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Accurate and Fast Simulation of Channel Noise in Conductance-Based Model Neurons by Diffusion Approximation

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  • Daniele Linaro
  • Marco Storace
  • Michele Giugliano

Abstract

Stochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically detailed model neurons calls for the availability of fast numerical methods. In fact, exact techniques employ the microscopic simulation of the random opening and closing of individual ion channels, usually based on Markov models, whose computational loads are prohibitive for next generation massive computer models of the brain. In this work, we operatively define a procedure for translating any Markov model describing voltage- or ligand-gated membrane ion-conductances into an effective stochastic version, whose computer simulation is efficient, without compromising accuracy. Our approximation is based on an improved Langevin-like approach, which employs stochastic differential equations and no Montecarlo methods. As opposed to an earlier proposal recently debated in the literature, our approximation reproduces accurately the statistical properties of the exact microscopic simulations, under a variety of conditions, from spontaneous to evoked response features. In addition, our method is not restricted to the Hodgkin-Huxley sodium and potassium currents and is general for a variety of voltage- and ligand-gated ion currents. As a by-product, the analysis of the properties emerging in exact Markov schemes by standard probability calculus enables us for the first time to analytically identify the sources of inaccuracy of the previous proposal, while providing solid ground for its modification and improvement we present here.Author Summary: A possible approach to understanding the neuronal bases of the computational properties of the nervous system consists of modelling its basic building blocks, neurons and synapses, and then simulating their collective activity emerging in large networks. In developing such models, a satisfactory description level must be chosen as a compromise between simplicity and faithfulness in reproducing experimental data. Deterministic neuron models – i.e., models that upon repeated simulation with fixed parameter values provide the same results – are usually made up of ordinary differential equations and allow for relatively fast simulation times. By contrast, they do not describe accurately the underlying stochastic response properties arising from the microscopical correlate of neuronal excitability. Stochastic models are usually based on mathematical descriptions of individual ion channels, or on an effective macroscopic account of their random opening and closing. In this contribution we describe a general method to transform any deterministic neuron model into its effective stochastic version that accurately replicates the statistical properties of ion channels random kinetics.

Suggested Citation

  • Daniele Linaro & Marco Storace & Michele Giugliano, 2011. "Accurate and Fast Simulation of Channel Noise in Conductance-Based Model Neurons by Diffusion Approximation," PLOS Computational Biology, Public Library of Science, vol. 7(3), pages 1-17, March.
  • Handle: RePEc:plo:pcbi00:1001102
    DOI: 10.1371/journal.pcbi.1001102
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    References listed on IDEAS

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    1. Antti Saarinen & Marja-Leena Linne & Olli Yli-Harja, 2008. "Stochastic Differential Equation Model for Cerebellar Granule Cell Excitability," PLOS Computational Biology, Public Library of Science, vol. 4(2), pages 1-11, February.
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    Cited by:

    1. Cofré, Rodrigo & Cessac, Bruno, 2013. "Dynamics and spike trains statistics in conductance-based integrate-and-fire neural networks with chemical and electric synapses," Chaos, Solitons & Fractals, Elsevier, vol. 50(C), pages 13-31.
    2. Kyriaki Sidiropoulou & Panayiota Poirazi, 2012. "Predictive Features of Persistent Activity Emergence in Regular Spiking and Intrinsic Bursting Model Neurons," PLOS Computational Biology, Public Library of Science, vol. 8(4), pages 1-15, April.
    3. Joshua H Goldwyn & Eric Shea-Brown, 2011. "The What and Where of Adding Channel Noise to the Hodgkin-Huxley Equations," PLOS Computational Biology, Public Library of Science, vol. 7(11), pages 1-9, November.
    4. Tommaso Costa & Giuseppe Boccignone & Franco Cauda & Mario Ferraro, 2016. "The Foraging Brain: Evidence of Lévy Dynamics in Brain Networks," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-16, September.
    5. Chitaranjan Mahapatra & Inna Samuilik, 2024. "A Mathematical Model of Spontaneous Action Potential Based on Stochastics Synaptic Noise Dynamics in Non-Neural Cells," Mathematics, MDPI, vol. 12(8), pages 1-13, April.
    6. Liu, Huixia & Lu, Lulu & Zhu, Yuan & Wei, Zhouchao & Yi, Ming, 2022. "Stochastic resonance: The response to envelope modulation signal for neural networks with different topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).

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