Data Assimilation Methods for Neuronal State and Parameter Estimation

• Published in: Journal of mathematical neuroscience Vol. 8; no. 1; pp. 11 - 38
• Main Authors: Moye, Matthew J., Diekman, Casey O.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 09-08-2018; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Bifurcations; Climate models; Data assimilation; Electric potential; Identification methods; Kalman filters; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Neurosciences; Parameter estimation; Parameter identification; Resistance; Review; Software; Third Annual International Conference on Mathematical Neuroscience; Variational methods; Weather forecasting; Conductance-based models; Parameter estimation; Neuronal excitability; Data assimilation
• ISSN: 2190-8567; 2190-8567
• DOI: 10.1186/s13408-018-0066-8

This tutorial illustrates the use of data assimilation algorithms to estimate unobserved variables and unknown parameters of conductance-based neuronal models. Modern data assimilation (DA) techniques are widely used in climate science and weather prediction, but have only recently begun to be applied in neuroscience. The two main classes of DA techniques are sequential methods and variational methods. We provide computer code implementing basic versions of a method from each class, the Unscented Kalman Filter and 4D-Var, and demonstrate how to use these algorithms to infer several parameters of the Morris–Lecar model from a single voltage trace. Depending on parameters, the Morris–Lecar model exhibits qualitatively different types of neuronal excitability due to changes in the underlying bifurcation structure. We show that when presented with voltage traces from each of the various excitability regimes, the DA methods can identify parameter sets that produce the correct bifurcation structure even with initial parameter guesses that correspond to a different excitability regime. This demonstrates the ability of DA techniques to perform nonlinear state and parameter estimation and introduces the geometric structure of inferred models as a novel qualitative measure of estimation success. We conclude by discussing extensions of these DA algorithms that have appeared in the neuroscience literature.