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Optimal control methods for nonlinear parameter estimation in biophysical neuron models

View ORCID ProfileNirag Kadakia
doi: https://doi.org/10.1101/2022.01.11.475951
Nirag Kadakia
1Department of Molecular, Cellular, and Developmental Biology, Yale University, New Haven, CT, USA
2Quantitative Biology Institute, Yale University, New Haven, CT, USA
3Swartz Foundation for Theoretical Neuroscience, Yale University, New Haven, CT, USA
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Abstract

Functional forms of biophysically-realistic neuron models are constrained by neurobiological and anatomical considerations, such as cell morphologies and the presence of known ion channels. Despite these constraints, neurons models still contain unknown static parameters which must be inferred from experiment. This inference task is most readily cast into the framework of state-space models, which systematically takes into account partial observability and measurement noise. Inferring only dynamical state variables such as membrane voltages is a well-studied problem, and has been approached with a wide range of techniques beginning with the well-known Kalman filter. Inferring both states and fixed parameters, on the other hand, is less straightforward. Here, we develop a method for joint parameter and state inference that combines traditional state space modeling with chaotic synchronization and optimal control. Our methods are tailored particularly to situations with considerable measurement noise, sparse observability, very nonlinear or chaotic dynamics, and highly uninformed priors. We illustrate our approach both in a canonical chaotic model and in a phenomenological neuron model, showing that many unknown parameters can be uncovered reliably and accurately from short and noisy observed time traces. Our method holds promise for estimation in larger-scale systems, given ongoing improvements in calcium reporters and genetically-encoded voltage indicators.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

  • ↵* nirag.kadakia{at}yale.edu

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted January 12, 2022.
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Optimal control methods for nonlinear parameter estimation in biophysical neuron models
Nirag Kadakia
bioRxiv 2022.01.11.475951; doi: https://doi.org/10.1101/2022.01.11.475951
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Optimal control methods for nonlinear parameter estimation in biophysical neuron models
Nirag Kadakia
bioRxiv 2022.01.11.475951; doi: https://doi.org/10.1101/2022.01.11.475951

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