,
, , p.20
22 Saturated calmodulin production 22 Binding of calmodulin to SK terminals 23 Calcium concentration, 23 Calcium concentration dynamics. . . . . . . . . . . . . . . 23 ,
, Full set of equations for the single SAC dynamics, p.25
, , p.25
, , p.25
25 Calibrating parameters from experiments, p.26 ,
, , p.26
, , p.26
, , p.26
28 Slow-fast analysis 28 Dynamical changes with respect to parameters variations. 28 Dynamically driven bursting, 29 Robustness with respect to parameters variations. . . . . 33 CONTENTS Fast dynamics of V, p.111 ,
, , p.112
, , p.112
, , p.112
, , p.113
, , p.113
, , p.113
, , p.113
, , p.114
114 Singular diffusion, p.114 ,
, , p.115
115 Single neuron dynamics in the presence of a tunable sAHP and Ach currents, p.115 ,
, Confronting our model to experimental recordings 119
, The role of potassium channels in waves characteristics, p.119
Exploring the effect of the cholinergic transmission on the spatio-temporal patterns of stage II retinal waves, p.125 ,
, , p.125
, , p.125
125 Recordings of retinal waves with MEA of 256 electrodes . 125 Analysis of the MEA recordings, p.125 ,
, The effect of hexametonium in early stage II retinal waves, p.126
, The effect of atropine in early stage II retinal waves, p.129
, , p.133
, , p.134
, 7 Conclusions and Perspectives 137
137 Synaptic coupling versus volume diffusion, p.137 ,
The role of variability in SACs on waves generation. . . . 138 Extending our model towards a generic dynamical system for retinal waves, p.139 ,
, Can we use retinal waves to restore plasticity in pathological retinas, p.139
Cessac A biophysical model explains the spontaneous bursting behavior in the developing retina Nature Scientific Reports, under review, 2018. ,
, Cessac Following stage II retinal waves with a biophysical model Bernstein Conference, p.2017
Cessac Mathematical and experimental studies of retinal waves ICMNS Conference, selected talk, 2016. ,
A Unique Role for Kv3 Voltage-Gated Potassium Channels in Starburst Amacrine Cell Signaling in Mouse Retina, Journal of Neuroscience, vol.24, issue.33, pp.337335-7343, 2004. ,
DOI : 10.1523/JNEUROSCI.1275-04.2004
The spikes trains probability distributions: A stochastic calculus approach, Journal of Physiology-Paris, vol.101, issue.1-3 ,
DOI : 10.1016/j.jphysparis.2007.10.008
,
Mechanisms and circuitry underlying directional selectivity in the retina, Nature, 2002. ,
Bifurcations in Morris???Lecar neuron model, Neurocomputing, vol.69, issue.4-6, pp.293-316, 2006. ,
DOI : 10.1016/j.neucom.2005.03.006
Variability, compensation and homeostasis in neuron and network function, Nature Reviews Neuroscience, vol.15, issue.7, pp.563-574, 2006. ,
DOI : 10.1016/j.neuint.2005.12.029
Retinal Wave Patterns Are Governed by Mutual Excitation among Starburst Amacrine Cells and Drive the Refinement and Maintenance of Visual Circuits, The Journal of Neuroscience, vol.36, issue.13, pp.36-3871, 2016. ,
DOI : 10.1523/JNEUROSCI.3549-15.2016
Retinal waves: mechanisms and function in visual system development Cell Calcium, 2004. ,
Relationships between intracellular neocortical pyramidal neurons calcium and afterhyperpolarizations in neocortical pyramidal neurons, J Neurophysiol, 2004. ,
A Reaction-Diffusion Model of Cholinergic Retinal Waves, PLoS Computational Biology, vol.19, issue.12, pp.1-14, 2014. ,
DOI : 10.1371/journal.pcbi.1003953.s006
Voltage oscillations in the barnacle giant muscle fiber, Biophysical Journal, vol.35, issue.1, pp.193-213, 1981. ,
DOI : 10.1016/S0006-3495(81)84782-0
,
Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality, Phys. Rev. E, vol.64, p.16133, 2001. ,
Coordinated Transitions in Neurotransmitter Systems for the Initiation and Propagation of Spontaneous Retinal Waves, The Journal of Neuroscience, vol.20, issue.17, pp.6570-6577, 2000. ,
DOI : 10.1523/JNEUROSCI.20-17-06570.2000
Zhang Dynamic Scaling of Growing Interfaces Phys, Rev. Lett, vol.56, issue.889 3, 1986. ,
noise, Physical Review Letters, vol.13, issue.4, p.381, 1987. ,
DOI : 10.1103/PhysRevB.13.556
Andrade Controlling self-organized criticality in sandpile models, Phys. Rev. E, vol.81, p.15102, 2010. ,
, , 2015.
Pharmacologically induced wave-like activity in the adult retina IOVS, p.2012 ,
The shape and arrangement of the cholinergic neurons in the rabbit retina Proc, 1984. ,
The Brian simulator Front Neurosci, 2009. ,
Full-length axon regeneration in the adult mouse optic nerve and partial recovery of simple visual behaviors, Proceedings of the National Academy of Sciences, vol.45, issue.12 ,
DOI : 10.1167/iovs.04-0541
Phasic acetylcholine release and the volume transmission hypothesis:time to move on, Nature Reviews. Neuroscience, 2009. ,
Smith The role of starburst amacrine cells in visual signal processing Vis Neurosci, 2012. ,
, Exp Eye Res, vol.33, issue.3, pp.315-347, 1981.
Virasoro Spin-glass theory and beyond World scientific Singapore, 1987. ,
, Starburst Amacrine Cells http://wiki.eyewire.org [29] Robert Clewley. Hybrid models and biological model reduction with pydstool, PLoS Computational Biology, 2012.
Cellular Mechanisms Underlying Spatiotemporal Features of Cholinergic Retinal Waves The Journal of Neuroscience, pp.850-863, 2012. ,
t Differential Effects of Acetylcholine and Glutamate Blockade on the Spatiotemporal Dynamics of Retinal Waves, The Journal of Neuroscience, vol.20, issue.2, p.56, 2000. ,
DOI : 10.1523/JNEUROSCI.20-02-j0004.2000
Eglen Homeostatic Activity-Dependent Tuning of Recurrent Networks for Robust Propagation of, Activity The Journal of Neuroscience, vol.20, p.56, 2000. ,
Tresser Transition to topological chaos for circle maps Physica D, 1986. ,
DS Rokhsar Retinal waves are governed by collective network properties, Journal of Neuroscience, vol.1, pp.9-9 ,
Shinichi Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation Phys, Rev. E, vol.82, p.11127, 2010. ,
Dynamic Processes Shape Spatiotemporal Properties of Retinal Waves, Neuron, vol.19, issue.2, pp.293-306, 1997. ,
DOI : 10.1016/S0896-6273(00)80940-X
Abstract, Visual Neuroscience, vol.10, issue.01, pp.61-71 ,
DOI : 10.1016/j.neuron.2010.01.035
URL : https://hal.archives-ouvertes.fr/hal-01375359
Retinal wave behavior through activity-dependent refractory periods, PLoS Comput Biol, vol.3, issue.11, p.245, 2007. ,
, , 2007.
Effect of acetylcholine on postjunctional membrane permeability in eel electroplaque, The Journal of General Physiology, vol.70, issue.1, pp.23-36, 1977. ,
DOI : 10.1085/jgp.70.1.23
Abbott A Model Neuron with Activity- Dependent Conductances Regulated by Multiple Calcium Sensors The Journal of Neuroscience, 1998. ,
Synaptic remodeling generates synchronous oscillations in the degenerated outer mouse retina Front Neural Circuits, 2014. ,
A theory of Plasma Membrane calcium pump function and its consequences for presynaptic calcium dynamics, 2003. ,
A Theory of Plasma Membrane Calcium Pump Stimulation and Activity, Journal of Biological Physics, vol.263, issue.2, pp.183-206, 2005. ,
DOI : 10.1042/bj3310763
Non linear oscillations, dynamical systems, and bifurcation of vector fields, 1983. ,
A forest-fire model and some thoughts on turbulence, Physics Letters A, vol.147, issue.5-6, pp.297-300 ,
DOI : 10.1016/0375-9601(90)90451-S
Self-organized critical forest-fire model, Physical Review Letters, vol.40, issue.11, pp.1629-1632 ,
DOI : 10.1103/PhysRevB.40.7425
Supplementary chapters of the theory of ordinary differential equations, S Nauka, 1978. ,
Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, 2007. ,
Theoretical models of spontaneous activity generation and propagation in the developing retina Molecular BioSystems, 2009. ,
Eglen Modeling developmental patterns of spontaneous activity, Curr Opin Neurobiol, 2011. ,
Characterization of Voltage-Gated Ionic Channels in Cholinergic Amacrine Cells in the Mouse Retina, Journal of Neurophysiology, vol.97, issue.6, 2007. ,
DOI : 10.1073/pnas.93.15.8057
Following the ontogeny of retinal waves: pan-retinal recordings of population dynamics in the neonatal mouse, The Journal of Physiology, vol.20, issue.7, pp.1545-1563, 2014. ,
DOI : 10.1113/jphysiol.2013.262840
Early-Stage Waves in the Retinal Network Emerge Close to a Critical State Transition between Local and Global Functional Connectivity, Journal of Neuroscience, vol.29, issue.4, 2009. ,
DOI : 10.1523/JNEUROSCI.4880-08.2009
Spontaneous Activity in Developing Turtle Retinal Ganglion Cells: Pharmacological Studies, The Journal of Neuroscience, vol.19, issue.10, 1999. ,
DOI : 10.1523/JNEUROSCI.19-10-03874.1999
Retinal Waves, 2012. ,
DOI : 10.1016/B978-0-12-397266-8.00151-4
, James van Coppenhagen, and Evelyne Sernagor Age-dependent Homeostatic Plasticity of GABAergic Signaling in Developing Retinal Networks Journal of Neuroscience, 2011.
MATCONT, ACM Transactions on Mathematical Software, vol.29, issue.2, pp.141-164, 2003. ,
DOI : 10.1145/779359.779362
A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, vol.117, issue.4, pp.500-544, 1952. ,
DOI : 10.1113/jphysiol.1952.sp004764
A Key Role of Starburst Amacrine Cells in Originating Retinal Directional Selectivity and Optokinetic Eye Movement, Neuron, vol.30, issue.3, 2001. ,
DOI : 10.1016/S0896-6273(01)00316-6
Vijverberg Potentiation and Inhibition of Neuronal Nicotinic Receptors by Atropine: Competitive and Noncompetitive Effects Molecular Pharmacology, 1997. ,
DOI : 10.1124/mol.52.5.886
URL : http://molpharm.aspetjournals.org/content/molpharm/52/5/886.full.pdf
A Developmental Switch in the Excitability and Function of the Starburst Network in the Mammalian Retina, Neuron, vol.44, issue.5, pp.851-864, 2004. ,
DOI : 10.1016/j.neuron.2004.11.015
A transient network of intrinsically bursting starburst cells underlies the generation of retinal waves, Nature Neuroscience, vol.94, issue.3, pp.363-371, 2006. ,
DOI : 10.1152/jn.00279.2005
, Nicotinic Cholinergic Receptors in the Rat Retina: Simple and Mixed Heteromeric Subtypes Molecular Pharmacology, pp.1656-1668, 2005.
Leonardo Collaborateur Introduction to the modern theory of dynamical systems, 1995. ,
Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-B??tzinger complex neurons, Journal of Computational Neuroscience, vol.95, issue.4, 2013. ,
DOI : 10.1152/jn.01308.2005
James Sneyd A mathematical model of calcium dynamics in HSY cells PLOS Comp Bio, p.2017 ,
Hermann Riecke Intrinsic bursting of AII amacrine cells underlies oscillations in the rd1 mouse retina, Journal of Neurophysiology, 2014. ,
Dynamics of Spontaneous Activity in the Fetal Macaque Retina during Development of Retinogeniculate Pathways, Journal of Neuroscience, vol.26, issue.19, 2006. ,
DOI : 10.1523/JNEUROSCI.0328-06.2006
Feldheim, Spatial-Temporal Patterns of Retinal Waves Underlying Activity-Dependent Refinement of Retinofugal Projections Neuron, 2009. ,
Direct Participation of Starburst Amacrine Cells in Spontaneous Rhythmic Activities in the Developing Mammalian Retina, The Journal of Neuroscience, vol.18, issue.11, pp.4155-4165, 1998. ,
DOI : 10.1523/JNEUROSCI.18-11-04155.1998
D Random Perturbations of Dynamical Systems Springer, Grundlehren der mathematischen Wissenschaften, 1998. ,
Nonlinear Dynamics and Chaos : with Applications to Physics, Biology, Chemistry, and Engineering. Boulder, CO, 2015. ,
Sur l'??quilibre d'une masse fluide anim??e d'un mouvement de rotation, Acta Mathematica, vol.7, issue.0, pp.259-380, 1885. ,
DOI : 10.1007/BF02402204