Keywords: axon, plasticity, nanoscale, STED axones, plasticité, super-résolution, STED

Investigating morpho-functional plasticity of CA3 axons in living brain slices by a combination of STED microscopy and electrophysiology.

I wish to thank my supervisor for giving me the opportunity to perform a PhD in his lab, supporting me over the years and giving me independence in my research. I started out in the team almost five years ago coming back from the US as a lab manager in a nascent team. It was a great experience to see the lab building up and the team growing over those years. I thank Dr. Daniel Cattaert for his collaboration in the project. His modeling approach and our fruitful discussions have shed new light on the project. I want to thank my buddy and brand new Doctor Philipp Bethge for joining me on our endeavor for an academic degree and countless off-hours in the streets of Bordeaux.

I also wish to thank for former members of the team: Fabien Nadrigny who always impressed me with his explanations every time I had a question about optics; Elena Avignone for biological discussions and her friendship; Martin Lenz, our expert in optics who I wish all the best in his next adventures. Special thanks to the members of the team: Julie Angibaud, Misa Arizono, Mirelle Ter Veer, Lasani Wijetunge, Thomas Pfeiffer, Jan Tonnesen for contributing to the great atmosphere in the lab and their friendship. Thanks to Aude Panatier for very helpful discussions and her friendship. Thanks to all the members of the institute that are all contributing in making this laboratory such a nice place to work and live.

List of Figures

ABSTRACT

Millisecond timing precision in the transfer of information between neurons is essential for the synchrony and plasticity of neural circuits in the brain. Axons are neuronal extensions that ensure the communication via brief electrical impulses called action potentials (AP).

Because they are unmyelinated and are extremely thin, hippocampal axons propagate APs slowly and thus generate long delays of conduction (up to 100 ms) that are traditionally considered invariant. However, recent studies have shown that activity changes the morphology of axons and modulate the latency of transmission, thus raising the question whether axons undergo activity-dependent structural changes that could influence the propagation of APs.

The diameter of hippocampal axons (ranging between 100-350 nm) are usually too thin to be properly resolved by conventional light microscopy. However, the development of super resolution STED imaging now enables the observation of their detailed morphological dynamics in living tissue.

Using a novel combination of STED microscopy, field recordings, patch-clamp electrophysiology in mouse brain slices and computer simulations we discovered that CA3 axons undergo long-lasting enlargement in their diameter after the induction of long term potentiation (LTP). We provide strong evidence that this diameter enlargement increases AP conduction velocity.

Taken together, our findings indicate that axons can dynamically tune AP propagation delays by changing their diameters, thereby altering the timing of information transfer in neural circuits. This study suggests a novel and powerful structural mechanism for neural plasticity.

Résumé détaillé en français

Un neurone est une cellule excitable électriquement et hautement polarisée qui reçoit, traite et transmet les informations au moyen de signaux électriques et chimiques. Les neurones peuvent se connecter les uns aux autres par l'intermédiaire de contacts appelés synapses et former des réseaux neuronaux. Typiquement, un neurone est composé de trois compartiments, un corps cellulaire (soma), une arborisation dendritique qui reçoit les signaux d'autres neurones et l'axone qui envoie l'information vers les neurones suivants.

L'axone est une extension protoplasmique mince et allongée qui part du corps cellulaire et qui s'étend jusqu'aux terminaisons nerveuses. Sa fonction est de conduire l'information par l'intermédiaire d'impulsions électriques, généralement des potentiels d'action (PA) partant du soma, se propageant pour atteindre différent neurones.

Traditionnellement les axones sont perçus comme des transmetteurs fiables de l'information générée au soma en véhiculant un code purement digital. Toutefois, les examens attentifs de l'organisation structurelle, de la composition en canaux et des différentes propriétés fonctionnelles des axones ont commencé à remettre en question cette vision simpliste. En effet, de nombreuses études ont démontré que la structure de l'axone peut exercer une influence profonde sur l'intégration d'entrée neuronale et la modulation de sortie, indiquant ainsi que le répertoire des axones fonctionnel est beaucoup plus large qu'on ne le pensait traditionnellement.

Un timing précis de la décharge neuronale est essentiel pour la synchronisation du réseau et la plasticité circuit dans le cerveau. Une synchronisation à l'échelle de la milliseconde est extrêmement importante dans l'intégration des signaux excitateurs et inhibiteurs qui module la fonction de sortie d'un neurone. En outre, la coïncidence entre les événements synaptiques et les décharges dendritiques est connue pour réguler la force de la transmission synaptique dans un processus communément appelé la plasticité dépendante du timing de décharge (en anglais: spike-timing dependent plasticity ou STDP). En ce qui concerne ces fonctions importantes du cerveau, le délai de conduction axonale des potentiels d'action (PA) est un paramètre souvent négligé, mais peut être très long. Du moment de l'initiation jusqu'à la terminaison nerveuse présynaptique, ce délai peut varier sensiblement d'une à plusieurs centaines de millisecondes.

Dans le cerveau des mammifères, la vitesse et la fiabilité de propagation des PA peuvent être assurées de deux manières : un large diamètre axonal ou la myélinisation. Cependant, la plupart des axones dans l'hippocampe sont non-myélinisés et ont des diamètres très minces qui expliquent les importants délais de propagation. Par exemple, en plus de leur topologie très ramifiée et de leur morphologie irrégulière du aux boutons présynaptiques dits 'en passants', les axones CA3 présentent de longues branches collatérales (jusqu'à 20 mm) et des diamètres compris entre 100-300 nm.

La difficulté d'isoler et d'évaluer les propriétés biophysiques de ces axones minces a forgé notre point de vue où le délai de la conduction axonale est un paramètre fixe qui ne contribue pas au codage de l'information. Néanmoins, quelques études indiquent que le délai de conduction des PA pourrait être régulé de manière dynamique. Des études de microscopie à deux photons ont révélé un important remodelage structurel des connexions synaptiques dans l'hippocampe durant des protocoles de plasticité synaptique. Cela représente la preuve la plus convaincante que la morphologie des axones est sensible à l'activité qui pourraient donc modifier la vitesse de conduction des PA. De plus, une régulation dynamique du diamètre axonal a déjà été suggérée par plusieurs études qui ont signalé des changements dans les latences synaptiques durant l'activité et pourrait être liés à un changement de délais axonaux.

Parce que la microscopie optique conventionnelle ne parvient pas à résoudre correctement la morphologie des axones allant bien au-dessous de 500 nm et la microscopie électronique ne peut pas être combinée avec des tests fonctionnels, c'est une possibilité encore inexplorée de savoir si minces axones non-myélinisés subissent des changements de diamètre dépendants de l'activité qui pourraient influencer la propagation des PA.

Par conséquent, la microscopie à super résolution STED, dont le pouvoir de résolution n'est pas limitée par la diffraction de la lumière, est bien adaptée pour l'imagerie des axones dans des tranches de cerveau vivant.

Dans cette étude, nous avons examiné si les axones peuvent être régulés de manière dynamique par l'activité. Nous avons combiné la microscopie STED, l'électrophysiologie avec des enregistrements d'activité de champs et de neurone unique en 'patch-clamp' sur des tranches en culture de cerveau de souris et des simulations informatiques afin de corréler les changements morphologiques dépendants de l'activité d'axones de la vitesse de conduction des PA. Nos résultats montrent que de façon concomitante avec l'induction de protocoles d'activité de potentialisation synaptique, le diamètre des axones s'élargit et la vitesse de conduction des PA augmente AP de conduction. Ces données suggèrent l'existence d'un nouveau type de plasticité par laquelle les diamètres des axones contrôlent dynamiquement les délais synaptiques dans les réseaux neuronaux.

Le travail de cette thèse comprend également le développement d'un nouveau genre de microscope à super-résolution STED qui permet d'observer les fines structures du système nerveux plus profondément dans des tranches de cerveau adulte mais également sur animal vivant. Les premiers développements de microscopes STED étaient basés sur une excitation à simple photon qui limite les observations sur les structures superficielles de culture de neurones dissociés ou de tranches fines de cerveau en culture. En revanche, la microscopie deux-photon est actuellement la méthode de choix pour l'imagerie dans des échantillons

The action potential

When an excitatory synapse is activated, an excitatory postsynaptic potential (EPSP) is generated and transiently depolarize the membrane. If the depolarization reaches a certain threshold such as through the simultaneous activation of several synapses, the neuron fires an AP which will travel down the axon. In contrast to EPSPs that spreads electrotonically; APs actively propagate along axons due to the voltage dependence of their ionic conductances.

This makes the AP a self-supporting or regenerative process.

The AP is an electrical impulse propagating rapidly along the axon. They are generated by sequential opening of various voltage-gated sodium and potassium channels (Nav and Kv channels, respectively) at the cell membrane. When the membrane is at its resting potential, Nav channels are closed but rapidly open when the potential reaches a specific threshold.

This produces an inward flow of positively charged, sodium ions that quickly increase the membrane potential (depolarization phase). This depolarization causes a change of membrane polarity which leads to the inactivation of the Nav channels. The depolarization also activates Kv channels allowing an outward flow of potassium ions returning the membrane potential to its resting potential (repolarisation phase). Their slow inactivation kinetics produces an undershoot called after-hyperolarisation. For chemical synapses, when the AP arrives at the presynaptic terminal, the change in membrane potential activates voltage-gated calcium channels (Cav channels) creating an inward current of calcium ions into the presynaptic terminal. Typically, this rise of calcium triggers the fusion of vesicles, liberating neurotransmitters into the synaptic cleft. As a consequence, the neurotransmitter molecules activate postsynaptic receptors which produce post synaptic currents.

A single AP is followed by an absolute refractory period during which another AP cannot be evoked, and a relative refractory period during which a stronger stimulus is required to elicit an AP. At the end of the depolarization phase, when Nav channels are closing, they enter in an inactivated state before going back to a resting state which makes them insensitive to any change in membrane potential -this phase corresponds to the absolute refractory period. This aspect is mainly responsible for the unidirectional propagation of AP. Indeed, in a propagating AP, the segment of axon behind the actively spiking part is refractory to the change in potential. The segment in front, yet not having been activated, is capable of being stimulated by the depolarization from the AP.

After the absolute refractory period, the axon undergoes the relative refractory period where activation of Nav channels can induce APs, albeit only after strong stimulation. This is due to an outward flow of potassium ions as a fraction of Kv channels are still open (slow kinetics of the Kv channels).

Classification of axons

Across species, organs and even within the same anatomical region, axons are very diverse in their structures and properties. Two main types of axons can however been distinguished: unmyelinated and myelinated axons. Myelinated axons refer to axons that are enwrapped by a myelin sheet from Schwann cells in the peripheral nervous system (PNS) or the oligodendrocytes in the central nervous system (CNS). These axons conduct electrical impulses much faster than their unmyelinated kin. The myelin sheath, arranged in segments along the axon and separated by the nodes of Ranvier, acts as an electric insulator preventing the electrical current from leaving the axon and hence, restricting the ionic exchanges to the nodes of Ranvier. Indeed, when impulses propagate continuously as waves along unmyelinated axons, relying on channel kinetics, they seem to hop from node to node in a combination of fast electrotonic spread and active propagation. This phenomenon is called the saltatory conduction and dramatically increases conduction speed.

In the mammalian CNS, the classification into grey and white matter arises from a whiteness of the myelin revealing the regions containing the fast conducting fibers. By opposition, the grey matter that does not contain myelin gets its color from the neuronal cell bodies, neuropil, glial cells and capillaries. Grey matter is found at the surface of the cerebral cortex and cerebellum, as well as in the depths of the cerebrum (thalamus; hypothalamus; subthalamus, basal ganglia -putamen, globus pallidus, nucleus accumbens; septal nuclei), cerebellar (deep cerebellar nuclei -dentate nucleus, globose nucleus, emboliform nucleus, fastigial nucleus), brainstem (substantia nigra, red nucleus, olivary nuclei, cranial nerve nuclei) and spinal grey matter (anterior horn, lateral horn, posterior horn). The white matter is composed of bundles of myelinated fibers connecting the various grey matter areas. For instance, the corpus callosum is the largest white matter structure of the brain and its role is to facilitate interhemispheric communication.

Hippocampal axons

The hippocampus, part of the grey matter, is one of the most studied regions of the brain.

There are two main reasons for this great interest. First, it is now well established that the hippocampus has a critical role in learning and memory processes. For instance, the hippocampus is involved in remembering information that can be described in a propositional or declarative manner [START_REF] Andersen | The Hippocampus Book[END_REF]. During the last decades, all the work that has focused on the function of the hippocampus has shaped our current concepts about memory organization in the brain. The second reason that gathers attention around the hippocampus is its extremely well oriented cellular organization that makes the hippocampal formation relatively easy to study (Figure 2). Indeed, neurons are organized in densely packed layers that are easily recognizable at low magnification. In this organization, two types of excitatory glutamatergic cells can be found: the pyramidal neurons and granule cells. The cell bodies of the granule cells compose the granular layer of the dentate gyrus (DG) whereas the cell bodies of pyramidal neurons lie in a single densely packed layer called stratum pyramidale that can be divided into four regions: Cornu Ammonis 1, 2, 3 and 4 (CA1 to 4).These cells form a tri-synaptic excitatory circuit where cells from entorhinal cortex send their axons through the perforant path to the DG granule cells. The granule cells contact CA3 pyramidal neurons via mossy fiber collaterals. Then, CA3 neurons send axonal projections called Schaffer collaterals (named after the Hungarian anatomist-neurologist Károly Schaffer) that contact pyramidal neurons of the CA1 layer [START_REF] Andersen | The Hippocampus Book[END_REF].

The two types of connections DG to CA3 and CA3 to CA1 involve two very distinct types of synapses. The mossy fibers display large varicosities (5-10 µm) named mossy fiber boutons due to their cushiony appearance. They form synapses with CA3 pyramidal cells in the proximal part of their dendrites on elaborate spines called "thorny excrescences". The CA3-CA1 connection involves a more typical excitatory glutamatergic synapse in the cortex. For this reason, many scientists use the Schaffer collateral synapse as a sample synapse, to study and identify the rules by which synapses undergo plastic changes. The axon initial segment (AIS) is the site of initiation of the AP. This highly excitable axonal compartment was first identified by the Swiss Rüdolf Alber von Kölliker [START_REF] Kölliker | Neurologische Bemerkungen[END_REF] and the German Robert Remak [START_REF] Remak | über den Bau der grauen Säuden im Rückenmark der Säugethiere[END_REF]. The AIS has a variable length of around 25µm and can be located directly at the axon hillock or up to tens of microns away from the hillock. The Nav and Kv channels composition of the AIS as well as its length and distance from the soma contributes to the spiking properties of the neuron. The AIS is characterized by a high density of Nav and Kv channels compared to the rest of the axon and the adjacent cell body. Combining electrophysiological recordings and computer simulations, sodium channels density in the AIS was evaluated to be 20 to 1 000 fold higher than in the soma or dendrite [START_REF] Mainen | A model of spike initiation in neocortical pyramidal neurons[END_REF] Christie & De Blas, 2003). Indeed, GABAergic Chandelier cells projects and form axoaxonic contacts on the AIS of hundreds of principal cells acting as "master breakers" of excitatory circuits.

The molecular organization of the AIS is mainly dependent of the scaffolding protein Ankyrin G (AnkG). Shortly after the beginning of the axon development, AnkG is targeted with a high degree of specificity to the proximal part of the axon and underlies the AIS formation. The localization of the AIS is mediated by -IV-spectrin, a protein associated to the actin cytoskeleton that binds to AnkG [START_REF] Yang | betaIV spectrin is recruited to axon initial segments and nodes of Ranvier by ankyrinG[END_REF]. It is also well established that AnkG retains Nav channels and is therefore responsible for their high density in the AIS [START_REF] Jenkins | Ankyrin-G coordinates assembly of the spectrin-based membrane skeleton, voltage-gated sodium channels, and L1 CAMs at Purkinje neuron initial segments[END_REF][START_REF] Zhou | AnkyrinG is required for clustering of voltage-gated Na channels at axon initial segments and for normal action potential firing[END_REF]. The fine tuning of Nav localization in the AIS is thought to also depend on auxiliary proteins such as Nav and intracellular fibroblast growth factors (iFGFs) that promote their surface expression [START_REF] Grieco | Open-channel block by the cytoplasmic tail of sodium channel beta4 as a mechanism for resurgent sodium current[END_REF][START_REF] Laezza | The FGF14(F145S) mutation disrupts the interaction of FGF14 with voltagegated Na+ channels and impairs neuronal excitability[END_REF].

Axon shaft

The axon trunk is the main part of the axon. Its role is to conduct APs generated at the AIS down to the presynaptic terminal. The channel composition in the distal axon can be very diverse. In the widely studied squid giant axon or more generally for invertebrates, the literature has described initiation and propagation typically based on only a few subtypes of Nav channels giving rise to a fast sodium current and few Kv channels that produce a delayed rectifier potassium current [START_REF] Goldin | Evolution of voltage-gated Na(+) channels[END_REF]Hodgkin & Huxley, 1952a;[START_REF] Loughney | Molecular analysis of the para locus, a sodium channel gene in Drosophila[END_REF].

However, in mammals, it is well known that many axons, myelinated or unmyelinated, central or peripheral, are equipped with many more Nav and Kv channel subtypes. Yet, the role of every channel subtype, their cooperative effect and the consequence for AP propagation are poorly understood. In thin unmyelinated axons, even less is known as their small diameter increases the difficulty to detect the channel composition reliably by [START_REF] Xu | Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons[END_REF]. Surprisingly, those actin-rings were found to be evenly spaced along the axon with a periodicity of ~180-190 nm. In addition, they found a similar periodic arrangement for spectrin, adducin and Nav (Figure 3). This new information about the unique cytoskeleton layout in axons will certainly change our understanding on how axons develop and how electrical signals propagate within this compartment.

Presynaptic compartment

The most fundamental function of the presynaptic compartment is to regulate the release of neurotransmitter via the fusion of synaptic vesicles with the presynaptic plasma membrane.

Typically, the presynaptic compartment of a chemical synapse is composed of synaptic vesicles, an active zone, scaffolding molecules, and trans-synaptic adhesion molecules [START_REF] Li | Synapse proteomics: current status and quantitative applications[END_REF][START_REF] Mcallister | Dynamic aspects of CNS synapse formation[END_REF].

The number of synaptic vesicles ranges between hundreds to thousands and can be divided into the readily releasable pool, located in the active zone, and the reserve pool. The segregation of those pools is mediated by the calcium sensitive phosphatase, calcineurin. The activation of calcineurin through the elevation of Ca 2+ concentration in the presynaptic bouton, dephosphorylate synapsin that is responsible for the clustering of the reserve pool vesicles, thus allowing vesicles to migrate to the active zone and become part of the readily releasable pool [START_REF] Cesca | The synapsins: key actors of synapse function and plasticity[END_REF]. The active zone, sometimes called presynaptic density, is the site of the presynaptic compartment mediating neurotransmitter release. It is formed by the presynaptic membrane and a protein dense material that tightly integrate in the membrane whereby neurotransmitter vesicles are tethered. The fusion of neurotransmitter vesicles at the membrane is highly regulated and utterly depends on the formation of a protein assembly called the SNARE complex (Soluble N-ethylmaleimide-sensitive factor Attachment protein

Receptor complex). The increase of presynaptic Ca 2+ , following the arrival of an AP, forces vesicles to fuse to the plasma membrane due to a change in conformation of molecules in the SNARE complex.

The assembly and stability of the synaptic cleft is mediated by trans-synaptic adhesion molecules that are thought to regulate structure and function of mature synapses during activity [START_REF] Knott | Formation of dendritic spines with GABAergic synapses induced by whisker stimulation in adult mice[END_REF][START_REF] Toni | LTP promotes formation of multiple spine synapses between a single axon terminal and a dendrite[END_REF].

Morphology of axons 2.2.1 Complexity of axonal arborization

Axons can contact neighboring cells that are few tens of microns away or project to other brain areas several centimeters away. Some neurons have a very simple axonal morphology, for instance, granule cell axons in the cerebellum are characterized by a single T-shaped branch node from which two parallel fibers extend. Others, like basket cell interneurons, that are present in the molecular layer of the cerebellum, the hippocampus and the cortex, densely collateralized in a confined area of tens of microns [START_REF] Andersen | The Hippocampus Book[END_REF]. This topology allows basket cells to synchronize firing of hundreds of principal cells through their divergent axon [START_REF] Cobb | Synchronization of neuronal activity in hippocampus by individual GABAergic interneurons[END_REF].

CA3 axons are traditionally seen as simple axons projecting in the CA1 area and are also known as Schaffer collaterals. In fact, CA3 pyramidal cells give rise to highly divergent projections in all areas of the hippocampus. In vivo reconstructions of CA3 axons in the rat have revealed their complex topology (Ishizuka et

Morphological heterogeneity of individual axons

Axon morphology is a fundamental parameter that determines its biophysical properties such as propagation of electrical signals (Hodgkin & Huxley, 1952b), likely influences biochemical diffusion and possibly active transport. The first noticeable feature of axon morphology is their calibers which greatly differ between 0.08 -10 µm in the CNS. Larger axons conduct APs faster and with high fidelity but are space and energy consuming. A variation in caliber which positively correlates with conduction speed was shown to be a compensatory mechanism of axon length to ensure synchronous depolarization of their synaptic targets [START_REF] Salami | Change of conduction velocity by regional myelination yields constant latency irrespective of distance between thalamus and cortex[END_REF][START_REF] Stanford | Conduction velocity variations minimize conduction time differences among retinal ganglion cell axons[END_REF][START_REF] Sugihara | Uniform olivocerebellar conduction time underlies Purkinje cell complex spike synchronicity in the rat cerebellum[END_REF]. In addition to their mean diameter, unmyelinated axons always exert irregular geometries [START_REF] Greenberg | Irregular geometries in normal unmyelinated axons: a 3D serial EM analysis[END_REF];

Shepherd & Harris, 1998) which have often been neglected in two dimensional EM morphometric analyses by representing axons as straight cylinders.

As the presynaptic compartment is a large regulatory machinery of neurotransmitter release, it requires space and makes the axon a varicose structure. In the neocortex, presynaptic boutons can be classified in two morphologically distinct categories, terminaux boutons and en passant boutons. Terminaux boutons resemble dendritic spines with a head containing the release machinery and a neck that links the head to the axon trunk. En passant boutons are presynaptic elements that are displayed in a "beads-on-string" fashion along the axon segment. Whereas layer 2, 3, 5 axons mostly exhibit en passant boutons, layer 6 axons display a high content of the terminal form (Figure 5). Interestingly, long term in vivo imaging revealed that terminaux boutons of layer 6 were more dynamic (De Paola et al,

2006

) whereby neck length adjustment allows for more potential synaptic partners [START_REF] Chklovskii | Cortical rewiring and information storage[END_REF][START_REF] Stepanyants | Geometry and structural plasticity of synaptic connectivity[END_REF]. The frequency of presynaptic boutons on an axon is also a cell specific feature that depends on the number and location of the synaptic partners. For instance, en passant boutons are on average spaced every 3µm along CA3 axons and also greatly vary in size ranging from 0.011-0.572µm 3 (Shepherd & Harris, 1998). The irregularity of the axon shaft, the segment between two presynaptic elements, is often under-appreciated due to the lack of resolution in conventional light microscopy. For example, the cross section diameter of the axon shaft of CA3 pyramidal neurons can substantially vary from 80 to 300 nm within a few microns distance (Shepherd & Harris, 1998) (Figure 6). The presences of organelles, such as mitochondria or synaptic vesicles often larger than 40nm contribute to its irregular shape. The membrane properties of the axon can be defined by the membrane resistance, r m , and capacitance, c m , both expressed per membrane length unit (.m and F/m). Both parameters depend on the specific membrane resistance (R m ), capacitance (C m ) and the circumference of the axon (of radius a) following the equations:

= 2 (1) = 2 (2)
The axoplasmic resistance (or axial resistance) affects the travel rate of APs down the axon.

The amount of molecules that are not electrically conductive is responsible for this resistance.

As a consequence, this will cause more ions to flow across the axolemma than laterally through the axoplasm. The axoplasmic resistance (r i ) is defined by the specific axoplasmic resistance (R i ), and the cross section area (of radius a) of the axon following the equation: The length constant, , defines the distance for which a graded electric potential passively travels along the axon (Figure 7). In other words, this represents the axonal distance whereby a passive spread of potential can depolarize the membrane to threshold. Interestingly, a large length constant can contribute to spatial summation in the axon. It depends on the membrane resistance (r m ), the axoplasmic resistance (r i ) and the extracellular resistance (r o ) following the equation:

= π (3)
= + (4)
Knowing that the effect of the extracellular resistance is negligible in normal conditions, the equation can then be simplified as:

= (5)
To understand how the length constant changes, one has to consider that the membrane resistance is a function of the number of open ion channels and that the axoplasmic resistance is inversely correlated with the axon diameter. A given voltage (V max ) will decay as a function of the distance (x) from the source following the equation:

( ) = (1 - ) (6)
A given voltage decays therefore by approximately 37% after travelling a distance corresponding to one length constant ().

The time constant, , defines the duration for which the membrane potential of the axon changes in response to a current change in the axoplasm. It describes how much the capacitance delays full depolarization. The time constant depends on the membrane resistance and membrane capacitance following the equation: =

The following cable equation including the time and length constant then describe how an electrical current injected at the position x travels along the axon:

= + (8)

The Hodgkin-Huxley model for active propagation

In addition to the cable theory, the Hodgkin-Huxley model describes how an AP actively propagates along an unmyelinated axon. In 1952, by impaling a squid giant axon with an electrode, Hodgkin and Huxley were the first to experimentally measure intracellular APs (Hodgkin & Huxley, 1952a). From those measurements, they could establish a conductancebased model that explains the ionic mechanisms underlying the initiation and propagation of action potentials in axons.

It integrates voltage-gated ion channels with non-linear conductance (g) and leak ion channels with linear conductance (G L ); the membrane capacitance (C m ); the equilibrium potential (E) for sodium, potassium and leak; m, n and h are steady-state values for activation and inactivation:

= + ̅ ℎ( - ) + ̅ ( -) + ( -) (9)
This equation faithfully reproduces many well known characteristics of AP propagation such as the sodium and potassium currents during an AP, the all-or-none firing pattern of AP, the AP waveform, the refractory period and the periodic firing properties.

AP propagation including geometrical constraints (Rall model)

Cable theory and Hodgkin-Huxley model set the fundamental basis for AP propagation in a fixed axonal cylinder. However, irregularities such as changes in diameter and bifurcations can have a large impact on AP propagation. Rall has established several numerical models to understand how AP propagation is affected by those irregularities (Goldstein & Rall, 1974;

Holmes [START_REF] Holmes | Electrotonic length estimates in neurons with dendritic tapering or somatic shunt[END_REF][START_REF] Rall | Theory of physiological properties of dendrites[END_REF]. In those studies, Rall and collaborators demonstrated that for an AP approaching a step decrease in the axon diameter, both velocity and AP peak amplitude increases while an AP approaching a step increase of axon diameter causes a decrease of velocity and peak height. Exploring the effect of tapering, they found that the velocity was proportional to the length constant when a linear change in diameter over the distance is taken in account.

As mentioned above, most axons in the mammalian brain are highly collateralized. From the hillock, an axon can give rise to many branches that can innervate different areas. In 1974, Goldstein and Rall, later followed by others, mathematically describe how an AP propagates through branch points (Goldstein & Rall, 1974;[START_REF] Manor | Effect of geometrical irregularities on propagation delay in axonal trees[END_REF]. They defined a geometrical parameter called geometric ratio (GR) that describes the ideal diameter (d) relationship between mother and daughter branches:

= / + / / (10)
For the case where the ratio equals 1, there is a perfect impedance matching and the AP propagates in the 2 daughter branches without alteration of waveform or velocity. When the ratio is higher than 1, the electrical load approaching the branch point is not sufficient to activate both daughter branches therefore the conduction is delayed and the waveform is transiently altered. In an extreme case, the AP could even fail to propagate, stopping at the branch point.

Although theoretically possible, it still remains unclear whether the axonal compartment uses such mechanism to filter information within its arborization. Modeling studies have suggested that action potentials could fail at branch points in an activity-dependent manner [START_REF] Luscher | Simulation of action potential propagation in complex terminal arborizations[END_REF]). Propagation failures have been reported experimentally in large invertebrate axons under specific conditions [START_REF] Luscher | Action potential propagation through embryonic dorsal root ganglion cells in culture. II. Decrease of conduction reliability during repetitive stimulation[END_REF]Parnas, 1972;Smith, 1980a;Smith, 1980b). In more complex arborizations (e.g., CA3 axons or basket cell axons) such mechanism has not been reported so far. Because of their small diameter (Shepherd & Harris, 1998)

Axon diameter and conduction velocity

The conduction velocity in axon is mainly dependent on membrane capacitance, membrane resistance, axial resistance and the types and density of voltage-gated ions channels (Del 1993). Therefore, the action potential velocity depends on both, passive propagation parameters and the non-linear membrane conductance that define the active propagation. As described above, the passive propagation is defined by the length and time constants of the membrane that are dependent on the membrane capacitance, resistance and axial resistance which in turn depends on the diameter. From the equations described above, large axons have large length constants and small time constants which propagate the impulses rapidly. A small time constant means that a depolarization affects more rapidly an adjacent section which brings it to threshold sooner and therefore increases the propagation velocity. For a large length constant, a potential change in a given segment spreads a greater distance along the axon and brings further distal segment to threshold sooner. The equation of the length constant can be written differently to highlight its diameter (d) dependence:

= 4 (11)
The propagation velocity is directly proportional to the length constant () and inversely proportional to the time constant () as illustrated by the following equations:

∝ / (12) ∝ 1 4 (13)
Thus, for given specific membrane properties in unmyelinated axons, velocity is proportional to the square-root of the axon diameter (Dayan & Abbott, 2001; Hodgkin & Huxley, 1952a).

To double the velocity in an axon, it is necessary to quadruple the diameter. It is important to mention that this relation does not hold true for myelinated axons. The coating of axons with a thick insulating sheath of myelin represents another way to decrease the membrane capacitance and therefore increasing the propagation velocity. In this case, with early empirical [START_REF] Gasser | Axon diameters in relation to the spike dimensions and the conduction velocity in mammalian A fibers[END_REF][START_REF] Hursh | Conduction velocity and diameter of nerve fibers[END_REF] and later theoretical investigations [START_REF] Rushton | A theory of the effects of fibre size in medullated nerve[END_REF], it is generally agreed that there is a linear relationship between the conduction velocity of myelinated axons and their diameter.

To determine the velocity of an actively propagating AP, it is possible to derive the Hodgkin and Huxley equation based on voltage-clamp data and include passive spread properties from the cable theory giving the following equation:

4 = + ̅ ℎ( - ) + ̅ ( -) + ( -) (14)

Short-term dynamics of action potential propagation

The various types of voltage-gated ion channels in the membrane can have substantially different voltage-dependences and time constants associated with activation and inactivation.

Therefore, properties of AP propagation, such as excitability and conduction velocity can change during repetitive stimulation. The first systematic inquiry on activity-dependent changes in spike conduction using earthworm lateral giant axon and frog sciatic A-fibers revealed a change in both excitability and conduction velocity [START_REF] Bullock | Facilitation of conduction rate in nerve fibers[END_REF]. When the interval between the two stimuli was only several milliseconds, excitability and conduction velocity were reduced (subnormal period). Interestingly, when the interval was longer, up to 100 ms, excitability and velocity were increased. This phenomenon is referred as the supernormal period. A similar change in excitability of CA3 Schaffer collaterals was showed later by Soleng et al. by using antidromic stimulation and recording from the soma [START_REF] Soleng | Activity-dependent excitability changes in hippocampal CA3 cell Schaffer axons[END_REF]. They found that the passage of a single AP initially reduces the excitability of the membrane for the first 15 ms and then increases excitability for the next 200 ms.

The shape of the presynaptic AP carries the electric load that determines the Ca 2+ current flow in the presynaptic compartment and hence neurotransmitter release. The AP waveform has long been considered highly stereotypical and faithful when propagating along axons.

However, several studies have shown that the amplitude and the duration of APs can be regulated by activity and hence modulate transmitter release [START_REF] Byrne | Presynaptic facilitation revisited: state and time dependence[END_REF][START_REF] Shapiro | Presynaptic membrane potential affects transmitter release in an identified neuron in Aplysia by modulating the Ca2+ and K+ currents[END_REF].

Geiger and Jonas were the first to demonstrate that the duration of APs is not fixed in the hippocampus [START_REF] Geiger | Dynamic control of presynaptic Ca(2+) inflow by fastinactivating K(+) channels in hippocampal mossy fiber boutons[END_REF]. By performing whole-cell recording of mossy fiber boutons from granule cells in the dentate gyrus, they found that APs get broader during repetitive stimulation. Kv channels, responsible for the AP broadening, rapidly inactivate during high frequency stimulation and slowly recover from inactivation. In addition, they measured the subsequent increase of presynaptic Ca 2+ inflow. Similarly, LTD causes spine shrinkage [START_REF] Zhou | Shrinkage of dendritic spines associated with long-term depression of hippocampal synapses[END_REF]). Although, it is often assumed that the presynaptic compartment also undergoes structural and morphological changes reflecting structural modifications during synaptic plasticity, there is surprisingly no clear evidence in the literature. It is possible however that significant functional changes occurring at presynaptic boutons might be reflected in much more subtle structural and morphological modifications compared to what spines experience.

Functional and structural modifications of the presynaptic compartment during synaptic plasticity

The involvement of the presynaptic compartment in the change of synaptic strength has been debated for long. Some argue for a dominant role of the postsynaptic compartment ( In the series of events occurring during the classical NMDAR-dependent LTP, the strengthening of the synapse is not homogenous across the pre and postsynaptic compartments. These processes include a rapidly developing postsynaptic component and a slowly developing presynaptic component [START_REF] Lisman | A unified model of the presynaptic and postsynaptic changes during LTP at CA1 synapses[END_REF].

Activity-dependent plasticity of intrinsic excitability

The plasticity of intrinsic excitability is a type of non-synaptic plasticity whereby the Burrone, using similar labeling techniques, they found that the auditory deprivation increases the length of the AIS but not the distance from the soma. Similarly, they correlated the increase in AIS length with an increase of neuronal excitability via patch-clamp recordings.

Long-term change of action potential conduction velocity

As described above, the conduction velocity in axons is mainly defined by two parameters: 1) the morphology by considering the core diameter of the axon and its irregularities and 2) the excitability of the axon membrane defined by types and numbers of ion channels. Because of their low optical and electrophysiological accessibility, so far, no study has shown an activity-dependent correlative change between the biophysical properties and conduction velocity.

Although there are few evidences demonstrating that axonal conduction delay can be a plastic feature. Variations in conduction delay were measured by electrophysiological recordings in rabbit visual corticotectal and callosum axons in vivo [START_REF] Swadlow | Impulse conduction in the mammalian brain: physiological properties of individual axons monitored for several months[END_REF][START_REF] Swadlow | Physiological properties of individual cerebral axons studied in vivo for as long as one year[END_REF].

Indeed, for some of the recorded axons, delays were continuously increasing or decreasing over several months period. By culturing cortical neurons on a multi-electrode array (MEA),

STED microscopy

Basic optical principle of STED microscopy

Fluorescence microscopy is one of the most widely used and powerful techniques in the life sciences, enabling the visualization of cell-biological structures and processes with extremely high specificity and sensitivity in living tissue samples. Fluorescence is the phenomenon whereby a fluorophore absorbs a photon (i.e., 488 nm for GFP) and produces the emission of another photon of lower energy (525 nm) defined by the Stoke shift. Interestingly, when the molecule is in the excited state, it can directly be de-excited by a photon that matches the energy difference between the excited state and the ground state (595 nm for GFP). Upon interaction of the photon with the excited fluorophore, the molecule returns to the ground state before spontaneous fluorescence emission can occur in a process called stimulated emission (Figure 9).

Stimulated emission depletion (STED) microscopy is an imaging technique that uses these

non-linear properties of fluorophores described above to achieve super resolution. It was invented by Stefan W. Hell who first described its principle in 1994 [START_REF] Hell | Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy[END_REF], and demonstrated it experimentally in 1999 [START_REF] Klar | Subdiffraction resolution in far-field fluorescence microscopy[END_REF]. In neuroscience, STED microscopy enables the observation of nanoscale dynamics of the finest structures of neurons and glia previously inaccessible with traditional light microscopy techniques.

In conventional light scanning microscopy like confocal or two-photon microscopy, the resolution of the optical system is limited by the diffraction of light. This means that when light is focused through a lens or objective, a pattern of diffraction is formed, called point spread function (PSF), and defines the volume of excitation of the fluorophores for a given position in the focal plane. The size of the PSF depends on the excitation wavelength and the numerical aperture (NA) of the objective. From this, it is then possible to determine the theoretical resolution limit (r) of the system given by Abbe's formula with , the wavelength used to excite the fluorophore and NA, numerical aperture of the objective.

∆ ≅ 2 (15)

PSF engineering

The second requirement to achieve super-resolution imaging using stimulated depletion is the ability to shape the PSF of the depletion beam at the focal plane in order to allow the excited molecule to emit exclusively in the center of the excitation PSF. This is achieved by the use of a helical vortex phase plate that allows the Gaussian STED beam to destructively interfere in the center so that a vortex of light is created. When an optical vortex travels through a focusing lens or an objective and is projected onto a flat surface, its intensity distribution will form a doughnut-like pattern in the focal plane (Figure 10). That way, the azimuthally distributed photons of the doughnut will quench the fluorescence at the rim of the excitation PSF. It is critical to the performance of a STED microscope that the center of the doughnut remains at a minimal value throughout the power range. For this reason, a /4 wave plate is used to create circular polarization of the STED light in the focal plane.

Improvement in spatial resolution

For STED microscopy, in addition to the excitation wavelength and the NA, the optical resolution will also be defined by the intensity of depletion saturation of the fluorophore image. The fluorescent photon yield of a molecule does not increase linearly with the excitation intensity. This non-linear process also exists for stimulated depletion and is responsible for the theoretically unlimited resolution. Indeed, using high intensity doughnutlike depletion beam allows the saturation of the quenching process around the excitation PSF.

As a result, the fluorescence is allowed to be emitted only from the center of the doughnut, giving an effective PSF below the diffraction limit of the optical system.

∆ ≅ 2. 1 + (16)
In theory, STED microscopy could provide an unlimited resolution. This implies that the power used for depletion is infinite. In practice, there are technical limitations such as the property of lasers which deliver a finite amount of light power. To date, the record for the best resolution in STED goes to Rittweger et al. where in 2009, by using nitrogen vacancies diamond and an average of 850 mW STED power, they achieved to obtain a resolution of ~5.8 nm (Figure 11) [START_REF] Rittweger | STED microscopy reveals crystal colour centres with nanometric resolution[END_REF]. In this case, the power remains a limiting factor to improve even more the resolution.

Development of STED imaging in living tissue

To perform STED imaging on live cells, the high light power can damage the integrity of the

STED imaging of the dynamics of axon morphology

Unmyelinated axons in the hippocampus are often too small to be properly resolved by conventional light microscopy (Shepherd & Harris, 1998). STED microscopy allows the observation of nanoscale features and permits quantitative morphological analysis of the axonal structure by extracting precise estimates of axon diameters. To understand how to perform measurements based on collected signal intensity, it is important to discriminate the evaluation of the performance of the optical system and the measurement of a biological structure.

The home-built STED microscope in the laboratory uses an excitation wavelength at 485 nm and a 1.4 NA objective. Applying Abbe's formula, the theoretical resolution limit in confocal mode of the system is then 173 nm. The experimental validation of the instruments resolution should be tested by using, for example, fluorescent nanobeads that are significantly smaller than the theoretical resolution of the system and can be approximated as point sources of light. In confocal imaging, the PSF at the focal point follows a 2D-Gaussian distribution in the lateral (xy) dimension. The distribution of the fluorescent signal must then be mathematically approximated as a 2D-Gaussian distribution and therefore the full width at half-maximum (FWHM) from the Gaussian fit gives the best approximation on the resolution of the system. If the measured FWHM value matches the theoretical resolution, the system is fully optimized and can be regarded as being truly diffraction limited.

The calculation of the theoretical resolution in STED imaging implies to have a good understanding of the photo-physical properties of the fluorophores which are likely to change depending on their environment (temperature, pH, medium). It is therefore easier to test experimentally the resolution using fluorescent beads. In STED microscopy, the resulting effective PSF at the focal plane is the result of the combination of the excitation beam and a doughnut shape depletion beam. In condition of saturated depletion of the fluorophore, the effective PSF is then following and well approximated by a Lorentzian distribution. By imaging 40 nm fluorescent beads in STED mode, the FWHM measurement that reflects the performance of the system can be around 40 nm when the system is optimized; therefore the size of the bead becomes a limiting factor to assess the resolution. For the experiments, we typically consider 40 nm as our resolution limit for STED imaging which is well below the size of the thinnest axons measured in electron microscopy (~ 80 nm) (Shepherd & Harris, 1998).

The improvement of resolution provided by STED microscopy enables to study the structural complexity of axon. In order to assess the diameter of axons, we measure the FWHM of the fluorescence intensity profile from the axon section area. The FWHM represents the extend of the intensity distribution and therefore is directly linked to the axon diameter. In opposition to the resolution of an optical system that purely depends on the size of the PSF, the measurement of a fluorescent structure is considered to be much larger than the resolution limit. In that case, no assumption can be made on the fluorescence distribution of a volume labeled axon. Therefore, the FWHM is directly extracted from the raw intensity profile and reflects the best estimate of the true size of the structure.

Aims of the study

In contrast to the somato-dendritic region, much less is known about if and how axonal compartment is dynamically regulated. Axons are classically viewed as static transmission cables that reliably transmit APs over long distances. However, recent studies have questioned this view, indicating that they are structurally and functionally dynamic.

Given that geometrical features shape the passive electrical properties of axons and hence should influence AP propagation, we wanted to explore the possibility that axons undergo dynamic modifications in their morphology in response to electrical stimulation. However, because axon morphology cannot be fully resolved in live tissue, little is known about their structural dynamics, let alone what its impact is for axon function. I overcame this technical limitation by using superresolution STED microscopy, allowing me to investigate the structure and function of CA3 axons in living hippocampal slices.

The central aims of my PhD thesis were the following:

1) To establish STED microscopy for imaging axon morphology in living brain slices in parallel with electrophysiological analyses.

2) To develop semi-automated image analysis tools for rapid and reliable quantification of axon morphology imaged by STED microscopy.

3) To examine the morphological dynamics CA3 axons by by time lapse imaging under control conditions.

4) To investigate activity-dependent structural changes in presynaptic boutons and axon shafts axons using common plasticity paradigms like LTP and LTD.

5) To evaluate the functional impact of the morphological changes on AP propagation using electrophysiological recordings and computer simulations.

MATERIALS AND METHODS

Animals

Organotypic hippocampal slice cultures

Organotypic hippocampal slices were prepared from 5-7 days old wild-type mice and cultured for 3-5 weeks using the Gähwiler technique (Gahwiler, 1987;Gahwiler et al, 1997).

The main advantage of this culturing method is the very good optical accessibility for an inverted setup as the slice grows directly on a coverslip. Moreover, it can easily be combined with electrophysiology.

The first step of the protocol consists in the preparation of the coverslips. 12x24 mm, 0,17

µm

Recording solutions

For the imaging experiments, slice cultures were mounted into a heated recording chamber For the experiments that didn't involve imaging, the composition of the ACSF was identical except that neither Trolox nor ascorbic acid was used.

Viral infection

For specifically labeling CA3 neurons, a glass micropipette backfilled with Sinbis-GFP diluted in TNE buffer containing 0.1 M NaCl, 0.05M Tris-Cl pH8, 0.5 M EDTA, 0.001% Tween-20, connected to a Picospritzer (Parker), and placed in the cell body layer of the CA3 area. The virus was injected into the tissue by applying a few pressure pulses (50-150 ms; 10-15 psi). The size of the injection area, which appears dark in transmission mode and was visually inspected to keep it confined so that approximately 30-50 neurons get infected (Figure 12). Experiments were conducted 36-48 h post-infection giving optimal GFP expression while [START_REF] Ehrengruber | Recombinant Semliki Forest virus and Sindbis virus efficiently infect neurons in hippocampal slice cultures[END_REF] preserving the physiological health of the cells (Jeromin et al, 2003).

Extracellular field recordings

For the imaging experiments, field excitatory postsynaptic potentials were recorded from the CA1 stratum radiatum using a glass microelectrode (3-5 M) filled with ACSF. In order to maximize the number of CA3 labeled fibers undergoing the stimulation, a glass microelectrode (3-5 M) filled with ACSF was placed in the middle of the labeled CA3 somata area. Short (0.2 ms) current pulses were delivered from a stimulus isolator (AMPI).

The stimulus strength (ranging between 10-35 µA) was adjusted to elicit a fEPSP of 50% of the noise coming from the measurement and the imaging, an average of 5 parallel lines is done. Considering that the cytoplasmic fluorescence concentration might be inhomogeneous,

no assumption was made on the intensity plot profile distribution; therefore the FWHM was directly extracted from the raw intensity profile. Diameter profiles of full axon stretches could then be generated and analyzed further. For the plasticity experiments, 1 µm axon shaft portions were selected from the automatically generated FWHM profiles excluding the varicosities by visual inspection. Average diameters were calculated over time for each 1 µm.

To determine the bouton size change over time, all boutons from all the experiments were automatically analysed by measuring the FWHM along the boutons. Bouton areas could be determined by summing all the FWHM measured and multiplied by the pixel size.

Simulations

The propagation of action potentials into axon branches was simulated using the

Geometry

The simulation model was made of 4 sections: to give the model a realistic behavior (i.e. in order to avoid sealed effects from interfering with the analysis), the simulated branch

(3) was included after a 500 µm proximal axon (2) (used to simulate realistic incoming spike), and before a distal axon (4) of 200 µm in which spikes propagate after traveling in the simulated branch. Spikes were initiated in an initial segment (1) in which a current pulse was generated before accessing the 500 µm axon. In each section, the number of segments was calculated to get a length/diameter ratio <=5. The temporal integration step was 100 µs.

Passive properties

The intra-compartmental potential, E, is described by the differential equation I core is the axial current to neighboring compartments summed over all neighbors

I E E G core c core c neighbors      ( )
The parameter G core (in S) denotes the core conductance from the compartment in question to the neighboring compartment:

G diam l R core a      2 4 1 1
where diam and l are diameter and length of the compartment (in cm), respectively ; Ra is the specific resistance of the axoplasm (in .cm). 1) is intrinsic currents. Intracellular current injection can be modeled by adding current to the compartment. The parameter cm (µF) describes the capacitance of the compartment cm = C m x area (area is the membrane surface of the compartment in cm 2 , C m is the specific capacitance in µF.cm -2 ) All compartments had the same specific membrane resistance (R m ) set to 10000 .cm 2 . All computations were carried out assuming a specific capacitance, C m of 1µF/cm 2 and a specific axoplasmic resistance, R a , of 100 .cm.

I ch in equation (

Sodium and potassium channels

Sodium (Na + ) current is computed as: I Na = (E Na -E).G Na .m 3 .h

The activation variable m is described by

  dm dt m m m m      . . 1 with rate functions  m and  m                       m m m d E k e d E k A m m m       1             m m m d E k e A m    
The inactivation variable h is computed in a similar way.

 

dh dt h h h h      . . 1 With rate functions  h and  h           h h d E k e A h h                  h h h d E k e A h     1
In most computations, we used the following values for the Na + channel parameters (IS):

A h = 1 ms -1 ; k h = -0.1 mV -1 ; d h = -35 mV
The maximum conductance density for Na + channels in a given compartment was G Na Max = 0.6 S.cm -2 in the initial segment, and G Na Max = 0.012 S.cm -2 in other sections of the model. The equilibrium potential for Na + ions was set E Na = +50 mV.

Potassium (K + ) current is computed as: I K = (E K -E).G K. n 4

Its activation variable, n , is described by the equation :

  dn dt n n n n      . . 1 with rate functions  n and  n ) ( 1 n n n n n d E k e d E k A n                     ) ( n n n d E k e A n        
In all computations, we used the following values for the K + channel parameters:

A n = 0.1 ms -1 ; k n = 0.1 mV -1 ; d n = -55 mV;

A n = 0.125 ms -1 ; k n = -0.0125 mV -1 ; d n = -65 mV

The maximum conductance density was G K Max = 0.19 S.cm -2 in the initial segment, and 0.0036 S.cm -2 in the other sections of the model. The equilibrium potential for K + ions was E K = -77 mV.

Statistics

For the plasticity experiments, we expressed the values as normalized mean ± standard error of mean. We performed a two-way repeated ANOVA, to test the effect of time, the interaction between groups and change over time, and the effect between groups. The homogeneity of variances for every timepoints was tested using a Levene test, for the timepoints that were not significant, a post-hoc Bonferroni test was performed otherwise we performed a post-hoc Dunnett test.

RESULTS

The results section is composed of two parts:

Aim of the study:

According to the traditional view axons are faithful and static conductors of action potentials (AP) generated at the cell body. However, recently it has become evident that axons can strongly and dynamically influence AP propagation, e.g. AP speed and waveform, which is thought to powerfully broaden the computational repertoire of neural circuits.

Axon morphology is likely to be an important determinant of AP propagation within the axonal tree, because basic structural parameters (such as axon diameter) largely define the passive electrical properties of axons. However, because most axons in the central nervous system are so thin, it has been impossible to image axons, let alone their activity-dependent dynamics, in live tissue using conventional light microscopy, which does not offer nearly enough spatial resolution.

To overcome this limitation and to investigate the plastic structural changes of hippocampal axons in living brain slices, we used a novel combination of superresolution STED microscopy, electrophysiology and biophysical modeling using the NEURON simulation environment.

Methodology:

We used a custom-built STED microscope (spatial resolution around 50 nm) for visualizing the structural dynamics of GFP-labeled Schaffer collateral axons. Axon diameters were monitored using quantitative analysis in baseline conditions and after HFS-induced LTP of CA3-CA1 synapses. Using the STED morphology data, we built a realistic NEURON model of Schaffer collateral axons to systematically explore the influence of nanoscale axon morphology on AP propagation. We performed antidromic AP latency measurements using patch-clamp recordings and extracellular stimulations of the axon.

Results:

STED imaging revealed that live CA3 axons are on average 200 nm wide, ranging from 100 to 350 nm, in keeping with previous EM reports. Axons can undergo local fluctuations in diameter under baseline conditions. However altogether, the populations of axons were very stable over a period of an hour. Interestingly, induction of LTP caused a significant and persistent enlargement of axon diameters. Using patch-clamp recordings and antidromic stimulation, we correlated the axon diameter increase with an increased conduction velocity of APs following LTP induction.

Taken together, our findings indicate that axons dynamically tune AP propagation by changing their diameters, thereby alter the timing of information transfer in neural circuits, suggesting a novel and powerful structural mechanism for neural plasticity.

Structural plasticity regulates propagation delays of action potentials in hippocampal axons

Ronan Chereau 1,2 , Daniel Cattaert 3 and U. Valentin Nägerl

INTRODUCTION

Precise timing of neuronal activity is essential for network synchrony and circuit plasticity in the brain. Timing variations of synaptic inputs on the order of a few milliseconds can decide over action potential firing 1 and the direction of synaptic plasticity 2, 3 .

Neural timing ultimately is defined by the anatomy and biophysics of the underlying neural structures, which impose characteristic time delays on electrical signals as they get integrated and transmitted. The possibility that time delays are plastic variables has not been explored much experimentally, for technical reasons but also because neural plasticity is mostly studied as a change in signal amplitude (rather than signal timing). Hence, we know very little about whether and how time delays are physiologically regulated and what this may mean for information processing in the brain.

A major source of time delay arises from the conduction of action potentials (AP) along axons. It can take tens of milliseconds for an AP to travel from the axon initial segment (AIS) to the presynaptic terminal, depending on distance 4 . To conduct APs at very high speed axons need to be myelinated or have large core diameters. However, most axons in the hippocampus, including the Schaffer collaterals from CA3 neurons, are unmyelinated and extremely thin (between 100-300 nm 5 ), conducting APs at a speed of less than 300 m/msec 4, 6 . This imposes long delays on AP propagation (between 5-10 milliseconds), despite short travel distances to postsynaptic targets in the CA1 area (less than a few millimeters).

The experimental difficulty to record electrophysiologically from single axon fibers and to measure accurately their nanoscale morphology in living tissue has hampered our ability to investigate whether the delay of axonal AP propagation is a dynamically regulated variable, let alone if and how it may be affected by structural changes in the axon. Recent studies based on two-photon imaging and/or electrophysiology have discussed this as a possibility, demonstrating that the induction of synaptic plasticity causes in tandem morphological and functional changes in axonal compartments 7-10 .

However, it remains an open question whether thin unmyelinated axons undergo activitydependent changes in their diameter that might influence the propagation of APs. This knowledge gap is largely because conventional light microscopy does not provide enough spatial resolution and electron microscopy cannot be used for longitudinal studies. By contrast, STED microscopy can faithfully resolve axon morphology and is compatible with functional assays in living brain tissue 11, 12 .

Here, we used a combination of time-lapse STED imaging, electrophysiology and biophysical modelling to investigate activity-dependent structural plasticity of axons and assess its impact on AP propagation in organotypic brain slices.

We demonstrate that the induction of LTP leads to orchestrated increases in presynaptic boutons and axon shafts, which are correlated with bidirectional changes in AP conduction velocity. Our study suggests a novel type of morpho-functional plasticity whereby axon morphology dynamically regulates AP conduction delays in hippocampal axons.

METHODS

Animals

Wild-type mice were kept under 12 h light/ 12 h dark cycle with ad libitum access to food and water (strain from Jackson Labs, Bar Harbor, ME). Experimental procedures were in accordance with the French National Code of Ethics on Animal Experimentation and approved by the Committee of Ethics of Bordeaux (no. 50120202).

Organotypic hippocampal slice cultures

Organotypic hippocampal slice cultures (Gähwiler type) were dissected from 5-to 7-day old pups of wild-type mice and cultured 3-5 weeks at 35 °C in a roller drum at 10 revolutions per hour as previously described 13, 14 . In brief, hippocampi were chopped coronally at 350 μm using a tissue chopper and embedded in a freshly mixed plasma/thrombin clot on the surface of a poly-l-lysine (PLL)-coated glass coverslip. After coagulation, the slice on the coverslip was cultured in a roller tube in 0.5 ml of medium consisting of 50% Eagle's basal medium, 25% horse serum and 25% Hank's balanced salt solution, supplemented with glutamine to a final concentration of 1 mM and glucose (11 g/l) (all from Sigma). The Gähwiler cultures are optically very accessible, as synapses close to the coverslip can be imaged on an inverted microscope setup.

Recording solutions

For the imaging experiments, slice cultures were mounted into a heated recording chamber (32°C) and continuously perfused with carbogenated (95% O2, 5% CO2) artificial cerebrospinal fluid (ACSF) at pH 7.4 with an osmolarity of 300-310 mOsm containing 124 mM NaCl, 3mM KCl, 2 mM CaCl2, 1 mM MgCl2, 10 mM glucose, 1.25 mM NaH2PO4, 26 mM NaHCO3, 2.5 mM sodium L-ascorbate, 2 mM trolox (Sigma-Aldrich). The use of antioxydants, ascorbic acid and Trolox helps preventing toxicity due to sample illumination by free radicals from reactive oxygen species. For the experiments that didn't involve imaging, the composition of the ACSF was identical except that neither Trolox nor ascorbic acid was used.

Viral infection

For specifically labelling CA3 neurons, a glass micropipette backfilled with Sindbis-GFP viral particles diluted in TNE buffer containing 0.1 M NaCl, 0.05M Tris-Cl pH8, 0.5 M EDTA, 0.001% Tween-20, connected to a pressure-injection device (Picospritzer, Parker), and positioned into the cell body layer of the CA3 area of the hippocampus. The virus was injected into the tissue by applying a few pulses of positive pressure (50-150 ms; 10-15 psi).

The size of the injection area, which appears dark in transmission mode and was visually inspected to keep it confined so that approximately 30-50 neurons get infected. Experiments were conducted 36-48 h post-infection giving optimal GFP expression 15 while preserving the physiological health of the cells 16 .

Electrophysiology

For the imaging experiments, field excitatory postsynaptic potentials were recorded from the CA1 stratum radiatum using a glass microelectrode (tip resistance 3-5 M) filled with ACSF. In order to maximize the overlap between fibers that are labelled and that experience the stimulation, a monopolar stimulating electrode (glass microelectrode 3-5 M filled with ACSF) was placed in the middle of the area of labelled CA3 cell bodies. Brief (0.2 ms) current pulses were delivered from a stimulus isolator (AMPI). The stimulus strength (ranging between 10-35 µA) was adjusted to elicit fEPSP corresponding to 50% of their maximal amplitude. The fEPSPs were recorded using a patch clamp amplifier (Multiclamp 700B; Molecular Devices). Amplifier gain was set at 20X and a Bessel filter of 2 kHz was

STED microscopy

For live-cell imaging of hippocampal brain slice cultures, we used a home-built STED microscope based on pulsed excitation and pulsed depletion in the visible range of the spectrum. A standard commercial inverted microscope (DMI 6000 CS Trino, Leica, Mannheim, Germany) equipped with a high-numerical-aperture objective lens (PL APO, 100×, oil, NA 1.4, Leica) served as a base. For excitation, a pulsed-laser diode (PDL 800-D, Picoquant, Berlin, Germany) was used delivering 90 ps pulse duration at 485 nm wavelength.

For depletion, 595 nm wavelength laser pulses for the STED beam were produced by an optical parametric oscillator (OPO BASIC Ring fs RTP, APE, Berlin, Germany) pumped by a Ti:Sapphire laser (MaiTai, Spectra-Physics, Darmstadt, Germany), operating at 80 MHz and emitting at 800 nm. The pulses of originally 200 fs duration were stretched to 68 ps by first dispersion in a glass rod 25 cm long (SF6) and then in a polarization-preserving fiber (Schäfter & Kirchhoff, Hamburg, Germany) of 20 m length. To create the STED focal doughnut, a polymeric phase plate (RPC Photonics, Rochester, NY) was introduced into the STED beam path. The STED and excitation pulses were synchronized at 80 MHz via external triggering of the laser diode using an electronic delay generator. The laser beams were combined using a dichroic mirror (AHF Analysentechnik, Tübingen, Germany). We used a telecentric beam scanner (Yanus IV, TILL Photonics, Gräfelfing, Germany) in combination with scan and tube lenses from the microscope manufacturer to stir the laser beams across the sample. The fluorescence signal was detected in a descanned fashion and separated from the excitation by a dichroic mirror (499 nm long-pass), then cleaned with a 525/50 band-pass filter and finally focused onto a multimode optical fiber connected to an avalanche photodiode (SPCM-AQR-13-FC, PerkinElmer, Waltham, MA). Image acquisition was controlled by the custom-written software IMSpector 17 .

Image acquisition

The parameters of acquisition were originally defined so that neither apparent photodamage nor excessive photobleaching was detected over the time course of the experiment. All the image acquisitions were performed with an excitation power of 4-6 µW and a STED power of 8 mW (measured at the objective back aperture). The images stacks were acquired with a voxel size of 19.5 nm (xy); 375 nm (z) and dwell time of 15 µs. Imaging depths into the slice, determined by the z-piezo focus, the fluorescence on top of the slice defining the zero zposition, was ranging between 5-15 µm. For the plasticity experiments, an area containing multiple and well separated axon stretches was selected. Z-stacks of 30x20x3µm (x, y and z dimensions respectively) were acquired every 10 min for 1 hour. Two acquisitions were performed before the stimulus and four after.

Image analysis

Images were exported from the IMSpector software into an 8-bit tiff file format. We used NIH ImageJ for processing the acquisitions. Image analysis was done on raw data and images presented in the figures were filtered by a 1-pixel median filter to reduce noise. A screening by visual inspection was performed and only the signal of the axon stretches that were fully contained into the volume of acquisition at all time points was selected for the morphometric analysis. A maximum intensity projection was performed on the regions of interest. To realize the automated morphometric measurement, a reference image that consist of a line of pixels running along the axon stretch was produced by first, thresholding and binarize the picture, then we used the skeletonize plugin from ImageJ. A custom written Matlab program was used to automatically measure the FWHM along the axon image using the reference image that determines the position of the measurement. At every position, it automatically estimates the best tangential fit and plots the intensity profile from its orthogonal. To reduce the noise coming from the measurement and the imaging, an average of 5 parallel lines is done. Considering that the cytoplasmic fluorescence concentration might be inhomogeneous, no assumption was made on the intensity plot profile distribution; therefore the FWHM was directly extracted from the raw intensity profile. Diameter profiles of full axon stretches could then be generated and analyzed further. For the plasticity experiments, 1 µm axon shaft portions were selected from the automatically generated FWHM profiles excluding the varicosities by visual inspection. Average diameters were calculated over time for each 1 µm.

To determine the bouton size change over time, all boutons from all the experiments were automatically analysed by measuring the FWHM along the boutons. Bouton areas could be determined by summing all the FWHM measured and multiplied by the pixel size.

Simulations

The propagation of action potentials into axon branches was simulated using the compartment model program NEURON version 7.3 18 . The properties of each compartment can be defined independently. Axon branches were measured with the STED microscope (see above). A text file containing the diameter profile along the studied branch was used to build a simulation model. The simulation model was composed of unmyelinated excitable compartments, described by standard 19, 20 channel kinetic equations.

Geometry of model axon

The simulation model was made of 4 sections: to give the model a realistic behavior (i.e. in order to avoid sealed effects from interfering with the analysis), the simulated branch (3) was included after a 500 µm proximal axon (2) (used to simulate realistic incoming spike), and before a distal axon (4) of 200 µm in which spikes propagate after traveling in the simulated branch. Spikes were initiated in an initial segment (1) in which a current pulse was generated before accessing the 500 µm axon. In each section, the number of segments was calculated to get a length/diameter ratio ≤5. The temporal integration step was 100 µs. The tested sequences consisted in a mirrored repetition of diameter profiles obtained after automated analysis of axon stretches acquired in STED mode and normalized to a length of 500 nm in order to avoid edge effects.

Passive electrical properties

The intra-compartmental potential, E, is described by the differential equation (Equation 1) where I leak is the passive leakage current: 2)

I leak = (E leak -E)  G leak (Equation
and E leak and G leak are the equilibrium potential and the leak conductance, respectively. The parameter G core (in S) denotes the core conductance from the compartment in question to the neighboring compartment:

where diam and l are diameter and length of the compartment (in cm), respectively ; Ra is the specific resistance of the axoplasm (in .cm). 1) is intrinsic currents. Intracellular current injection can be modeled by adding current to the compartment. The parameter cm (µF) describes the capacitance of the compartment cm = C m x area (area is the membrane surface of the compartment in cm 2 , C m is the specific capacitance in µF.cm -2 ) All compartments had the same specific membrane resistance (R m ) set to 10000 .cm 2 . All computations were carried out assuming a specific capacitance, C m of 1µF/cm 2 and a specific axoplasmic resistance, R a , of 100 .cm.

I ch in equation (

Sodium and potassium channels

Sodium (Na + ) current is computed as:

I Na = (E Na -E).G Na .m 3 .h
The activation variable m is described by with rate functions  m and

 m I E E G core c core c neighbors      ( ) G diam l R core a      2 4 1 1   dm dt m m m m      . .
The inactivation variable h is computed in a similar way.

With rate functions  h and  h

In most computations, we used the following values for the Na + channel parameters (IS):

Activation m:

A m = 1 ms -1 ; k m = 0.1 mV -1 ; d m = -40 mV; A m = 4 ms -1 ; k m = -0.055 mV -1 ; d m = -65 mV
Inactivation h:

A h = 0.07 ms -1 ; k h = -0.05 mV -1 ; d h = -65 mV;

A h = 1 ms -1 ; k h = -0.1 mV -1 ; d h = -35 mV
The maximum conductance density for Na + channels in a given compartment was G Na Max = 0.6 S.cm -2 in the initial segment, and G Na Max = 0.012 S.cm -2 in other sections of the model. The equilibrium potential for Na + ions was set E Na = +50 mV.

Potassium (K + ) current is computed as:

I K = (E K -E).G K. n 4
Its activation variable, n , is described by the equation :

with rate functions  n and  n

In all computations, we used the following values for the K + channel parameters:

A n = 0.1 ms -1 ; k n = 0.1 mV -1 ; d n = -55 mV;                       m m m d E k e d E k A m m m       1             m m m d E k e A m       dh dt h h h h      . . 1           h h d E k e A h h                  h h h d E k e A h     1   dn dt n n n n      . . 1 ) ( 1 n n n n n d E k e d E k A n                     ) ( n n n d E k e A n        
A n = 0.125 ms -1 ; k n = -0.0125 mV -1 ; d n = -65 mV

The maximum conductance density was G K Max = 0.19 S.cm -2 in the initial segment, and 0.0036 S.cm -2 in the other sections of the model. The equilibrium potential for K + ions was E K = -77 mV.

Statistics

For the plasticity experiments, we expressed the values as normalized mean ± standard error of mean. We performed a two-way repeated ANOVA, to test the effect of time, the interaction between groups and change over time, and the effect between groups. The homogeneity of variances for every timepoints was tested using a Levene test, for the timepoints that were not significant, a post-hoc Bonferroni test was performed otherwise we performed a post-hoc Dunnett test.

RESULTS

Quantitative analysis of axon morphology at the nanoscale

To visualize axonal projections in 3-5 weeks organotypic hippocampal slices, CA3 pyramidal neurons were locally infected using Sindbis virus expressing GFP (Fig. 1a,b). The Schaffer collateral projections were imaged in the CA1 stratum radiatum by STED microscopy. Our home-built STED microscope offers a spatial resolution in the focal plane of around 50 nm (Fig. S1), providing sufficient resolution to reliably quantify morphological parameters of thin unmyelinated axons that can be as small as 100 nm regarding previous electron microscopy studies 5 .

The images reveal irregular geometries of axon morphologies and high variability across axon segments (Fig. 1c). In order to comprehensively analyze axonal morphology, we measured both inter-varicosity shaft segment diameters and presynaptic boutons sizes. Axon shaft diameters were symmetrically distributed around a median of 203 nm, ranging from 70 to 420 nm (n = 26574, only values above 0.1% were represented, Fig. 1d), while median bouton size was 0.53 µm² ranging between 0.2-2.2 µm² (n = 319, Fig. 1e). The distributions of the morphological parameters appeared smooth and unimodal (Fig. 1d,e).

We observed slight dynamic changes in the axonal morphology, however the overall aspect of the structure is stable over the course of an hour (Fig. 1g,h). Both boutons size and shaft diameter did not undergo directional changes over time (Kruskall-Wallis test P bouton >0.40, n=63, P shaft >0.54, n=113 segments of 1µm; Fig. 1i-k) indicating that the morphology of those structures are largely stable over periods of an hour and that repeated STED imaging did not induce visible photodamage.

LTP induction leads to structural plasticity in axons

We investigated how CA3 axons morphology changes during LTP at CA3-CA1 synapses.

We measured field excitatory postsynaptic potentials (fEPSPs) in the CA1 stratum radiatum after electrical high-frequency stimulation (HFS) in the CA3 pyramidal layer in order to maximize the overlap between stimulated and imaged axons (Fig. 2a). HFS led to a strong increase in fEPSP responses (potentiation at 30-40 minutes post-induction, 81%; Fig. 2b; average potentiation at 30-40 minutes post-induction, 65 ± 16%, n=8, p<0.002; Fig. 2d). At the same time, STED image stacks were acquired around every 12 minutes, with two reference stacks before the stimulation and four stacks after it.

The STED time lapse imaging series revealed a substantial increase in the diameter of CA3 axon concomitant with LTP induction (Fig. 2c with corresponding LTP recording Fig. 2b).

The effect appears to be evenly expressed along axons and builds up over tens of minutes after LTP induction (at 45 minutes: 5.0 ± 0.8%; LTP: n=8; Fig. 2e) leading to statistically significant differences between "before" and "after" stimulation groups (p<0.05), as well as between stimulated and unstimulated conditions (control: n = 7; p<0.05).

Because LTP might not be evenly expressed throughout the CA1 stratum radiatum and that the imaging protocol limits us to relatively small fields of view, we sorted LTP experiments by the ones that showed in average the largest diameter increase over the ones that showed a minimal change (Fig. 2f). The average diameter increase for the experiments that showed the largest change is about 7% (at 45 minutes: 6.9 ± 0.6%; n=4) which amounts to a 14% increase in axonal cross section over the control conditions.

In order to check whether the morphological effect induced by HFS depends on the expression of LTP, we repeated the experiments in the presence of an NMDA receptor antagonist (50µM APV). Whereas the induction of LTP was completely abolished by bath application of the drug (Fig. 2d), the morphological effect on axon diameter was only visible at 45 minutes after HFS (3.6 ± 1.6%, n=6) (Fig. 2f). However, it appears to build up more slowly compared to without the drug.

We also compared the distributions of diameter changes for individual axon segments in an hour for the control condition and after LTP induction (Fig. 2g). This analysis reflects the important variability in diameter change in both control and LTP condition. It also further support the hypothesis that some of the axons did not experience the stimulation as a small fraction showed almost no change (fraction 0%;).

We analyzed the bouton morphology separately from the shaft segments. We observed a much more subtle increase of the bouton size during LTP and no significant difference in APV conditions (Fig. 2h).

Taken together, the combination of time lapse STED microscopy and electrophysiological experiments reveals that axons can undergo activity-dependent structural plasticity whereby electrical stimulation leads to nanoscale changes in axon diameter.

LTP leads to an increase of APs conduction velocity

Knowing that AP conduction is largely predicted by morphological parameters, we investigated whether a change in AP velocity would corroborate the morphological data. We performed patch-clamp recordings from CA3 pyramidal neurons together with direct axonal stimulation in the CA1 stratum radiatum. We monitored simultaneously antidromic AP propagation latencies at the soma and fEPSP in the CA1 stratum radiatum during LTP induction (Fig. 3a). The current-clamp waveform following the electrical stimulation was characterized using drugs to discriminate AP generated by direct axonal stimulation and synaptically evoked AP (Supplementary Fig. 4a). In addition, synaptic transmission was blocked by 2mM kynurenic acid (KYN) at the end of every recording to validate the experiment (Supplementary Fig. 4b).

Interestingly, we found a significant long-lasting reduction of APs latencies 20 minutes after LTP induction reflecting an increase of conduction velocity in the axonal compartment (Fig. 3c,d with corresponding LTP recording Fig. 3b). In average, we found that the AP latency was significantly reduced by 2.2 ± 0.77% at 30-40 minutes after induction of LTP (n=10, P<0.02, with an average potentiation at 30-40 minutes post-induction of 81 ± 22%, P<0.006) and this change was completely abolished when LTP was blocked (APV, n=8, at 30-40 minutes post-induction: average decrease of latency of 0.12 ± 0.42%, p>0.78; average potentiation of 11 ± 9%, p>0.26) (Fig. 3e-g).

LTP induction increases boutons

In order to know if morphological changes of the axon geometry could explain the initial slow down of conduction velocity, we imaged CA3 axons right after HFS. Interestingly, we observed that 2 minutes after HFS, boutons undergo an increase in size by 20 ± 2.5% (n=148, from 4 experiments; p<0.05) while the axon shaft diameter increases by 2.3 ± 1.4% (n=148, p>0.05; Fig. 4a-c). This rapid change appears to be transient as the 8 minutes after the stimulation, the size of the bouton partially decreases (9.8 ± 2.7%, n=148, p<0.05) while the axon shaft diameter keeps increasing by 3.8 ± 1.5% (n=148, p<0.05; Fig. 4b,c). In addition, by plotting the relative change of bouton size with the measured adjacent shaft diameter, we show that the irregularity of the axon structure is much greater 2 minutes after the stimulation compared to after 8 minutes (Fig. 4d).

These results indicate that HFS transiently increases irregularity of the axon structure could be the cause for the initial slow down in conduction velocity observed previously.

Axon structural plasticity correlates with changes in AP propagation delays during LTP

While basic biophysical principles explain directional changes of geometry and AP conduction velocity, we investigated their correlation based on realistic model simulations. In the model used, we tested different axon stretch geometry based on real morphological data (Fig. 5a). We found a high correlation between AP conduction velocity and the square-root of the average axon shaft tested (r² = 0.94) (Fig. 5b). We also tested the impact of the degree of irregularity generated by the average increase of boutons size on an axon segment (Fig. 5c and Supplementary Fig. 6). The increase by 10 and 20% of the bouton size increases the delay of propagation hence decreases the conduction velocity. The changes in conduction velocity calculated from the AP latency recordings correlates well with the simulation based on the morphological changes after HFS and during the establishment of LTP (Fig. 5d).

DISCUSSION

Our experimental approach based on a combination of STED microscopy (with a spatial resolution of around 50 nm) and electrophysiology in living brain slices made it possible to visualize nanoscale changes in axon morphology and to carry out electrophysiological experiments to induce synaptic plasticity and to assess the impact on AP propagation.

We obtained direct evidence that axons become wider and propagate APs faster after the induction of LTP. Both the morphological and functional effects were rapidly expressed and persisted for at least an hour, suggesting a novel form of neural plasticity, which may have important implications for temporal coding in neural circuits of the mammalian brain.

Morphological dynamics of axons in living brain slices

Hyperthin unmyelinated axons are an anatomical hallmark of the hippocampus, with shaft diameters oftentimes narrower than 200 nm 5 . As conventional light microscopy does not provide sufficient spatial resolution for accurate measurements on this spatial scale, very little is known about the morphological dynamics of axon shafts, let alone its regulation by neuronal activity or its effects on AP propagation. By contrast, the morphological dynamics of presynaptic boutons, which are much larger than axon shafts, have been studied before by two-photon microscopy, revealing that they undergo a modest amount of structural remodelling under baseline conditions, but significantly reduce their contacts with dendritic spines after the induction of long-term depression (LTD) at hippocampal synapses 9, 10 .

Coordinated changes in axon morphology and function

Consistent with the previous work, we observed very little structural remodelling of presynaptic boutons and axon shafts under baseline conditions. However, the induction of LTP led to clear-cut bouton enlargement and shaft widening, which were detectable within minutes and persisted for more than one hour after stimulation. The time-lapse data indicate that the structural changes followed a differential time course, where the boutons swelled up transiently before the shafts became wider.

Importantly, these changes would be entirely invisible to conventional light microscopy, because they were on the order of tens of nanometers, necessitating the use of superresolution microscopy.

LTP induction also led to clear changes in AP propagation delay, which at first increased, and then decreased to significantly below baseline levels for the remainder of the experiment.

These findings confirm and extend previous reports on changes in synaptic latency after LTP induction. However, these changes were attributed to activation of silent synapses 21 or to changes in presynaptic release probability 7 . In contrast, our experiments provide direct evidence for a drop in AP propagation delay after LTP, which is consistent with a study in cultured neurons using multi-electrode arrays 8 .

The changes in shaft diameter and AP propagation delay after LTP correspond well with cable theory that predicts that the speed of AP conduction in unmyelinated axons depends on the square root of axon diameter 22 , indicating that the decreased AP propagation delays reflect a widening of axon shafts that accelerates AP conduction, as opposed to axon excitability changes independent of any structural effects. Moreover, the model simulations, which were based on accurate morphological reconstructions using the STED data, also corroborate the conclusion that AP conduction velocity is increased after LTP. Interestingly, the model predicted the increase in AP propagation delay from the transient swelling of the boutons after LTP induction.

Potential mechanisms of axon widening

The increase in axon diameter after LTP implies a gain in surface area of the axon, which must be sourced either by de novo membrane synthesis or redistribution of existing membrane pools. A local redistribution of membranes cannot account for the net gain, because the effect was globally expressed and affected the average diameter. Moreover, according to membrane biophysics, stretching or unfolding of axon membranes can also be ruled out as mechanisms, because lipid bilayers are unlikely to be elastic enough or to behave like an accordion.

Alternatively, a substantial increase in surface membrane could derive from the exocytosis of presynaptic vesicles due to the intense electrical stimulation of the axons during the induction of LTP. The estimated size of the total membrane added by the release of synaptic vesicles, based on the net loss of vesicles seen ultrastructurally after LTP 23 , could in fact readily account for the increase in bouton size and axon diameter. The differential time course we observed for the structural changes suggests a scenario where the addition of the membrane of the vesicles first drives an expansion of the boutons, which then diffuses laterally to cause widening of the adjacent axon shafts, providing a plausible cell biological mechanism, which is both rapid and metabolically cost-efficient. However, the partial blockade of the morphological effects by APV experiments argue somewhat against this model, because a priori APV should not affect the release of synaptic vesicles during LTP induction.

Finally, the concept whereby axons act as dynamic delay lines for information transfer has been debated for a long time. In the auditory system, the interaural time difference to achieve coincidence detection in sound localisation requires sub-millisecond precision and was thought to rely on axon length 30 (i.e. Jeffress model 31 ). But recent findings showed that the topological organization of delays were poorly correlated with axon length and demonstrated that axon diameters and distances between nodes of Ranvier were mechanisms for adjusting interaural delay differences 32 .

In summary, our study amends the classic view of structural plasticity as primarily reflecting a change in synaptic strength by demonstrating structural changes that dynamically regulate the speed of AP conduction and hence are likely to substantially impact the timing of information transfer in neural circuits. objective provides access to combine superresolution imaging with electrophysiological recording as well as performing in vivo STED imaging.

Additional results

Morphological dynamics of CA3 axons during LTD

We found that LTP modulates the axonal morphology by overall increasing the diameter of the axonal shafts. We also investigated whether LTD (i.e. functional counterpart of LTP) that leads to synaptic depression could also produce a directional change in the axonal morphology and examine whether the morphological effect observed on the axons during LTP depended on the type of electrical stimulation and the direction of synaptic plasticity. Indeed, the application of LFS (900 pulses, 1 Hz), which reliably induced LTD (Figure 14a), led to a small but statistically significant decrease in the diameter of CA3 axon shafts coinciding with the LTD induction phase. However, the effect was only short-lived and the axon diameters recovered at 45 minutes after LFS (Figure 14b). In addition, no morphological change was observed on boutons (Figure 14c).

Topological organization of CA3 axon trees

The rules whereby an AP propagates through a complex unmyelinated axonal arborization are still elusive. When some studies show that once initiated, APs reliably reach their presynaptic targets [START_REF] Cox | Action potentials reliably invade axonal arbors of rat neocortical neurons[END_REF][START_REF] Hu | A supercritical density of Na channels ensures fast signaling in GABAergic interneuron axons[END_REF], others indicate that geometric constrains might alter propagation and even produce conduction failures (Goldstein & Rall, 1974;[START_REF] Luscher | Action potential propagation through embryonic dorsal root ganglion cells in culture. II. Decrease of conduction reliability during repetitive stimulation[END_REF]. Branch points represent a biophysical constrain that may alter this propagation. A large geometrical ratio (GR) calculated between the cross sectional diameter of a mother branch and its two daughter branches can serve as an indication to predict if AP may slow down passing through branch point or even fail to propagate in one of the daughter branches. Preliminary results show that due to large diameters the GR ratio is often close to 1 in the proximal part of the arborization and substantially increase in the distal part of the axon when the collaterals are much thinner (Figure 18). These data indicate the proximal part of the tree should conduct APs reliably whereas it could be altered in the distal region. Further investigations will be required to determine whether rules of propagation are different between the proximal and distal part of the axon. While EM studies have exquisitely described geometry and ultrastructure of unmyelinated axons of principal neurons in fixed preparations, little is known about their dynamics in living tissue. Limited by the diffraction of light, conventional light microscopy has failed to study their dynamics at the nanoscale hence calling for a novel imaging approach. The development of superresolution STED microscopy, overcoming light diffraction limit and providing a optical resolution down to 50 nm, bridges this gap allowing for live observations of these hyperthin structures.

Summary of the findings

In this study, we report a new type of plasticity whereby axons can dynamically modulate their diameters hence changing its properties for the propagation of APs. We combined STED imaging and electrophysiology in life brain tissue and computer simulations to investigate the activity-dependent dynamics of axons. We found that HFS-induced LTP leads to a persistent increase of axon shaft diameters that is largely repressed when the LTP expression is pharmacologically prohibited. In addition, we observed that boutons swell transiently shortly after the HFS stimulus, thus, increasing the morphological irregularity of the structure. Extracting conduction latencies from antidromically propagating APs, we show that AP conduction velocity is altered by the induction of LTP with an initial slowing down followed by a persistent increase of the velocity during the establishment of LTP. These data strongly corroborate what was observed in superresolution imaging experiments, hence confirmed by simulation models using our acquired morphological data.

Knowing now that the geometry of axons can be modulated by activity raises many new questions to understand the causes and the consequences for the physiology of the neuron and the impact on the neuronal circuitry and network behaviour.

Effect of structural factors on AP propagation

There are two structural mechanisms employed by axons that warrant fast AP propagation.

One of the strategies, largely used by invertebrates, is to set up large axon diameters. For instance, the well studied squid giant axon has a typical 0.

Morpho-functional changes on axons depend on LTP induction

In this study we found that the axonal structure was sensitive to the HFS-induced LTP. This type of stimulation protocol has been widely used in the literature to explore and unravel synaptic plasticity mechanisms at CA3-CA1 synapses. While postsynaptic NMDA receptors are an established mediator of the expression of LTP, there are also indications for either direct or indirect structural and functional modifications on the presynaptic element. Indeed, some studies suggest that the functions of the pre-and postsynaptic elements are enhanced in a well coordinated fashion [START_REF] Lauri | Presynaptic mechanisms involved in the expression of STP and LTP at CA1 synapses in the hippocampus[END_REF]. Following a fast postsynaptic potentiation, a slow presynaptic component was shown to appear during LTP [START_REF] Bayazitov | Slow presynaptic and fast postsynaptic components of compound long-term potentiation[END_REF]. It consists in the enhancement of the release probability of vesicles and depends on the activation of L-type voltage-gated calcium channels. Furthermore, it has been shown that LTP induction enhances presynaptic neuronal excitability [START_REF] Ganguly | Enhancement of presynaptic neuronal excitability by correlated presynaptic and postsynaptic spiking[END_REF][START_REF] Li | Bidirectional modification of presynaptic neuronal excitability accompanying spike timing-dependent synaptic plasticity[END_REF].

Even though there is an extensive literature on the postsynaptic morphological changes, little is known about the structural modifications on axons during LTP. Recent studies revealed that the number of synaptic vesicles was persistently reduced after LTP induction (Bourne et al, 2013) and that bouton sizes increase following glutamate uncaging protocols to strengthen synapses (Meyer et al, 2014).

In our experiments, we partially but not fully blocked the increase of axon shaft diameter when LTP was blocked by the NMDAR antagonist APV, although we did not observe a reduction of AP latencies. Knowing that NMDA receptors are present at the axon membrane

Putative mechanisms axon structural plasticity

We can emit several hypotheses that could explain the dynamic modulation and more specifically the enlargement of axons during HFS-induced LTP. Some would involve mechanical tension of the plasma membrane and others involve dynamic redistribution of membrane.

The recent discovery of unique cytoskeleton architecture of the axon proper triggers the imagination for novel axonal properties [START_REF] Xu | Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons[END_REF]. The actin rings displayed along the axon and periodically spacing every 180-190 nm with an incredible accuracy raise new questions. First being: are those rings regulated by activity? In the case of our study, we could assume that the global axon enlargement is the consequence of the modulation of those actin rings. Every ring could be seen as a tunable pattern imposing a form on the axon that could both modulate its electrical and biochemical compartmentalization.

A possible scenario involves the release machinery of presynaptic boutons. Even though we have a good understanding of the molecular and structural determinants of neurotransmitter release through the fusion of vesicles at the plasma membrane, it is not yet clear how the presynaptic compartment deals with this membrane dynamics. We wondered whether the source of membrane producing the enlargement of axons could come from neurotransmitter vesicles. A strong argument supporting this hypothesis comes from recent studies. First of all, in vivo studies have clearly shown that the number of presynaptic vesicles in boutons scales with the surface area of the postsynaptic density [START_REF] Harris | Dendritic spines of CA 1 pyramidal cells in the rat hippocampus: serial electron microscopy with reference to their biophysical characteristics[END_REF][START_REF] Harris | Variation in the number, location and size of synaptic vesicles provides an anatomical basis for the nonuniform probability of release at hippocampal CA1 synapses[END_REF][START_REF] Lisman | Quantal analysis and synaptic anatomy--integrating two views of hippocampal plasticity[END_REF][START_REF] Schikorski | Morphological correlates of functionally defined synaptic vesicle populations[END_REF]. Since the postsynaptic density size increases with LTP, one could assume that the number of vesicles increases as well.

Although, early EM observations from single section analyses suggested that the number of presynaptic vesicles was reduced after induction of LTP [START_REF] Applegate | Redistribution of synaptic vesicles during long-term potentiation in the hippocampus[END_REF][START_REF] Fifkova | Long-lasting morphological changes in dendritic spines of dentate granular cells following stimulation of the entorhinal area[END_REF]Meshul & Hopkins, 1990). This was recently confirmed through 3D reconstructions from serial EM sections revealing a strong depletion of about 100 vesicles out of 300 in average, 30 minutes and 2 hours after LTP induction (Bourne et al, 2013). Thus, one could suspect that this depletion of vesicles represents the source of membrane that contributes to the overall increase of axon diameter.

Knowing that the size of a vesicle is about 40 nm in diameter, and on average, the axon structure is composed of an axon shaft of 200 nm and displays oblong-shaped boutons of 1 µm long and 500 nm large with a frequency of 3 µm along the axon; the exocytosis of 100 vesicles per bouton would yield an average axonal diameter increase of ~ 20%. Performing the reverse calculation from a 5-7% increase in axonal diameter observed in our study, we The release probability at hippocampal synapses was shown to be highly heterogeneous and positively correlates with bouton volume and active zone area [START_REF] Holderith | Release probability of hippocampal glutamatergic terminals scales with the size of the active zone[END_REF]. This parameter is also non-linear with the frequency of stimulation. Typically, HFS produces a facilitation quickly followed by a depletion of the readily-releasable pool [START_REF] Dobrunz | Release probability is regulated by the size of the readily releasable vesicle pool at excitatory synapses in hippocampus[END_REF][START_REF] Dobrunz | Heterogeneity of release probability, facilitation, and depletion at central synapses[END_REF]. Considering the stimulus protocol employed in our study (3 times 1 second at 100 Hz) and taking a conservative estimate of the release probability at single boutons of 0.2 in average [START_REF] Dobrunz | Release probability is regulated by the size of the readily releasable vesicle pool at excitatory synapses in hippocampus[END_REF][START_REF] Hanse | Vesicle release probability and pre-primed pool at glutamatergic synapses in area CA1 of the rat neonatal hippocampus[END_REF][START_REF] Holderith | Release probability of hippocampal glutamatergic terminals scales with the size of the active zone[END_REF], an average of 60 vesicles have fused to every boutons on the axon during the stimulation.

In addition, a recent study brought the evidence that exocytosis of neurotransmitter was followed by rapid bulk endocytosis within 50-100 ms [START_REF] Watanabe | Ultrafast endocytosis at mouse hippocampal synapses[END_REF] which means that a part of the membrane coming from the 60 vesicles calculated would be endocytosed.

Altogether, this scenario involving a net change in the number of vesicles after LTP could explain the overall increase axon diameter (Figure 19).

Functional impact of axonal AP velocity modulation on information processing in the brain

The timing of signal transmission between neurons in the hippocampus can be substantial but is most of the time ignored in computational studies. This delay in transmission is generally described as the sum of axonal conduction that depends on the conduction velocity, the axonal length, and the synaptic delay.

In that regard, CA3 axons conduct APs relatively slowly (0. Therefore, propagation times in axons can be as long as 100 ms.

In our study, we observed a consistent change in the population of axons measured. However, STED microscopy limits the imaging to a set of axon stretches in a relatively small field of view (~ 30 x 20µm). Therefore, we cannot rule out that the increase of diameter is homogenous throughout the axon arborisation. But, assuming that the change is global, the acceleration of the conduction could shorten the AP arrival time by a few milliseconds in the distal axon (Figure 20). There is evidence that milliseconds time difference would have a significant impact on several hippocampal functions. First, some hippocampal rhythms such as gamma and ripples (140-200 Hz) are very fast and suggest that submilliseconds synchronization may be important. Second, delays of propagation are crucial in the context of spike-timing dependent plasticity (STDP). The time window for supralinear summation of calcium caused by dendritic spikes and synaptic events is on the milliseconds scale and determines whether synapses are potentiated or depressed. Knowing that STDP is responsible for the formation of synchronized groups of neurons that are strongly interconnected, a slight change in axonal delay could remodel those polysynchronous groups (Izhikevich, 2006). Third, a few milliseconds change in delay of propagation could largely alter the disynaptic inhibition of the postsynaptic neuron.

Thus, it will be interesting to evaluate whether axon geometry-dependent variations in AP delay further increase storage capacity.

In addition to the modulation of AP propagation properties, it would be interesting to investigate whether structural modifications of axon morphology are reflected in a change in diffusive properties which would impact axonal transport.

Outlook

This work, going along with recent discoveries, outline more generally that the computational power of axons and their functional impact has been largely underestimated. In biology, it is considered that the level of structural complexity scales with the diversity of functions. In that regard, both the diversity of the large scale organization of axonal trees, the ultrastructural organization of the axon trunk and presynaptic boutons gives us as many indications for a variety of functions that remains to be discovered.

For instance, by picturing the complexity of axon arborisations in the hippocampus (Major et al, 1994;Wittner et al, 2007), emerging ideas supported by biophysical principles are challenging the view that APs have a smooth ride from the soma to the presynaptic targets.

The highly collateralized organization and the presence of many varicose en passant boutons may substantially decrease conduction speed and could even lead to failure of propagation. It would be interesting to see whether in non-pathological conditions, axons use such mechanism to control APs propagation in an arborisation. One could imagine that every branch points within a tree would act as a gate for allowing or blocking the passage of an AP. This failure of AP propagation was suggested many times [START_REF] Bucher | Beyond faithful conduction: short-term dynamics, neuromodulation, and long-term regulation of spike propagation in the axon[END_REF][START_REF] Debanne | Information processing in the axon[END_REF][START_REF] Debanne | Axon physiology[END_REF] and experimentally shown, but only in specific conditions [START_REF] Luscher | Action potential propagation through embryonic dorsal root ganglion cells in culture. II. Decrease of conduction reliability during repetitive stimulation[END_REF][START_REF] Manor | Effect of geometrical irregularities on propagation delay in axonal trees[END_REF].

Another aspect to consider is that the axonal protrusion can be very isolated biochemically and electrically from the neuronal cell body. For some cell types, axons can extend up to several meters making any signalling from the soma a very slow and non-reliable process. It is then likely that the distal axon would be largely influenced by local signalling from its glial environment. This concept has emerged recently with two studies from the same group. One of those studies demonstrated that the distal part of the axon is electrically isolated as compared to the proximal part (Sasaki et al, 2012a). The other shows the influence of astrocytes on the local regulation of AP propagation [START_REF] Sasaki | Action-potential modulation during axonal conduction[END_REF].

Concluding remarks

In conclusion, this work serves us with novel indicators that beyond the classical scope of AP propagation, axons are capable of many structural rearrangements for the plasticity of neuronal circuitry.

We showed that the morphology with both the irregularity of the structure and the average diameter can be directly modulated by neuronal activity. Biophysical theory, computer simulations as well as electrophysiological recordings indicate that changes in AP conduction velocity are the direct result of structural changes in the axons.

The emergence of new technologies and the conceptual refinement about axonal properties will help to discover many interesting facets of axon physiology and unravel its significance for neural computations.

Figure 1 :

 1 Figure 1: Drawings of stained neurons in the spinal cord with soma, nucleus, dendrites and axons, by Otto F K. Deiters, 1865. .....................................................................................

Figure 2 :

 2 Figure 2: The structural organization of the hippocampus. .........................................................

Figure 3 :

 3 Figure 3: Structural arrangement of actin, spectrin and associated proteins in the axon trunk. ....

Figure 4 :

 4 Figure 4: NeuroLucida reconstruction of a CA3 pyramidal neuron. ...........................................

Figure 5 :

 5 Figure 5: Morphology of boutons in the neocortex. ...................................................................

Figure 6 :

 6 Figure 6: Electron micrograph and 3D reconstruction of CA3 axons. ........................................

Figure 7 :

 7 Figure 7: Electrical model of a passive axonal cable. .................................................................

Figure 8 :

 8 Figure 8: Expression mechanism of presynaptic LTP and LTD: prototypical mechanisms. ........

Figure 9 :

 9 Figure 9: Simplified Jablonski diagram of GFP for fluorescence and stimulated depletion. .......

Figure 10 :

 10 Figure 10: Point spread function engineering for STED microscopy. .........................................

Figure 11 :

 11 Figure 11: Stimulated emission depletion microscopy reveals densely packed nitrogenvacancy centres in diamond. ..............................................................................................

Figure 12 :

 12 Figure 12: Local infection CA3 pyramidal neurons using sinbis-GFP. .......................................

Figure 13 :

 13 Figure 13: Optical design of the home-built inverted STED microscope for opto-physiology in brain slices. ...................................................................................................................

Figure 14 :

 14 Figure 14: Structural plasticity of axon shafts and boutons during LTD. ..................................

Figure 15 :

 15 Figure 15: The inhomogeneous distribution of fluorophores in the axon structure makes intensity-based measurement of diameters inaccurate. .....................................................

Figure 16 :

 16 Figure 16: The imaging of axonal structures was performed in non-saturated conditions. ........

Figure 17 :

 17 Figure 17: The FWHM measurement does not depend on the intensity of the signal. ...............

Figure 18 :

 18 Figure 18: Geometric ratio measurement on the proximal axon tree. .......................................

Figure 19 :

 19 Figure 19: Proposed mechanism of axonal diameter enlargement. ...........................................

Figure 20 :

 20 Figure 20: Hippocampal axons may serve as dynamic delay lines for information transfer. .....

1 The axon as a transmission cable 1 . 1

 111 vivant épais que ce soit dans les tranches aigues ou sur animal vivant. Etant une méthode de microscopie photonique classique, la résolution spatiale d'un microscope deux-photon est limitée à environ 350 nm à cause de la diffraction de la lumière, et donc ne permet pas l'observation détaillée d'importantes structures neuronales comme les épines dendritiques ou les axones. Nous avons construit un nouveau microscope basé sur une excitation à deux photons et à déplétion stimulée pulsée. Sa polyvalence permet l'imagerie des fluorophores classiquement utilisés comme la GFP, YFP et Alexa488. Nous illustrons le potentiel du microscope pour la résolution de structures cérébrales minces telles que des épines dendritiques, les axones et lesINTRODUCTION General introductionA neuron is an electrically excitable and highly polarized cell that receives processes and transmits information through electrical and chemical signals. Neurons can connect to each other via contacts called synapses and form neuronal networks. Typically, a neuron is composed of 3 compartments, the cell body (or soma), the input region called dendrites and the output region called axon.The axon (from Greek, axis) is a thin and elongated protoplasmic protrusion that projects away from the cell body to terminal endings. Its function is to conduct information via electrical impulses, typically action potentials (APs) from the soma to different neurons, muscles or glands. Its discovery, during the 19 th century, is usually attributed to the German anatomist Otto Friedrich Karl Dieters[START_REF] Deiters | Untersuchungen über Gehirn und Rück-enmark des Menschen und der Säugethiere[END_REF] being the first to distinguish the axon from the dendrite which is the other type of neuronal protrusions that receive information from other neurons via synapses (Figure1). The functional role of the axon as the output compartment of the neuron was first suggested by the pioneer work of the Spanish anatomist Santiago Ramón y Cajal (Ramon y Cajal, 1897). A few years later, JuliusBernstein (1902) correctly postulated the fundamental biophysical properties of the neuronal membrane. He used the term "membrane breakdown" to describe the transient lost of membrane negativity during the propagation of an AP. In the 1930's, Cole and Curtis experimentally measured the change in membrane resistance in the squid giant axon during the passage of an AP[START_REF] Cole | Electric Impedance of the Squid Giant Axon during Activity[END_REF]. This work was then followed by Hodgkin, Huxley and Eccles who received the Nobel prize in physiology and medicine in 1963 for the discovery the ionic mechanisms involved in the excitation and inhibition of the nerve membrane[START_REF] Hodgkin | The relation between conduction velocity and the electrical resistance outside a nerve fibre[END_REF].Ever since, axons were seen as reliable transmission cables, conveying a purely digital code, where information is composed of the rate and timing of stereotypical APs traveling to downstream targets. However, close examination of the structural organization, various channel compositions and functionally diverse properties of axonal arbors has begun to challenge this simplistic view. Indeed, numerous studies have demonstrated that the axon structure can exert profound influence on neuronal input integration and output modulation, thus indicating that the functional repertoire of axons is much broader than traditionally thought[START_REF] Bucher | Beyond faithful conduction: short-term dynamics, neuromodulation, and long-term regulation of spike propagation in the axon[END_REF][START_REF] Debanne | Information processing in the axon[END_REF][START_REF] Debanne | Axon physiology[END_REF].

Figure 1 :

 1 Figure 1: Drawings of stained neurons in the spinal cord with soma, nucleus, dendrites and axons, by Otto F K. Deiters, 1865.

Figure 2 :

 2 Figure 2: The structural organization of the hippocampus.The dentate gyrus (DG) that exclusively receives inputs from the entorhinal cortex (EC) is composed of granule cells. Typically, granule cells project to the CA3 area via the morphologically distinct mossy fibers. The CA3 is composed of excitatory pyramidal neuronsand sends projections called Schaffer collaterals to the CA1 region. Similarly, CA1 is composed of excitatory pyramidal cells that are projecting toward the Subicullum and other layers of the entorhinal cortex.(modified drawing from Ramon yCajal, 1911)

Figure 3 :

 3 Figure 3: Structural arrangement of actin, spectrin and associated proteins in the axon trunk. (Top) Super resolution STORM microscopy reveals the periodic structural organization of actin in the axon. Conventional fluorescence image of the actin (green) and dendritic marker,MAP2 (magenta), in a cultured hippocampal neuron fixels at 7 DIV (D). 3D STORM image of actin in a region containing axons (E). (Bottom) Periodic organization of thecytosketeton,with actin that forms rings and its associated proteins in the axon trunk.(adapted from[START_REF] Xu | Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons[END_REF]

Figure 4 :

 4 Figure 4: NeuroLucida reconstruction of a CA3 pyramidal neuron. (a) Coronal view of the entire axonal arbor. The green triangle shows the location of the cell body, the axons are white, the dentate granule cell layer is marked with yellow line, CA1-3 pyramidal cell layer with red line. D dorsal, V ventral, L lateral, M medial, A anterior, P posterior. (b) This rotated view shows that CA3 pyramidal cell axon collaterals follow the curve of the Cornu Ammonis. (c) View of the axonal arbor from dorsal. (d) View from medial.(fromWittner et al., 2007)

Figure 5 :

 5 Figure 5: Morphology of boutons in the neocortex. The 2 types of boutons that can be observed in the neocortex are the terminaux boutons and en passant boutons, which are cell-type specific. Layer 2, 3, 5 axons preferentially exhibit en passant boutons whereas layer 6 axons exhibit more terminaux boutons.

Figure 6 :

 6 Figure 6: Electron micrograph and 3D reconstruction of CA3 axons. Left, Full-field view of a representative micrograph from the stack of images used for threedimensional reconstructions. The shaft and two varicosities (var) of an axon are indicated. Right, Eight reconstructed axons from serial sections, at the same scale as the micrograph. Some axons extend beyond the area of the micrograph because of the three-dimensional perspective. The axons travel in many different directions, rather than parallel to each other. Scale bar, 1.0 µm.(from Shepherd and Harris, 1998).

Figure 7 :

 7 Figure 7: Electrical model of a passive axonal cable. The model is composed of parallel segments of capacitances c m and resistance r m . The resistance in series along the fiber r i characterize the intracellular movement of electric charges.

  , those thin unmyelinated axons remained out of reach for direct electrophysiological measurements. Calcium imaging of presynaptic terminals revealed a high reliability of AP propagation through branch points in cortical pyramidal neurons (Cox et al, 2000) but those measurement were confined to the proximal part of the arbor where collaterals are the largest. New emerging techniques, like direct extracellular recording of APs (Sasaki et al, 2011; Sasaki et al, 2012b) at axons collaterals and latest improvement of voltage-sensitive dyes (Foust et al, 2010) will certainly help to provide a definitive answer.

  By numerically solving this equation, the AP propagation velocity remains proportional to the square-root of the axon diameter. The accumulation of experimental measurements has confirmed that the axon diameter is a good indicator of the propagation velocity within and across species. For examples, the squid giant axon can approach a millimeter in diameter and propagate APs at a speed range of 10-25 m/s[START_REF] Rosenthal | Seasonal variation in conduction velocity of action potentials in squid giant axons[END_REF]. Peripheral crustacean axons display velocities of 1-10 m/s with a diameter range of 1-10 µm[START_REF] Young | The effects of temperature on peripheral neuronal function in eurythermal and stenothermal crustaceans[END_REF]. At the other end of the spectrum, CA3 axons, which are among the smallest axons with a diameter range of 100-350 nm, the speed of AP propagation was estimated to be around 0.25-0.38 m/s[START_REF] Andersen | The hippocampal lamella hypothesis revisited[END_REF] Meeks & Mennerick, 2007).

4 Long-term plasticity of unmyelinated axons 4 . 1 Presynaptic changes associated with synaptic plasticity 4 . 1 . 1

 441411 Performing extracellular recording on CA3 axons, Sasaki et al. demonstrated that the AP waveform broadens locally in response to local application of glutamate and adenosine A 1 receptor antagonist on the axon shaft[START_REF] Sasaki | Action-potential modulation during axonal conduction[END_REF]. The authors demonstrated that axonal AMPA receptors activation causes a local depolarization that broadens APs while traveling down the axon. As a consequence of large APs, they showed that synaptic transmission is enhanced. In addition, they provided evidence that astrocytes, known to play an important role in local synaptic transmission, could regulate peri-axonal glutamate concentration and be responsible for the local broadening of APs in the distal part of the axon.Later, using a similar approach, Sasaki et al. demonstrated that network activity, responsible for sustained depolarization of the resting membrane potential in the soma, does broaden APs in the proximal part of CA3 axons(Sasaki et al, 2012a). They could show that somatic depolarization of CA3 pyramidal cells facilitates neighboring CA3 to CA3 but not distal CA3 to CA1 synaptic transmission. Moreover, they illustrated the importance of the axonal topology showing that AP broadening decays with the distance from the soma and the branching pattern. Synaptic plasticity Learning and memory refers to the ability of the brain to encode, store and retrieve information. This ability relies on the plastic nature of neural networks, allowing the brain to adapt itself in response to experience. Among these adaptations, synaptic strength enduring patterns of activity can be modulated in a phenomenon known as synaptic plasticity. The concept was first introduced by Donald Hebb more than 60 years ago: 'When an axon of cell A is near enough to excite cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic changes takes place in one or both cells such that A's efficiency, as one of the cells firing B, is increased' (Hebb 1949). However, it took more than 20 years to get the first experimental evidence of synaptic plasticity. In 1973, by stimulating the perforant path and recording field potentials in the dentate gyrus in anesthetized rabbits, Bliss and Lømo discovered that strong synaptic activity can result in a persistent increase of synaptic strength, a phenomenon referred as long-term potentiation (LTP)[START_REF] Bliss | Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path[END_REF]. The functional counterpart of LTP that is an activity-dependent and input specific decrease of synaptic strength, known as long-term depression (LTD), was experimentally demonstrated a few years later[START_REF] Lynch | Heterosynaptic depression: a postsynaptic correlate of long-term potentiation[END_REF].Since then, LTP and LTD are the most extensively studied paradigms of plasticity and were shown to occur in most synapses of the brain[START_REF] Cooke | Plasticity in the human central nervous system[END_REF]. To date, LTP and LTD are believed to be important cellular correlates of learning and memory.Over the past 40 years, much attention was focused on understanding the structural and functional changes occurring at the post-synaptic compartment. Many forms of synaptic plasticity have been described involving several biochemical pathways. The most stereotypical form of LTP and LTD occurs at the Schaffer collaterals-CA1 synapse and depends on the activation of postsynaptic NMDA receptors. Typically, expression of LTP and LTD can be decomposed in an early and a late phase. During LTP, NMDA receptors activation produces a rapid and high increase of Ca 2+ in the post-synapse that leads to the phosphorylation of CaM-kinase II. In the early phase, AMPA receptors sensitivity increases usually producing a large potentiation of the synapse. Later, the increase of the global phosphorylation rate in the post-synaptic compartment leads to a long lasting recruitment of AMPA receptors to the synaptic membrane increasing the synaptic efficacy[START_REF] Lisman | A mechanism for the Hebb and the anti-Hebb processes underlying learning and memory[END_REF].On the other hand, LTD is induced by a moderate and prolonged increase of Ca 2+ concentration that leads to the activation of calcineurin. The phosphatase activity of calcineurin reduces the synaptic weight by decreasing the number of AMPA receptors at the synapse.Many structural correlates have been established to underlie the expression of synaptic plasticity. The recruitment of receptors to the postsynaptic density that is responsible for the synaptic strengthening during LTP is often correlated with an increase in spine volume[START_REF] Harvey | Locally dynamic synaptic learning rules in pyramidal neuron dendrites[END_REF][START_REF] Kopec | Glutamate receptor exocytosis and spine enlargement during chemically induced long-term potentiation[END_REF][START_REF] Matsuzaki | Structural basis of longterm potentiation in single dendritic spines[END_REF][START_REF] Yang | Spine expansion and stabilization associated with long-term potentiation[END_REF].

  By monitoring the level of neurotransmitter release together with synaptic activity at CA3-CA1 synapses, Bayazitov et al. explored the differential contribution of the pre and postsynaptic compartment during the strengthening of synapses (Bayazitov et al, 2007). The induction of LTP was performed by different stimulation protocols. They found that 50 Hz and short theta-burst stimulation (TBS) favors postsynaptic strengthening while 200 Hz and TBS promotes a compound LTP that is expressed both pre-and postsynaptically. In this compound LTP expression, the postsynaptic component is fast and strongly dependent on the activation of NMDA receptors whereas the presynaptic component is slower and requires the activation of L-type Cav channels (Grover & Teyler, 1990; Zakharenko et al, 2001) and depends on protein kinase A (PKA) activation (Castillo, 2012) (Figure 8). Other investigations showed that R-type Cav channels are involved in the presynaptic component of LTP in the mossy fiber CA3 pathway (Breustedt et al, 2003; Dietrich et al, 2003). Along with the increase in release probability following the induction of LTP, Bourne et al. have shown that ultrastructural modifications occur in the presynaptic compartment (Bourne et al, 2013).Performing 3D reconstructions of axons from serial section electron microscopy 30 minutes and 2 hours after induction of LTP, they observed a persistent reduction of the vesicle pool of around 30% and a transient decrease in the readily releasable pool.

Figure 8 :

 8 Figure 8: Expression mechanism of presynaptic LTP and LTD: prototypical mechanisms. Voltage-gated calcium channel mediated Ca 2+ influx responsible for neurotransmitter release is involved in some forms of presynaptic LTP/LTD. The activation of mGluR7 produces a depression of P/Q types Cav channels via the activation of the PKC pathway hence reducing neurotransmitter release during LTD. During LTP, R type Cav channels are thought to activate the PKA pathway facilitating neurotransmitter vesicle fusion.(adapted from[START_REF] Castillo | Presynaptic LTP and LTD of excitatory and inhibitory synapses[END_REF]

  threshold voltage for the initiation of APs is regulated upon activity. A change in postsynaptic excitability was already suggested in the early descriptions of LTP at hippocampal synapses[START_REF] Bliss | Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path[END_REF] and it is now well established that changes in pre-and postsynaptic intrinsic excitability plays an important role in synaptic plasticity[START_REF] Campanac | Plasticity of neuronal excitability: Hebbian rules beyond the synapse[END_REF][START_REF] Debanne | Brain plasticity and ion channels[END_REF][START_REF] Debanne | Spike-timing dependent plasticity beyond synapse -pre-and post-synaptic plasticity of intrinsic neuronal excitability[END_REF][START_REF] Zhang | The other side of the engram: experience-driven changes in neuronal intrinsic excitability[END_REF]. As the excitability of the cell membrane depends on the ionic environment and the channel composition, it is becoming increasingly clear that every sub-cellular compartment can differentially regulate their own excitability. This is certainly true for dendrites, where an increase of local excitability has been measured following the induction of LTP[START_REF] Campanac | Downregulation of dendritic I(h) in CA1 pyramidal neurons after LTP[END_REF][START_REF] Frick | LTP is accompanied by an enhanced local excitability of pyramidal neuron dendrites[END_REF]. Concerning the axonal compartment, there are only a few reports indicating a change in excitability associated with synaptic plasticity. Xu et al. have demonstrated a synergic effect between the induction of synaptic LTP in CA1 pyramidal cells and an increase in the sensitivity of Nav channels for more hyperpolarized potentials in the presynaptic cell[START_REF] Xu | Activity-dependent long-term potentiation of intrinsic excitability in hippocampal CA1 pyramidal neurons[END_REF]. Interestingly, this presynaptic change in excitability was blocked by NMDA receptor antagonist APV, Ca 2+ chelators, CaM kinase inhibitors and protein synthesis inhibitors. This indicates that the change of excitability shares common mechanisms with the late phase of synaptic LTP. However, since the presynaptic effects were recorded at the soma, it remains unclear whether the locus of expression of this change in excitability is in the axonal trunk or in the AIS. Earlier, a similar concomitant change of synaptic strength and presynaptic excitability was found in cultured hippocampal neurons[START_REF] Ganguly | Enhancement of presynaptic neuronal excitability by correlated presynaptic and postsynaptic spiking[END_REF]. The authors could prevent the increase of intrinsic excitability by inhibiting a retrograde signaling pathway involving presynaptic PKC. This would suggest that the change in excitability occurs near the presynaptic compartment, hence the axonal trunk.The AIS is a key structure that controls the overall excitability of neurons. In 2010, two groups have reported novel mechanisms of activity-dependent change in neuronal excitability involving structural modifications of the AIS.By labeling and imaging the AIS in dissociated hippocampal neurons, Grubb and Burrone showed that neurons can regulate the position of the entire AIS compartment according to ongoing activity[START_REF] Grubb | Activity-dependent relocation of the axon initial segment fine-tunes neuronal excitability[END_REF]. The AIS moves away from the soma in response to a persistent increase of extracellular potassium. Performing current-clamp recording combined with AIS imaging, they demonstrated that the AIS relocation is associated with a decrease in neuronal excitability. In another study, Kuba et al. demonstrate that deprivation of auditory input in avian brainstem auditory neuron also leads to structural changes of the AIS[START_REF] Kuba | Presynaptic activity regulates Na(+) channel distribution at the axon initial segment[END_REF]. Interestingly, unlike the relocation of the AIS described byGrubb and

  Bakkum et al. could to induce, detect and track changes of a small neuronal network and measure how they adapt to various patterns of stimulation. Using this approach, they demonstrated that along with changes in synaptic efficacy, APs propagation delays and amplitude were modulated(Bakkum et al, 2008). Performing repeated stimulation patterns (0.5 Hz) at various location of the reduced network, they observed that, in some axons, the conduction velocity and the amplitude of APs were modulated. The absence of correlation between AP amplitude and velocity may indicate changes in the morphology in addition to channel densities. However, there are numerous reports on both, structural modifications (Bastrikova et al, 2008; Becker et al, 2008; De Paola et al, 2006) and excitability changes (Bi & Poo, 2001; Ganguly et al, 2000; McNaughton et al, 1994) in axons; those were always the result of local measurements or from reduced preparation. For this reason, people could not reliably assess conduction velocity measurements on such short axonal distance.

Figure 9 :

 9 Figure 9: Simplified Jablonski diagram of GFP for fluorescence and stimulated depletion.(A) The GFP molecule is excited from its ground state (S0) to a higher energy level (mostly S1) by a blue photon (488 nm). After vibrational relaxation to the lowest S1 level, the molecule emits a red-shifted photon (green) and returns back to its ground state by a process called fluorescence.(B) In case of stimulated depletion, similarly, the GFP molecule is excited from its ground state (S0) to a higher energy level (S1) by a blue photon (488 nm). Before spontaneous fluorescence occurs, a red-shifted photon (595 nm) de-excites the molecule from (S1) to its ground state (S0) which leads to the emission of a photon has the same properties (such as wavelength, polarity) as the incident photon.

Figure 10 :

 10 Figure 10: Point spread function engineering for STED microscopy. (A) Reflections of the laser beams from gold particles used for visualization and spatial alignment of the excitation and STED beams. The laser beams are routed through a pellicle beam splitter so that the reflections can be detected by a photomultiplier tube. This allows for the characterization of the excitation and STED beams and illustrates the doughnut-like intensity distribution of the STED laser. Scale bar: 200 nm. (B) Intensity profiles along the optical axis of the excitation and STED PSF shown in (A), indicated by the white dashed line.

  STED microscopy was the first technique that was not limited by the diffraction barrier of optical microscopy. The resolution in STED imaging is theoretically unlimited and can be expressed by a modified Abbe's equation where I is the STED beam intensity used and I s is the STED beam intensity required to reduce the fluorescence by a factor of 1/e (Harke et al, 2008):

Figure 11 :

 11 Figure 11: Stimulated emission depletion microscopy reveals densely packed nitrogenvacancy centres in diamond. Confocal (a) and STED (b) images from the same crystal region. (c) The individual centers resolved in b automatically yield the effective PSF of the STED recording whose y-profile exhibits a FWHM of y = 16.0 nm. (d) The coordinate of each centre can be calculated with 0.14 nm precision. Comparing (a) with (d) highlights the dramatic gain in spatial resolution resulting from the unique increase in resolution. (e,f) Applying I maxSTED = 3.7 GW cm -2shrinks a confocal spot of 223 nm diameter (FWHM) down to 8 nm. Note that the increase in resolution is a purely physical phenomenon.(from[START_REF] Rittweger | STED microscopy reveals crystal colour centres with nanometric resolution[END_REF]

  structure. The photo-damage is a consequence of light absorption by the biological tissue and hence produces heat. Therefore it is necessary to use modest amounts of light without compromising resolution. By using pulsed lasers, it is possible to image with low average STED power to preserve the sample and high peak intensity to obtain super resolution. This requires that both excitation and depletion pulses are synchronized and differentially delayed. Several studied have demonstrated that STED imaging is compatible with live-cell observations achieving a spatial resolution of around 60-100 nm with STED intensities comparable to what is being used for two-photon imaging (Nagerl et al, 2008; Rankin et al, 2011; Willig & Nagerl, 2012).

Wild-type mice

  were kept under 12 h light/ 12 h dark cycle with ad libitum access to food and water (strain from Jackson Labs, Bar Harbor, ME). All experiments were in accordance with the National Code of Ethics on Animal Experimentation (Carte Nationale d'éthique sur l'expérimentation animale; Ministère de l'enseignement supérieur et de la recherche, Ministère de l'agriculture de l'agroalimentaire et de la forêt) and approved by the Committee of Ethics of Bordeaux.

  thick coverslips are first heated in ethanol for 30 minutes. Then the coverslips are dryed and heated in an oven for at least 3 h at 225 °C. After this step, they are then coated with a poly-L-lysine solution for 20-30 minutes. After drying, the coverslips are washed in distilled water for 20 minutes. The dissection itself consists of the extraction of the hippocampi from the 5-7 days old mice by decapitating the mice, removing the scalp, opening the skull, removing and submerging the brain in cooled and freshly prepared dissection solution with the following composition: 98 ml GBSS (containing in g/L: 0.220 CaCl 2 * 2 H 2 O; 0.740 KCl; 0.030 KH 2 PO 4 ; 0.210 MgCl 2 * 6 H 2 O; 0.070 MgSO 4 * 7 H 2 O; 8 NaCl; 0.227 NaHCO 3 ; 0.120 Na 2 HPO 4 ; 1.100 D(+)-Glucose * H 2 O); 18,92 mg of kynurenic acid; and 1 ml of glucose solution (1.1g in 1mL of distilled water). The pH was adjusted with 1M HCl to 7.2, sterile filter and stored at 4 °C. The hippocampi are then isolated and placed on the teflon disk of the tissue chopper (McIlwain) that is equipped with a razor blade. Coronal slices of 350 µm are produced and transferred in a new petri dish containing cooled dissection solution for 30-60 minutes. The next step consists in mounting the slices on the glass coverslips by embedding them into a clot of thrombin and chicken plasma. 10 µL of chicken plasma is deposited on the center of the coverslip. A slice is then transferred on the chicken plasma drop before adding 10 µL of thrombin solution (742.5 μl of GBSS; 7.5 μl of glucose solution; 500 μl of thrombin). The chicken plasma and the thrombin are then mixed before leaving the clot to coagulate around the slice for 30 minutes. The coverslips are then transferred into delta tubes (Nunc) before adding 750 µL of culture medium with the following composition: 100 ml of BME medium; 50 ml of HBSS; 50 ml of horse serum; 1 ml of glutamine; 2 ml of glucose. The tubes containing the slices are then placed on a roller-drum incubator set at 35 °C with a rotation speed of 0.1 rpm.

Figure 12 :

 12 Figure 12: Local infection CA3 pyramidal neurons using sinbis-GFP. Left. A glass pipette filled with sindbis-GFP viral particles solution is inserted into the stratum pyramidale of the CA3 area. Few pulses of positive pressure are applied and the affected area is controlled by visual inspection by contrast change (dotted red circle). Right. High magnification fluorescence image of the CA3 pyramidal layer 36 h post-infection. Only a small section of CA3 pyramidals are labeled. Scale bar: 20 µm.

6 MgCl 2 ,

 62 the maximal amplitude for LTP and control experiments and 66% for LTD experiments. The fEPSPs were recorded from Digidata 1440A and Multiclamp 700B (Axon CNS; Molecular Devices). Amplifier gain was set at 20 and a Bessel filter of 2 kHz was applied. A test pulse was recorded every 15 s (0.067 Hz) through the whole experiment. The stimuli protocols consisted of 3 trains with 20 s interval of 100 pulses delivered at 100 Hz to induce LTP; 900 pulses delivered at 1 Hz to induce LTD and started after recording a baseline of 20 min. The initial slopes of the fEPSPs were determined with Clampfit 10.1 (Axon instruments). Some experiments were performed in the presence of the NMDA receptor antagonist, D-APV, to prevent the induction of an LTP.For the electrophysiological experiments that involved patch-clamp recording of CA3 pyramidal neurons, the stimulation pipette was placed in the CA1 radiatum in between the extracellular field recording electrode (placed in the distal part of the CA1) and the CA3.Patch-clamp recordingsCurrent-clamp recordings were obtained from CA3 pyramidal cells to record the arrival time of an antidromic AP generated distally on the axon. Patch-clamp glass electrodes (1.5 x 1.17mm, Harvard Apparatus, 3-5 MΩ) were filled with the following solution (in mM) : 115 KMeSO3, 10.3 Na + (NaOH, Na-ATP, Na-GTP), 4.40 HEPES, 1 EGTA, 4 ATP, 0.3 GTP, osmolarity =275-280, pH: 7.3. Once the seal between the cell membrane and the glass electrode reached 1GΩ, whole-cell mode was used and cells were clamped at -70mV. Those presenting an access resistance (Ra) greater than 25 MΩ or and injected current greater than -100 pA were excluded from the experiment. CA3 cells were recorded in current clamp with a dynamic current injection correction to maintain the resting membrane at -70 mV. Amplifier (Multiclamp 700A) gain was set at 1 and a Bessel filter of 2 kHz was applied. To elicit an antidromic AP, a glass electrode back-filled with ACSF was placed in the distal part of the CA1 and then moved toward the CA3 until an AP could be recorded reliably at the soma. Short (0.1 ms) current pulses were delivered from a stimulus isolator (AMPI) with a stimulation strength ranging between 25-75 µA. Excitatory field recordings was performed simultaneously with the same stimulation electrode in order to monitor the induction of plasticity.Inverted single-photon STED setupFor live-cell imaging of hippocampal brain slice cultures, we use a custom-built STED microscope based on pulsed excitation and pulsed depletion in the visible range of the spectrum (Figure13). A standard commercial inverted microscope (DMI 6000 CS Trino, Leica, Mannheim, Germany) equipped with a high-numerical-aperture objective lens (PL APO, 100×, oil, NA 1.4, Leica) served as a base. For excitation, a pulsed-laser diode (PDL 800-D, Picoquant, Berlin, Germany) was used delivering 90 ps pulse duration at 485 nm wavelength. For fluorescence quenching, 595 nm wavelength laser pulses for the STED beam were produced by an optical parametric oscillator (OPO BASIC Ring fs RTP, APE, Berlin, Germany) pumped by a Ti:Sapphire laser (MaiTai, Spectra-Physics, Darmstadt, Germany), operating at 80 MHz and emitting at 800 nm. The pulses of originally 200 fs duration were stretched to ∼68 ps by first dispersion in a glass rod 25 cm long (SF6) and then in a polarization-preserving fiber (Schäfter & Kirchhoff, Hamburg, Germany) of 20 m length. To create the STED focal doughnut, a polymeric phase plate (RPC Photonics, Rochester, NY) was introduced into the STED beam path. The STED and excitation pulses were synchronized at 80 MHz via external triggering of the laser diode using an electronic delay generator. The laser beams were combined using a dichroic mirror (AHF Analysentechnik, Tübingen, Germany). We used a telecentric beam scanner (Yanus IV, TILL Photonics, Gräfelfing, Germany) in combination with scan and tube lenses from the microscope manufacturer to stir the laser beams across the sample. The fluorescence signal was detected in a descanned fashion and separated from the excitation by a dichroic mirror (499 nm longpass), then cleaned with a 525/50 band-pass filter and finally focused onto a multimode optical fiber connected to an avalanche photodiode (SPCM-AQR-13-FC, PerkinElmer, Waltham, MA). Image acquisition was controlled by the custom-written software IMSpector (IMSpector).

Figure 13 :

 13 Figure 13: Optical design of the home-built inverted STED microscope for optophysiology in brain slices. The diode laser used for excitation is routed through a beam scanner into an upright microscope and synchronized with the STED laser (Ti:Sa/optical parametric oscillator (OPO)). Femtosecond pulses emitted from the Ti:Sa/OPO are broadened by a 20-m-long polarization-preserving single-mode fiber. The doughnut is formed by a helical phase mask (Vortex phase plate). An oil immersion objective is used. /2, half-wave plate; /4, quarterwave plate; DC, dichroic mirrors, NA, numerical aperture; t, pulse broadening fiber; xyscan, scanner for x and y dimension; APD, avalanche photodiode; EOM, electro-optical modulator.

compartment model program NEURON version 7 . 3 (

 73 Carnevale & Hines, 2006). The properties of each compartment can be defined independently. Axon branches were measured with the STED microscope (see above). A text file containing the diameter profile along the studied branch was used to build a simulation model. The simulation model was composed of unmyelinated excitable compartments, described by standard(Hodgkin & Huxley, 1952a; Hodgkin & Huxley, 1952b) channel kinetic equations.

  is the passive leakage current:I leak = (E leak -E)  G leakand E leak and G leak are the equilibrium potential and the leak conductance, respectively.

  Activation m: A m = 1 ms -1 ; k m = 0.1 mV -1 ; d m = -40 mV; A m = 4 ms -1 ; k m = -0.055 mV -1 ; d m = -65 mV Inactivation h: A h = 0.07 ms -1 ; k h = -0.05 mV -1 ; d h = -65 mV;

Part 1 Part 1 :

 11 is a research article in preparation and formatted in the style of a scientific journal describing the activity-dependent regulation of axon morphology and function in living brain slices. In this project, I designed, performed and analyzed the imaging and electrophysiological experiments. The computer models were built by our collaborator, Daniel Cattaert; he and I ran the simulation-based experiements. Part 2 is a research article published in Biophysical Journal on February 2013 describing the development of a novel type of STED microscope based on two-photon excitation. In this project, I contributed to the design and building off the microscope. Activity-dependent morphological dynamics of CA3 axons and modulation of action potential conduction velocity.

  applied. A test pulse was recorded every 15 s (0.067 Hz) throughout the experiment. The stimulus protocol consisted of 3 trains of 100 pulses delivered at 100 Hz and 20 seconds apart to induce LTP and started after recording a baseline of 20 min. The initial slopes of the fEPSPs were determined with Clampfit 10.1 (Molecular Devices). Some experiments were performed in the presence of the NMDA receptor antagonist, D-APV. Whole-cell patch clamp recordings were performed using glass capillaries (tip resistance 3-5 M) with the following solution (in mM): 115 KMeSO3, 10.3 Na + (NaOH, Na-ATP, Na-GTP), 4.6 MgCl2, 40 HEPES, 1 EGTA, 4 mM ATP, 0.3 GTP, osmolarity = 275-280 mosmol, pH 7.3. Recordings where the access resistance (Ra) exceeded 25 MΩ or with holding currents greater than -100 pA were excluded from analysis. CA3 cells were recorded in current clamp mode with a dynamic current injection correction to maintain the resting membrane at -70 mV. The gain of the patch clamp amplifier was set at 1X and a Bessel filter of 2 kHz was applied. To elicit an antidromic AP, a glass electrode back-filled with ACSF was placed in the distal part of the CA1 area and then moved toward the CA3 until an AP could be recorded reliably at the soma. Short (0.1 ms) current pulses were delivered from a stimulus isolator (AMPI) with a stimulation strength ranging between 25-75 µA. Excitatory field recordings was performed simultaneously with the same stimulation electrode in order to monitor the induction of plasticity.

  is the axial current to neighboring compartments summed over all neighbors (Equation3)

Figure 1

 1 Figure 1 Heterogeneity and dynamics of CA3 axons

  (d-e) Distribution of morphological parameters of axons. (d) Distribution of axon diameters (n=26574). Curved line is a Gaussian fit, where R²=0.99. The inset shows median diameter; 203 nm, interquartile and range. (e) Distribution of bouton size (n=319). Curved line is a lognormal fit, where R²=0.98. The inset shows median size; 0.53 µm², interquartile and range. (f) Example of an axon segment imaged over more than an hour (scale bar, 1 µm) (g) Diameter profile of the axon shown in (f). The average diameter in time is represented (black line) with SD (grey). (h) Time-lapse imaging over 1 hour (geometric mean with 95% CI) for boutons (n=85) and 1 µm axon shaft segments (n=113).

  (i-j) Standard deviation of the normalized changes over 1 hour.

Figure 2 Figure 3

 23 Figure 2 Structural plasticity of axon shafts and boutons during LTP

Figure 4 LTP

 4 Figure 4 LTP induction increases presynaptic boutons

Figure 5

 5 Figure 5 Biophysical modeling of impact of axon structural plasticity on AP

Figure S1

 S1 Figure S1Resolution improvement of STED microscopy over confocal microscopy.

Figure S2

 S2 Figure S2Raw data of the maximum intensity projection image shown in Figure1.

Figure S3

 S3 Figure S3 Example of axon shaft diameter increase after LTP induction

Figure S4

 S4 Figure S4Electrophysiological approach to measure axonal propagation delays of APs.

Figure S5

 S5 Figure S5Velocity comparison between orthodromic and antidromic AP propagation.

Figure S6

 S6 Figure S6Boutons swelling slow down conduction velocity.

  These results indicate that LTD leads to a different type of morphological change on axon whereby the axon shaft diameters transiently decrease after LFS and recover later. The morphological dynamics of CA3 axons is specific to the type of stimulation and synaptic plasticity.

Figure 14 :Figure 15 :

 1415 Figure 14: Structural plasticity of axon shafts and boutons during LTD.

Figure 16 :

 16 Figure 16: The imaging of axonal structures was performed in non-saturated conditions.(A) Plot representing the number of counts performed by the APD detector increasing the flux of photons (a low power green diode was used as a light source). The data is well fitted by a exponential curve (R²=0.96; red line). The detection starts to be highly non-linear after 75 counts in 15 µs (black dotted rectangle). (B) Histogram of intensity distribution from 10representative imaging sessions (30x20x3 μm maximum intensity projections, containing 6 timepoints each, pulled together acquired with a 15 μs dwell time). The inset shows the expanded y-axis scale showing that less than 0.3% of the pixels are detected non-linearly.

Figure 17 :

 17 Figure 17: The FWHM measurement does not depend on the intensity of the signal. (A) STED images from the same axon stretch acquired with high and low excitation power in a living sample. The scale of pixel intensities is represented in the top right corner. (B) Comparison of the FWHM measurement along the axon stretch shown in A. The two profiles are very similar and highlight the independence of the measurement from the fluorescence intensity of the structure. The slight differences observed denote the dynamic fluctuations of the structure.

Figure 18 :

 18 Figure 18: Geometric ratio measurement on the proximal axon tree. (a) Confocal image of a GFP-labeled CA3 pyramidal neuron by single-cell Sindbis-GFP viral infection. The axon branches extensively and contacts local CA3 neurons (axon around the dendritic tree) and CA1 neurons (extensions on the right part of the image). (b) Tracing of the proximal part of the axon and STED image corresponding to the region shown in the schematic (red square). Axon diameters and calculated geometric ratio (GR) are shown. The arrow indicated the direction of orthodromic AP propagation. (c) GR ratio as a function of the mother branch diameter. (d) GR ratio as a function of the branch point order.

  5 mm cross sectional diameter and can conduct AP at 25 m/s. Myelination, specific to vertebrates, insulate axons and ensure fast propagation through saltatory conduction. None of those strategies are used by CA3 axons in the hippocampus where axon diameters range around 200 nm and myelination is absent (Ishizuka et al, 1990; Meeks et al, 2005; Shepherd & Harris, 1998; Soleng et al, 2003a; Westrum & Blackstad, 1962). Hence, APs are conducted slowly, increasing the importance of the topological organization of the synaptic targets which will receive the information with a variable temporal delay. Do the differences in axonal latencies influence hippocampal function? First, regarding that some hippocampal rhythms such as gamma (20-70 Hz) and ripples waves (140-200 Hz) are very fast, the synchronization within a millisecond might be important. Gamma oscillations are known to be important for exploratory behaviour and sharp wave ripples play a role in memory consolidation during rest. Those network rhythms have to be extremely precise and utterly depend on neuronal connectivity, therefore axonal delays could substantially modify those oscillation patterns. Second and partially related to the first argument, few milliseconds difference may be critical in the context of disynaptic inhibitory signals. Third, in the context of STDP, excitatory synapses are either potentiated or depressed in a time window of 10-20 ms which reflects the maximal supralinear calcium summation between dendritic spike and synaptic event.

(

  Li et al, 2004; Pina-Crespo & Gibb, 2002; Siegel et al, 1994), we can hypothesize that the blockade of axonal NMDA receptors during HFS could either reduce axonal membrane excitability.

  could estimate a depletion of about 20-30 vesicles in average per bouton. This difference with the study from Bourne et al. might be due to the type of preparation and stimulation employed therefore giving different probability of vesicular release during HFS and bulk endocytosis mechanisms following exocytosis (Bourne et al, 2013).

Figure 19 :

 19 Figure 19: Proposed mechanism of axonal diameter enlargement.High-frequency stimulation of axons promotes the exocytosis of neurotransmitter release inthe presynaptic element leading to an increase in the size of the bouton. This makes the overall axonal structure more irregular hence slowing down AP conduction velocity. The excess of membrane in boutons subsequently diffuses in the adjacent axon shaft enlarging its cross sectional diameter concomitantly with LTP induction. In consequence, larger axon diameter and fewer irregularities lead to faster propagation of APs.

  37 m/s (Meeks et al, 2005); 0.2 m/s (Soleng et al, 2003b)) because there are thin, irregular and unmyelinated ((Ishizuka et al, 1990; Meeks et al, 2005; Shepherd & Harris, 1998; Soleng et al, 2003a; Westrum & Blackstad, 1962). In addition, an in vivo reconstruction of a full CA3 axon arborisation in the rat revealed that some of its collaterals can extend up to 20 mm (Wittner et al, 2007).

Figure 20 :

 20 Figure 20: Hippocampal axons may serve as dynamic delay lines for information transfer.The activity-dependent modulation of axonal geometry leading to a change in conduction delay could represent a novel type of plasticity whereby axons could control delays of transmission impacting several important functions in the hippocampus.

  of the AIS to promote AP initiation, the proximal Nav1.2 channels contribute to AP back-propagation at the soma and dendrites[START_REF] Hu | Distinct contributions of Na(v)1.6 and Na(v)1.2 in action potential initiation and backpropagation[END_REF]). In the same way, Kv channels are distributed at high densities in the AIS. In layer 5 of the cortex and in CA3

	pyramidal cells, Kv1.1 and 1.2 are mainly located distally, together with Nav1.6 (Lorincz &
	Nusser, 2008). Other neuron types have different Kv1 subunit distribution and even though it
	is known that Kv1.1 and 1.2 have different kinetics (Grissmer et al, 1994) it remains unclear
	how the difference in Kv subunit composition affects AIS function. In addition, Kv7.3 and

; Moore et al, 1983; Rapp et al, 1996) resulting in a boost of inward sodium current that initiates the AP. The structural organization of the AIS is very different from the rest of the axon. Electron microscopy observations indicated several specific features of AIS. The AIS is rich in microtubule bundles and their membrane is rich in proteins similar to what was observed in the nodes of Ranvier of myelinated fibers (Bender & Trussell, 2012; Palay et al, 1968). Later, electrophysiological and immunocytochemical techniques provided evidence for a specific arrangement of Na + , K + and Ca 2+ channels that determines action potential generation and shape. Indeed, the distribution of Nav channel subtypes in the AIS is highly polarized. Whereas dense clusters of fast activating and fast inactivating Nav1.6 channels are located at the distal part Kv7.4 are also present in the AIS of CA3 and CA1 pyramidal neurons and were shown to play a critical role controlling the resting membrane potential and action potential threshold (Pan et al, 2001; Shah et al, 2002; Shah et al, 2008; Yue & Yaari, 2006). More recently, Bender et al., reported the presence of Cav channels in the AIS and demonstrated their implication in AP initiation and control of AP firing pattern (Bender et al, 2010; Bender & Trussell, 2009; Bender et al, 2012).

Initial segments also contain high concentration of GABA A receptors

[START_REF] Brunig | Intact sorting, targeting, and clustering of gamma-aminobutyric acid A receptor subtypes in hippocampal neurons in vitro[END_REF]

  1,2 1 Interdisciplinary Institute for Neuroscience (IINS), Université de Bordeaux, France 2 UMR 5297, Centre National de la Recherche Scientifique (CNRS), Bordeaux, France 3 Centre de Neurosciences Intégratives et Cognitives, CNRS-UMR 5228 et Université de

	Bordeaux, France
	Running Title: Axon plasticity regulates velocity of action potentials

Acknowledgments V Acknowledgements This work was conducted at the Interdisciplinary Institute for Neuroscience (UMR 5297 CNRS) in Bordeaux in the group of Prof. U. Valentin Nägerl from October 2010 until June 2014.

First of all I would like to thank the committee members for the evaluation of this work, Dr. Dominique Debanne and Prof. Juan Burrone for their judgment, Dr. Andreas Frick and Prof.

Peter Kind for their examination and Dr. Stéphane Oliet for being the chair of the defense.

PhD fellowship from the Conseil Region Aquitaine (3 years) PhD extension fellowship from the Fondation Recherche Médicale (FRM) (9 months

Image acquisition

The parameters of acquisition were originally defined so that neither apparent photodamage nor excessive photobleaching was detected over the time course of the experiment. All the image acquisitions were performed with an excitation power of 4-6 µW and a STED power of ~8 mW (objective back aperture measurements). The images stacks were acquired with a voxel size of 19.5 nm (xy); 375 nm (z) and dwell time of 15 µs, unless stated otherwise.

Imaging depths into the slice, determined by the z-piezo focus, the fluorescence on top of the slice defining the zero z-position, was ranging between 5-15 µm. For the plasticity experiments, an area containing multiple and well separated axon stretches was selected. Zstacks of 30x20x3µm (x, y and z dimensions respectively) were acquired every ~10 min for 1 hour. Two acquisitions were performed before the stimulus and four after.

Image analysis

Images were exported from the IMSpector software into an 8-bit tiff file format. We used NIH ImageJ for processing the acquisitions. Image analysis was done on raw data and images presented in the figures were filtered by a 1-pixel median filter to reduce noise. A screening by visual inspection was performed and only the signal of the axon stretches that were fully contained into the volume of acquisition at all time points was selected for the morphometric analysis. A maximum intensity projection was performed on the regions of interest. To realize the automated morphometric measurement, a reference image that consist of a line of pixels running along the axon stretch was produced by first, thresholding and binarize the picture, then we used the skeletonize plugin from ImageJ. A custom written Matlab program was used to automatically measure the FWHM along the axon image using the reference image that determines the position of the measurement. At every position, it automatically estimates the best tangential fit and plots the intensity profile from its orthogonal. To reduce ABSTRACT Precise timing of electrical signalling is critically important for many kinds of computations performed by neural circuits, such as action potential firing, spike-timing dependent synaptic plasticity and temporal coding of sensory inputs.

The transmission of APs over unmyelinated axons is an inherently slow process, which causes major time delays for synaptic communication, taking up to hundreds of milliseconds.

While it is clear that travel distance and morphological properties of the axon largely set this conduction delay, very little is known about whether and how it may be physiologically regulated.

We combined time-lapse superresolution stimulated emission depletion (STED) microscopy with electrophysiology and computer simulations to investigate the relationship between axon morphology and AP conduction in CA3 pyramidal neurons in living mouse organotypic hippocampal brain slices.

Our study reveals that axon morphology, which is very heterogeneous, is largely stable under baseline conditions. By contrast, after the induction of LTP in the CA3-CA1 synaptic pathway we observed remodelling of presynaptic boutons and axon shafts that correlates with bi-directional changes in AP conduction velocity measured by patch clamp recordings and predicted by biophysical modeling.

Our findings indicate that AP propagation delay is regulated by activity-driven changes in axon morphology, suggesting a novel structural mechanism for fine-tuning the timing of information transfer in neural circuits.

Functional implications for neural timing

The changes in AP propagation delay during LTP were recorded over relatively short distances, and hence amounted to just a couple of hundreds of microseconds. However, if axon widening affects AP conduction uniformly along the axon, the reduction of AP propagation delay should scale with the length of the axons. Given that CA3 axons can be as long as 20 mm in vivo in rats 24 , the AP propagation delay for distal synapses would build up to several tens of milliseconds, which would be expected to strongly impact synaptic integration in the postsynaptic neurons.

What is the functional significance of variations in axonal delays for network performance? Propagation delays could be important in the context of spike-timing dependent plasticity (STDP). The time window for supralinear summation of calcium caused by dendritic spikes and synaptic events is on the milliseconds scale and determines whether synapses get potentiated or depressed. Given that STDP might be responsible for the formation of synchronized groups of neurons that are strongly interconnected, slight variations in propagation delays could remodel those poly-synchronous groups 25 . Variations in delay at excitatory synapses may also produce substantial changes in the temporal integration by changing the balance during di-synaptic inhibition and therefore may change the output properties.

Several studies have indicated that CA3 axons, known to branch extensively 24, 26 do not propagate APs reliably throughout their complex arbor and might exhibit failures at branch points under certain conditions 27-29 . The enlargement of axon shafts may affect the reliability of AP propagation by altering the impedance mismatch at branch points.

Part 2: Development of two-photon excitation STED microscopy in two colors in acute brain slices

Aim of the study:

To understand how neural cells shape and react in physiological and pathological conditions, it is necessary to observe them in the most intact preparation. STED microscopy enables for observing nanoscale dynamics of cellular morphology and organelles where conventional light microscopy failed to resolved them. However, the first developments of STED microscopy were based on single photon excitation thus limiting observations to superficial structures in dissociated cultures and organotypic brain slices. On the other hand, two-photon microscopy is currently the method of choice for imaging in thick living tissue preparations, both in acute brain slices and in vivo. As a conventional light microscopy method, the spatial resolution of a two-photon microscope is limited to ~350 nm by the diffraction of light, hence missing important structural details like spine and axon morphological features.

We aimed to develop a 2-photon excitation STED depletion microscope providing unprecedented spatial resolution and excellent experimental access in acute brain slices.

Results:

We built a new microscope based on two-photon excitation and pulsed stimulated depletion.

Its versatility allows for imaging the classical green fluorophores such as GFP, YFP and Alexa488. We illustrate the potential of the microscope for resolving thin brain structures such as dendritic spines, axons and microglia processes in acute brain slices at more than 50µm from the surface. We also show the potential for two colors superresolution imaging using linear unmixing. Its upright design and the long-working distance water dipping

APPENDIX

The following pages correspond to the algorithm written in Matlab used for the automated analysis of the axon diameters.

It consists in a main program called 'axomorph' and a series of functions used in this program.

The figure next page illustrates how the automatic measurement is performed by the program.

From the image of an axon stretch, a reference line of pixels corresponding to the center of the axon stretch (or skeleton) is generated using ImageJ or the home-made function 'refcreator' (A). In order to realize the measure of the cross section diameter, it is necessary to find the best orthogonal line at every position. Therefore, for every position (pixel of the reference line) a linear fit is performed based on a group of pixels around the position. Then, the orthogonal line passing thru the pixel position is calculated (B). The pixel coordinates of the orthogonal line are used to collect the intensity values of the axon cross section for the position and built the Gaussian-like intensity profile (C). From this, the FWHM value is extracted by detecting the edges of the curve at 50 % the maximum. The maximum is defined as the average of the three brightest pixels. Then the measurement is reported for the position and repeated for the next pixel of the reference line (D). %% Function that plots the FWHM of an axon at any given section. The x-axis % is in µm and the y-axis is in nm. %%%%%% Ronan Chéreau %%%%%%% REVISION: November 29, 2012 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %INPUTS: axoimage = the real image containing the axon to be measured % ref = reference line going thru the center of the axon (usually a skeletonization of the axon in imagej) % pixsizenm = enter the value of the pixel size resolution of the picture (assuming that the pixel is not rectangular) % (auto defined) lfitvector = number of pixels used to make the linear fit at every section % (auto defined) limplot = number of pixels value from the axoimage to plot at every step % linewitdh = width of the line in pixels % nf = noise filter: allow the user to choose the number of data % points to average in order to smoothen the plot % flip = if you want to inverse the data, flip=1 % visual = if you want to visualize the measurement process,visual=1 % %OUTPUTS: %

In the figure: show the original axon image; the reference line; % the plot of all the raw data collected; the linear transformation % of the axon and the plot of the calculated FWHM over the distance. %The idea of this is to avoid mistakes for complex forms of axons where in %an extreme case, it would make loop, therefore in this case the find %function is not strong enough %detect the succession of pixels in a line %The first part is to identify one end of the line by screening the binary %matrix %The second part collect the pixels in a new matrix going from one end to %the other %Made for axomorph %The contour of the image has to be zero in order the the program to not %look at the neighbor outside of the picture. And also to make sure that %there was no weired processing that gives a contour line on the image. binref=binref>0; size_mat=size(binref); binref(1,:)=0; binref(:,1)=0; binref(size_mat(1),:)=0; binref(:,size_mat(2))=0; %since I'm going to erase the values to find one end of the line, I have to %duplicate the matrix. binref1=binref; %%%%1st part: take the coordinates of any pixel of the line%%%% [xlin,ylin]=ind2sub(size(binref),find(binref)); %find(binref) returns only the pixels containing a 1 %ind2sub use the size of the matrix to transform the values in x,y %coordinates because by default it gives % 1 position value per pixel (i.e. 2050 > (50,20)) x=xlin(1); y=ylin(1); %this returns the coordinates of the first pixel in the %find list pixel which is not necessarily the first of the line %%%%%2nd part: finding the pixel coordinates of one of the 2 end of the %%%%%line. It's screening the positive pixels in the neighourhood, and %%%%%since we want to go over all the pixels, it's looking first in %%%%%horizontal, then vertical, then both diagonals. Horizontal and %%%%%vertical have the priority because in some cases one pixel can have 2 %%%%%postives neighbours. for i=1:size