Dynamical Parameter and State Estimation in Neuron Models

Henry D. I. Abarbanel, Paul H. Bryant, Philip E. Gill, Mark Kostuk, Justin Rofeh, Zakary Singer, Bryan Toth and Elizabeth Wong

in The Dynamic Brain

Published in print January 2011 | ISBN: 9780195393798
Published online September 2011 | e-ISBN: 9780199897049 | DOI:
Dynamical Parameter and State Estimation in Neuron Models

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Using the “dynamical parameter estimation” (DPE) formulation of parameter and state estimation in models of nonlinear systems, we study the estimation of all parameters in two neuron models, including the four-dimensional standard Hodgkin-Huxley model and the two-dimensional Morris-Lecar model. DPE couples data from an observed system to synchronize the model and the data in a balanced manner. Parameters, unobserved states, and coupling/control variables are determined by the minimization of a synchronization cost function subject to the model equations of motion. In the implementation of DPE, this chapter uses the “direct method” for the numerical solution of the equivalent optimal tracking problem, employing the numerical optimization package SNOPT. The chapter finds that the numerical procedure for searching in parameter and state space performs in an accurate manner when the system is significantly perturbed from its attractor by external forcing. By driving the neuron off its attractor, it is forced to explore, in a transient manner, the phase space of the system, thus distinguishing distinct models with similar attractors. The model neurons also act to reduce additive noise in voltage data, and we analyze the source of this noise reduction.

Keywords: dynamical parameter estimation; SNOPT; chaos; noise reduction; Hodgkin-Huxley model; Morris-Lecar model; Gaussian distributed noise

Chapter.  15538 words.  Illustrated.

Subjects: Neuroscience

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