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Section COMPUTATIONAL NEUROSCIENCE
duce a higher degree of order (Prigogine, 1984). However, since all of his Nobel-Prize winning discussions have been philosophical and mathematical, some scientists criticized his view on evolution from chaos to order, saying that such phenomena may be manipulated on paper or on a computer screen, but not in real life. The manifestation of the emergence of regularity in interacting chaotic systems may shed light on understanding of essential mechanisms leading to self-organization of nature. Indeed, synchronization of chaotic systems is an example of self-organization in nature, and it is usually assumed that interaction between coupled oscillators enhances their synchronization. However, this is not always true. An increase in coupling between chaotic systems may result in unexpected behaviors, such as, e.g., oscillation death or deterministic coherence resonance. The latter has been theoretically predicted in two coupled chaotic Rossler oscillators (Pisarchik, 2015). The natural question arises: Can this phenomenon occur in a biological system? Our research gives a positive answer to this question. Here, we report on the first observation of resonant coherence enhancement in a deterministic neuron model. Through numerical simulations and electronic experiments we demonstrate the improved regularity in inter-spike intervals (ISI) of a chaotic Hindmarsh-Rose neuron affected by another chaotic neuron. Resonant chaos suppression is detected when the neurons are in a phase synchronization state. This surprising phenomenon resembles "stabilization of chaos by chaos", i.e., the chaotic signal from the presynaptic neuron makes the dynamics of the postsynaptic neuron more regular if there is a small mismatch between their parameters.
References
1. PRIGOGINE I. & STENGERS I. (1984): Order Out of Chaos (New York: Bantam Books).
2. PISARCHIK A.N. & JAIMES-REATEGUI, R. (2015): Deterministic coherence resonance in coupled chaotic oscillators with frequency mismatch, Phys. Rev. E 92, 050901(R).
Modeling Stochastic Processes in Neurons
Erik De Schutter*
Okinawa Institute for Science and Technology Graduate University, Japan. * Presenting e-mail: erik@oist.jp
Many aspects of neuronal function, for instance spiking and synaptic transmission, are very noisy. To achieve a better understanding of how this noisiness can contribute to neural coding it is important to understand the causal processes. Detailed modeling using accurate stochastic methods is an essential tool because stochasticity can be manipulated in models, something that is often difficult to achieve in experiments.
To facilitate such modeling we have been developing the STEPS software, which is an efficient implementation of the Inhomogeneous Stochastic Simulation Algorithm (ISSA, also known as spatial Gillespie) applied on tetrahedral meshes to allow for accurate representation of neural morphology. Using STEPS we have investigated the role of stochasticity in the induction of synaptic plasticity and in the generation of dendritic calcium spikes in cerebellar Purkinje cells.
Dendritic calcium spikes vary a lot in shape but the underlying mechanisms were unclear. We showed that a system including calcium-activated channels behaves quite differently from one containing only voltage-gated channels. In the latter case stochastic effects disappear rapidly when the number of channels increases, but this is not true for calcium-activated channels. This leads to large variability in the number of spikes fired during a calcium burst when simulated in an unbranched cable and additional large spatial variability in membrane potential and calcium concentrations when simulated in a branched dendrite.
Unfortunately simulating stochastic processes in neuronal dendrites is very time consuming and we were limited to only simulating a small part of a dendrite because of runtime considerations. The ISSA method used in STEPS is inherently serial and cannot be parallelized. Recently we have described an effective and accurate approximate method on tetrahedral meshes that overcomes this limitation by using an operator splitting approach. The implementation in the STEPS software is the first truly accurate parallelization of an ISSA-like method and allows for good scaling of the parallel computation provided the meshes are partitioned properly. Using this approach we can now apply stochastic simulation to models of the complete Purkinje cell and study the mechanisms of variability of dendritic calcium spikes and other forms of spiking at the cellular level.
52 Opera Med Physiol 2016 Vol. 2 (S1)
