Computational methods for stochastic modeling and parameter fitting of models based on Hodgkin-Huxley formalism
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1
Tampere University of Technology, , Finland
Stochasticity plays a crucial role in shaping the dynamic behavior of a neuron. Therefore, it is important to take this stochasticity into account when modeling, for example, the electroresponsiveness of a neuron. In this work, we demonstrate the use of stochastic differential equations (SDEs) in neuronal modeling. We introduce an SDE model of a single cerebellar granule cell (Saarinen et al. PLoS Computational Biology, 2008) where the description of the ion channel kinetics incorporate the natural stochasticity observed in the dynamic behavior of these channels. We present also ways of incorporating stochasticity to the well-known Hodgkin-Huxley (HH) model of action potential generation in a squid axon and a methodology for fitting these stochastic models to irregular current-clamp data. These data contain subthreshold oscillations, spontaneous action potentials, and clusters of action potentials, among other stochastic features. This kind of fitting and use of irregular data have not been possible with the existing deterministic models and deterministic parameter estimation techniques. We use a Bayesian estimation technique which relies on transforming the probability distributions of the estimation problem into distributions which are easy to sample. This transformation allows us to use Sequential Monte Carlo (SMC) techniques to draw samples from the desired posterior distributions. Based on these samples, a Maximum Likelihood (ML) estimation technique in utilized to produce ML estimates for the selected model parameters; these include maximal conductances of ionic currents and the intensity of random fluctuations in the current-clamp data. We show that we are able to obtain accurate ML estimates for the selected model parameters based on the learning data. These data have been corrupted with different levels of measurement noise. The approximation of the likelihood function allows us to study also the sensitivity of the model parameters and effects of the changes in their values to the model behavior. The sharper the peak is in the likelihood, around the correct parameter value, the more sensitive is the model behavior with respect to value of that parameter. In conclusion, the use of SDEs in neuronal modeling enables more accurate reproduction of the irregular electrophysiological activity of a neuron. The presented method offers also an attractive way to perform parameter estimation in situations where it has not been possible with the deterministic models and methods. Our approach provides a comprehensive set of analytical tools to analyze model behavior and the estimation problem, since the theory of stochastic calculus has been widely studied in the field of mathematics. However, our estimation method is, in its present form, rather computationally heavy. Therefore, we are studying the possibilities of distributed computing, including GRID technology, in our studies. In the future, other methods of approximating the likelihood and speeding up the computations will be considered. In spite of the heavy computing, SMC methods offer a set of methods which are very flexible, relatively easy to implement, parallelizable, and applicable in very general settings.
Conference:
Neuroinformatics 2008, Stockholm, Sweden, 7 Sep - 9 Sep, 2008.
Presentation Type:
Poster Presentation
Topic:
Computational Neuroscience
Citation:
Saarinen
A,
Ylipää
A,
Yli-Harja
O and
Linne
M
(2008). Computational methods for stochastic modeling and parameter fitting of models based on Hodgkin-Huxley formalism.
Front. Neuroinform.
Conference Abstract:
Neuroinformatics 2008.
doi: 10.3389/conf.neuro.11.2008.01.032
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Received:
28 Jul 2008;
Published Online:
28 Jul 2008.
*
Correspondence:
Antti Saarinen, Tampere University of Technology,, Tampere, Finland, antti.saarinen@cs.tut.fi