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The human brain is the most biologically complex organ, composed of eighty-six billion individual neurons that mesh together to form an incredibly intricate neural network. How do billions of neurons facilitate our behavior? The field of computational neurosciences takes a mathematical approach to uncover the mysteries of the brain. The field uses models, computer simulations, and theoretical analyses to study the principles that govern our cognitive capacity and the physiology of the nervous system. One challenge of establishing a biophysical neuron model that accurately predicts the behavior of a neuron is estimating fixed parameters—measurements representative of other undeterminable variables. For example, the conductivity of a neuron’s ion channels must be modeled by an indirect parameter since it cannot be directly measured. These critical parameters dictate neuron interactions and overall firing behavior. “All these responses depend on the interplay between the parameters,” said Nirag Kadakia, a postdoctoral researcher in the Department of Molecular Cellular Developmental Biology at Yale.
Kadakia proposed a new algorithm tailored to “noisy” systems with nonlinear dynamics to infer the parameters of individual neurons. “If you really want to understand the system at its fullest detail, you have to include those nonlinear responses,” says Kadakia. His proposed algorithm utilizes an engineering technique called optimal control theory. This mathematical optimization finds the best estimate for a parameter in the most efficient way possible, given the system’s constraints. This model builds upon previous traditional modeling approaches and has significantly improved prediction accuracy. Older and more classic algorithms are inadequate in this context and may not ultimately converge on the best parameter estimate that fits the data. Kadakia’s work demonstrates that unknown parameters can be inferred from nonlinear, high-dimensional systems despite noise and low observability, giving rise to rich data and more accurate model predictions.