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in the directed cycle of simple oscillators. Numerical simulations confirm this hypothesis. Second, in addition to nodes with identical dynamics, we numerically investigate the case in which individual oscillators differ; their parameters are randomly sampled from a distribution centered at fixed nominal values. We observe that, provided that coupling within individual modules is strong enough, solutions resembling rotating waves emerge in this system, too. The latter regime co-exist with nearly synchronous state giving rise to coupling strength-modulated multi-stability and coherence in such systems.
Acknowledgements
The first author is thankful to the RFBR (grant 15-38-20178) for partial support of this work. References
1. W. Strogate. Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life. Hyperion, 2003.
2. A. Pikovsky, M. Rosenblum, and J. Kurths. Synchroniozation A universal concept in nonlinear sciences. Cambridge University Press, 2001.
3. M. Golubitsky, I. Stewart, I., and A. Torok SIAM Journal on Applied Dynamical Systems, 2005, 4(1), 78-100.
4. A.Y. Pogromsky. Int. J. of Bifurc. and Chaos, 1998, 8(2), 295-319.
5. L. Scardovi, M. Arcak, and E. Sontag. IEEETransactions on Automatic Control, 2010, 55, 1367-1379.
6. A. Pogromsky, G. Santoboni, and H. Nijmeijer. Physica D : Nonlinear Phenomena, 2002, 172(1-4), 65-87.
7. I. Belykh, V. Belykh, and M. Hasler. Physical Review E, 2000, 62(5), 6332-6345.
8. I. Belykh, V. Belykh, and M. Hasler. Physica D: Nonlinear Phenomena, 2004, 195(1-2), 159-187.
9. V. Chandrasekar, J. Sheeba, B. Subash, M. Lakshmanan, and J. Kurths. Physica D: Nonlinear Phenomena, 2014, 267, 36-48.
10. A. Gorban, N. Jarman, E. Steur, H. Nijmeijer, C. van Leeuwen, and I. Tyukin Proceedings of the 4-th IFAC Conference on Control of Chaotic Systems, 2015.
11. A. Gorban, N. Jarman, E. Steur, C. van Leeuwen, and I. Tyukin. Mathematical Modelling of Natural Phenomena, 10, 212-231.
Cocaine Addiction as a Homeostahc Reinforcement Learning Disorder
Boris S. Gutkin1,2*
1 Group for Neural Theory, LNC INSERM U960, Ecole Normale Superieure, Paris, France;
2 Center for Cognition and Decision Making, NRU Higher School of Economics, Moscow, Russia. * Presenting e-mail: boris.gutkin@gmail.com
Background
Current addiction theories diverge and depict cocaine addiction as a disorder of either reinforcement learning or hedonic homeostatic regulation. The learning-based theories, in particular, suggests that addiction results from transition from a voluntary and goal-directed, to a habitual decision process. Underlying all of these computational theories is the central role of the dopaminergic system signaling reward information. Under cocaine, as under other addictive drugs, this signaling is pathologically influenced by the pharmacological action of the drug.
Methods
Here we propose a new theory of addiction that integrates the brain reinforcement learning and hedonic homeostatic regulation systems. As opposed to habit-based theories, we postulate that in addicts, a goal-directed planning system remains in charge of fulfilling drug-related homeostatic needs of the organism, while drugs gradually modify the need structure, as well as associative learning mechanisms. Formal mathematical modeling and simulation, as well as cocaine self-administration paradigm in rats are combined to test key predictions of our theory.
Results
Simulations show that our new theory accounts for key behavioral and neurobiological features of addiction, most notably, escalation of cocaine use, drug-primed craving and relapse, individual differences underlying susceptibility to addiction, and dopamine D2-receptor down-regulation in addicts. The theory also generates unique predictions about cocaine self-administration behavior in rats that are confirmed by new experimental results.
Conclusion
We show that our integrative theory explains many behavioral and neurobiological aspects of cocaine addiction that
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Section COMPUTATIONAL NEUROSCIENCE
were previously explained by different theories. We also discuss the limitations of previous theories, particularly that viewing addiction as a habit-based disorder can be fundamentally inconsistent with certain aspect of addiction.
Electro-Diffusion in Dendritic Spines and the I-V Relation
David Holcman*
Ecole Normale Superieure, France. * Presenting e-mail: david.holcman@ens.fr
Electrical activity of dendritic spines in cellular microdomains in general remains unclear unresolved. The electrical current is carried by moving ions and induces a local change in the voltage, which can modulate the opening of channels and contribute to the initiation of an action potential. The ionic flow in dendritic spines is driven by the coupled electric field to the charge densities that interact through the non-cylindrical spine geometry.
Due to small nanometric scale and the charge-voltage interaction, the voltage-current (I-V) relation and its regulation by geometry remains difficult to investigate. I will present here our recent effort to deconvolve the response of the slow genetically encoded voltage sensor in hippocampal neurons and to compute from the electro-diffusion theory, the electric field and the ionic flows in the spine head. We resolve here the I-V relation and extract the spine resistance, which is certainly insufficient to characterize the nonlinear I-V interaction. Coll. R. Yuste (Columbia).
Delayed and Asynchronous Neurotransmitter Release
Maciej (Martin) Krupa* Inria, France.
* Presenting e-mail: maciej.p.krupa@gmail.com
Asynchronous release of neurotransmitter is an important phenomenon known to occur in certain neurons. It is linked to short term synaptic plasticity, memory formation, modulation of inhibition, etc.
We have designed a model system describing the exocytotic cycle of vesicles at excitatory and inhibitory synapses that accounts for asynchronous release. Our system models the interaction of the SNARE and SM proteins and predicts a delayed inertial protein unbinding associated with the SNARE complex assembly immediately after vesicle priming. The underlying mathematical mechanism is bifurcation delay, which is a phenomenon known to occur in systems with multiple time-scales.
Fig.1. Time-coded neurotransmitter release at excitatory and inhibitory synapses, S. Rodrigues, M. Desroches, M. Krupa, J. Cortes, T. J. Sejnowski, A. B. Ali, PNAS 2016
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