Keywords: temporal reasoning, Event Calculus, mechanical ventilation management, patient monitoring, knowledge-based systems, PROLOG

In this paper, we propose to use one of the well-known general theories of time and change, namely the Event Calculus [1], to represent temporal aspects in intelligent medical monitoring systems. In particular, we explore the application of CEC [2] (an efficient implementation of the Event Calculus) to the management of mechanical ventilation. First, we present the prototype we have built, which has been extensively tested on patient's data from real clinical cases. Then, we provide a thorough evaluation of the obtained results, pointing out both strengths and weaknesses of the approach, and identifying a number of extensions which can be extremely useful to scale up the medical application of the approach.

Introduction and Motivation

In data-rich clinical environments such as Intensive Care Units (ICUs) or operating rooms, there is a crucial need for intelligent monitoring systems that can help the clinician to deal with the massive flux of information. These systems should be able: (i) to acquire and exploit the mass of data available to propose a diagnosis of the patient's state, (ii) to filter the numerous alarms from monitors to indicate only those that require a human intervention, and (iii) to propose specific therapeutic strategies depending on the evolution of the patient's state. Explicit time and change representation is essential for building such intelligent monitoring systems. In this Section, we point out the motivations for our work, both from the temporal reasoning and the application point of view.

The Temporal Dimension

Time is a central factor in intelligent monitoring systems that are supposed to interact with real dynamic environments. The need for time representation in these systems concerns two major aspects:

-Modelling of temporal concepts and inferences performed by the physician: the physician i) builds dynamically an interpretation of the time course of the patient's disease, ii) predicts the patient's evolution with regard to previous states, and iii) constructs and executes a plan of actions to drive the patient to an expected state. The physician adapts his/her strategy to the history of the patient's disease and to the time the patient spent in a given state. To build a global dynamic interpretation of the patient's behaviour, he/she must construct gradually specific abstractions at several levels, recognizing relevant changes for each level [3].

-Respect of real-time constraints: the system should be able to i) acquire physiological data provided by several monitors and the clinical staff, ii) plan the sequencing of the three fundamental tasks in medical reasoning [4] -observation, diagnosis, and then therapy -each task being in turn decomposable in several sub-tasks, and iii) have a prompt reaction in alarming situations, which impose to short-cut some sub-tasks.

The need for an explicit representation of time in medical systems has been advocated by several researchers, but very few clinical decision support systems incorporate clear formalisms for temporal reasoning [5]. Recently, several research efforts have been devoted to define ontologies and mechanisms for medical temporal reasoning and abstraction independently of a specific medical application [3,6,7,8,9]. From this point of view, the Event Calculus (EC), the well-known general theory of time and change proposed by [1], appears to be an interesting framework. In particular, EC (i) is a general and thus likely to be re-usable approach, (ii) is wellfounded and has been thoroughly formally studied (some works dealing with formal aspects of EC are [10,11,12,13], just to mention the most recent ones), and (iii) adheres to a model with events, states and cause-effect relationships, which seems well adapted for temporal reasoning in medical domains [3,6,14]. The Situation Calculus [15] shares the same general aim of EC, i.e.

to formalise common sense reasoning about the initiation and persistence of properties and relationships over the course of time. We prefer EC for our domain, because, as pointed out by [16]: (i) whereas EC was intended primarily for reasoning about actual events, the Situation Calculus was designed primarily for reasoning about hypothetical actions and situations (which is not our case), and (ii) whereas the Situation Calculus deals with transitions between global situations, EC allows to deal with the effect of actions on local states.

Although EC derives a significant representational power from its roots in Logic Programming augmented with negation-as-failure as a mechanism for default reasoning, it was found to be rather inefficient to meet the harsh requirements of fast decision-support response [12]. For this reason, EC has not been used for the design of intelligent monitoring systems up to now, but an efficient implementation [2] of EC has been recently proposed. In this paper, we exploit this implementation in order to explore the application of EC in the context of mechanical ventilation management, with the general aim of testing the adequacy of EC to model temporal reasoning in medical monitoring.

Intelligent Systems for Mechanical Ventilation Management

A typical clinical application of intelligent monitoring systems is the management of the mechanical respiratory assistance provided to patients who suffer from a lung disease and are hospitalised in ICUs. Recent physiological studies [17,18] have convinced physicians to mechanically ventilate patients as soon as possible with partial assistance modalities: a variable level of mechanical assistance is added to the spontaneous respiratory activity of the patient.

Although partial mechanical support such as pressure support ventilation (PSV) [19] is simple in its principle, its use generally requires the presence of a trained and experienced physician who adapts the level of assistance to the evolution of the patient's state. This is emphasised when the physician, applying specific strategies, tries to decrease gradually the assistance and appreciates the patient's capability to breathe alone. This procedure (called weaning procedure) must be performed carefully to improve the quality and the success rate of such a difficult process.

Many decisions and adjustments performed on the ventilator settings are based on objective data and can be formalised and modeled with appropriate knowledge representation techniques.

Ideally, the advantages of a knowledge-based system for the management of ventilator therapy are: (i) to function on a 24 hours per day basis, allowing a continuous adaptation of the level of the assistance and a reduction of total duration of ventilation, and (ii) to develop specific weaning strategies, including a gradual decrease of the mechanical support, difficult to obtain in clinical practice without the assistance of a computerised system. Such a system must work in a closedloop to be useful to the clinical staff. Recently, clinical studies have validated this approach [20,21].

Since the precursor work of Fagan [22], several systems have been designed to assist respiratory management (see [23] for a broad survey on recent intelligent patient monitoring projects). Briefly, systems can be divided in two categories:

-Systems solving a practical clinical problem: for example, [24] deals with the complex task of ventilating patients with Acute Respiratory Distress Syndrome, while [25] tackles the problem of assisting therapists and nurses in weaning post-operative cardiovascular patients from mechanical ventilation. These systems are hardly adaptable to other clinical contexts.

-General architectures for intelligent monitoring: these are long term research projects, such as [26], which proposes a general architecture for intelligent agents and is applied to intensive care monitoring problems, and [27], which mixes qualitative and quantitative computation in a ventilator-management advisor. The first objective of these researches is not to design a prototype working at the patient's bedside, but to explore novel AI techniques potentially useful to solve medical problems.

Our project is intermediate. On one hand, our goal is to solve a clinical problem (i.e. the management of PSV) and to test a closed-loop prototype at the patient's bedside. On the other hand, we aim at generic reasoning mechanisms for temporal medical reasoning validated in the clinical environment. Existing systems often use an embedded implicit temporal representation (e.g. [22], [28]). Unlike these systems, we adopt an explicit and general representation of temporal knowledge and reasoning (i.e., the Event Calculus [1]), to monitor and control ventilator therapy in real-time. Therefore, the prototype we built serves also the purpose of evaluating strengths and weaknesses of the Event Calculus in the medical monitoring domain.

Temporal Ontology and Inference in EC

Kowalski and Sergot's Event Calculus (EC) is a general approach to representing and reasoning about events and their effects in a logic programming framework [1]. From a description of events which occur in the real world and properties they initiate or terminate, EC derives the maximal validity intervals (MVIs) over which properties hold. It takes the notions of event, property, time-point and time-interval as primitives and defines a model of change in which events happen at time-points and initiate and/or terminate time-intervals over which some property holds. It embodies a notion of default persistence according to which properties are assumed to persist until an event occurs that interrupts them * . A model of the world based on events, whose occurrence modifies the state of the world and properties that have a tendency to persist during time, is well adapted to our applications [3].

In the following axioms, we adopt PROLOG's convention of beginning variables' names with an uppercase letter and constants with a lowercase letter. In order to help the reader who is not familiar with PROLOG syntax, we provide a natural language formulation to the right of each axiom we introduce.

Basic Event Calculus

Formally, we represent an event occurrence by means of the happens_at(event, timePoint) clause † . The relation between events and properties is defined by means of initiates_at and terminates_at clauses: The initiates_at (terminates_at) clause states that each event of type event1 (event2) initiates * The implicit default persistance assumption of EC may not be natural in some medical problems. For these cases, some authors (e.g. [3], [9], [22]) allow also the use of explicit persistence functions to determine intervals of validity. † In general, the requirement of knowing the exact time point when each event happened can be relaxed (we dealt with the case of partially ordered events in [29]) at the expense of efficiency. Fortunately, all the events in the considered application can be time-stamped.

(terminates) a period of time during which property prop holds, provided that a number (possibly zero) of given conditions hold at instant T. In EC, both initiates_at and terminates_at are context-independent predicates: they do not admit preconditions. However, even when modeling very simple real-world examples, the context is essential to decide which properties are initiated or terminated by the occurrence of an event. For example, the event "turn on the switch" in a simple light bulb circuit, initiates the property "the light is on" at a given instant, only if the property "electrical power is supplied" holds at that instant [2]. Thus, as indicated above, we added preconditions to initiates_at and terminates_at in order to model complex domains, such as mechanical ventilation management.

Initial conditions describe the (possibly partial) initial state of the world and are specified by means of a number of events of type initially(prop).

The EC model of time and change is defined by means of the following axioms: The mholds_for axiom states that a property P maximally holds between events Ei and Et, if Ei initiates P and occurs before Et that terminates P, provided there is no known interruption in between (the negation involving the broken_during predicate is indeed interpreted using negationas-failure). The interval [Start,End] is thus a Maximal Validity Interval (MVI) for property P. The broken_during axiom states that a given property P is interrupted between Start and End if there is an event E that happens between them and terminates P. This axiom provides a so-called weak interpretation [30] of initiates_at clauses (in a strong interpretation [30], the broken_during axiom would consider also initiating events for P and not just terminating ones as possible interruptions for the interval [Start,End]). In general, the choice between weak and strong interpretation is domain-dependent [30].

Finally, the holds_at axiom relates a property to a time-point rather than to a time-interval:

  , T < End. "property P maximally holds over interval [Start,End], if event Ei initiates P at instant Start, and event Et terminates P at instant End, and Start is before End, and P is not broken during [Start,End]" "property P maximally holds over interval [Start,+∞], if event Ei initiates P at instant Start, and P is not broken during [Start,+∞]" "property P is broken during [Start,End], if event E terminates P at instant T, and T is between Start and End"


Model selection via the lasso in conditional logistic regression

Marta Avalos

To cite this version:

Marta Avalos. Model selection via the lasso in conditional logistic regression. Second International Biometric Society Channel Network Conference, Apr 2009, Ghent, Belgium. pp.Model selection and clustering session. inserm-00402434

Conference abstracts 2nd Channel Network Meeting, Ghent, Belgium, April 6-8, 2009 Model selection via the lasso in conditional logistic regression

Marta Avalos

Biostatistics team of INSERM U897 and University of Bordeaux 2, France marta.avalos@isped.u-bordeaux2.fr

We propose a model selection procedure in the context of matched case-control studies and, more specifically, for the conditional logistic regression. The method is based on penalized conditional likelihood with an L 1 -type penalty of the regression coefficients, the so-called lasso. This penalty, which shrinks coefficients to improve the accuracy of prediction, is particularly adapted when the number of covariates is large (with respect to the number of events) or in case of collinearity between them. An attractive property of the lasso is that it performs parameter estimation and variable selection simultaneously. The implementation of the method is based on a simple modification of the R-package penalized for fitting generalized linear and Cox proportional hazard models with L 1 or L 2 penalties, developed by J. Goeman. The effectiveness of the algorithms allows the use of resampling methods for choosing the regularization term and for evaluating the stability of the selected model. Thus, K-fold likelihood cross-validation and bootstrap are applied, both taking into account the dependent nature of data. The methodology is illustrated with some examples.


Dr Svetlana Samokhvalova

J.-F Lutz
email: jflutz@unistra.fr

Informational Polymers Macromolecular Information Transfer

Keywords: Artificial Translation, Molecular Replication, Precision Polymers, Sequence-Controlled Polymers, Template-Directed Synthesis

Macromolecular information transfer can be defined as the process by which a coded monomer sequence is communicated from one macromolecule to another. In such a transfer process, the information sequence can be kept identical, transformed into a complementary sequence or even translated into a different molecular language. Such mechanisms are crucial in biology and take place in DNA!DNA replication, DNA!RNA transcription and RNA! protein translation. In fact, there would be no life on Earth without macromolecular information transfer. Mimicking such processes with synthetic macromolecules would also be of major scientific relevance because it would open up new avenues for technological applications (e.g. data storage and processing) but also for the creation of artificial life. In this important context, this minireview summarizes recent research about information transfer in synthetic oligomers and polymers. Medium-and long-term perspectives are also discussed.

Introduction

Life cannot proceed without information. [1] Indeed, the characteristics of all known living terrestrial organisms are encoded in genes, which are sequence-defined informational polymers. [2] Yet, the purpose of genes is not only to store information. Genes can be permanently altered (i.e. mutations), reversibly-modified (i.e. epigenetics) and copied. Furthermore, as long as the host organisms are alive, genes are regularly expressed to produce functional proteins. All this biological machinery requires molecular mechanisms for information transfer such as replication, translation and transcription.

Applying such biological principles to synthetic molecules has been a dream for chemists for many years. Mimicking important biological features such as biocatalysis [3] and replication [4] is a central topic for decades in organic synthesis and supramolecular chemistry. However, most of this research has been dedicated to small molecules and attempts for developing life-inspired macromolecular systems are quite rare. [5] In recent years, the information storage principle (i.e. sequence control) of biological polymers has been mimicked in a wide variety of synthetic polymers. [6] Such informational macromolecules have been proven to be useful in a variety of applications, including molecular data storage, [7] cryptography [8] and traceability applications. [9] Still, in all these examples, information is stored passively into the macromolecules and is not processed or transferred. As underlined in a recent essay, [5] there are currently no synthetic polymer enabling fast and reliable information transfer as it is occurring in biological systems. However, achieving such a property could be a major discovery that could have implications for applied chemistry but also for the development of artificial Life. In this context, the aim of this minireview is to summarize and critically analyze the efforts that have been made towards macromolecular information transfer.

General Mechanisms

Figure 1 shows some possible mechanisms for macromolecular information transfer. The presented situations are theoretical and are not necessarily existing in natural or synthetic systems. Two main mechanisms can be considered for information transfer, i.e. with or without molecular contact. In the contact mechanism (Figure 1a), a sequencedefined parent strand acts as a template to guide the synthesis of a daughter strand. This situation is the most familiar to chemists because it is the one selected by nature for genetic information transfer, [10] as described in the following section. Yet, several versions of such a mechanism can be imagined. In the simplest case (i), the parent strand is copied into an exact replica containing the same information sequence. This implies that the coded monomers selfassociate to guide the synthesis of the daughter strand. Alternatively, the coded monomers may interact through complementary AÀ B interactions, as schematized in (ii). Hence, the parent!daughter information transfer leads to the formation of a complementary sequence. In some other situations, the parent and daughter strands may also have different molecular structures. For instance, the original informational polymer may be transcribed into a related macromolecule with slightly different backbone or coding monomers. Such a transcript can be attained through the formation of twin or complementary monomer pairs, as schematized in (iii) and (iv). Furthermore, as described in (v), the sequence of a parent strand may be translated into a completely different informational macromolecule, i.e. having unrelated backbone chemistry and coding alphabet. In all these contact mechanisms, the two strands can be in direct contact through covalent and/or non-covalent interactions but they can also be associated with the help of intermediate molecules.

From a purely theoretical point of view, it is also possible to transfer information from one macromolecule to another without having any contact between them (Figure 1b). This, of course, can be achieved at the macroscale using a computer or a human brain as intermediate. Yet, it would also be interesting to achieve autonomous contact-free mechanisms at the molecular scale. An informational sequence can first potentially be transformed into a physical-(e.g. electrical, optical) or chemical-(e.g. ligands, ions) signal with the help of a molecular transducer. This can be attained, for example, with a nanopore that transforms a coded macromolecular sequence into an electrical signal. [11] Afterwards, the transmitted signal can be exploited for the synthesis of a sequence-defined macromolecular replicate; for example with the help of processive catalysis. [12] Although never achieved, such a contact-free mechanism may potentially also lead to macromolecular information transfer. Yet, it deals more with signal transduction rather than classical molecular replication.

Information Transfer in Biology

Even though the focus of this minireview is mainly on synthetic polymers, the purpose of this first section is to describe how macromolecular information transfer proceeds in biology. Indeed, since most of the synthetic systems described in the following pages are bio-inspired, it is useful to remind briefly how things work in nature. Yet, only a general summary is provided here and more detailed University (2001-2003), leader of the research group Nanotechnology for Life Science at the Fraunhofer Institute for Applied Polymer Research (2003-2010), and leader of the Precision Macromolecular Chemistry group at the Institut Charles Sadron (2010-2022). His research interests include the synthesis of sequence-controlled polymers and the design of informational polymers. In 2018 he received the Silver Medal of the French CNRS and in 2022 was appointed as a Senior distinguished member of the French Chemical Society. Comparable situations may also be obtained with expanded alphabets. For simplicity purposes, chain directionality (i.e. parallel versus antiparallel parent-daughter association) is also not considered in this Figure . a) Mechanisms involving molecular contact between parent and daughter strands: (i) Formation of a twin daughter strand that is an exact replica of the parent strand; (ii) Formation of a complementary strand driven by the association of complementary monomer pairs. (iii, iv) Examples of daughter strands, in which the informational chemistry of the parent strand is transcribed into a related alphabet. The molecular structure of the backbone and some letters of the alphabet may be changed in the process (e.g. B!C). v) Translation of a parent strand into an informational daughter strand with a fully different backbone and X/Y coding chemistry. b) Macromolecular information transfer without molecular contact. In such cases, the informational chemistry of the parent strand is transduced to the daughter strand through the formation of a physical or chemical message.

information can be found in classical textbooks. [10] Nucleic acids such as DNA and RNA are informational macromolecules because they store genetic information. This information is written using four monomers (ATGC for DNA and AUGC for RNA). Furthermore, nucleic acids can transfer their information through three main mechanisms: replication, transcription and translation.

Replication is an information transfer from a parent DNA chain to a daughter strand. It relies on the complementary association of base pairs AÀ T and GÀ C. Consequently, the formed daughter strand has a complementary sequence, as compared to the initial strand (mechanism (ii) in Figure 1a). Yet, since natural DNA exist under the form of a double-stranded complementary duplex, the replication of the two parent strands (parents 1 and 2) results in the formation of the exact same duplex (i.e. daughter 1 has the same sequence as parent 2 and daughter 2 has the same sequence as parent 1). Although nucleobases are crucial recognition motifs that ensure molecular contact between parent and daughter strands, phosphate and pentose ring of the repeat units also play an important role in the process. [13] Replication is enabled by enzymes including polymerases, helicases and ligases and is overall highly reliable. However, it has been achieved through a very long evolutionary process and it is therefore restricted to a limited set of molecules. [14] In other words, even subtle variations from the canonical reaction conditions can influence the fidelity of enzymatic replication. [15] While replication allows to copy information, transcription is an information transfer from DNA to messenger RNA, which acts as a mediator between the genetic storage medium (i.e. DNA) and the ribosomal machinery that synthesizes proteins. In this process, the backbone of the daughter strand contains ribose repeat units and therefore differs from the deoxyribose-based parent strand. Furthermore, the coding alphabet of mRNA is slightly different from the one of DNA since it contains uracil units instead of thymine. Information transfer is therefore based on the complementary base pairs AÀ U, TÀ A and GÀ C. Overall, the transcription process selected by nature corresponds to mechanism (iv) in Figure 1a.

Finally, the translation of mRNA into protein sequences is more than a simple data transmission. Indeed, in such a process, the information content of the parent strand is transformed into a different molecular language, as schematized by mechanism (v) in Figure 1a. For instance, the 4symbols alphabet of mRNA is translated into the 22 aminoacids of proteins. Such a transformation is made possible by transfer RNAs that contain both nucleobases (that associate with the mRNA parent strand) and amino acids (that polymerize into the daughter strand). The molecular translation is enabled by the classical codon system, in which a triad of nucleobases codes for a given amino acid or stop instruction. The codon system is probably one of the many reasons why evolution retained a quaternary code for genetic polymers. Indeed, trimer codons based on a 4symbols alphabet lead to 4 3 = 64 translation possibilities, which largely covers the 22 proteinogenic amino acids. In comparison, with a binary alphabet, pentamer codons would be needed to cover all situations (2 5 = 32), which probably would be less practical.

Replication of DNA, RNA, XNA, and Peptides

The natural information transfer mechanisms described in section 3 proceed in biological medium and in the presence of enzymes or ribozymes. Their discovery inspired chemists for developing artificial molecular replicating systems in laboratory conditions; in particular, in the absence of biocatalysts. Most of this research has been conducted with natural or altered biopolymers, such as DNA, RNA, XNA and peptides. These approaches are described in seminal reviews under the generic names "molecular replication" or "non-enzymatic replication". [4,16] One of the first example of non-enzymatic templatedirected syntheses of oligonucleotides was reported by Naylor and Gilham in 1966, who synthesized thymidine homo-oligomers of various chain-length using complementary polyadenylic acid as a template. [17] Afterwards, numerous examples have been reported, in particular by Orgel who has extensively studied the synthesis of oligonucleotides on DNA or RNA templates. [18] However, early examples dealt mainly with the synthesis of homo-oligomers, in which the information content is limited. [19] The first convincing example of non-enzymatic templated synthesis of a sequence-defined strand was reported by Orgel and co-workers in 1984. [20] Following nature's strategy, a complementary daughter strand was synthesized in this example (mechanism (ii) in Figure 1a). However, its catalytic behavior was not demonstrated. This was later achieved by von Kiedrowski who described the autocatalytic replication of a sequencedefined hexanucleotide. [21] Similar concepts have also been investigated with socalled xeno nucleic acids (XNA), which have backbones that differ from those of natural DNA and RNA. [22] A particular attention has been paid to peptide nucleic acids (PNA) that are consisted of a peptide backbone with pendant nucleobases. [23] Shortly after the first studies about the hybridization of PNA with DNA or RNA, [24] PNA was tested as a template for information transfer to RNA. [25] The opposite situations RNA!PNA and DNA!PNA were also investigated, [25,26] although these studies resulted in low transcription efficiency. This situation was later improved by Liu and co-workers who have shown that it is possible to connect short sequence-defined PNA oligomers via DNAtemplated reductive amination. [27] Alternative polymerization concepts such as sequence-selective base filling were also described for PNA!PNA information transfer. [28] Apart from classical PNA, other families of XNA have been investigated for macromolecular information transfer. Holliger and co-workers have recently summarized the potential of different synthetic nucleic acids with artificial base pairs to be enzymatically synthetized, to be amplified via the PCR technique, as well as to participate in replication, transcription and translation both in vitro and in vivo. [29] For example, it was shown that the development of specific polymerase variants allows information transfer from DNA to hydrohexitol, cyclohexenyl, locked and threofuranosyl nucleic acids. [30] Furthermore, the use of XNA as mediator for reverse transcription of DNA (DNA!XNA!DNA) has been assessed. [30,31] Besides nucleic acids, the replication of peptides was also studied, [32] even though such events do not take place in nature. For instance, Ghadiri and co-workers have used leucine zippers, which are dimers of two α-helical peptide chains, to achieve peptide self-replication. [33] In this case, a 32-mer parent strand was used as a template to catalyze the ligation of 15-mer and 17-mer sub-oligomers. The daughter strand is an exact clone of the parent strand and has therefore the same amino acid sequence (mechanism (i) in Figure 1a). The product then becomes a part of the autocatalytic cycle to promote further peptide fragments condensation. Based on this finding the authors suggested the possibility of self-replication of proteins with the conservation of enzymatic activity. Yet, in terms of information transfer, this example remains limited since the reactive 15-mer and 17-mer sub-oligomers contain long preformed information sequences.

Information Transfer in Synthetic Polymers

The purpose of this section is to describe recent advances for achieving macromolecular information transfer with synthetic systems. It therefore focuses on manmade molecules that can store several bits of information; i.e. oligomers or polymers that are composed of at least a few monomer units. Thus, the self-replication of small molecules is intentionally kept out of the scope of this section. Numerous contributions have been made to this field and detailed information can be found in comprehensive reviews. [34]

Artificial Hybridization and Replication

Supramolecular Strand Association

As described in section 3, replication and transcription rely on the complementary association of nucleobases, which is a recognition process involving hydrogen bonds. In other words, macromolecular information transfer is due to supramolecular strand association. Significant effort has been made to achieve similar processes with synthetic oligomers. The first step in this direction is the formation of perfectly-matching supramolecular duplexes between complementary synthetic strands. [START_REF]Hybridization shall be distinguished from conventional polymer-polymer complexation, in which several polymer chains interact via random non-covalent interactions[END_REF] Interesting examples have been reported using H-bond strand association, i.e. by mimicking the main strategy of nature. For example, Hunter and co-workers have described several examples of synthetic dimers stabilized by H-bond recognition. [37] Such situations can be obtained using self-complementary [37b] (i.e. a single type of strand that forms a supramolecular dimer) or complementary strands [37a] (i.e. two distinct strands with complementary structures). Comparable examples have been reported by other groups. For instance, Lehn and coworkers have described double helices formed through the self-recognition of pyridine-amide units. [38] Yet, H-bonds are not the only type of supramolecular interactions that can be used to drive duplex formation. In an early publication, Lehn and co-workers have demonstrated that metal-ligand interactions can also be exploited for that purpose. [39] Another efficient supramolecular motif for inter-strand recognition are salt bridges that have been used by Yashima and co-workers for double-helix formation. [40] However, in most of these examples, the strands were homopolymers and did not contain sequence-coded information. Some of the very first examples of duplexes involving defined informational sequences have been reported by Gong and co-workers. [41] They developed oligoamides with defined sequence of H-donors an H-acceptors that form duplexes with a complementary strand. [42] Lehn and co-workers have prepared sequence-defined oligomers containing bidentate bipyridine and tridentate terpyridine ligands and described that they are able to form sequencespecific duplexes by binding metal ions with corresponding coordination numbers. [43] Among other research on the topic, [44] the work of Hunter and co-workers shall be highlighted. These authors have developed different families of synthetic sequence-defined duplexes using various types of backbones and supramolecular recognition units, [45] and in particular have studied in details the competition between duplex formation and intramolecular folding. [46] Beyond duplex formation, very few studies describe macromolecular information transfer based on supramolecular associations between synthetic strands. One example was reported very recently by Hunter and coworker using supramolecular salt bridges Figure 2). [35] That system was designed to synthesize an exact copy of the parent strand (mechanism (i) in Figure 1a). One crucial aspect in supramolecular strategies is that the non-covalent associations between the monomers and the parent strand are strong enough to be stable in the dilute conditions used for daughter strand polymerization. This condition was verified in this example and it was reported that the daughter strand was obtained as the major product. Yet, it was underlined that this strategy is overall less efficient than some of the covalent approaches described in the following section.

Covalent Strand Association

Supramolecular interactions are sensitive to external parameters such as pH, temperature, ionic strength and concentration. For those reasons, dynamic covalent bonds, [47] which are more robust but easily breakable in mild conditions, appear as an interesting alternative for macromolecular information transfer. One of the earliest examples of a synthetic duplex stabilized by dynamic imine bonds was reported by the group of Moore using molecularly-defined phenylacetylene matching strands. [48] However, it was observed in this work that, above a critical strand length, the formed ladder coexist with a large amount of undefined high-molecular weight aggregates. More recently, Scott and co-workers have exploited dynamic imine bonds to obtain defined molecular ladders from complementary peptoid strands bearing aniline and benzaldehyde side-chains. [49] Interestingly, this strategy was used shortly after for the preparation of sequence-specific duplex. [50] Informational polymers capable of undergoing dynamic imine bonds have also been reported by Szostak and co-workers. [51] The solidphase synthesis of sequence-defined oligoarylacetylenes with aniline and benzaldehyde side-groups was described [51b] and the competition between intramolecular folding and duplex formation was explored. [51c] Perhaps more importantly, together with Prywes, these authors have studied replication and information transfer in oligoarylacetylenes. [51a] They have synthesized dimers, in which information is encoded by aniline and benzaldehyde sequences. As shown in Figure 3, such dimers form complementary duplexes which can be successfully replicated with the use of Sonogashira cross coupling to connect the monomer units. In such a process, the two strands of the parent duplex are copied into complementary daughter strands. In a sense, this mechanism is comparable to the replication of doublestranded DNA described in section 3.

Although dynamic covalent chemistry has demonstrated its potential for artificial information transfer, the intrinsic properties of such reactions bring up certain limitations. This is linked to the existing equilibria between different competing structures, such as a template with pre-organized building blocks vs a folded template or a template with only partially bound building blocks. The group of Hunter has addressed such limitations in a recent overview and highlighted the advantages of using conventional covalent chemistry for more reliable recognition in artificial macromolecules. [52] For instance, they have suggested to use ester chemistry as a recognition pattern for the synthesis of a complementary copy of an oligomer. [53] In this approach, molecular recognition was facilitated by phenol and benzoic acid moieties attached to oligotriazoles obtained via coppercatalyzed azide-alkyne cycloaddition (CuAAC). The authors have shown that it is possible to isolate the complementary copy and recover the template by hydrolyzing the ester bonds. A hybrid situation, in which the duplex is formed via H-bonds templating with the use of a covalent primer has been very recently reported by the same authors. [54] A complementary copy of a parent triazole trimer was obtained through this strategy (mechanism (ii) in Figure 1a). The covalent primer (i.e. first unit of the complementary sequence) was first attached to the template and was used to guide the attachment of a H-bond-forming dimer (i.e. additional units of the complementary sequence).

Artificial Translation

In all examples discussed in section 5.1, the chemical nature of the parent and daughter strands is the same, which resembles replication and to some extent transcription of biological polymers. To our knowledge, there is currently no reported example of translation-like mechanisms (mechanism (v) in Figure 1a) involving fully synthetic parent and daughter strands. However, sequence-defined biological templates such as peptide and nucleic acids has been studied for the preparation of synthetic polymers. Attempts for translating the information sequence of peptide templates to synthetic polymers have been so far restricted to small model molecules. [START_REF] Ouchi | Sequence-Controlled Polymers: Synthesis, Self-Assembly, and Properties[END_REF] Yet, DNA-templating was more broadly applied for the preparation of synthetic polymers. Most examples deal with the synthesis of polymers that are not sequence-defined, thus not informational, and are therefore not discussed in this minireview. [56] Still, in some cases, nucleic acids have been used to template the synthesis of sequence-defined polymers. [START_REF] Chen | Sequence-Controlled Polymers[END_REF] In these approaches, information transfer from parent to daughter strand is not directly mediated by nucleobase recognition (this would lie in the broad category of XNAs discussed in section 4), but using other concepts. For instance, Schuster and co-workers have exploited the major groove of DNA double-stranded duplexes to synthesize molecularly-defined conducting oligomers. [57,59] In this strategy, synthetic building blocks are covalently immobilized on DNA nucleobases and polymerized enzymatically. Horseradish peroxydase-mediated oxidative polymerization, guided by DNA-templating, was used to synthesize copolymers with defined sequences of aniline and benzene units. [59b] A comparable strategy was used afterwards for the synthesis of sequence-defined polymers containing aniline and 2,5-bis(2-thienyl)-pyrrole. [57] As schematized in Figure 4, before polymerization, the aniline building blocks are covalently attached to one strand of the DNA duplex, whereas the pyrrole building blocks are attached to the other strand. Consequently, the information that is transferred to the conducting daughter strand comes originally from two parent strands.

Liu and co-workers have also developed strategies for macromolecular translation. [60] They have first described a DNA-walker that enables translation from a DNA strand into a peptide chain. [60a] In a later work, the authors translated DNA sequences into synthetic copolymers using PNA-adapters (Figure 5). [60b] In this strategy, the role of the PNA adapters can be compared to the one of transfer RNAs in biology (see section 3) since they act as intermediates between the parent and daughter strands. Moreover, a bio-inspired codon system was used in this approach. Indeed, each PNA adapters carry a sequence of five nucleobases and one synthetic building block. Consequently, five coded bits of the parent informational sequence result in the incorporation of one coded bit in the daughter strand. Ultimately, the daughter strand can be separated from the adapters due to the use of cleavable disulfide linkers.

Molecular machines are also relevant for macromolecular information transfer. In a sense, the interlocked architecture described by Leigh and co-workers can be seen as a translation machine because it allows translation from a synthetic track into a peptide strand. [61] This system is conceptually close to some covalent replication approaches developed by Hunter (see section 5.1.2). The main difference between both strategies is somehow the way the daughter strand is polymerized. Nevertheless, in the approach reported by Leigh and co-workers, there is no parent strand per se, because the synthetic track contains the amino acids from the very beginning and was not described as a bare informational macromolecule.

Outlook

The objective of this Minireview was to describe and classify recent synthetic efforts leading to macromolecular information transfer. As described in the previous pages, substantial progress has already been achieved. However, on the whole, manmade strategies are far from optimal. Three main criteria shall be considered to assess the quality of macromolecular information transfer: (i) efficacy, (ii) exponenntially and (iii) informational content. Efficacy can simply be assessed by estimating the yield of the formed daughter strands with correct sequence (i.e. excluding defects with truncated sequences). Based on that criterion, most of the systems described herein are valid, even though some of them lead to low or moderate yields. Exponentiality reflects the fact that a formed daughter strand may catalyze the synthesis of further macromolecular copies. Here, manmade systems remain overall rather limited because of the dissociation of parent-daughter duplexes and other limitations. Yet, together with molecular mutations, [2b] autocatalytic replication of informational polymers remains one of the keys toward open-ended chemical evolution. [62] Information content can be quantified as the number of bits that is transferred from one macromolecule to another. That number is not necessarily equal to the number of monomers in the parent sequence, since information density can be in some cases higher than 1 bit/monomer. [6b] Nevertheless, that criterion is currently the most limiting one in manmade systems. In most of the examples described above, the transferred information content is minimal (i.e. at the scale of 2 or 3 bits). In other words, these proofs-of-concept deal mainly with oligomers rather than real informational polymers. Therefore, one of the major targets of the field in the future will be to develop strategies for transferring longer informational sequences.

To achieve further progress in the field, biology can of course be used as a source of inspiration, which is actually already the case in most works described herein. As described in section 3, macromolecular information transfer proceeds with very high efficiency in nature. However, there are still large differences between biological and manmade mechanisms. One of them is the efficiency of biocatalysis, which is much higher than in most human approaches. Furthermore, macromolecular information transfer is not an isolated process in biology but occurs in a complex environment (i.e. as a part of a complex system). These considerations may guide further research on this topic. Yet, one potential limit is to mimic biological concepts too closely and to design artificial macromolecules that remains conceptually and structurally very close to biological polymers (e.g. XNA). Indeed, future breakthroughs in the field may also result from approaches that are very different from the solutions selected by nature.

Figure 1 .

 1 Figure 1. Some possible mechanisms for macromolecular information transfer. The examples shown here are only presented for a 2-symbol A/B molecular alphabet. Comparable situations may also be obtained with expanded alphabets. For simplicity purposes, chain directionality (i.e. parallel versus antiparallel parent-daughter association) is also not considered in this Figure. a) Mechanisms involving molecular contact between parent and daughter strands: (i) Formation of a twin daughter strand that is an exact replica of the parent strand; (ii) Formation of a complementary strand driven by the association of complementary monomer pairs. (iii, iv) Examples of daughter strands, in which the informational chemistry of the parent strand is transcribed into a related alphabet. The molecular structure of the backbone and some letters of the alphabet may be changed in the process (e.g. B!C). v) Translation of a parent strand into an informational daughter strand with a fully different backbone and X/Y coding chemistry. b) Macromolecular information transfer without molecular contact. In such cases, the informational chemistry of the parent strand is transduced to the daughter strand through the formation of a physical or chemical message.

Figure 2 .

 2 Figure 2. Example of macromolecular information transfer involving supramolecular associations between the parent and the daughter strand:(i) attachment of complementary motifs, (ii) polymerization of the daughter strand, (iii) strands separation. Redrawn and adapted from Ref.[35].

Figure 3 .

 3 Figure 3. Replication of information-containing oligoarylacetylene. (i) Formation of a diimine duplex by recognition of complementary sequences. (ii) Addition of monomers A and B breaks the duplex and lead to sequence-specific associations between the monomers and the parent strands. (iii) Polymerization of the templated monomers leads to two daughter copies of the original duplex. Redrawn and adapted from Ref. [51a].

Figure 4 .

 4 Figure 4. Schematized representation of the double-stranded DNA templating strategy used for the synthesis of sequence-defined conducting polymers. Redrawn and adapted from Ref. [57].

Figure 5 .

 5 Figure 5. Translation of a DNA sequence into a synthetic copolymer. a) Schematized representation of the interaction between a PNA adapter and the DNA template. b) Example of a PNA adapter bearing an oligo(ethylene glycol) building block. Redrawn and adapted from Ref. [60b].

Angew. Chem. Int. Ed. 2023, e202300014 (5 of 9) © 2023 The Authors. Angewandte Chemie International Edition published by Wiley-VCH GmbH 15213773, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/anie.202300014 by Cochrane France, Wiley Online Library on [10/03/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Acknowledgements

This work was supported by the Interdisciplinary Thematic Institute SysChem via the IdEx Unistra (ANR-10-IDEX-0002) within the program Investissement d'Avenir. The PhD fellowship of S.S. was supported by the CSC Graduate School funded by the French National Research Agency (CSC-IGS ANR-17-EURE-0016).

Conflict of Interest

The authors declare no conflict of interest.

Minireviews Informational Polymers

S. Samokhvalova, J.-F. Lutz* e202300014

Macromolecular Information Transfer

The transfer of information from one macromolecule to another is a cornerstone of heredity, evolution, and Life. However, it is very difficult to achieve comparable mechanisms with manmade polymers. So far, artificial replication has mainly been demonstrated with small molecules with low information content. Here, we describe and categorize recent efforts that have been made to achieve macromolecular information transfer with synthetic polymers.


Dr Simone Di Noja

Dr Marina Garrido

Dr Lorenzo Gualandi

Dr Giulio Ragazzon
email: ragazzon@unistra.fr

Control over Dethreading Kinetics Allows Evaluating the Entropy Stored in an Interlocked Molecular Machine Out-of-Equilibrium

Keywords: Calorimetry, Molecular Machines, Non-Equilibrium, Rotaxanes, Supramolecular Chemistry

The operation of nanomachines is fundamentally different from that of their macroscopic counterparts. In particular, the role of solvent is critical yet rarely associated with machine functionality.

Here we study a minimal model of one of the most advanced molecular machines to gain control of its operation by engineering components and the employed solvent. Operation kinetics were changed over more than four orders of magnitude and could be modulated by solvent. Leveraging solvent properties, it was possible to monitor the relaxation of the molecular machine towards equilibrium and measure the heat exchanged in the process. Our work expands the capabilities of acid-base powered molecular machines, confirming experimentally that such systems have a dominant entropy content.

Introduction

Artificial molecular machines have held the limelight of the scientific community due to their potential to bridge the gap between the natural and artificial worlds. [1][2][3][4][START_REF] Liang | Proc. Natl. Acad. Sci[END_REF] The term "molecular machine" [2,3] encompasses a broad range of molecular architectures. The simplest case is represented by molecular switches, which interconvert between two states as a consequence of perturbed environmental conditions. [START_REF] Aprahamian | [END_REF][START_REF] Feringa | Molecular Switches[END_REF] At an increasing level of complexity, [START_REF] Chatterjee | [END_REF] we find systems that can undergo a cyclic sequence of reactions. The ability to perform cyclic reaction sequences is particularly relevant because it enables repeating endergonic processes. Indeed, from the point of view of the underlying physics, cyclic chemical reaction networks that are traveled unidirectionally represent a clear demarcation point between networks that can or cannot absorb work from the environment repeatedly, operating as molecular ratchets. [9][10][11][12][13][14][15][16][17][18] Thus, cyclic reaction sequences are a prerequisite to performing more elaborated tasks. [4,19] As a general example, we consider a square reaction scheme for pseudorotaxane assembly that can be traveled unidirectionally upon alternating acid-base stimuli, leading to the relocation of a macrocycle to an energeticallyunfavored location along a molecular axle (Figure 1). [20][21][22][23] This choice stems from the simplicity of pH changes as stimuli to power molecular machinery and the importance of simplicity for the progress of the field. [24] When the axle is deprotonatedstate ithe separated components are thermodynamically more stable than the pseudorotaxane; however, protonation of the axle forms a recognition site for the ringin state iileading to thermodynamically favored assembly in state iii. Addition of a base will ultimately revert the system to state i. In principle, this process can occur via either state ii or state iv. Indeed, dethreading from protonated state iii, followed by deprotonation of the uncomplexed axle, might take place, given the reversibility of self-assembly processes, and the high basicity of basic sites encircled by macrocycles, an established effect in interlocked structures. [25][26][27] In this scenario, dethreading occurs via the microscopic reverse process of threading under acidic conditions, and the machine does not complete a cyclic process. Therefore, it is important to distinguish if relaxation occurs via state iv or ii. The norm is to observe the conversion of each of the explored states into the following one of the sequence. [11,28] Here, this implies observing the formation of state iv from state iii, and then following dethreading relaxation from high-energy state iv to state i. This observable dynamic is considered a dissipative process, of high current interest in relation to transient supramolecular assemblies. [29][30][31][32][33][34][35][36][37] Engineering dethreading kinetics in crown ether rotaxanes is challenging, because subtle changes in stopper structure often lead to a sharp transition from pseudorotaxane to rotaxane-like character of the complex, an effect termed "all-ornothing" substituent effect. [38,39] So far, studies that approached self-assembly kinetics investigated the threading processes affording thermodynamically stable complexes, whereas the dethreading kinetics from high-energy states remained essentially unexplored. [22] To advance the understanding of minimal molecular ratchets, we focused on a versatile molecular pump module developed by Leigh and coworkers, capable of accumulating macrocycles in a high-energy state upon a sequence of acid-base stimuli. [20,40] The operating mechanism in action is based on the self-assembly of a crown ether macrocycle onto a dibenzyl ammonium ion. [START_REF] Bruns | The Nature of the Mechanical Bond : From Molecules to Machines[END_REF][START_REF] Ashton | [END_REF] A key design element is a benzyl aldehyde terminal in the axle component, which under acidic conditions can react with a hydrazide to form a hydrazone. If the hydrazide bears sufficiently bulky substituents, the hydrazone acts as a stopper, affording a rotaxane. The dibenzyl ammonium recognition site is lost if a base is added, resulting in kinetic trapping of the threaded crown ether in a high-energy state. [20,40] Here, we study the dethreading process from high-energy states in a minimalistic machine powered by acid-base stimuli. Control of its operation was gained, modulating the relaxation kinetics over four orders of magnitude by appropriate choice of the stopper unit, which allowed measurement of the heat exchanged during the dethreading process.

Results and discussion

Leveraging Leigh's design, we prepared axle 1aH + as a minimal molecular ratchet capable of trapping a macrocycle in a highenergy state (Figure 2a). Axle 1aH + comprises two key functional elements: a dibenzyl ammonium recognition site and symmetric terminal aldehydes. The synthesis of 1aH + is achieved using a convergent 6-step strategy, having an overall yield of 34% (SI section 3.1). As macrocyclic component we selected the extensively used crown ether dibenzo-24-crown-8 (DB24C8, Figure 2a), which is known to have a high affinity for dibenzyl ammonium ion in non-polar organic solvents. [43] The addition of DB24C8 to 1aH + resulted in the formation of pseudorotaxane [1aH + ⊂ DB24C8], as evidenced by the appearance of new upfield shifted signals for the protons of the macrocycle, both in the aromatic (e.g., from 6.91 to 6.81 ppm) and in the aliphatic region (e.g., from 4.10, 3.80 and 3.69 ppm to 4.05, 3.77 and 3.59 ppm, respectively, Figure S47). While pseudorotaxane formation is slow on the NMR time-scale, as increasing amounts of DB24C8 are added, the resonances of uncomplexed 1aH + progressively shifts towards lower frequencies (e.g. from 7.04 to 7.02 ppm), disclosing the underlying rapid equilibrium associated with ion pair formation between 1aH + and its counterion PF6 -, in agreement with previous reports. [44] Addition of 1.1 equivalents (eq.) of phosphazene base P1-t-Bu-tris(tetramethylene) (P1-t-Bu) resulted in complete dethreading, as revealed by the disappearance of signals associated with pseudotoraxane, and the appearance of peaks related to free, deprotonated 1a species. (Figure S47). Threading and dethreading processes occurred on a timescale slower than the NMR timescale, yet faster than the time required to record an NMR spectrum, indicating that benzaldehyde terminals do not provide a significant kinetic barrier for DB24C8 slippage on this time scale. Having established the ability of 1aH + to thread DB24C8, we focused our attention on hydrazone stopper features, selecting as starting point hydrazide 2a (Figure 2a), which was previously employed to stopper the larger dibenzo-30-crown-10 macrocycle. [20] Optimization studies associated with hydrazone formation were performed using commercially available 3-(2hydroxyethoxy)benzaldehyde (3, Figure 2a), which served as a minimal model of 1aH + terminals. Solutions of 3 and hydrazide 2a (6 mM of both components in CD3CN or CDCl3:CD3CN 3:1) were kinetically stable over time, showing no evidence of hydrazone formation under neutral conditions. The nucleophilic addition of hydrazide could be promoted by addition of acids, such as trichloroacetic acid (TCA) or triflic acid, CF3SO3H (TfOH). In particular, a screening of experimental conditions indicated that hydrazone formation could take place quantitatively (>95%), either upon addition of 0.2 eq. of TCA over 30 min, or alternatively upon addition of 0.05 eq. of TfOH over 90 min (Figure S50). When using higher amounts of acid, the extent of hydrazone formation to afford 2a•3 (Figure 2a) was lower in the same time range, possibly due to competitive protonation of the hydrazide. Hydrazone formation could also be monitored via UV-Vis absorption spectroscopy, following the formation of a new band at 295 nm (Figure S51). By using optical spectroscopy, we could confirm hydrazone formation even at a concentration of 120 µM for both components and observed that the rate of hydrazone formation under the employed conditions strongly depends on the total acid concentration. Indeed, in the presence of 220 µM TCA the reaction did not proceed, while in the presence of 15 mM TCA, the kinetic of hydrazone formation was comparable to that observed using 6 mM components. Control experiments excluded the relevance of light-induced isomerization of hydrazone under our experimental conditions. Indeed, we observed identical outcomes when performing hydrazone formation reaction in the dark or under ambient light.

By combining pseudorotaxane self-assembly with hydrazone formation it was possible to obtain complex [1a•2a2H + ⊂DB24C8], which however remains stable in CD3CN only for a few minutes, after which the solution becomes slightly turbid. Addition of DB24C8 to 1a•2a2H + promoted precipitation, indicating that pure CD3CN is not an optimal solvent for the present system. Since 1a•H + is not well soluble in pure CDCl3, we identified CDCl3:CD3CN 3:1 as a suitable mixed solvent system, which could ensure solubility of both 1aH + , and 1•2a2H + alone and in the presence of DB24C8. To obtain a high-energy state, 1.1 eq. of phosphazene base P1-t-Bu was added to preassembled [1a•2a2H + ⊂ DB24C8]. Contrary to what was observed in the absence of 2a, the signals of uncomplexed DB24C8 did not increase their intensity, with evidence from 1 H-NMR spectroscopy potentially compatible with the deprotonation of [1a•2a2H + ⊂ DB24C8] to afford a high-energy rotaxane [1a•2a2⊂DB24C8], in which DB24C8 resides onto the hydrazone moiety (Figure S48,49). However, the need to operate in a mixed solvent system and the lack of indicative peaks in the 1 H-NMR complicated monitoring machine operation. To improve system solubility and monitoring, we prepared axle 1bH + (Figure 2a) to be operated according to the reaction scheme in Figure 2b. 1bH + can be obtained with an overall 9% yield as a result of a convergent 8-step synthesis, based on the preparation of an asymmetric dibenzyl ammonium core having a pendant propargyl moiety and subsequent click reaction to afford a triazolium secondary station upon methylation (SI section 3.2). The as-synthetized axle 1bH + has an additional positive charge, improving the solubility in CD3CN, which was complete under all employed experimental conditions. Moreover, the triazolium moiety, along with the ethylic chain attached to it, offered distinctive 1 H-NMR signals for HB, HC HD, and HE (Figure 2a), facilitating monitoring machine operation. [45] Indeed, a stability constant of 225 M -1 in CD3CN for the assembly of [1bH + ⊂ DB24C8] was obtained from the integral ratio of peaks at 5.32 ppm and 5.14 ppm, ascribed to HB in uncomplexed and complexed 1bH + , respectively (Figure 3 [45,46] Considering the low acidity of protons encircled by crown ethers, [26] most likely the ring first shuttles thanks to Brownian motion away from the ammonium ion, followed by deprotonation; however, in the absence of spectroscopic evidence, shuttling and deprotonation are considered as a single process in Figure 1 We then turned our attention to controlling the relaxation kinetics from high-energy state IV to V, corresponding to the dethreading of DB24C8 from deprotonated axles of type 1b•2. Indeed, while triazolium has some binding affinity for DB24C8, the selfassembly equilibrium is shifted completely to the separated components at the employed mM concentration. [45] We therefore subjected 1bH + to stepwise reaction sequences from state I to state IV using hydrazides 2a-2m (Figure 2). Hydrazides 2a-2e were selected because they have a progressive decrease in steric hindrance and offer the possibility to investigate the effect of changing i-Pr position on the phenyl ring. Hydrazide 2f was selected because CF3 group is an isostere of i-Pr. [47] . Hydrazides 2i-2l provide information on OMe substitutions on the different positions of the phenyl ring, while hydrazide 2m can be compared with 2g and 2h to gain insights on methyl substituents. Investigated hydrazides displayed a sharp all-or-nothing substituent effect in terms of dethreading kinetics to afford state V. High-energy structures of type [1b•2⊂DB24C8] obtained from hydrazides 2a-2c, 2i, and 2l, were stable over time, and no changes were observed over at least 48 h in the 1 H-NMR spectrum. In sharp contrast, the addition of P1-t-Bu to pseudorotaxanes obtained from hydrazides 2d-2h and 2j-2k led to the formation of respective 1b•2 adducts in a time shorter than that required to record the first NMR spectrum after base addition (ca. 160 s). This evidence implies that the corresponding dethreading rate constants are either larger than 1.9×10 -2 s -1 or smaller than 3.0×10 -7 s -1 . On the basis of the present experimental data, it is not possible to unambiguously determine if the formation of state V from III occurred via intermediate IV or VI.

To rationalize these findings, we calculated the Boltzmannweighted Sterimol steric parameters for all the hydrazides investigated. [48] We found it insightful to represent the kinetic behavior as a function of parameters wL and wB5 (Figure 4), which report on the length of the substituent and longest dimension perpendicular to the L axis. In this representation, the two families of hydrazides occupy different regions, with hydrazides affording kinetically trapped states lying at the periphery of the graph. This representation suggests hydrazides having a large wB5 parameter and large wL facilitate blocking DB24C8. The peculiar behavior of 2b, [49] which blocks the macrocycle despite a relatively small wB5 might be rationalized considering that wB1, the shortest dimension perpendicular to L axis is 2.71 Å, a value larger than any other wB1 parameter associated with hydrazides that do not stopper DB24C8. (SI section 7).

To observe experimentally the dethreading kinetics associated with relaxation from state IV to state V, ensuring that the molecular machine performs a cyclic reaction sequence, we focused our attention on i-Pr substituted hydrazides 2c-2e: the fact that 2c afforded a kinetically trapped state, while 2d and 2e afforded the equilibrium state rapidly, as well as the fact that 2e is characterized by wSterimol parameters very similar to kinetically trapped 2b, was taken as an indication that dethreading was likely close to an experimentally accessible kinetics, having t1/2 in the minutes to hours timescale. [50] 10.1002/chem.202300295

Accepted Manuscript

Chemistry -A European Journal

This article is protected by copyright. All rights reserved. By comparing literature data on the threading kinetics of pseudorotaxanes based on dibenzyl ammonium/crown ether recognition, we observed that when an analogous axle was investigated in CD3CN or dichloromethane (DCM), the threading rates were similar in the two solvents, while complex thermodynamic stability was much higher in DCM (ca. 10 5 M -1 vs 10 2 M -1 ). [51,52] Thus, we reasoned that since NMR studies suggest that DB24C8 interacts via hydrogen bonds also in the high-energy state IV (with triazolium station), the solvent composition could be used to stabilize such interaction, slowing down the dethreading kinetics. [53][54][55][56] Since some hydrazides are not soluble in pure CDCl3, we decided to operate in the mixed solvent system CDCl3:CD3CN 3:1 because CDCl3 is a less competitive solvent for hydrogen bonding interactions with respect to CD3CN. Experimental confirmation of hydrogen bond stabilization in the chosen solvent was the increase of the association constant for pseudorotaxane [1bH + ⊂DB24C8], from 225 M -1 to 1800 M -1 . We thus focused on hydrazides affording pseudorotaxanes which dethreaded rapidly in CD3CN, and measured their dethreading kinetics in the mixed solvent system.

In contrast with previous experiments performed in CD3CN, when 2e and 2m were employed, it was possible to observe a dethreading kinetics from state IV to state V. Indeed, the addition of 1.1 eq. of P1-t-Bu to [1b•2eH + ⊂DB24C8] afforded the highenergy complex [1b•2e⊂DB24C8], state IV, as evidenced by the appearance of signals similar to those observed in kinetically trapped states. However, the intensity of these signals progressively decreased (Figure S53a), due to the dethreading of DB24C8 to afford uncomplexed 1b•2e. In the case of [1b•2e⊂DB24C8], complete dethreading occurs in less than 10 min. Nonetheless, the dethreading kinetics depends critically on both the dimension and position of hydrazide substituents: as a matter of fact, for [1b•2d⊂DB24C8] and [1b•2f⊂DB24C8], obtained with 3-isopropyl benzohydrazide and with 4trifluoromethyl benzohydrazide respectively, the dethreading occurs in a time shorter than that required to record a single NMR spectrum also in the mixed solvent system. Instead, for [1b•2m⊂DB24C8], the process advances in nearly 3 days. (Figure S54a) Fitting of the dethreading data confirmed that the process follows a first-order kinetics, with dethreading constants of (6.7±0.7)×10 -3 s -1 and (1.07±0.03)×10 -5 s -1 obtained when using hydrazide 2e and 2m, respectively (Table 1 and Figure S53b,54b). type complexes upon addition of 1.1 eq. of P1-t-Bu in the mixed solvent The slower dethreading kinetics observed using hydrazide 2m could be accelerated (t1/2 = 15 min instead of 18 h) by operating in the more polar mixed solvent CDCl3:CD3CN 1:1. Overall, these data demonstrate that it is possible to modulate kinetics to confirm stepwise evolution from state III to state V via state IV, by using a suitable solvent system. Being able to observe the dethreading relaxation kinetics allows investigating the heat exchanged in this process. To this aim, pseudorotaxane [1b•2eH + ⊂DB24C8] was prepared in the same conditions used in NMR studies, and 1.1 eq. of P1-t-Bu was added inside a calorimeter. The fast acid-base reaction afforded a highly exothermic process, which dominated the first 5 min of the dethreading experiment (Figure S56). Our interpretation was supported by control experiments of TfOH neutralization (Figure S56). After 5 min, an endothermic process was observed, which decayed exponentially over time (Figure 5 andS56). We could successfully use the rate constant determined in 1 H-NMR studies to fit the endothermic decay kinetics, confirming that the observed process occurs on the same time scale of dethreading. Our ability to monitor the dethreading kinetics is corroborated by control experiments performed by adding 1.1 eq. of P1-t-Bu to the noninterlocked mixture of 1b•2eH + and DB24C8, which do not show any heat exchange after 5 min (Figure S56), indicating that the observed process should be attributed to the thread and axle being interlocked. Since the dethreading reaction is exergonic (G ≤ -12 kJ mol -1 under the present experimental conditions, SI section 6.2 for details), the observed endothermic process implies that the dethreading reaction is entropy-driven. In particular, under the experimental condition employed, the calorimetry data afford a H of 20±7 kJ mol -1 for the relaxation to equilibrium, leading to an entropic contribution TS ≥ 32 kJ mol -1 . Considering the interactions involved, it seems reasonable to expect similar characteristics in other pseudorotaxanes bearing the same triazoliumcrown-ether recognition motif. As a comparison, this value is roughly twice as much as the total energy that can be stored in light-driven molecular whirligig, i.e., a derivative of Feringa rotary motor entangling glycol chains upon rotation. [57] 10.1002/chem.202300295

CDCl3:CD3CN 3:1 at 298 K. Hydrazide kout [s -1 ] [a] t1/2 [min] [b] ΔG ǂ [kJ mol -1 ] [a,c]

Accepted Manuscript

Chemistry -A European Journal

This article is protected by copyright. All rights reserved. Leveraging the observed dethreading kinetics, we addressed the possibility of performing multiple cycles of threading and dethreading via states (III→IV→V→VI→III). Initially, state VI was prepared by reacting axle 1bH + and hydrazide 2e in the presence of 0.05 eq of TfOH. Then, adding 1 eq. of DB24C8 afforded [1b•2eH + ⊂DB24C8], which formed over 90 h, as evidenced by 1 H-NMR spectra (Figure S55). Under the present experimental conditions, state III is likely formed directly via threading from state VI, i.e., hydrazone dynamic formation does not play a role because in an identical experiment performed using bulky hydrazide 2a no threading was observed. Addition of 1.05 eq. of P1-t-Bu to [1b•2eH + ⊂ DB24C8], state III, afforded IV, which relaxed spontaneously to 1b•2e and DB24C8, as evidenced by the convergence of the HB peaks to a single signal at 5.27 ppm. Next, 1.1 eq of TfOH is added to form the ammonium station of 1bH + again, thus [1b•2eH + ⊂DB24C8]. Under these conditions, it was possible to perform three subsequent cycles (III→IV→V→VI→III, Figure 6, SI section 6) powered by the addition of TfOH and P1-t-Bu. Formation of [1b•2eH + ⊂DB24C8] for the fourth cycle could not be accomplished, presumably due to a progressive hydrolysis reaction of hydrazone to form starting aldehyde (hydrolysis was never observed in shorter kinetic studies).

Conclusions

In conclusion, we have studied a minimal molecular machine capable of trapping a macrocycle in a high-energy state according to an energy ratchet mechanism, powered by acidbase inputs. On-demand selection of stoppering units allowed controlling the dethreading kinetics over four orders of magnitude, from a persistent kinetically trapped state to a rapid equilibration. Remarkably, the careful selection of solvent allowed fine-tuning dethreading kinetics, making it possible to gain direct evidence of the machine exploring the square reaction network in a directional fashion. Importantly, through kinetic calorimetry measurements, it was possible to experimentally quantify the entropy stored in the investigated high-energy pseudorotaxane. While the considerable entropy content of high-energy pseudorotaxanes was already anticipated, [58] our work evaluates experimentallyto the best of our knowledge for the first timethis energetic contribution. Employing calorimetry to study molecular machines that operate away from equilibrium expands the toolbox available to gain insights into such systems. Monitoring the heat exchanged in time allows discriminating between fast reactions (here acid-base) and slow reactions (here dethreading) associated with the same process. By operating the machine under optimized conditions, it was possible to repeat the machine ratcheting cycle three times. Our work illustrates how tailoring structural details and solvent can afford on-demand functionality of molecular machines and sheds light on the energetic features of ordered supramolecular structures obtained as a result of endergonic processes.

Experimental Section

Materials & synthesis: Unless otherwise stated, all reagents and solvents were purchased from commercial sources and used as received. Commercial reagents included hydrazides 2b, 2e, 2f, 2g, 2h, 2i, 2j, 2k and macrocycle DB24C8. Hydrazides 2a, 2c, 2d, 2l, and 2m, were synthesized from corresponding carboxylic acids or esters. A complete description of the synthetic protocols and characterization data of synthesized compounds, including 1aHPF6 and 1bHPF6, are reported in the Supporting Information.

NMR experiments: In a typical cycling experiment, the NMR tube was charged with 500 μL of a 1bH + solution (3.6 μmol). After that, in sequence, 60 μl (3.6 μmol, 1 eq.) of a DB24C8 macrocycle solution, 100 μL (3.6 μmol, 1 eq.) of hydrazide 2 and 2.5 μL (0.18 μmol, 0.05 eq.) of TfOH are added. Spectra are recorded after every new addition. The spectrum is monitored until the disappearance (i.e., integration <5%) of the peak ascribed to the aldehyde proton (9.99 ppm). Finally, 22 μL (4 μmol, 1.1 eq.) of a P1-t-Bu solution (35 μmol, 175 mM) are added and quickly mixed. The final concentration after all the additions is 5.25 mM. Further details are reported in the Supporting Information.

Calorimetry experiments: Samples were prepared according to the same protocol used in NMR experiments. However, after hydrazone formation, the solvent was removed under reduced pressure, and 3.6 mL of CHCl3:CH3CN 3:1 were added. The resulting 1 mM solution is used for the measurement. Further details are reported in the Supporting Information.

Methods:

The stability constants were obtained from the 1 H-NMR spectra of equimolar solutions (6•10 -3 M) of DB24C8 and either axle 1aHPF6 or 1bHPF6, at r.t., using the single-point method. [59,[START_REF] Connors | Binding Constants: The Measurement of Molecular Complex Stability[END_REF] The concentration of all the species at equilibrium was determined using the initial concentrations and the integration of the protons of the complexed and uncomplexed species. The stability constant was calculated according to a 1:1 binding model. Data fitting of the exponential kinetics was performed using a homemade Python code. wSterimol parameters were calculated using the procedure described in ref. [48] with minimal modifications. Further details are reported in the Supporting Information.

Figure 1 .

 1 Figure 1. (a) Minimal scheme for the operation of a molecular ratchet mechanism driven alternating acid and base inputs, leading to the relocation of a macrocycle onto a thermodynamically unfavoured recognition site. Purple and olive units serve as recognition sites. (b) Kinetic traces associated with a relaxation from iv to ii that is too fast to be experimentally observed (left), slow enough to be observed (centre), or very slow leading to a kinetically trapped state (right) depending on the size of the stopper.

Figure 2 .

 2 Figure 2. (a) Molecular structure of investigated compounds, with indicative protons labeled. (b) Reaction network for the operation of 1bH + and a generic hydrazide 2 leading to kinetic trapping of DB24C8 in high-energy state (IV) as a result of sequential acid-base additions.

  -I,II). Hydrazone formation occurred effectively upon the addition of hydrazide 2a and 0.05 eq. of TfOH, as indicated by the disappearance of HA signal at 9.99 ppm and the progressive rise of the HF signal of 2a in [1b•2aH + ⊂DB24C8] at 10.26 ppm (Figure 3-III). Addition of 1.1 eq. of P1-t-Bu to [1b•2aH + ⊂DB24C8] afforded the high-energy complex [1b•2a⊂DB24C8], as evidenced by the disappearance of the HB signal at 5.14 ppm and the appearance of a new set of peaks, including a singlet at 9.11 ppm and a singlet at 4.73 ppm, relative to HC and HB, along with two triplets at 5.45 and 4.70, relative to HD and HE (Figure 3-IV); the observed signals are in line with DB24C8 encircling the triazolium station, and interacting via hydrogen bonds.

and 2 .

 2 The obtained high-energy, kinetically-trapped state was stable in solution for at least 48 h at r.t., during which the 1 H-NMR spectrum remained unchanged, indicating the kinetic stability of [1b•2a⊂DB24C8]. 10.1002/chem.202300295 Accepted Manuscript Chemistry -A European Journal This article is protected by copyright. All rights reserved. 15213765, ja, Downloaded from https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/chem.202300295 by Cochrane France, Wiley Online Library on [10/03/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Figure 3 .

 3 Figure 3. Partial 1 H-NMR spectra (500 MHz, CD3CN, r.t.) describing states I -IV (Figure 2b) for axle 1bH + and hydrazide 2a. (I) 7.2 mM axle 1bH + alone, (II) upon addition of 1 eq. of DB24C8, (III) upon subsequent addition of 1 eq. of hydrazide 2a and 0.05 eq. of TfOH to form [1b•2aH + ⊂DB24C8], and (IV) upon subsequent addition of 1.1 eq. of P1-t-Bu to form [1b•2a⊂DB24C8]. Full spectra are reported in Figure S52.

Figure 4 .

 4 Figure 4. a) Schematic representation of the Sterimol parameters L and B5 for 2a. The view is perpendicular to the L-axis, i.e. the direction along the connecting point of the examined parent molecule. b) Kinetic properties for the dethreading of DB24C8 from [1b•2H + ⊂DB24C8] type complexes upon addition of 1.1 eq. of P1-t-Bu in CD3CN. at 298 K, with respect to wSterimol parameters of corresponding hydrazides, to which notation refers.

  Apparent dethreading rate constant. Upper and lower bound values were calculated assuming a first-order kinetic with a residual fraction of complex of 0.05 after 160 s for fast processes. [b] Half-life of the complex, calculated as t1/2 = ln2/kout. [c] Calculated from the measured rate constants using the relationship ΔG ǂ = -RT ln(kout h/kb T), where R, h, and kb correspond to the gas, Planck and Boltzmann constants. [d] Investigated only in mixed solvent due to poor solubility in CD3CN.

Figure 5 .

 5 Figure 5. a) Heat exchanged over time from [1b•2eH + ⊂DB24C8] (1 mM) upon addition of 1.1 eq. of P1-t-Bu in the mixed solvent CHCl3:CH3CN 3:1 at 298 K. Solid black line refers to the fit of the experimental data (red circles) according to a first-order dethreading process, having kout = 6.7×10 -3 s -1 , as determined in 1 H-NMR experiments. b) Thermodynamic parameters, determined from calorimetry measurements.

Figure 6 .

 6 Figure 6. Repeated acid-base cycles ratcheting DB24C8 onto 1b•2e thread to form [1b•2e⊂DB24C8]. Initial conditions: CDCl3:CD3CN 3:1, components 5.4 mM subsequent additions of 1.1 eq. base P1-t-Bu and 1.05 eq. of TfOH acid. Association % are obtained from the integration of 1 H-NMR signals. The reported values are an average of two independent experiments. TfOH is added ca. 30 min after the addition of base; P1-t-Bu is added ca. 90 h after addition of acid. Lines are intended as a guide to the eye.

  10.1002/chem.202300295Accepted ManuscriptChemistry -A European JournalThis article is protected by copyright. All rights reserved.

  15213765, ja, Downloaded from https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/chem.202300295 by Cochrane France, Wiley Online Library on [10/03/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

  , ja, Downloaded from https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/chem.202300295 by Cochrane France, Wiley Online Library on [10/03/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

	10.1002/chem.202300295
	Accepted Manuscript

Chemistry -A European Journal

This article is protected by copyright. All rights reserved. 15213765

  15213765, ja, Downloaded from https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/chem.202300295 by Cochrane France, Wiley Online Library on [10/03/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Table 1 .

 1 Kinetic data for the dethreading of DB24C8 from [1b•2H + ⊂DB24C8]

  15213765, ja, Downloaded from https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/chem.202300295 by Cochrane France, Wiley Online Library on [10/03/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Acknowledgments

This work was supported by the University of Trieste (MAC Microgrant), the Interdisciplinary Thematic Institute ITI-CSC via the IdEx Unistra (ANR-10-IDEX-0002) within the program Investissement d'Avenir, and the European Research Council (ERC-2021-StG n. 101041933). The authors thank Prof. Maurizio Prato for supporting research activities and helpful discussions, Prof. Paolo Samorì and Dr. Fanny Richard for help in calorimetry experiments, Dr. Stephanie Federico for kindly providing some commercial compounds, Prof. David A. Leigh and Dr. Massimo Baroncini for helpful discussions and David Russell for proofreading the manuscript.

We studied a minimal model of an acid-base powered molecular machine, gaining control on its dethreading kinetics by engineering its components. Leveraging solvent properties, we could monitor the relaxation of the molecular machine from a high energy state to equilibrium. By measuring the heat exchanged in this process, we could confirm experimentally that such systems have a significant entropy content.

Twitter usernames: @giuliosflask @simonedinoja @marina_gar_ser @lab_carbon 10.1002/chem.202300295

Conflict of interest

The authors declare no conflict of interest.

Accepted Manuscript

Chemistry -A European Journal

This article is protected by copyright. All rights reserved.


Parsimonious additive logistic models

Logistic regression is a standard tool in statistics for binary classification. The logistic model relates the logarithm of the odds-ratio to the predictors via a linear regression model. A generalization is the additive logistic model, which replaces each linear term by an unspecified smooth function, allowing for more flexibility while preserving interpretability.

Another variant is penalized logistic regression, which shrinks coefficients to improve the accuracy of prediction. Ridge regression (L2-penalization) and lasso (L1-penalization) are the main penalization procedures. An attractive property of the later is that it performs parameter estimation and variable selection simultaneously. New theoretical results, efficient algorithms, and available software play a major role in the recent popularization of lasso. In this study, L1-penalization is adapted to additive logistic regression fitted by smoothing splines.

Coefficients associated to predictors. Coefficients associated to predictors with little effect on the response may be shrunk (some of them to zero). This approach gives parsimonious models, removes irrelevant variables, and identifies non linear trends. The estimates are computed via the usual Newton-Raphson update, combined with the lars-lasso algorithm, to resolve the penalization problem, and the backfitting algorithm to fit additive models.

Different criteria based on the effective degrees of freedom are proposed to choose the penalization parameters. Performance is illustrated with some examples.