode23s solver.

Parameter identification

To obtain calibration data, we performed 6 experiments differing by the initial state of the cell population and by the temporal profiles of the inducers and probing in various ways the dynamics of the system (see section 3.1 of chapter 3). Model fitting was made using the global optimization tool CMA-ES [START_REF] Hansen | Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation[END_REF]. We used the measured fluorescence values for RFP and GFP directly as proxies for measured molecule numbers per cell, which means that the transcription, translation, degradation and dilution rates as well as Hill half occupation levels are fitted to fluorescence levels. As a first approximation, we assume the measured fluorescence levels per cell to be proportional to molecule numbers. The objective for CMA-ES was to minimize the mean squared relative deviations between model predictions and averaged measured fluorescence.

The optimization was repeated 8 times. Despite the use of a simple model not all parameters were fully constrained by the data, however all estimations produced similar dynamics and similar equilibrium points could be inferred from the different sets of parameters. We picked the set of parameter that produced the unstable equilibrium point with the highest levels of LacI and TetR to maximize the signal-to-noise ratio during our control experiments.

The final parameter values obtained were:

Controllers

The main controllers used in this study are fairly simple although we did use model predictive control algorithms in early theoretical studies of toggle switch controllability. We used the same algorithms for in vivo control and in silico simulations.

Bang-bang control

The so-called bang-bang controller, also known as a hysteresis controller, is a feedback controller that switches abruptly between two states. Although bang-bang controllers can produce optimal control strategies in some cases, they are often implemented because of simplicity or convenience. The input delivery technique can also restrict actuation to a binary all-or-nothing choice in some microfluidic devices. However in our case, the use of a bangbang controller was dictated by early theoretical results that indicated that PI controllers with a strong proportional term would perform better on a population of cells (see chapter 3). This incited us to try the extreme case of bang-bang control: Code implementation of this control algorithm that was used both in silico and on real control experiments can be found in our github repository 14 .

Proportional-integral control

A Proportional-Integral (PI) controller continuously calculates an error value that is the difference between a desired setpoint and the measured level of fluorescence. The controller attempts to minimize the error over time by adjusting the level of inducer. But contrary to the bang-bang controller, the PI controller does not completely open or close the valves, but it can take advantage of the pulse-width modulation implemented with the 3-way valves (see section 3.1.6) With the and as the proportional and integral parameters respectively, the reference levels of aTC or IPTG obtained experimentally (20 ng/mL of aTC and 0.25 mM of IPTG for all toggle switch control experiments), and the time delay before the integral term is applied. The last element, the time delay, was added later in the experimental process to avoid overshoot effects caused by the error just after the objective is applied before the system can be in the vicinity of the objective, which typically takes about two hours.

Code implementing this control algorithm and that was used both in silico and on real control experiments can be found in our github repository15 .

Conclusion

In this chapter we presented the materials and methods used in this thesis to control a genetic toggle switch. In the first part of this chapter, the biological side of the problem was presented, with details on possible implementation choices that did not work to expose the limits of the approach as well as some of the possible ways of improvements over the current implementation. For example, while the fusion protein design was not adapted to our problem, in other problems it should be possible to use this type of design for sensing the level of a protein of interest. Another important contribution is the development of a chassis strain for IPTG-and aTC-based induction that can be used for other control applications. To the best of my knowledge, no bacterial strain was ever optimized for simultaneous induction of the lac and tet systems. Finally, as a general remark on biological systems development, the construction of a chassis and circuit is a time-consuming process in the workflow of external cell control that should not be overlooked when undertaking such a task.

In the second part of the chapter, hardware and software choices are discussed. In particular, a 3-way pulse-width-modulation mixing apparatus is described in what is, to the best of my knowledge, the first attempt at double chemical induction in microfluidic devices. Variants of the mother-machine microfluidic device are also presented to facilitate long-term acquisition and image analysis. This setup allows us to robustly extract single-cell fluorescence data and control single-cells over extended periods of time. The efforts put into the development, automation and integration of the different parts of the platform can be re-invested in single cell control of other genetic circuits, with the possibility to rapidly modify different parts of the platform thanks to its modular nature. One important aspect of the methodology of external control of gene expression that will make reproducibility possible is opening the design of different elements of the platform, and I have already released parts of the designs presented here, and will release the rest of the platform under open-source and open-hardware licenses.

In the third part of this chapter, we discussed the elaboration of an ODE model and an SSA model of the genetic toggle switch to perform deterministic and stochastic simulations of the genetic toggle switch. In the next chapter we use this model to evaluate the possibility to control the toggle switch with different control strategies. Throughout the process of characterization we observed delays in the system that we incorporated into the model. We also discuss fitting of the model to characterization data, and our choices in implementation of the control strategies. A number of improvements could be added to the control strategies, as the two control strategies presented here have been studied extensively and a number of improvements on those techniques as well as other techniques have been presented in the literature.

One of the main domains of application of this in silico feedback platform would be automated characterization of genetic circuits in bacteria, synthetic or endogenous. The control algorithm and the induction techniques presented here are generic enough that the method could be applied to various genetic networks with minor modifications.

Introduction

With the 2-inputs-2-outputs feedback platform presented in the previous chapter, we investigated the possibility of controlling the genetic toggle switch. The toggle switch system is a fundamental element in numerous natural and synthetic gene regulation networks. In this chapter I am going to present dynamical control attempts, and successes, at stabilizing single toggle-switch-bearing cells in the unstable area of this double-negative feedback system. I start by presenting the characterization experiments used for fitting the model of our system, and then present a study of the stability of the fitted model for different values of the inducer concentrations. The main in silico and in vivo results of this thesis are then presented, demonstrating the possibility to control the bistable toggle switch in real-time in the vicinity of the unstable point. Finally, surprising results for population control of toggle-switchbearing cells are analyzed and a new regime of stability for the genetic toggle switch is demonstrated.

Characterization experiments

In order to gather some knowledge on the system as well as identify parameters for the toggle switch model, the selected toggle switch circuit (see section 1 of chapter 2) was submitted to a series of characterization experiments. In the first series of experiments the cells were submitted to long-term exposure to either of the two inducers IPTG or aTC to observe basic dynamic switch responses. A surprising result contrasting with the overnight experiments in batch cultures was that the toggle switch, in absence of inducers, would not remain in its LacI-RFP-dominant state, and would instead drift towards a TetR-GFP-dominant state, even when switched in the opposite state initially. Less surprisingly, this TetR-GFP-dominant state would produce a lower level of green fluorescence than fully activated. Although models predict that this monostable behavior in the absence of inducers is possible, it is relatively surprising that microfluidics experiments provoke a behavior that differs from the batch culture ones. It should be noted however that cells in mother machine devices are submitted to a constant flow of nutrients, which both washes the inducers away continuously and efficiently after they are removed, and puts the cells in a continuous exponential growth phase since they never lack nutrients. Microfluidic device culture conditions and batch culture conditions differ significantly.

Theory suggests that, when a toggle switch can be switched between its too stable states, there exists a concentration of base levels of aTC and IPTG that should transform the landscape of the toggle switch into a so-called "balanced" landscape where the system is bistable and the basins of attraction are symmetrically separated. We empirically obtained concentrations of aTC and IPTG, subsequently called reference concentrations, for which both states were stable in microfluidic experiments. If, when "releasing' the system, we switched to those reference concentrations of aTC and IPTG instead of no inducers, the system would stay in whichever state (LacI-RFP-high/TetR-GFP-low or LacI-RFP-low/TetR-GFP-high) it was before the release. These concentrations for which our cells are bistable are aTC = 20 ng/mL and IPTG = 0.25 mM. behavior from the others, and from any predicted behavior. Our stochastic simulations are based on the Gillespie algorithm (see chapter 2), which can produce an exact simulation of noise in biochemical reactions, but is limited to intrinsic noise. The study of noise and cell-tocell variability in gene expression is a well-studied problem but has remained largely limited to simulations of stochasticity in gene expression. Only recently were models fitted to highquality single-cell datasets to represent the variability of gene expression between cells as a consequence of phenotypic differences in the population (Llamosi et al. 2016). Although, for the purpose of our study the Gillespie-based simulation framework allowed us to test the behavior of our control algorithms when exposed to noisy gene expression, it does not accurately simulate the extrinsic variability of gene expression in a population of different cells. With the quality of the data acquired for this study, an interesting development of our modeling approach would be to apply the aforementioned population models, known as mixed-effect models, to the study of noise and cell-to-cell variability in a populations of toggle-switch-bearing bacteria.

State space analysis

To better understand the behavior of our toggle switch and be able to intuitively investigate its response to external stimuli, we computed the vector field, nullclines and equilibrium points of our ODE system. The graphical representation helped us visualize the underlying rules that govern the dynamics of our system.

The vector field consists of computing the derivative of our system in its state space (or, in our case, the protein space). It is then typically represented by a so-called "quiver" plot in which arrows represent the gradient vectors for each of the evaluated elements of the state space. Because it is impossible to represent the vector field in the five dimensions that counts our ODE model, and because we are primarily interested in the evolution of the protein level, we did a quasi-steady-state approximation on the mRNA and IPTG levels and used this reduced model to compute the vector field presented in Figure 3-2. The quasi-steady-state approximation of our system can be performed because of the timescale separation of the transcription and translation processes: The time constants for mRNA expression differ from the protein expression time constants by at least one order of magnitude. The pahse portrait is a powerful representation to illustrate key concepts in the dynamics of the genetic toggle switch. In a similar spirit we also represented the nullclines of the toggle switch, which are the curves representing the steady state values for each of the two proteins as a function of other variables of the system. Again, to be able to represent the nullclines in 2 dimensions, the additional approximation of quasi-steady-state mRNA levels was made, i.e. the represented curves are solutions to the ODE model such that: and , for all values of TetR, and and , for all values of LacI.

for the PI control algorithms (see parameter in section 4.3.2 of chapter 2). However in Figure 3-6A we present all the possible levels of aTC and IPTG concentrations that could make the toggle switch bistable. An interesting combination of Figure 3-5 and Figure 3-6A is Figure 3-6C where the TetR to LacI ratio of equilibrium points vs inducer levels is presented.

The surface created by all the equilibrium points is similar to a cusp catastrophe curve [START_REF] Strogatz | Nonlinear Dynamics and Chaos[END_REF]. The hysteresis behavior that is typically associated with toggle switches can be seen as a trajectory over this landscape. Although catastrophe theory has been applied early on to biological problems [START_REF] Poston | Catastrophe Theory and Its Applications First Edit[END_REF], to my knowledge the parallel between the toggle switch and catastrophe theory has not been drawn before.

scale separation: subjected to fast periodic stimulations, the comparatively slower genetic circuit approximately follows a dynamics corresponding to the time-averaging of two opposing vector fields that presents a globally-stable equilibrium point at intermediate concentrations for LacI and TetR proteins.

As a contribution to in silico cybergenetics, we demonstrated that single-cell control of a bistable system can be achieved with relatively simple control frameworks and very little a priori knowledge of the system. This result opens the door to the study of gene regulation networks of increased complexity and in operating domains unreachable or unsustainable thus far. The architecture of our control framework demonstrates the possibility for two controllers to steer two connected processes without communicating with each other. It illustrates the possibility to perform multiple-input-multiple-output control studies of genetic networks, which would facilitate and accelerate the examination of internal network dynamics, but it also demonstrates that control can be performed on networks where, due to only partial knowledge of the regulatory linkage, the controllers might compete against each other.

The quality of the single-cell data obtained with our platform and the prolonged observations of the toggle switch system in its domain of unstability also allowed us to expand the general knowledge on this fundamental circuit. Toggle switches, and multistable systems in general, are known to play a central role in cell fate determination. Indeed, decision processes are understood as the continuous transformation of a stable equilibrium in which cells reside into an unstable one, separating the state space in several basins of attractions of novel equilibria, corresponding to the different possible futures of the cells [START_REF] Waddington | The strategy of the genes[END_REF][START_REF] Balázsi | Cellular decision making and biological noise: from microbes to mammals[END_REF][START_REF] Wang | Quantifying the Waddington landscape and biological paths for development and differentiation[END_REF]. The toggle switch is also a fundamental component of synthetic biology circuits. Therefore, in addition to its importance as a test assay for control of complex circuits in living organisms, the control methods we outlined in this article are relevant to drive and understand cell decisions, cell fate, differentiation and dedifferentiation dynamics, but also analyze the input-output functions of core elements of synthetic biology circuits.

Finally, the stabilization of an entire population of toggle switch cells in the unstable area of the system in open-loop experiments is a new observation that was suggested by closed-loop control experiments and new knowledge acquired on the dynamics of the system. This dynamic stabilization phenomenon, similar to the inversion of stability in the Kapitza pendulum [START_REF] Kapitza | Dynamic stability of a pendulum with an oscillating point of suspension[END_REF], could be used both as a control approach for multistable systems, possibly to reset the state of cellular decision making circuits, but also in general dynamic stabilization could be studied as a possible range of operation for multistable networks. Oscillating morphogen stimulations have already been shown to trigger differentiation processes in embryos [START_REF] Kirst | Dynamic information routing in complex networks[END_REF]Sorre et al. 2014;[START_REF] Aulehla | Signaling gradients during paraxial mesoderm development[END_REF]. The study of dynamic stability in cellular decision networks in fluctuating concentrations of inducers can expand our understanding of those processes and create a new framework of analysis for those systems.

Introduction: Automated cell segmentation, a core problem for single-cell control

The amount of data available to biologists dramatically increased at the turn of the century.

With the democratization of next generation sequencing techniques, microarrays, RNA-Seq, and imaging techniques, the field has definitively entered the era of high throughput acquisitions and big data analysis. A new field, quantitative biology, emerged out of these innovations and draws upon a multitude of approaches from the physical sciences and engineering to make biology quantitative and predictive. However, even though progresses were made in the field of multi-channel time-lapse microscopy imaging, the analysis of the formidable amount of data generated by such methods still often requires manual input from the experimenter. Such a procedure typically requires a lot of work from the experimenter and not only limits the throughput of the approach, but also makes on-the-fly segmentation impossible, which is crucial in the case of single-cell control.

Cell segmentation: Filtering, mathematical morphology and active contours

Before the changes brought about by microscope automation and microfluidics on one hand, and the advent of digital image processing on the other, cell segmentation and data extraction used to be performed manually. Since then a number of image analysis and segmentation tools have been developed to help the experimenters in their task. So far, the tools proposed can be considered semi-automatic as they require a significant amount of post-processing to achieve satisfactory segmentation results and make cell tracking possible.

The first, simplest form of automatic image segmentation is filtering and thresholding. In cases where the cells are well separated and their pixel intensity is homogeneous and different from the background (for example, in phase contrast microscopy images or in fluorescence imaging), a simple histogram threshold can segment cells at minimal computational cost. It can also be quite robust: Automatic threshold selection [START_REF] Otsu | A Threshold Selection Method from Gray-Level Histograms[END_REF][START_REF] Glasbey | An Analysis of Histogram-Based Thresholding Algorithms[END_REF]) is usually preferred to hard-set thresholds, which has the double advantage of finding an optimal threshold value without the need for heuristics and allows the algorithm to adapt to changes in illumination between images. Another improvement is the use of adaptive thresholding [START_REF] Yanowitz | A new method for image segmentation[END_REF], which partitions an N x M image in overlapping windows of n x m pixels and finds local thresholds for each. A thresholding map is then interpolated for the entire image. This partitioning approach is especially useful in images where, due to uneven illumination, the luminosity and contrast between the cells and the background varies within the image. However these thresholding methods become insufficient as soon as the cells in the image are not well separated, which is almost always the case in time-lapse movies of growing populations of cells.

The next level of cell segmentation is feature extraction. A more robust approach is to identify cell features, usually cell boundaries. Instead of identifying the cell region entirely, the boundaries are identified and cell region is inferred from it. This type of approach uses a variety of linear image filters that transform the image into a map of the features of the image first and then applies a threshold to the result to identify the borders. One of the advantages of

The number of parameters in this type of networks increases exponentially with the number of neurons in each layer, and one might fear that training a model with such a high number of parameters would require impractically long computational times. While this is mostly true, and one of the reasons why it took about 50 years for large-scale artificial neural networks to emerge, two things must be noted: First, ANNs require a surprisingly low number of training inputs compared to the number of parameters they use to produce satisfactory classification/identification results. This is probably related to the yet-unknown reason why they are better than other learning algorithms at generalizing their results to completely new observations [START_REF] Nielsen | Neural Networks and Deep Learning[END_REF]. For that reason, even small networks were able to perform reasonably well compared to other image classification/segmentation algorithm, if only a bit slower. The second, more remarkable thing is that developments on ANN training since the 1950s have greatly sped up the training process by a) an optimization of error gradient computation for each neurons layer, called the backpropagation algorithm [START_REF] Rumelhart | Learning representations by backpropagating errors[END_REF]), b) a drastic reduction of total computation time by randomly subsampling training data, called stochastic gradient descent [START_REF] Bottou | The Tradeoffs of Large Scale Learning[END_REF], and c) improvements in the implementation of the algorithms that made massive parallelization on GPUs possible [START_REF] Raina | Large-scale deep unsupervised learning using graphics processors[END_REF]. All these improvements ultimately led to the multi-record-breaking deep learning revolution: The development and training of large-scale networks was possible at last, and the large number of neurons layers made it possible to estimate intricate recognition functions. For a review of the history of deep learning as well as a discussion on recent advances in the field see (LeCun et al. 2015).

Convolutional Neural Networks

The CNN class of network architectures has proven especially efficient in image analysis and segmentation (LeCun et al. 2015). Convolution is a fundamental operation in image analysis and signal processing. In image processing it consists in evaluating for each pixel a weighted sum between the pixel and its neighborhood, with a mask, or kernel matrix, of weights applied to each pixel. This approach is used to implement image filters, including average, Gaussian, or gradient-type filters, amongst others. But the same principle can be applied to layers of neurons: Instead of fully connecting layers of neurons, i.e. using all the outputs of a layer as inputs for each neuron of the next layer and fitting the weights, the convolutional approach connects a small local set of neurons on one layer to one corresponding neuron on the next layer. Another property of CNNs is that the parameters for all neurons on a convolutional layer are shared, which means that different sets of weights are not fitted per neuron, but instead one "global" set of weights is fitted for each convolutional layer, and the same local operation is applied to the whole image. We can immediately see how this approach drastically reduces the number of parameters to fit. From an image processing point of view, convolutional layers also make sense since they can also mimic the actions of traditional image processing operators such as de-noising filters, gradient estimation and feature extraction, or even thresholding. Finally Convolutional Neural Networks usually consist of a number of different convolutional layers that are then used as an input to more inter-connected layers as one goes deeper in the network, up to the point where the layers become fully interconnected like in a perceptron type of architecture. These more fully connected layers usually perform more advanced, or "high-level" functions, while the less the choice of this reduced view of the entire image deprives the network of some of the context in the entire image that could have improved its performance. It is fairly easy to understand though why the authors chose to implement their network this way: Historically deep learning algorithms have been developed to classify images, not to segment them. The networks had been structured to take an image as an input, and identify what type of food or dog breed was in the image, but not delimitate where it was. The most straightforward way to apply these structures to segment images was then to use it on sliding windows and classify each of them as "image-with-a-neuron-membrane-in-the-center" or not.

The necessary tradeoff between localization and context remained a central problem in deep learning until very recently, when a team proposed a new network architecture that contracts from convolutional layers to a fully connected network, and then expands progressively back into convolutional layers until its output layer produces a segmented mask of the original image [START_REF] Long | Fully convolutional networks for semantic segmentation[END_REF]. This architecture was soon applied to cell segmentation, breaking preceeding records in a number of segmentation challenges by large margins (Ronneberger et al. 2015). Another interesting aspect of their work is the procedure devised for data augmentation, namely random elastic deformations, which is important in deep learning since those networks require a large number of training samples to be able to fit the millions of parameters they are using. With this procedure they were able to train their relatively large network with only 20 original training images. Although the segmentation results are still not perfect, the U-Net architecture is a leap in cell segmentation with 77.5% correct segmentation, to be compared to the previous record of 46% for the same image set.

exceeding the performance of the more traditional support vector machines (SVMs) only recently [START_REF] Chen | Deep Learning-Based Classification of Hyperspectral Data[END_REF]; see [START_REF] Zhang | Deep learning for Remote Sensing Data[END_REF] for a review).

Support Vector Machines

Spectral signature identification is a classification problem: Whether some region of the image represents a type of soil, buildings or cellular organelles boils down to a classification choice. Out of the myriad of classification algorithms developed for different statistical problems, SVMs have long offered the best results for hyperspectral data analysis, and are today second only to recently developed Deep Neural Networks.

SVMs, Support Vector Machines, have been around since the 1960s [START_REF] Vapnik | Pattern recognition using generalized portrait method[END_REF] and rely, in their simplest form, on identifying a hyperplane that can separate (with a maximal margin) all n-dimensional observations in a provided training set of m observations. In less obscure terms, SVMs (or, more precisely, linear SVMs) identify and optimize linear boundaries between classes of training points. To reduce computational cost, instead of estimating the coordinates of the optimal hyperplane by using all datapoints, support vector machines use a subset of the datapoints that lie at the boundary between classes, which are called support vectors. It has been demonstrated that the optimal hyperplane for separating the two classes and maximizing generalization performance is the one maximizing the margin between the itself and the support vectors of the two classes [START_REF] Vapnik | Estimation of dependences based on empirical data[END_REF].

Once the optimal hyperplane has been estimated, when new data is acquired and needs to be classified the algorithm evaluates whether a new observation is situated on one side or the other of this boundary. The result, usually called a prediction, determines whether this new observation is part of one class or another, but it also provides an estimate of how "certain" that classification is: The Euclidean distance from the estimated boundary is usually extracted from the algorithm as a classification score, which can be useful a posteriori to assert the validity of segmentation results.

Of course, linear classifiers like linear SVMs are often not adapted to real-life data, in which the different classes are often spread in complex intertwined regions of their feature space. A workaround for this problem was developed in the early 1990s [START_REF] Boser | A Training Algorithm for Optimal Margin Classifiers[END_REF]) and made SVMs the go-to classifiers for almost 20 years. The idea was not only to transform the feature space of the observations into another, where the differences could be separated linearly, but also creating new dimensions from the ones existing if necessary. This method is called the kernel trick, because the new dimensions are created through so-called kernel functions, which allow the SVM classifier to operate in a high-dimensional, implicit feature space without ever computing the coordinates of the data in that space. Instead, the dot products that are normally used on the data to compute their classification score in linear SVMs are replaced by the kernel functions. This operation is computationally cheaper than the explicit computation of the coordinates, and makes the separation of nonlinear data possible. A lot of kernel functions have been used in the literature, but in the field of hyperspectral imaging Gaussian radial basis functions typically yield higher performance with respect to speed and accuracy [START_REF] Mountrakis | Support vector machines in remote sensing: A review[END_REF]:

are given a misclassification weight depending on some mislabeling score2 . A tradeoff parameter between the sum of weighed misclassifications and the size of the feature space is set by the experimenter, and is typically determined empirically [START_REF] Steinwart | Support Vector Machines[END_REF].

Finally, the curse of high-dimensionality is a problem in SVMs too, and the number of features, or wavelengths, in hyperspectral data reduces the performance of the classifiers (this behavior is known as the Hughes phenomenon [START_REF] Hughes | On the mean accuracy of statistical pattern recognizers[END_REF])). The common procedure is therefore to reduce the dimensionality of the feature space while minimizing information loss via so-called feature extraction procedures. Although a number of algorithms for feature extraction has been used for specific applications, one of the first and most straightforward algorithms to be used and that dominated the field in the early years of hyperspectral imaging is principal component analysis [START_REF] Hotelling | Analysis of a complex of statistical variables into principal components[END_REF]) and a number of its variants [START_REF] Mountrakis | Support vector machines in remote sensing: A review[END_REF].

The analysis of hyperspectral data with SVMs was first suggested in the late 1990s [START_REF] Gualtieri | Support vector machines for hyperspectral remote sensing classification[END_REF] but the first paper to compile all the improvements on SVM performance mentioned above and to establish SVMs as the undisputed hyperspectral data classifiers for more than a decade appeared only five years later [START_REF] Melgani | Classification of hyperspectral remote sensing images with support vector machines[END_REF]. For an indepth technical discussion on SVMs see [START_REF] Steinwart | Support Vector Machines[END_REF]. For an extensive review of SVMs and their ameliorations in hyperspectral data analysis, see [START_REF] Mountrakis | Support vector machines in remote sensing: A review[END_REF].

As a side note, SVMs have also been used for microscopy image analysis, and cell segmentation in particular. But because SVMs are primarily classifiers that must be wrapped in several layers of image analysis and feature extraction to transform input images into a myriad of observations to classify, their usage remained largely confined to niche applications, like white blood cell identification [START_REF] Ramoser | Leukocyte segmentation and classification in blood-smear images[END_REF][START_REF] Osowski | Application of Support Vector Machine and Genetic Algorithm for Improved Blood Cell Recognition[END_REF]).

The framework of hyperspectral imaging

To summarize, the typical workflow of hyperspectral data analysis with support vector machines is as follows: This procedure inspired the segmentation algorithm I am going to present in this chapter, which replaces the spectral signatures from hyperspectral imaging with so-called "focal signatures" that are acquired by imaging focal plans above and below the cells' imaging plane. The focal signatures are the pixel illumination levels acquired at each focal plane, which vary depending on the element of the in-focus image. Basic optics suggests that these changes in signature between the different elements depend on the shape and composition of the object being observed, thus making object class identification possible in theory.

Z-stacks and focal signatures

While working on autofocussing techniques to try to obtain stable time-lapse movies and minimize measurement noise, I had to acquire a number of Z-stacks to use as inputs for the algorithms I was developing (see section 3.1.7 of chapter 2). So-called Z-stacks are stacks of images acquired at different focal planes, usually around the focal plane of interest where the cells are most discernable. If we adopt the usual convention of naming the 2 dimensions along which the images are taken x and y, the axis along which the focal-plane stack is acquired is logically labeled z, hence the name Z-stack. The development of autofocussing techniques was an ongoing task throughout my PhD, but I rapidly realized that, instead of trying to simply identify the best frame in the stack according to some criterion (image sharpness, histogram levels…), results that were both more precise and accurate would be achieved by measuring the same feature in all stacks in the image and then comparing it to some reference "signature" acquired at the beginning of the experiment.

Around the same time, I was also trying machine learning algorithms for cell segmentation. I did not know then of the results acquired with DNNs on neurons membranes [START_REF] Ciresan | Deep Neural Networks Segment Neuronal Membranes in Electron Microscopy Images[END_REF], and was trying to use methods typically used for pedestrian identification in images based on SVMs and HOG transforms3 [START_REF] Dalal | Histograms of Oriented Gradients for Human Detection[END_REF]. While this method gave satisfactory results on another project I was collaborating on for ant segmentation, it became rapidly clear that the method was not adapted to bacterial cell detection. Somewhat paradoxically, the complex shapes humans or ants can adopt made them more easily discernable from other objects or between themselves, while the simple shape of bacteria coupled with the quality of the images at this level of magnification made the approach irrelevant.

But eventually one day, in a perfect illustration of the Eureka phenomenon (Asimov 1971), while precariously riding home on my bicycle after one too many beers and a frustrating number of desperate attempts at segmenting cells with dubious combinations of SVMs and feature extractors, I finally thought of using the information that I knew could be found in Zstacks to identify cells.

After acquiring new Z-stacks with hundreds of frames 4 and analyzing what would later be called the focal signature of specific objects in the stack, it became evident that not only did the "signature" of some criterion along the Z-axis was specific to the object that was being observed and hence identifiable (see autofocussing method in section XX of chapter 2), but also that the signature of each z-pixel5 in the stack was closely related to the class of object they were part of. The acquisition process as well as the typical shape of the signatures is detailed in Figure 2-1.

The Z-stacks were acquired on a number of different automated microscopes, two of which, referenced here and amongst labmates as Mustard and Marple, are in our lab and are based on the IX71 and IX81 Olympus chassis and feature a variety of different equipment. The most notable piece of equipment on the IX71-based microscope Mustard is the piezo-driven motorization of the objective nosepiece along the Z axis, which allows for precision positioning with a resolution in the tens of nanometers. For that reason, and also that Mustard was the microscope on which I implemented the control platform and was the most familiar with, the majority of acquisitions were performed on this microscope. Unless otherwise specified, the Z-stacks were acquired on it. Two other microscopes were used by collaborators to acquire Z-stacks for evaluating the performance of the algorithm, one located in the lab of the Biologie et Dynamique des Chromosomes group of CNRS UMR 7212 at Hôpital Saint-Louis in Paris, and another located in the lab of the Molecular Microbial Ecology group at the Department of Environmental Systems Science of ETH Zurich. These two microscopes will be referred to here as St-Louis and Zurich.

The stacks were acquired with varying distance steps (z-steps) between each frame, from 100nm to 1μm. The original number of frames per stack was 100, with 100nm steps between all stacks, but eventually it became clear that much lower numbers of frames were sufficient to achieve satisfactory signature classification performance for robust segmentation, although higher frame numbers increased the performance marginally (see section 4.2.1). I also the histograms of all the training stacks and, once the SVM were trained, on all new Z-stacks as well, to ensure that all data were spread over the same intensity scale.

The second problem, shifting, does not happen in hyperspectral data. It consists in a shift of the signatures along the Z axis caused by autofocussing error. Because the training Z-stacks are acquired around the focal plan at which the cells are precisely in focus, the frames are taken always at the same distance from the central in-focus frame. That means that the features of the training signatures are acquired at specific points in Z around the in-focus point. However autofocussing is not always perfect, or the specimen observed can be tilted, and this can lead to a shift of the signature in Z. In this case, the shape of all signatures in the stack will appear drastically different to the SVM.

The physics of hyperspectral sensors make such a shift impossible in this type of data, so unsurprisingly there were no solutions to be found in the literature. For a time we experimented with pre-processing methods to re-shift the data in such cases or iterative prediction steps to select the best result. But in the end, a more elegant solution was to simply train the SVM on shifted data: The stacks for training at a high resolution in z were acquired, and then subsampled for the frames we needed in the stack to train for in-focus data. Then, an artificial shift in Z would be applied by re-subsampling for the frames with a shift in Z. Subsamples were acquired for an arbitrary shift range and the SVM were trained on all those data: the in-focus data, but out-of-focus data as well. This procedure not only made the z-pixel classification more robust to autofocussing errors, up to the point where the autofocus could be so wrong that cells could not be identified anymore in the supposedly in-focus frame and still the z-pixels could be identified properly, but it also made the results more accurate when there were no autofocussing errors. We think that the latter is because the shifting procedure works as a sort of data-augmentation method that made the SVMs better at generalizing to new observations. Another advantage of this method is that, except for the shifting range that is decided at the beginning and that can be seen as the "range of robustness to autofocussing error", the algorithm does not require any arbitrary parameter to be decided upon by the user or any knowledge of signal or image processing for correcting focusing errors.

A third problem, which we are currently working on but that only arises when lamp alignment was not performed properly prior to the acquisition, can be referred to as "skewing'. It consists in a shift of the objects in the image along the X and Y axes when the frames are acquired along the Z axis. In other terms, images are not well-aligned between focal plans. The shift appears to be linear, i.e. the image is shifted by a constant vector ( ) every fixed z-step. We still have not found a way to robustly and automatically identify the shift to correct it.

Classification

Class prediction and confidence map

Once a set of SVMs has been trained, it is used for "production', or to identify new stacks for cell identification and segmentation.

When a new stack is acquired, it is first scaled to the same dynamic range as the training stacks (basically the histogram of the entire stack is equalized over the maximum range of the training data type, which is usually uint16)

It is then transformed into the principal components base by multiplying the z-pixels by the principal coefficients from the feature extraction step described in section 3.3.

The SVM is used on the transformed data, and for each z-pixel a set of classification scores that correspond to each of the classes the SVMs were trained for is produced. Because all zpixels are independent from each other and their classification does not depend on the classification of other pixels, parallelization of the prediction process is trivial. Unfortunately Matlab does not feature a GPU-accelerated SVM library, which can decrease processing time by two orders of magnitude [START_REF] Catanzaro | Fast support vector machine training and classification on graphics processors[END_REF]. Parallelization can still be performed at the CPU level. We used a Dell Precision T7910 with a 20-core Xeon ES-2650v3 processor, that allowed us to significantly decrease processing time, down to a bit more than a minute for an entire stack of 100 frames and 1392x1040 pixels per frames. Processing time can of course be reduced by defining regions of interest in the image and not classifying the rest of the image.

The SVMs raw scores are also used to establish a confidence map of the classification in the image. To produce this so-called confidence map, we apply the softmax function to the SVM classification results for each result, and pick the score of the best class as the classification "confidence". The softmax function is commonly used in deep neural networks and is used to normalize classification scores. It is defined as:

∑ , With
being the vector of the SVM classifications scores ( ) of the m SVMs for each of the m classes in the training set, for a z-pixel p of coordinates (x,y).

is the softmax function evaluated for class i on the classifications scores of z-pixel p. We call ( ) the vector containing the m softmax evaluations of each class for a z-pixel p. The softmax function restricts the scores to the interval [0, 1], where the initial SVM classification scores could be any element of . The second interesting property of the softmax vector is that the sum of its elements ∑ equals one. For those reasons the vector can be interpreted as a probability distribution, and as the probability that pixel p is of class i. The vector can also be seen as a sort of composition of the signature of zpixel p in terms of the archetypal signatures for each of the classes. The confidence map is constructed for any of its pixel of coordinates (x,y) from the softmax vectors of the corresponding z-pixel p as the highest softmax score for that z-pixel:

‖ ‖

The confidence maps can be seen in the results in section 4.2 and inform the experimenter or a downstream algorithm on the reliability of different parts the classified image. The class map defined as = of a specific class i can be used to improve segmentation as we will see in section 5.3.

Results

The results presented here are classification results obtained on different organisms. In section 5 I present how these results can be used to segment cells. Unless otherwise specified, the results were obtained on different stacks than the ones used for training the SVMs

Escherichia coli -Mother Machine

The mother machine type of Z-stacks are the ones I worked on the most since I did most of my work on the toggle switch in this microfluidic device. The SVMs were trained to identify 6 classes:

 Inside: The inner part of the cells.  Membrane: The outer part of the cell.

While the distinction between those two parts of the cells is not strictly necessary and a single class for the entire cell gives equivalent results, this partition of the cell simplifies segmentation, and can be used for simple watershedding as demonstrated in section 5.1.  Halo: The region of the mother machine chambers that is in between the cells and the PDMS wall.  PDMS wall: The PDMS wall of the chambers.  Chamber: Empty mother machine chambers.  Empty: Empty parts of the image.

The training set was constructed with regions in the vicinity of the chambers because it was the only part of the images we were interested in. The classification is therefore not as good or relevant in other parts of the image. In section 5.1 we reduce the classified image to a region of interest (ROI) to avoid dealing with misclassified parts of the region.

In the results presented on Figure 4-1, we can see that different regions in the image are correctly labeled, except for a few mistakes that are caused by glitches in the image. Such minor errors can be ignored altogether or can be corrected a posteriori with morphological rules.

The effect of the number of frames per stack on performance was also studied. From the same stack and labeled z-pixels, different subsets of frames in the 100 that counted the stack were used, with different subsampling methods. We used between 3 and 99 frames per stack and performed feature extraction, training, and mislabeling evaluation on those subsets (see section 3). Once the SVMs were trained, we classified entire frames and recorded the total classification time. We discovered that, while higher numbers of frames would tend to increase performance, the gains were marginal after 10-20 frames per stack (see Figure 4-3A). We were able to obtain segmentable results with only 7 frames per stack (see Figure 4-3B), which could also be brought down by identifying the most informative frames in the stacks from feature extraction. This result can be particularly interesting in cases where time is an issue (for example in multi-position time-lapse acquisitions) or in cases where cells are sensitive to long exposure times. Here the quality of segmentation is a bit lower, especially around the empty part of the image. In section 5.3 I discuss a method that uses the confidence maps for closing the contours of the cells and segmenting them.

Segmentation

I do not consider cell segmentation to be part of this algorithm, because almost all types of cell segmentation techniques can be used downstream of this classification/identification step. Traditional methods like watershedding or active contours can be used, or even deep learning approaches, although if one is to go through the trouble of implementing a deep learning algorithm, with a little extra effort the performance should be greatly improved by fusing the identification and segmentation step as I discuss in section 7.

However, here I will present simple implementations of cell segmentation to illustrate how easy cell segmentation becomes once the different parts of a microscopy image are identified, but also to illustrate how confidence maps and classification scores can be used to improve segmentation.

It should be noted that none of the segmentation procedures presented here use active contours or deformable models. Hence no assumption on the shape of the cells is made by the experimenter, which should improve the segmentation performance if chosen properly.

Escherichia coli -Mother Machine

This example illustrates the simplest form of segmentation that can be used to identify single cells in classified images. I will apply this procedure to the results described in section 4.2.1 because it is the most relevant to this thesis, although a similar approach can be used on the results presented in section 4.2.2.

A simplified form of 2-step watershedding is applied to the classified image as follows: The different watershedding objects/regions are seeded as the "cytoplasm" regions of the bacteria and are then spread into the membrane regions until they connect, thus delimiting the borders of each cell. The procedure as well as the results are described in Figure 5-1.

generally for quantitative biology the possibility to generate single-cell data robustly and with minimal human inputs would allow for a finer level of analysis of gene expression in gene regulation networks at the population level but also, with sufficiently good data, at the lineage level.

Chapter V Conclusion and perspectives

Table of Contents

Contributions

In this dissertation, I presented several tools for implementing a platform for single-cell control of gene expression in bacteria. I propose this platform to control a bistable, 2-inputs 2outputs genetic circuit, the genetic toggle switch, to illustrate the possibilities offered by external control of gene expression, but also to study the dynamics of this fundamental network. A seducing aspect of the control results presented here is that a diffcult task like stabilizing the genetic toggle switch in its unstable area was performed with a simple control framework and minimal a priori knowledge of the controlled system. In general, the shift of the implementation of the regulatory process from in vivo to in silico allows for faster implementation-experimentation cycles, and more importantly allows for the development of control strategies that are significantly more complex than what can currently be designed for in vivo regulation.

The online single-cell aspect of the platform and acquired data presented here is also important. Single-cell data measures gene regulation networks dynamics at a finer level of details than population or flow cytometry measurements, and is crucial for the study of some aspects of gene expression. For example distinguishing intrinsic and extrinsic noise in the dynamic study of stochastic gene expression would be impossible without long-term singlecell definition. The study of inheritance in populations of cells would also be impossible without single-cell data, tracking, and lineage reconstruction in timelapse microscopy images. In this study, controlling a multistable system like the toggle switch would not have been possible without single-cell timelapse data: On one hand, if fluorescence had been extracted from timelapse data at the population level, like in [START_REF] Fracassi | Automatic Control of Gene Expression in Mammalian Cells[END_REF][START_REF] Fiore | An experimental approach to identify dynamical models of transcriptional regulation in living cells[END_REF] , and not at the single-cell level, it would have been impossible to distinguish cells in the unstable area from a mixed population of cells in either of the two basins of attraction, since the fluorescence in those states would have been averaged. On the other hand, flow cytometry or similar methods used in other control platforms [START_REF] Melendez | Real-time optogenetic control of intracellular protein concentration in microbial cell cultures[END_REF][START_REF] Milias-Argeitis | In silico feedback for in vivo regulation of a gene expression circuit[END_REF][START_REF] Milias-Argeitis | Automated optogenetic feedback control for precise and robust regulation of gene expression and cell growth[END_REF] would not have provided the history of the measured cells and it would have been impossible to know whether cells were really maintained in the unstable area or simply transiting through it.

With this platform, we studied the possibility of real-time control on a synthetic bistable gene regulation network, the LacI-TetR genetic toggle switch. As illustrated in the state-of-the-art of this thesis, toggle switches, and multistable systems in general, are known to play a central role in cellular decision-making, and to be a key component of synthetic biology circuits. We showed two approaches to maintain this bistable genetic circuit close to its unstable equilibrium state: closed-loop control and periodic stimulation. We demonstrated that singlecell control of a bistable system can be achieved with relatively simple control frameworks and very little a priori knowledge of the system. We also demonstrate the possibility to perform multiple-input-multiple-output control studies of genetic networks, which would facilitate and accelerate the examination of internal network dynamics. Finally, the dynamic stabilization of an entire population of toggle switch cells in the unstable area of the system in open-loop experiments is a new observation that suggests that multistable genetic networks could be extracted from, and maintained outside of, their stable states without observing their state in real-time. Another implication is that gene regulation networks can feature hidden stable states that could occur because of dynamic stabilization phenomena. Therefore, with the advent of the dynamic study of gene regulation networks, it should be possible to look for such effects that could not be discovered throughout the simple study of static connections between different elements of a gene regulation network.

One of the important aspects of single-cell control of gene expression is the ability to segment and track single cells. In the previous chapter of thesis I presented a new concept for automated cell segmentation. An untapped amount of optical information about the objects observed through a microscope is hidden in focal planes above and below the focal plane of the specimen. I developed a machine-learning algorithm that exploits this information to accurately identify regions of the image as part of different classes of objects. The procedure can be applied to mixtures of various types of objects like yeast cells, bacteria, mammalian cells, but also microfluidic structures. I also demonstrate that with this identification of the different regions of the image cell segmentation is facilitated and can be achieved with rudimentary image analysis tools. The development of machine learning-based tools for robust image analysis should lower the necessary efforts to control and investigate new gene regulation networks at the single-cell level in new organisms.

Limitations

The approach, of course, has its limitations. The use of chemical inducers like IPTG and aTC forced us to modify the host strain to ensure it would not interfere with the concentrations of inducers applied to the cells. The modifications increased delays in our system which limited the control performance. It also made the cells less more sensitive to environmental stresses, which also made control experiments more challenging since the cells had a tendency to filament during experiments. The use of chemical inducers should not be abandoned however, but used in conjunction with optogenetic induction mechanisms to expand the number of possible input knobs. Optogenetics and chemical inducers can also be used to examine the interplay between environmental changes and intracellular phenomena. Also, the platform as it is implemented now only controls fluorescence level, and not actual proteins levels or the level of some biologically relevant element. It appears that in all applications of external control platforms so far, the state variable that is actually controlled is the one that is directly measurable, i.e. fluorescence. It is possible to estimate the levels of the system variables that are not directly measurable though, through state estimation techniques that have been part of control theory for a long time. In (Uhlendorf et al. 2012;[START_REF] Milias-Argeitis | In silico feedback for in vivo regulation of a gene expression circuit[END_REF][START_REF] Fiore | In-vivo real-ti e control of gene expression : a comparative analysis of feedback control strategies in yeast -Supporting Informations Appendix -GAL1 promoter mathematical model derivation[END_REF][START_REF] Milias-Argeitis | Automated optogenetic feedback control for precise and robust regulation of gene expression and cell growth[END_REF]) such state estimation filters were used, to not only estimate the state of the observed fluorescent probes that were being controlled, but also estimate the state of internal variables of their models. Those internal variables could also be controlled. In biological systems, most often the variable/process to control is not directly measurable and its observation is hidden behind intricate dynamics and noise. The ability to control hidden state variables in gene regulatory networks would be a remarkable development in external cell control and would expand the area of its possible applications.

The application of model-predictive control has not been performed on our control problem. Although plugging this new controller into the platform would be facilitated by its modular structure, and we now have the knowledge necessary to establish a new model of the dynamics for controlling our toggle switch (since models used for model-predictive control are usually simpler than the one we have described here) we have not experimented with this approach yet, except in preliminary in silico studies. One of the possible extensions of the work presented here would be the analysis of control performance of the genetic toggle switch with this type of approach.

Several limitations are also inherent to the various elements of the platform. In the next section I discuss recent developments in various related domains that might trigger other progresses in the field of external control of gene expression.

Developments of the control platform

The field of in silico cybergenetics has emerged from recent developments in microfluiduics, molecular biology, systems biology, image analysis and in vivo measurement automation that made the assembly of external control platforms possible. Naturally, the range of applications of the field is going to expand with progresses made in those areas over the years to come. Some recent progresses have not been integrated to the platforms yet, or only partially, and here I am going to discuss some of those recent advances that could benefit our domain.

Active microfluidics

In our platform, and in all microfluidics-based platforms used for control so far, the valves and mixing apparatus were not fully integrated to the chip. It is possible however to integrate various valves and pumps to the microfluidic device [START_REF] Unger | Monolithic Microfabricated Valves and Pumps by Multilayer Soft Lithography[END_REF][START_REF] Li | Parallel mixing of photolithographically defined nanoliter volumes using elastomeric microvalve arrays[END_REF][START_REF] Sundararajan | Microfluidic operations using deformable polymer membranes fabricated by single layer soft lithography[END_REF]. Those mechanisms have since been used to develop highthroughput labs-on-a-chip for chemistry and molecular biology, but they have also been used successfully for high-throughput studies of gene expression in live cells (Sorre et al. 2014;[START_REF] Dénervaud | A chemostat array enables the spatio-temporal analysis of the yeast proteome[END_REF]. Such systems could be used in control platforms to parallelize the study over different gene networks, different strains, or different independent stimulations.

Optogenetics

Optogenetics is a biological technique which involves the use of light-sensitive proteins to control intracellular processes, such as gene expression, protein recruitment, or enzymatic activity. The field is relatively recent, with the first system for controlling gene expression in yeast [START_REF] Shimizu-Sato | A light-switchable gene promoter system[END_REF] appearing in the early 2000s. Over the following decade other optogenetic systems were developed in bacteria [START_REF] Levskaya | Synthetic biology: Engineering Escherichia coli to see light[END_REF][START_REF] Tabor | Multichromatic control of gene expression in Escherichia coli[END_REF][START_REF] Kaberniuk | A bacterial phytochrome-based optogenetic system controllable with near-infrared light[END_REF]) and mammalian cells [START_REF] Strickland | Light-activated DNA binding in a designed allosteric protein[END_REF][START_REF] Gunaydin | Ultrafast optogenetic control[END_REF]Toettcher et al. 2011a) to control either gene expression, signaling, or enzymatic activity.

Although optogenetic has been used in some control platforms [START_REF] Milias-Argeitis | In silico feedback for in vivo regulation of a gene expression circuit[END_REF][START_REF] Melendez | Real-time optogenetic control of intracellular protein concentration in microbial cell cultures[END_REF][START_REF] Milias-Argeitis | Automated optogenetic feedback control for precise and robust regulation of gene expression and cell growth[END_REF]) its integration into microfluidic platforms is more difficult, although not impossible [START_REF] Renault | Combining Microfluidics, Optogenetics and Calcium Imaging to Study Neuronal Communication In Vitro S. Martinoia[END_REF]. Integrating optogenetic actuation into the light path of the microscope makes it even possible to illuminate the cells with chosen patterns [START_REF] Levskaya | Spatiotemporal control of cell signalling using a light-switchable protein interaction[END_REF][START_REF] Yang | A light-inducible organelle-targeting system for dynamically activating and inactivating signaling in budding yeast[END_REF], which would open the door to independent single-cell actuation of all cells within a population.

Fluorescence

Fluorescent probes design has gone through a rebirth in the last few years with the advent of super-resolution imaging [START_REF] Mishin | Novel uses of fluorescent proteins[END_REF]. One of the interesting developments for external control of gene expression is that new fluorescent probes have been developed that span new regions of the visible spectrum, therefore making it possible to observe higher numbers of fluorescent proteins at once. A promising result in this regard is the expansion of the space of discrimination between proteins into a new dimension: Time-modulation of light inputs, in addition to the traditional discrimination through the wavelengths of excitation and emission of the proteins, should make it possible in the near future to discriminate between a number of fluorescent proteins never reached before [START_REF] Querard | Photoswitching Kinetics and Phase-Sensitive Detection Add Discriminative Dimensions for Selective Fluorescence Imaging[END_REF]. Other remarkable advances in this direction are made to expand the usable spectrum for illumination and observation into the infra-red [START_REF] Filonov | Bright and stable near-infrared fluorescent protein for in vivo imaging[END_REF]. But infrared fluorescent proteins do not only expand the range of usable wavelength, they also permit deeper penetration of the light input into biological materials, and could be used in the future to image and control cells or cell populations inside colonies, biofilms or even tissues. The development of photoacoustic probe proteins goes even further in this direction, recently making the observation of gene expression up to 10 millimeters deep within tissues possible in live mice at high spatial resolution and in 3 dimensions [START_REF] Yao | Multiscale photoacoustic tomography using reversibly switchable bacterial phytochrome as a near-infrared photochromic probe[END_REF].

The problems of fluorescent protein maturation delays and photobleaching limit the resolution of discernable dynamics in timelapse fluorescent imaging, and this can reduce the control performance. Fast-maturing fluorescent proteins have been developed over the years [START_REF] Bevis | Rapidly maturing variants of the Discosoma red fluorescent protein (DsRed)[END_REF][START_REF] Fiore | In-vivo real-ti e control of gene expression : a comparative analysis of feedback control strategies in yeast -Supporting Informations Appendix -GAL1 promoter mathematical model derivation[END_REF]) but a recent shift in the field of fluorescent probe design that solves both maturation delays and bleaching issues uses so-called fluorogen-activating proteins [START_REF] Schwartz | Fluorogen-activating proteins provide tunable labeling densities for tracking Fc??RI independent of IgE[END_REF][START_REF] Plamont | Small fluorescence-activating and absorption-shifting tag for tunable protein imaging in vivo[END_REF]): Instead of waiting for the protein to fold completely for the chromophore to be activated, a synthetic chromophore is provided in the growth media. Fluorescence is activated by the genetically-encoded protein, which is simpler and smaller than fluorescent proteins and does not require chromophore maturation.

Image analysis

Image analysis was discussed extensively in chapter 4. New techniques for cell segmentation and tracking were developed in recent years, and the emergence of machine learning methods is a game-changer in the field, not only in cell segmentation but also in other sub-domains of image analysis (LeCun et al. 2015). Beyond the cell segmentation methods proposed in this thesis and in the U-net architecture (Ronneberger et al. 2015), machine learning could be used for robust tracking and lineage reconstruction, as such methods have been applied to similar problems in other areas of image analysis [START_REF] Wang | Learning a Deep Compact Image Representation for Visual Tracking[END_REF][START_REF] Shen | Efficient multiple faces tracking based on Relevance Vector Machine and Boosting learning[END_REF]. Robust cell segmentation, tracking and lineage reconstruction combined with the single-cell optogenetic control procedure described earlier, would open the door to the study of epigenetic and transmission phenomena in gene regulation networks within populations of cells.

Cloning and genome engineering

In our study, the cellular chassis is considered part of the study. Indeed, now that a cellular chassis has been developed for long-term control in Escherichia coli with the lac and tet systems, other circuits can be constructed and transformed in this host cell for control experiments. The development of such chassis strains is a tedious process and can be accelerated by recently developed techniques in DNA manipulation and cloning. This also applies to the development of synthetic circuits for control, or to the integration of actuation and observation elements in the gene regulation networks to study. Although external control platforms require much less modifications of the genome or less complex synthetic networks, cloning and genome engineering are still necessary, and any progress made in this direction would benefit the study of those systems.

The recent revolutions of the ZFN, TALE and CRISPR/Cas9 systems [START_REF] Gaj | ZFN, TALEN, and CRISPR/Cas-based methods for genome engineering[END_REF]) are of course possible ways to speed up the control workflow. But not only can those systems be used for genome engineering, they can also be used as custom recombinases, transposases, and more importantly transcription factors [START_REF] Kabadi | Engineering synthetic TALE and CRISPR/Cas9 transcription factors for regulating gene expression[END_REF]. The possibility to design custom-target transcription factors would make it possible to control the dynamics of arbitrary genes in gene regulation networks. Recently, a photoactivable version of the CRISPR/Cas9 system was developed for optogenetic genome editing [START_REF] Nihongaki | Photoactivatable CRISPR-Cas9 for optogenetic genome editing[END_REF], and one can expect the design of custom optogenetic transcription factors to become possible in the near future.

New cloning techniques developed over the past decade, like the Golden Gate technique (Engler et al. 2008) and its standardized version the Modular Cloning technique (Weber et al. 2011), or the Gibson assembly [START_REF] Gibson | Enzymatic assembly of DNA molecules up to several hundred kilobases[END_REF]) made it faster and easier to assemble long circuits into plasmids, which in turn can speed up the workflow of control-based analysis of genetic networks. De novo synthesis also became one of the preferred method for developing new circuits [START_REF] Kahl | A survey of enabling technologies in synthetic biology[END_REF] thanks to a drop in price over the past few years, and we can hope that these methods will eventually replace the tedious process of parts assembly in the long run.

Perspectives

In silico feedback control of biological processes in vivo has just emerged recently as I have detailed in the state-of-the-art of this dissertation, but it already sparked interest in the community (Del Vecchio et al. 2016) with possible applications speculated in medicine [START_REF] Menolascina | Engineering and control of biological systems: A new way to tackle complex diseases[END_REF], optimal experimental design [START_REF] Ruess | Iterative experiment design guides the characterization of a light-V-Conclusion inducible gene expression circuit[END_REF][START_REF] Ruess | Designing experiments to understand the variability in biochemical reaction networks[END_REF], metabolic engineering [START_REF] Shiue | Synthetic biology devices as tools for metabolic engineering[END_REF], or even space exploration [START_REF] Menezes | Grand challenges in space synthetic biology[END_REF]. It has to be noted though, that the work I presented here should be seen as a proof-ofconcept implementation of a feedback control system for gene expression of multistable systems in bacteria, and significant work remains to be done to actually apply feedback control systems for the generation of precise perturbations of any chosen biological system. In this final section however, I will detail possible long-term applications of in silico cybergenetics.

The recent success of systems biology illustrates the importance of investigating not only the structure and function, but also the dynamics of biological systems. In this respect, recent progresses in cloning, genome engineering and custom transcription factors fabrication should make it possible to control arbitrary genes in endogenous gene regulation networks to dissect their dynamics. Another interesting domain progressing quickly is the field of iterative, optimal experimental design. Given some initial information on a biological system, along with a defined objective (e.g. estimating the parameters of a model of the system, being able to perform the best predictions of a given situation etc.), it is possible to optimize the choice of experiments to be conducted to reach that objective. This method is particularly relevant to reverse-engineer complex genetic networks for which intuition is not sufficient to estimate the best course of action to extract a maximum of information out of all the expectable consequences of given perturbations. Control platforms could be used as automated tools for optimal experimental design to achieve on-the-fly, optimal, and possibly high-throughput scrutiny of endogenous networks.

Another closely related area of research that could benefit from external control of gene expression is circuit testing and characterization. By automating the process and parallelizing the platforms, library of circuits could be tested in different settings, with different dynamic perturbations. A significant obstacle for the construction of novel functions in synthetic biology is the integration of low-level modules together to obtain high-level signal processing functions in the biochemical network. Because the dynamics of the different modules are often poorly characterized, as we saw with the genetic toggle switch in this thesis, assembling them together to produce a desired function is often a difficult task. Parallelized control platforms could be used to characterize precisely those modules, and the inferred models could be used to predict the behavior of assembled circuits.

In a different domain, bioreactors used for industrial production of chemicals of interest are notoriously difficult to calibrate and batch-to-batch reproducibility and yield maximization are often imperfect [START_REF] Polizzi | Genetically-encoded biosensors for monitoring cellular stress in bioprocessing[END_REF]. External control of gene expression could help solve these problems [START_REF] Milias-Argeitis | Automated optogenetic feedback control for precise and robust regulation of gene expression and cell growth[END_REF]) and lower the costs of production of the chemicals by minimizing chemical inducers and culture costs. Several problems remain to scale up the processes described in batch culture control of gene expression, especially input delivery, but this should be one of the most direct contributions of current gene expression control platforms to the industry.

One related domain where control platforms could also be applied in the near future is metabolic engineering. It has been shown that the yield of synthetic metabolic pathways can be optimized by integrating control loops between the metabolic layer and the genetic layer of the patway [START_REF] Zhang | Design of a dynamic sensor-regulator system for production of chemicals and fuels derived from fatty acids[END_REF][START_REF] Oyarzùn | Synthetic gene circuits for metabolic control: design tradeoffs and constraints[END_REF]. Optogenetic tools for driving enzymatic activity already exist [START_REF] Beyer | Optogenetic control of signaling in mammalian cells[END_REF] and a plethora of biosensors for various metabolites have been developed over the years [START_REF] Okumoto | Quantitative imaging with fluorescent biosensors[END_REF][START_REF] Su | Microbial biosensors: A review[END_REF][START_REF] Polizzi | Genetically-encoded biosensors for monitoring cellular stress in bioprocessing[END_REF]. The seminal work of (Toettcher et al. 2011b) in this regard proves that similar intracellular processes can be controlled over short timescales, and it should be possible to adapt control platforms to the synthesis of chemicals of interest like biofuels.

Finally the recent development of infrared fluorescent proteins [START_REF] Filonov | Bright and stable near-infrared fluorescent protein for in vivo imaging[END_REF]) and photoacoustic tomography [START_REF] Yao | Multiscale photoacoustic tomography using reversibly switchable bacterial phytochrome as a near-infrared photochromic probe[END_REF] makes it possible to observe gene expression in live mammalians, and with the development of those techniques, one of the possible future domains of applications for external gene expression control platforms is real-time control of gene expression in live animals, with possible biomedical applications.

To summarize, in silico control of intracellular processes is still in its infancy, and we are still a long way from routine utilization of those methods to dissect genetic network dynamics, or to optimally produce chemicals of interest in bulk. On the other hand, this is the closest we have ever been to reaching those goals, and the field of in silico cybergenetics should play a major role in the years to come in the broader domains of synthetic biology and systems biology. Developing a platform for single-cell control of gene expression in bacteria, controlling a landmark bistable genetic network like the genetic toggle switch, and the surprising result of dynamic stabilization in a gene regulation network it entailed, will hopefully contribute to the development of the field into an established discipline. Transcription units, made of different level 0 parts, express one or, in the case of operons, several genes downstream of a promoter. They are assembled together into level 2 circuits to form synthetic genetic networks. The level 1 assemblies are made into different backbones that are designed to assemble into a specific order: The overhangs on the backbones are organized such that a pL1-F1 transcription units will ligate to level 2 backbone on one end, and to a pL1-F2 unit on the other. A pL1-F2 unit assembles with a pL1-F1 and a pL1-F3 unit and so on until pL1-F7, which ligates back with the level 2 backbone, thus closing the assembly. Of course not all 7 level 1 units are necessary to construct a level 2 circuits, and one can assemble only one transcription unit into a level 2 backbone if they wish. The numbering of the circuits of the library of toggle switches is as follows:

pTet-mKate2-LacI branches pLac-mEGFP-TetR branches The greyed-out circuits could not be constructed. The orange circuit 2.31 is the selected circuit for the control experiments.

Strains

Name

1

  Motivation: From steam to electronics to cybergenetics. ................................................... 1.1 Control Theory ............................................................................................................. 1.2 Control engineering and biology ................................................................................. 1.3 Externalizing Control ................................................................................................... 2 Scientific problem: Long-term and real-time control of a bistable genetic system in single-cell bacteria ...................................................................................................................... 3 Approach ............................................................................................................................. 4 Contributions ....................................................................................................................... 5 Outline ............................................................................................................................... Foreword 5 2002

Figure 2 - 1

 21 Figure 2-1 From (Toettcher et al. 2011a). a) Schematic of the Phy-PIF recruitment optogenetic system. Under different light conditions, the Phy domain switches between a closed state and an open state that triggers recruitment of the PIF-tagged proteins. The feedback control loop senses membrane recruitment by image analysis, and applies the appropriate amount of light to control the amount of recruitment at the membrane. b) The schematic of the feedback control loop. The user specifies a target function, and the controller compares it to the observed cell level and corrects the light input accordingly. c) Setpoint control results for different feedback parameters. The blue curves represent the binding of the PIF-tagged protein to the membrane. The red curve is the amount of light input sent to the cells by the controller. The black dashed line represents the objective. d) Control experiments of time varying profiles.

Figure 2 - 2

 22 Figure 2-2 From (Milias-Argeitis et al. 2011). a) The in silico feedback control loop. A batch of cells are illuminated in red and far-red light to drive a synthetic genetic system. b-c) Regulation of the fluorescence level around the setpoint (black line). The controlled system, in orange, is compared to a numeric simulation of the cells, in gray, and to an open-loop dynamic stimulation. The red and black bars at the bottom represent the light pulses in red and far-red, respectively. d) Setpoint control from different random initial points.

S

  it h. Biotechnology and Bioengineering 94(1):1-4. He se , Pas al, Mega N. M Clea , L. Mahadeva , a d Sha ad Ra a atha . . Sig al P o essi g the HOG MAP Ki ase Path a . Proceedings of the National Academy of Sciences 105(20):7165-70.Johnston, Robert J., Sarah Chang, John F. Etchberger, Christopher O. Ortiz, and Oliver Ho e t. 5. Mi oRNAs A ti g i a Dou le-Negative Feedback Loop to Control a Neu o al Cell Fate De isio . Proceedings of the National Academy of Sciences of the United States of America 102(35):12449-54. Kim, Keun-You g, a d Ji Wa g. . Pote tial E e g La ds ape a d Ro ust ess of a Gene Regulatory Network: Toggle S it h. PLoS Computational Biology 3(3):e60. Kita o, H. . S ste s Biolog : A B ief Ove vie . Science 295(5560):1662-64. Kobayashi, Hideki et al. 2004. P og a a le Cells: I te fa i g Natu al a d E gi ee ed Ge e Net o ks. Proceedings of the National Academy of Sciences of the United States of America 101(22):8414-19. Kotula, Jo atha W. et al. . P og a a le Ba te ia Dete t a d Re o d a E vi o e tal Sig al i the Ma alia Gut. Proceedings of the National Academy of Sciences of the United States of America 111(13):4838-43. Kramer, Beat P. et al. 2004. A E gi ee ed Epige eti T a sge e S it h i Ma alia Cells. Nature biotechnology 22(7):867-70.Le a , Ti a et al. . A Bista le Ge eti S it h Based o Desig a le DNA-Binding Do ai s. Nature communications 5:5007. Le is, Ki . . Pe siste Cells, Do a a d I fe tious Disease. Nature reviews Microbiology 5(1):48-56. Lipshtat, Azi, Adiel Loi ge , Nathalie Q. Bala a , a d Ofe Biha . . Ge eti Toggle S it h ithout Coope ative Bi di g. Physical Review Letters 96(18):1-4. Loi ge , Adiel, Azi Lipshtat, Nathalie Q. Bala a , a d Ofe Biha . . Sto hasti Simulations of Genetic Switch S ste s. Physical Review E 75(2):21904. Lu, Mi g a g et al. . T ista ilit i Ca e -Associated MicroRNA-TF Chimera Toggle S it h. The Journal of Physical Chemistry B 117(42):13164-74. Lutz, R., a d H. Buja d. . I depe de t a d Tight Regulatio of Transcriptional Units in Escherichia Coli via the LacR/O, the TetR/O and AraC/I1-I Regulato Ele e ts. Nucleic acids research 25(6):1203-10. Ma, Rui, Ji hao Wa g, Zho ghuai Hou, a d Hai a Liu. . S all-Number Effects: A Third Stable State in a Ge eti Bista le Toggle S it h. Physical review letters 109(24):248107. Mackey, Michael C., and Marta Tyran-ka i. 5. The Li iti g D a i s of a Bista le Mole ula S it h With a d Without Noise. Journal of mathematical biology 1-20.

1

  Introduction ....................................................................................................................... 2 Synthetic biology............................................................................................................... 2.1 Chassis development .................................................................................................. 2.2 LacI-TetR toggle switch ............................................................................................ 2.3 Modular Cloning (MoClo) and toxicity issue ............................................................ 2.4 Operon branches design ............................................................................................. 2.5 Fusion protein branches design .................................................................................. 2.6 The toggle switch library ........................................................................................... 3 Microfluidics & automation .............................................................................................. 3.1 Microfluidics .............................................................................................................. 3.1.1 Molded PDMS devices ....................................................................................... 3.1.2 Microfluidic wafers fabrication methods ........................................................... 3.1.3 Main device -Mother Machine.......................................................................... 3.1.4 Early device designs: Population chambers ....................................................... 3.1.5 Surface passivation, clogging, and flushing ....................................................... 3.1.6 Input delivery ......................................................................................................

Figure 3 - 3 -

 33 Figure 3-3 -Adapted from Uhlendorf et al.(Uhlendorf et al. 2012) The first device that I used was based on this design. (left) the general microfluidic setup, the device is connected to a valve that selects between two media. The media are flown through the channels and end up in the waste (purple tubing). The chambers are between the two channels and nutrients and drugs are transmitted to the bacteria by diffusion. Epifluorescence microscopes are used to image the cells from below, inside the chambers. (middle and right) The chambers are 0.4mm in length, and about 0.7 µm in height. The channels are 40 µm in height.To work around this issue I then adapted another device developed for yeast by Clément Vulin, another Ph.D. student on the team, to my organism. This second device was similar to the previous one, except that it featured chambers of various widths, which solved the collapsing ceiling problem. I was able to obtain good images of my bacteria where they would grow as a single layer. Those two devices did not feature details smaller than 5 microns, and I used only photolithography (section 3.1.2.1) to create their molds.

Figure 3 - 4 -

 34 Figure 3-4 -Images obtained with the second device. The cells do not move in the device or grow as multiple layers and the quality is good enough to try single cell segmentation. (left) Phase contrast 100X imaging of E.coli cells. (right) 100X composite image of red fluorescence imaging and transmitted light imaging of E.coli cells.I could not use those devices for single-cell control experiments. I did use them at the beginning of my PhD for population control, but the lack of robust segmentation algorithms for single-cell tracking and the rapid and free movement of cells in and out the field of view made them not adapted to online single-cell tracking. However the number of cells in the field of view is 10 to 100 times higher than in mother machine devices, and population effects can also be observed in this type of devices. Recent progresses made in cell segmentation might make it possible to monitor the fluorescence level of thousands of single-cells in a 2D layer on-the-fly (see chapter 4 for a short review of the state of the art in cell segmentation).

Figure 3 - 7

 37  The simplest, and most robust method, relies on the shape of the mother machine device, where mother cells are trapped at the end of the growth chambers, to extract fluorescence from a pre-arranged ROI. Motion compensation algorithms are used to ensure that the same part of the chamber is sampled at every timepoint.

Figure 3 -

 3 Figure 3-10 Mathematical morphology and active contour methods are often not robust enough for online segmentation. In this example, obtained with MAMLE(Chowdhury et al. 2013) but characteristic of other similar programs, 4 cells are not segmented properly. The details of the borders between cells are below the optical resolution of normal microscopes, and finding segmentation parameters that work for all cells in the image is often impossible, thus requiring user supervision.

  objectives chosen for control, and and as parameters indicating the minimum and maximum values reachable by the input device (Here the maximally closed/open states of the valves).

Figure 4 - 7

 47  Identification results on HeLa cells. Stacks of 150 frames with 0.3um z-steps were acquired on Marple with a 60X oil objective, in transmitted light. Here the quality of segmentation is a bit lower, especially around the empty part of the image. In section 5.3 I discuss a method that uses the confidence maps for closing the contours of the cells and segmenting them.

1

  Contributions ................................................................................................................... 2 Limitations ...................................................................................................................... 3 Developments of the control platform ............................................................................ 3.1 Active microfluidics ................................................................................................ 3.2 Optogenetics ............................................................................................................ 3.3 Fluorescence ............................................................................................................ 3.4 Image analysis .......................................................................................................... 3.5 Cloning and genome engineering ............................................................................ 4 Perspectives .....................................................................................................................

  are the basic building blocks of MoClo circuits. In our case a MoClo transcription unit is composed of 4 level 0 parts: Promoter (pL0-P plasmids), RBS/5' UTR (pL0-U plasmids), Gene/coding sequence (pL0-SC plasmids), and Terminator (pL0-T). The overhangs of each of those parts are organized such that they assemble in the right order.Part no. Designation (Geneious)Designation (short)

Table of Contents

 of

1 Genetic networks as dynamical systems. .......................................................................... 2 External control ................................................................................................................. 2.1 External control of gene expressionfirst results 2011-2012 .................................. 2.2 External control of gene expression -2014-2016 ..................................................... 3 The genetic toggle switch .................................................................................................. 3.1 Double repressive loops in natural gene regulatory networks ................................... 3.2 The genetic toggle switch in synthetic biology.......................................................... 3.3 Theoretical studies of the genetic toggle switch ........................................................ 3.4 Theoretical control of the toggle switch ....................................................................

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Table 2 .

 2 6-1 RBS strengths as calculated by the Salis RBS Calculator v2.0. Note the importance of the context of the RBS.

	RBS reference pTetO-lacI-mKate2	pLacO-tetR-
		branch	mEGFP branch
		Translation	Translation
		Initiation Rate (au)	Initiation Rate (au)
	B0030	3440	7734
	B0031	53	458
	B0032	12	8788
	B0033	27	301
	B0034	1035	1624
	B0035	251	520
	pTet-mKate2-LacI

Table 4 .

 4 . 3-1 Pseudo-reactions and propensities used in the Stochastic Simulation Algorithm

	Reaction	Propensity
	transcription	⁄
		⁄
	translation
	degradation
	13 github.com/Lab513/ToggleSwitch/blob/reOrg/CoreFunctions/CoreModel/toggle_props_stoich.m

Table 4 .

 4 4-1 Parameter values after CMA-ES identification after fitting the model to characterization data.

	Transcription rates	1.607 1.009 0.0238 0.1715	molec./min	Hill coefficients	2.093 2.000 2.000 2.000
	Translation rates Degradation rates	7.268 1.906 0.1477 0.1386		Half occupation levels	123.0 molec. 226.8 molec. 38.9 ng/mL 0.300 mM
	Dilution rate	0.0199

  and provide intermediary concentrations of inducers to the cells. It also takes into account past errors in an integral term to correct offset errors over time.

		{
	With	{	(	(	)		∫ (	)	)
				{
	With		{	(	(	)	∫ (	)	)

14 github.com/Lab513/ToggleSwitch/blob/reOrg/CoreFunctions/Control/BBcontrollerNew.m

  The classification performance of each SVM is then assessed on the evaluation set, and the best result is used for identification, or the experimenter can go back to step 3 to try to improve performance based on those results. 2. Prediction/Production 2.1. Acquire new unlabeled hyperspectral data. 2.2. Transform data into the new feature space from training step 1.2. 2.3. Classify the signatures of each pixel into the classes from step 1.1. 3. (Optional) Use classified images for target recognition/detection (Vehicles, infrastructures, forests…) with traditional image segmentation techniques.

	1.4.
	1. Training
	1.1. Hyperspectral training and evaluation datasets are acquired, and experts label the
	different classes in it.
	1.2. A feature reduction step is applied, thus drastically reducing the number of
	dimensions while preserving a maximum of the original information in the data.
	1.3. A number of SVM are fitted to the labeled training set after feature extraction, each
	with different sets of parameters (kernel function, misclassification/dimensions
	tradeoff, maximum number of support vectors…)

Level 2 -Circuits Level

  2 circuits are assembled from level 1 transcription units are the final product of Modular Cloning. Some of the plasmids presented here were then transformed into the chassis strains. The orange element represents toggle switches.

						F2a
						pL1-
	1.47 pTet	B0031		LacI_mKate2 FAB816	F2a	Cm ACYC pTet-lacIToggle switch branch -operon
						pL1-
	1.48 pTet	B0032		LacI_mKate2 FAB816	F2a	Cm ACYC pTet-lacIToggle switch branch -operon
						pL1-
	1.49 pTet	B0033		LacI_mKate2 FAB816	F2a	Cm ACYC pTet-lacIToggle switch branch -operon
						pL1-
	1.50 pTet	B0034		LacI_mKate2 FAB816	F2a	Cm ACYC pTet-lacIToggle switch branch -operon
						pL1-
	1.51 pTet	B0035		LacI_mKate2 FAB816	F2a	Cm ACYC pTet-lacIToggle switch branch -operon
						pL1-			plac-tetR "wildcard"Toggle switch branch -
	1.52 pLac	RBS swapper AarI TetR_mEGFP FAB815	F1a	Cm ACYC	operon
		RBS	swapper			pL1-			pTet-lacI "wildcard"Toggle switch branch -
	1.53 pTet	Esp3I		LacI_mKate2 FAB816	F2a	Cm ACYC	operon
		1.4 Name	Pos. 1	Pos. 2	3	4	5	6 7	Re s	Origi n	Description
											Single	transcription
		2.1		1.1					Cm ACYC	unit
											Single	transcription
		2.2		1.2					Cm ACYC	unit
		2.3	1.22		1.2 1	1.2 0	1.1 9	1.2 4	Cm ACYC	Toggle switch -fusion proteins
	Name Prom	RBS		CDS	Term	bckbn Res Ori 1.2 1.1 1.2	Description	Fusion	proteins
	pL0-P pL0-U 2.4 pLac B0034 pTet B0034 2.5 j23119 B0034 pLac B0034 2.6 pTet B0034 j23119 B0034 2.7 pLac B0034 pTet B0034 2.8 j23119 B0034 1.10 pLac 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 B0034 2.9 2.10 to	pL0-SC 1.4 mKate2 mKate2 1.2 mKate2 mEGFP 1.1 mEGFP mEGFP 1.2 EYFP EYFP 1.17 EYFP 1.4 mEGFP::TetR FAB815 pL1-F2 Cm ACYC Single FP transcription unit pL0-T pL1-0 9 4 Cm ACYC testing FX 1.2 1.1 1.2 Fusion FAB801 pL1-F2 Amp pUC Single FP transcription unit 1 9 4 Cm ACYC testing FAB801 pL1-F2 Amp pUC Single FP transcription unit 1.1 1.2 Single transcription proteins FAB801 pL1-F2 Amp pUC Single FP transcription unit 9 4 Cm ACYC unit FAB822 pL1-F2 Amp pUC Single FP transcription unit 1.1 1.2 Single transcription FAB822 pL1-F2 Amp pUC Single FP transcription unit 9 4 Cm ACYC unit FAB822 pL1-F2 Amp pUC Single FP transcription unit 1.2 FAB822 pL1-F2 Amp pUC Single FP transcription unit 6 Cm ACYC acrA-B knockout FAB822 pL1-F2 Amp pUC Single FP transcription unit 1.1 1.2 Single transcription FAB822 pL1-F2 Amp pUC Single FP transcription unit 9 4 Cm ACYC unit 1.40 to 1.22 1.22 1.22 1.22 1.25 1.22 1.46 to
		2.45	1.45	1.51					Cm ACYC Toggle switches -operons
		2.46	1.52	1.53					Cm ACYC Toggle switch -"wildcard"

Optogenetics is a biological technique which involves the use of light-sensitive proteins to control intracellular processes, such as gene expression, protein recruitment, or enzymatic activity.

Bet-hedging is the process by which, in some species, a variety of different phenotypes exist within a population of to ensure that a subpopulation is well prepared for environmental changes. The phenomenon is well documented in antibiotic resistance and biofilms formation in bacteria(Lewis 2007).

Conclusion ........................................................................................................................

The engineered Escherichia coli strains in which the genetic circuits to control will be transformed are referred to as "chassis" strains. We refer to the original BW25113 strain as "wild-type".

Isopropyl β-D-1-thiogalactopyranoside, or IPTG, is a molecular mimic of allolactose that cannot be metabolized by the cell. Allolactose is an isomer of lactose and is the actual inhibitor of the LacI protein. Lactose is converted to allolactose by the β-galactosidase enzyme of the lac operon.

Modular cloning, or MoClo, is a standardized cloning method based on the Golden gate protocol. This methodology was used extensively during my PhD because it offers a number of advantages for synthetic circuits construction. The method and its usage are described in section 2.2. The MoClo plasmids bearing the homology regions are described in appendix A as level 1 plasmids 1.25 to 1.27.

The Shine-Dalgarno (SD) sequence is a part of ribosomal binding sites in prokaryotic messenger RNA. The RNA sequence helps recruit the ribosome to the messenger RNA to initiate protein synthesis by aligning the ribosome with the start codon. The six-base consensus sequence is AGGAGG. Variants of this sequence have more or less chances of recruiting the ribosome.

Table 2.6-2 Summary of early characterization results. A corresponding table listing the circuit numbers can be found in appendix A.

MCP23017 are port expansion chips, made specifically for increasing the number of I/O ports on a microcontroller, like an arduino. Up to 8 chips can be connected on a 2-wires i2c serial bus, which means a single arduino could drive up to 128 valves.

github.com/Lab513/ValveControllerNano

Dimer versions of the lac repressor can also bind the operator site on the promoter and can also be bound by IPTG. However, for simplicity here we consider only the binding of the tetrameric version. The binding events linked to the other versions are taken into account (among other things) later on in the associated Hill

github.com/Lab513/ToggleSwitch/blob/reOrg/CoreFunctions/CoreModel/toggle_derivative_sim.m

github.com/Lab513/ToggleSwitch/blob/reOrg/CoreFunctions/generate_data.m

Because the ODEs of the deterministic model and the propensities of this model are based on the same network of pseudo-reactions, and because they use the same rates and assumptions, I could use the same parameter values in both approaches.

github.com/Lab513/ToggleSwitch/blob/reOrg/CoreFunctions/Control/PIcontrollerNew.m

Open-loop dynamic stabilization ....................................................................................

Conclusion .......................................................................................................................

This family of methods is called loss functions. The most common one used with SVMs is the hinge loss function[START_REF] Gentile | Linear hinge loss and average margin[END_REF][START_REF] Steinwart | Support Vector Machines[END_REF]

Histogram of oriented gradients, or HOG, is a feature extractor for 2D images that splits an image into overlapping windows and computes for each of them a histogram of the gradient for different orientations.

I will refer to single images acquired at specific focal plans in a Z-stack as frames.

I call a z-pixel the vector of intensity values along the Z axis that are acquired in each frame of the Z-stack for a specific set of pixel coordinates (x, y) along the X and Y axis. The term might be used interchangeably with focal signature, but is generally preferred here when referring specifically to raw data, while the term signature will be used in a more conceptual way and regardless of the feature space it is represented in.

Acknowledgements

Chapter IV Stack segmentation "Many facets of [cell segmentation] appear to be well within the grasp of present-day technology."

Prewitt & Mendelsohn

Table of Contents

Towards 3D segmentation

To my knowledge, there have been no algorithms proposed for 3D segmentation of cells in Zstacks of transmitted light images. While this problem is even more difficult than cell segmentation in a single focal plane, the possibility to segment colonies of cells freely growing in 3 dimensions would make the study of complex ecosystems of cells possible, or the evolution and growth of tissues, biofilms or embryo without requiring complex, and sometimes impossible, cloning procedures.

In this section I present a slight modification of the procedure described in previous sections that gave encouraging results in this direction. I used stacks of Staphylococcus aureus and mammalian red blood cells in solution. One particularity of those stacks is that cells are not all in the same focal plane, with red blood cells being in-focus about 7 microns above the bacteria. Because of this wide variety in focus I decided to try to segment the cells in 3D.

Instead of using the entire stack to train and segment the cells, I used only 20 frames around the focal plan of the different parts of the training set and trained the SVMs on those local signatures. I then ran the classification on all possible moving stack of 20 frames along the Z axis through the entire 300-frame stack. For each center frame the local stack would be classified and the classification scores were kept.

In Figure 6-1, the in-focus frame, as well as the corresponding classification map, are represented for different local Z-stacks. The different parts of the image are correctly classified when they are in focus, but are incorrectly classified when out of focus. This error can probably be blamed on bad dataset construction, which is a tedious task in 3 dimensions, and also on the long computation times: The software has not been developed, and therefore not optimized, for this 3-dimensional approach, and the classification time for an entire stack is counted in hours. This puts a hard limit on the speed of development of this aspect of the algorithm. Furthermore, 3D convolutional neural networks might be more adapted to this type of application, as discussed in section 7.

The classes used in this training set were the following ones: The MoClo backbones, parts, transcription units and cricuits are presented here, as well as the chassis strains that were developed in this PhD as well as those that were transformed with synthetic circuit plasmids for control. Not all strains were used in this PhD nor were all Level 2 MoClo plasmids transformed into specific strains.

List of plasmids and strains

Table of Contents

1 Plasmids

Backbones

The backbones are used to assemble the different levels of the MoClo process into. They are organized such that they always assemble in the same order.

Name