Global parameter estimation of an Hodgkin-Huxley formalism using membrane voltage recordings: Application to neuro-mimetic analog integrated circuits

Conductance-based models of biological neurons can accurately reproduce the waveform of the membrane voltage, as well as the spike timing in response to injected currents. Nevertheless, finding the good model parameter set to fit membrane voltage recordings is often a very time-consuming and complex task, difficult to achieve manually. We present a new variant of an optimization algorithm, the differential evolution. We specifically designed this technique for the automated tuning of neuro-mimetic analog integrated circuits based on an Hodgkin-Huxley formalism for a point-neuron model. It indeed enables us to estimate all the parameters of the model, while avoiding local minima. The method is first tested on three types of neuron models (fast spiking, regular spiking, and intrinsically bursting), and then applied to the automated tuning of a neuro-mimetic circuit from the reference membrane voltage of a fast spiking neuron model.

[1]  Noam Peled,et al.  Constraining compartmental models using multiple voltage recordings and genetic algorithms. , 2005, Journal of neurophysiology.

[2]  René Thomsen,et al.  A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[3]  J. Bower,et al.  Exploring parameter space in detailed single neuron models: simulations of the mitral and granule cells of the olfactory bulb. , 1993, Journal of neurophysiology.

[4]  Michael L. Hines,et al.  The NEURON Book , 2006 .

[5]  Yannick Bornat,et al.  Adjusting the neurons models in neuromimetic ICs using the voltage-clamp technique , 2008, 2008 IEEE International Symposium on Circuits and Systems.

[6]  Stefan Janaqi,et al.  Generalization of the strategies in differential evolution , 2004, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings..

[7]  Henry Markram,et al.  Minimal Hodgkin–Huxley type models for different classes of cortical and thalamic neurons , 2008, Biological Cybernetics.

[8]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[9]  S. Renaud,et al.  Automated tuning of analog neuromimetic integrated circuits , 2009, 2009 IEEE Biomedical Circuits and Systems Conference.

[10]  John Guckenheimer,et al.  Parameter estimation for bursting neural models , 2008, Journal of Computational Neuroscience.

[11]  Erik De Schutter,et al.  Complex Parameter Landscape for a Complex Neuron Model , 2006, PLoS Comput. Biol..

[12]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[13]  Allan R. Willms,et al.  NEUROFIT: software for fitting Hodgkin–Huxley models to voltage-clamp data , 2002, Journal of Neuroscience Methods.

[14]  Henry Markram,et al.  A Novel Multiple Objective Optimization Framework for Constraining Conductance-Based Neuron Models by Experimental Data , 2007, Front. Neurosci..

[15]  James M. Bower,et al.  A Comparative Survey of Automated Parameter-Search Methods for Compartmental Neural Models , 1999, Journal of Computational Neuroscience.

[16]  Y. Ho,et al.  Simple Explanation of the No-Free-Lunch Theorem and Its Implications , 2002 .

[17]  Sylvie Renaud,et al.  New variants of the differential evolution algorithm: Application for neuroscientists , 2009, 2009 17th European Signal Processing Conference.

[18]  Cyrille Rossant,et al.  Automatic Fitting of Spiking Neuron Models to Electrophysiological Recordings , 2010, Front. Neuroinform..

[19]  Liam Paninski,et al.  Efficient estimation of detailed single-neuron models. , 2006, Journal of neurophysiology.

[20]  Sylvie Renaud,et al.  Automated Parameter Estimation of the Hodgkin-Huxley Model Using the Differential Evolution Algorithm: Application to Neuromimetic Analog Integrated Circuits , 2011, Neural Computation.

[21]  S. Renaud,et al.  A Conductance-Based Silicon Neuron with Dynamically Tunable Model Parameters , 2005, Conference Proceedings. 2nd International IEEE EMBS Conference on Neural Engineering, 2005..

[22]  Sylvie Renaud,et al.  A $Q$ -Modification Neuroadaptive Control Architecture for Discrete-Time Systems , 2010 .

[23]  Yannick Bornat,et al.  A Library of Analog Operators Based on the Hodgkin-Huxley Formalism for the Design of Tunable, Real-Time, Silicon Neurons , 2011, IEEE Transactions on Biomedical Circuits and Systems.

[24]  John Guckenheimer,et al.  An Improved Parameter Estimation Method for Hodgkin-Huxley Models , 1999, Journal of Computational Neuroscience.

[25]  A. Hodgkin,et al.  Measurement of current‐voltage relations in the membrane of the giant axon of Loligo , 1952, The Journal of physiology.

[26]  Kenji Doya,et al.  A Hodgkin-Huxley Type Neuron Model That Learns Slow Non-Spike Oscillations , 1993, NIPS.