The topic of this dissertation is the study of the emergence of higher-order correlations in recurrentlyconnected populations of brain cells.Neurons have been experimentally shown to form vast networks in the brain. In these networks, eachbrain cell communicates with tens of thousands of its neighbors by sending out and receiving electricalsignals, known as action potentials or spikes. The effect of a single action potential can propagate throughthe network and cause additional spikes to be generated. Thus, the connectivity of the neuronal networkgreatly influences the network's spiking dynamics. However, while the methods of action potentialgeneration are very well studied, many dynamical features of neuronal networks are still only vaguelyunderstood.The reasons for this mostly have to do with the difficulties of keeping track of the collective, non-linearbehavior of hundreds of millions of brain cells. Even when one focuses on small groups of neurons, all butthe most trivial questions about coordinated activity remain unanswered, due to the combinatorialexplosion that arises in all questions of this sort. In theoretical neuroscience one often needs to resort tomathematical models that try to explain the most important dynamical phenomena while abstractingaway many of the morphological features of real neurons.On the other hand, advances in experimental methods are making simultaneous recording of largeneuronal populations possible. Datasets consisting of collective spike trains of thousands of neurons arebecoming available. With these new developments comes the possibility of finally understanding the wayin which connectivity gives rise to the many interesting dynamical aspects of spiking networks.The main research question, addressed in this thesis, is how connectivity between neurons influences thedegree of synchrony between their respective spike trains. Using a linear model of spiking neurondynamics, we show that there is a mathematical relationship between the network's connectivity and theso-called higher-order cumulants, which quantify beyond-chance-level coordinated activity of groups ofneurons. Our equations describe the specific connectivity patterns that give rise to higher-ordercorrelations. In addition, we explore the special case of correlations of third-order and find that, in large,regular networks, it is the presence of a single subtree that is responsible for third-order synchrony.In summary, the results presented in this dissertation advance our understanding of how higher-ordercorrelations between spike trains of neurons are affected by certain patterns in synaptic connectivity.Our hope is that a better understanding of such complicated neuronal dynamics can lead to a consistenttheory of the network's functional properties. / <p>QC 20161003</p>

Effective movement is central to survival and it is essential for all animals to react in response to changes around them. In many animals the rhythmic signals that drive locomotion are generated intrinsically by small networks of neurons in the nervous system which can be switched on and off. In this thesis I use a very simple animal, in which the behaviours and neuronal networks have been well characterised experimentally, to explore the salient features of such networks. Two days after hatching, tadpoles of the frog Xenopus laevis respond to a brief touch to the head by starting to swim. The swimming rhythm is driven by a small population of electrically coupled brainstem neurons (called dINs) on each side of the tadpole. These neurons also receive synaptic input following head skin stimulation. I build biophysical computational models of these neurons based on experimental data in order to address questions about the effects of electrical coupling, synaptic feedback excitation and initiation pathways. My aim is better understanding of how swimming activity is initiated and sustained in the tadpole. I find that the electrical coupling between the dINs causes their firing properties to be modulated. This allows two experimental observations to be reconciled: that a dIN only fires a single action potential in response to step current injections but the population fires like pacemakers during swimming. I build on this hypothesis and show that long-lasting, excitatory feedback within the population of dINs allows rhythmic pacemaker activity to be sustained in one side of the nervous system. This activity can be switched on and off at short latency in response to biologically realistic synaptic input. I further investigate models of synaptic input from a defined swim initiation pathway and show that electrical coupling causes a population of dINs to be recruited to fire either as a group or not at all. This allows the animal to convert continuously varying sensory stimuli into a discrete decision. Finally I find that it is difficult to reliably start swimming-like activity in the tadpole model using simple, short-latency, symmetrical initiation pathways but that by using more complex, asymmetrical, neuronal-pathways to each side of the body, consistent with experimental observations, the initiation of swimming is more robust. Throughout this work, I make testable predictions about the population of brainstem neurons and also describe where more experimental data is needed. In order to manage the parameters and simulations, I present prototype libraries to build and manage these biophysical model networks.

Traveling wave solutions of integro-differential equations for modeling one-dimensional neuronal networks, are studied. Under moderate continuity assumptions, necessary and sufficient conditions for the existence and uniqueness of monotone increasing (decreasing) traveling wave solutions are established. Some faults in previous studies are corrected.

Networks at various levels of the nervous system coordinate different motor patterns such as respiration, eye or hand movements and locomotion. Intrinsic rhythm-generating networks that are located in the spinal cord generate motor behaviors that underlie locomotion in vertebrates. These networks give a continuous and measurable coordinated rhythmic motor output and are referred to as locomotor central pattern generators (CPGs). Characterization of the mammalian locomotor CPG and its molecular control is depending on the identification of participating neurons and neuronal populations. In this thesis I present work where we have studied the significance of subpopulations of neurons in the formation and function of the left-right circuitry. In summary, we show that the axon guidance receptor DCC has a central role in the formation of spinal neuronal circuitry underlying left-right coordination, and that both Netrin-1 and DCC are required for normal function of the locomotor CPG. Commissural interneurons (CINs), which send their axons across the ventral midline in the spinal cord, play a critical role in left–right coordination during locomotion. A complete loss of commissural axons in the spinal cord, as seen in the Robo3 null mutant mouse, resulted in uncoordinated fictional locomotor activity. Removing CIN connections from either dorsal or ventral neuronal populations led to a shift from alternation to strict synchronous locomotor activity. Inhibitory dI6 CIN have been suggested as promising candidate neurons in coordinating bilateral alternation circuitry. We have identified that Dmrt3, expressed in inhibitory dI6 CINs, is a crucial component for the normal development of coordinated locomotor movements in both horses and mice. We have also concluded that the prominent hopping phenotype seen in hop/hop mice is a result of abnormal developmental processes including induction from the notochord and Shh signaling. Together, these findings increase our knowledge about the flexibility in neuronal circuit development and further confirm the role of dI6 neurons in locomotor circuits.

Traveling wave solutions of integro-differential equations for modeling one-dimensional neuronal networks, are studied. Under moderate continuity assumptions, necessary and sufficient conditions for the existence and uniqueness of monotone increasing (decreasing) traveling wave solutions are established. Some faults in previous studies are corrected.

Graph theoretical approaches have become a powerful tool for investigating the architecture and dynamics of complex networks. The topology of network graphs revealed small-world properties for very different real systems among these neuronal networks. In this study, we observed the early development of mouse retinal ganglion cell (RGC) networks in vitro using timelapse video microscopy. By means of a time-resolved graph theoretical analysis of the connectivity, shortest path length and the edge length, we were able to discover the different stages during the network formation. Starting from single cells, at the first stage neurons connected to each other ending up in a network with maximum complexity. In the further course, we observed a simplification of the network which manifested in a change of relevant network parameters such as the minimization of the path length. Moreover, we found that RGC networks self-organized as small-world networks at both stages; however, the optimization occurred only in the second stage.

Low intensity and low frequency ultrasound has been shown to modulate ion channel currents, membrane capacitive currents, and as a result, neuronal activity. Ultrasound has been used as a non-invasive way to modulate neuronal activity in vivo using mice as well as human subjects. Ultrasound with acoustic frequency as low as 0.35 MHz can be focussed on a region as small as 2 mm with reversible effects and no increase in temperature. In this study, two ultrasound transducers with different resonant frequency have been used to excite neuronal cultures. The resulting changes in the network properties such as synchronised network burst frequency, density, clustering and path length have been analysed. The study shows that ultrasound stimulation at acoustic frequency 450 kHz (ISPPA =11.3 mW/cm2) significantly modulates the above mentioned parameters and causes deviations from small world network properties of the control network.

La respiration est une activité motrice autonome rythmique au cours de laquelle de nombreux muscles se contractent de manière coordonnée afin de produire des mouvements ventilatoires adaptés aux contraintes environnementales et aux exigences de l'organisme. Cette fonction vitale doit être fiable et adaptable à très court terme, c’est pourquoi elle est influencée, entre autres, par un grand nombre d’activités motrices. Par exemple, lors d’exercices physiques, le rythme respiratoire peut se coupler au rythme locomoteur. Les objectifs de ce travail doctoral sont centrés sur l’exploration des mécanismes neurogènes à la base du couplage entre ces deux fonctions motrices chez le rat nouveau-né. Pour une grande partie, cette étude a été réalisée sur préparation isolée in vitro de tronc cérébral-moelle épinière de rat nouveau-né (0 à 3 jours), ce modèle permettant de conserver dans leur intégrité les centres responsables des rythmes respiratoire et locomoteur. Compte tenu de l’accessibilité directe aux réseaux neuronaux, les mécanismes de couplage et d'entraînement respiratoire ont été abordés par des approches combinées électrophysiologique, neuroanatomique, pharmacologique et lésionnelle. Dans ce contexte, un des principaux résultats de ce travail doctoral est le rôle crucial joué par les informations sensorielles en provenance des membres antérieurs et postérieurs dans l'entraînement respiratoire observé lors de séquences locomotrices. Ainsi, les afférences proprioceptives spinales capables de réinitialiser et d'entraîner l’activité des centres respiratoires bulbaires via un relais pontique, établissent également des connexions sur l’ensemble des populations de motoneurones spinaux respiratoires phréniques, intercostaux et abdominaux. / Respiration is an autonomous rhythmic motor activity that requires the coordinated contractions of diverse muscles to produce ventilatory movements adapted to organismal needs. This crucial physiological function must be reliable and adaptable on a short-term basis, and requires coordianted movements with various other motor activities. For instance, respiratory rhythmicity becomes coupled to locomotion during physical exercise. My doctoral work aimed to explore the neurogenic mechanisms underlying the interactions between these two motor functions in the neonatal rat. This work was mainly conducted on isolated in vitro brain stem-spinal cord preparations of newborn rats (0-3 days), an experimental model that allows the maintenance of the still functional respiratory and locomotor CPGs in vitro. Due to the easy access to the neuronal networks in these preparations, locomotor-respiratory coupling and respiratory entrainment mechanisms were investigated by combined electrophysiological, neuroanatomical, pharmacological and lesional approaches. A major finding was the crucial played by sensory information from fore- and hindlimb in respiratory entrainment induced by locomotor rythmicity. Spinal sensory afferents can reset and entrain the activity of the medullary respiratory centres via a pontine relay, as well as making direct connections with the various spinal respiratory motoneuron (phrenic, intercostal and abdominal) populations.

Glutamate is the essential neurotransmitters in pain pathways. The discovery of the vesicular glutamate transporters (VGLUT1-3) has been a fundamental step on the way to describe glutamate-dependent pain pathways. We used the Cre-lox system to construct conditional knockouts with deficient Vglut2 transmission in specific neuronal populations. We generated a Vglut2f/f;Ht-Pa-Cre line to selectively delete Vglut2 from the peripheral nervous system. These Vglut2 deficient mice showed decreased acute nociceptive responses and were less prone to develop an inflammatory state. They did not develop cold allodynia, or heat hyperalgesia and were less hypersensitive to mechanical stimuli in the PSNL chronic pain model. Further analyses of genes with altered expression after nerve injury, revealed candidates for future studies of chronic pain biomarkers. Interestingly, the Vglut2f/f;Ht-Pa-Cre mice developed an elevated itch behavior. To investigate more specific neuronal populations, we analyzed mice lacking Vglut2 in the Nav1.8 population, as inflammatory hyperalgesia, cold pain, and noxious mechanosensation have been shown to depend upon Nav1.8Cre positive sensory neurons. We showed that deleting Vglut2 in Nav1.8Cre positive neurons abolished thermal hyperalgesia in persistent inflammatory models and responses to noxious mechanical stimuli. We also demonstrated that substance P and VGLUT2-dependent glutamatergic transmission are co-required for the development of formalin-induced inflammatory pain and heat hyperalgesia in persistent inflammatory states. Deletion of Vglut2 in a subpopulation of neurons overlapping with the vanilloid receptor (TRPV1) primary afferents in the dorsal root ganglia resulted in a dramatic increase in itch behavior accompanied by a reduced responsiveness to thermal pain. Substance P signaling and VGLUT2-mediated glutamatergic transmission in TRPV1 neurons was co-required for the development of inflammatory pain states. Analyses of an itch phenotype uncovered the pathway within TRPV1 neurons, with VGLUT2 playing a regulatory role and GRPR neurons, which are to plausible converge the itch signal in the spinal cord. These studies confirmed the essential role of VGLUT2-dependent glutamatergic transmission in acute and persistent pain states and identified the roles of specific subpopulations of primary afferent neurons. Additionally, a novel pain and itch transmission pathway in TRPV1/VGLUT2 positive neurons was identified, which could be part of the gate control of pain.

La perception de la douleur résulte de l'intégration dans la moelle épinière des informations sensorielles et nociceptives transmises par les afférences primaires. Parmi celles-ci, les Mechanorécepteurs C à bas seuil (C-LTMR), exprimant la chimiokine TAFA4, ont été identifiés comme des modulateurs de la douleur. Cependant, les mécanismes sous-jacents au contrôle de l'intégration sensori-nociceptive par TAFA4 restent mal compris. Grâce aux enregistrements obtenus in vitro par patch clamp chez des souris naïves, nous montrons que l'application exogène de TAFA4 induit une diminution de la fréquence des courants post-synaptiques excitateurs spontanés (CPSE). A l’inverse nous observons une augmentation de la fréquence des événements synaptiques inhibiteurs spontanés (CPSI). Cette modulation de l'activité synaptique est préservée avec TTX, indiquant que TAFA4 modifie la transmission synaptique par des mécanismes présynaptiques. En stimulant les fibres nociceptives à haut seuil d’activation, nous démontrons que TAFA4 induit une augmentation du ratio des réponses synaptiques des interneurones évoquées par des stimulations d’impulsions pairées. Par conséquent, TAFA4 renforce l'inhibition présynaptique des fibres nociceptives. Nous démontrons également que les effets de TAFA4 sur la transmission excitatrice spontanée et évoquée sont bloqués par des antagonistes des récepteurs GABA, indiquant que les C-LTMRs interagissent principalement avec les neurones GABAergiques. De plus, des expériences de microscopie électronique ont révélé la présence de contacts synaptiques directs entre les C-LTMRs et les terminaisons GABAergiques dans la lamina IIi. Pour aller plus loin dans la caractérisation des effets de TAFA4 sur la transmission de la douleur, nous avons induit une inflammation de la patte arrière des souris (modèle CFA). Chez ces souris, l'effet de TAFA4 sur la fréquence EPSC et IPSC est conservé. Nous constatons que chez les souris CFA, TAFA4 diminue la décharge neuronale enregistrée in vivo suite à une stimulation mécanique nociceptive de la patte inflammée. Cet effet est bloqué par une injection d'antagonistes des récepteurs GABA. En effectuant le test Von Frey sur des souris inflammées, nous montrons que l’action anti-allodynique induite par l'injection intrathécale de TAFA4 est bloquée par les antagonistes des récepteurs GABA. Nous avançons l’hypothèse que les C-LTMRs contactent directement les interneurones GABAergiques de la corne dorsale et, via la libération de TAFA4, renforcent l'activité synaptique inhibitrice participant à l’effet anti-nociceptif de TAFA4. En outre, TAFA4 favorise la rétraction microgliale chez les animaux inflammés, ainsi qu'une augmentation du nombre de synapses inhibitrices sur les somas des neurones de la lamina IIi. En conclusion, ces résultats identifient les interneurones GABAergiques comme premier relais d'intégration pour les C-LTMRs et mettent en évidence une nouvelle interaction entre les neurones sensoriels, les cellules microgliales et les interneurones de la moelle épinière, permettant une modulation fine de l'activité inhibitrice et de la transmission nociceptive en situation pathologique. / Pain elaboration results from the integration within dorsal spinal cord of sensory and nociceptive information conveyed by primary afferents. Among these, C low-threshold Mechano Receptors (C-LTMR), expressing the chemokine TAFA4, were identified as modulators of pain. However, mechanisms underlying the control of sensori-nociceptive integration by TAFA4 remains poorly understood. Using in vitro patch clamp recording on spinal cord slices of naïve mice we show that, bath application of TAFA4 induces a decrease in frequency of spontaneous excitatory post synaptic currents (EPSCs). This effect is mirrored by an increase in frequency of spontaneous inhibitory synaptic events (IPSCs). This modulation of synaptic activity is preserved with TTX, indicating that TAFA4 alters synaptic transmission through presynaptic mechanisms. By recruiting high threshold nociceptive fibers, we demonstrate that TAFA4 induces an increase in the paired pulse ratio of evoked synaptic responses in interneurons, and thus, reinforces presynaptic inhibition of nociceptive fibers. We also demonstrate that the effects of TAFA4 on spontaneous and evoked excitatory transmission are blocked by antagonists of GABA receptors, indicating that -C-LTMRs mainly interact with GABAergic neurons. Moreover, Electron Microscopy provides evidence of direct synaptic contacts between C-LTMRs and GABAergic terminals in lamina IIi. To further characterize the effects of TAFA4 on pain transmission, we inflamed mice using Complete Freund Adjuvant (CFA). In CFA mice, the effect of TAFA4 on EPSC and IPSC frequency is preserved. We find that in CFA mice, TAFA4 decreases the neuronal discharge recorded in vivo following a nociceptive mechanical stimulation in inflamed hindpaw. This effect is blocked by an injection of GABA receptors antagonists. By performing Von Frey test on inflamed mice, we show that intrathecal injection of TAFA4 provides anti-allodynic effects blocked by GABA receptors antagonists. We propose that C-LTMR directly contact GABAergic interneurons in dorsal horn, and, through the liberation of TAFA4 reinforce inhibitory synaptic activity which may in turn promote their anti-nociceptive activity. Furthermore, TAFA4 promotes microglial retraction in CFA inflamed animals, together with an increase in the number of inhibitory synapses on lamina IIi somata. Altogether, these results identify GABAergic interneurons as the first integration relay for C-LTMRs and highlight a novel interplay between sensory neurons, microglial cells and spinal interneurons leading to a fine tuning of inhibitory activity and nociceptive transmission in pathological conditions.