Optimal control methods for nonlinear parameter estimation in biophysical neuron models

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, neuron 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.Author Summary: Systems neuroscience aims to understand how individual neurons and neural networks process external stimuli into behavioral responses. Underlying this characterization are mathematical models intimately shaped by experimental observations. But neural systems are high-dimensional and contain highly nonlinear interactions, so developing accurate models remains a challenge given current experimental capabilities. In practice, this means that the dynamical equations characterizing neural activity have many unknown parameters, and these parameters must be inferred from data. This inference problem is nontrivial owing to model nonlinearity, system and measurement noise, and the sparsity of observations from electrode recordings. Here, we present a novel method for inferring model parameters of neural systems. Our technique combines ideas from control theory and optimization, and amounts to using data to “control” estimates toward the best fit. Our method compares well in accuracy against other state-of-the-art inference methods, both in phenomenological chaotic systems and biophysical neuron models. Our work shows that many unknown model parameters of interest can be inferred from voltage measurements, despite signaling noise, instrument noise, and low observability.