Mathematical and experimental studies on retinal waves

Abstract : Retinal waves are spontaneous bursts of activity propagating in the developping retina and thought to play a central role in shaping the visual system and retinal circuitry. They first occur at early embryonic stages of development and gradually disappear upon maturation. Understanding their generating mechanisms may help to control and use them in order to re-train the retina for rewiring and possibly improve vision restoration, after treatment, in some degenerative retinal diseases. Retinal waves emergence is shown experimentally to depend on autonomous local cellular mechanisms combined with neurons coupling [1]. In order to describe, reproduce and explain experimental results, there is a need for careful biophysical modelling of the underlying cellular mechanisms, specific to the population of neurons involved. Our goal is also to link biophysical mechanisms to dynamical systems theory. From this perspective, a retinal wave is a spatiotemporal activity which is generated by the conjunction of local (cell level) nonlinear characteristics and network effects, can have different forms (fronts, spiral, standing waves, spatio-temporal chaos) and is induced by generic dynamical mechanisms, associated with typical bifurcations. We have developed a biophysical model of developmental stage II retinal waves, close enough to biology to reproduce several prominent experimental results, and accessible to dynamical systems analysis. We reproduce the spontaneous intrinsic cell-autonomous rhythmic bursting in Starbust Amacrine Cells (SACs) and the slow After Hyperpolarisation Current (sAHP), [2], which modulates the refractory process inbetween two consecutive bursts, observed experimentally in [1]. We describe the dynamical influence of cholinergic synapses, ensuring the level of SAC synchrony necessary for the emergence of waves, as shown in [1]. To summarize we obtain: a) a plausible generic mechanism generating spontaneous retinal waves in development, without any need for external stimulation as opposed to existing models [3],[4] and b) a mathematical characterization of retinal waves. Especially, a biophysical parameter controls the wave arousal and the corresponding shape (e.g. spirals). In this conference, we shall present the biophysical grounds of this model, the mathematical analysis of its behaviour, and experimental results confirming its validity. [1] J. Zheng, S. Lee, J. Zhou, A transient network of intrinsically bursting starbust cells underlies the generation of retinal waves, Nature Neuroscience, Volume 9, 2006 [2] H. J. Abel, J. C. F. Lee, J. C. Callaway, R. C. Foehring, Relationships between Intracellular calcium and Afterhyperpolarizations in Neocortical Pyramidal Neurons, JNeurophysiol:91, 324-335, 2004 [3] M. Hennig, C. Adams, D. Willshaw, E. Sernagor, Early-Stage Waves in the Retinal Network Emerge Close to a Critical State Transition between Local and Global Functional Connectivity, Journal of Neuroscience, 2009 [4] B. Lansdell, K. Ford, N. Kutz, A Reaction-Diffusion Model of Cholinergic Retinal Waves, PLOS Computational Biology, 2014
Type de document :
Communication dans un congrès
2nd International Conference on Mathematical Neuroscience (ICMNS), May 2016, Juan les Pins, France. 2016
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Contributeur : Dora Karvouniari <>
Soumis le : mardi 31 mai 2016 - 20:59:31
Dernière modification le : vendredi 31 août 2018 - 09:13:20

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Dora Karvouniari, Lionel Gil, Olivier Marre, Serge Picaud, Bruno Cessac. Mathematical and experimental studies on retinal waves. 2nd International Conference on Mathematical Neuroscience (ICMNS), May 2016, Juan les Pins, France. 2016. 〈hal-01324365〉

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