Optimality and identification of dynamic models in systems biology: an inverse optimal control framework

Motivation: Optimality principles have been used to explain many biological processes and systems. However, the functions being optimized are in general unknown a priori. Here we present an inverse optimal control framework for modeling dynamics in systems biology. The objective is to identify the underlying optimality principle from observed time-series data and simultaneously estimate unmeasured time-dependent inputs and time-invariant model parameters. As a special case, we also consider the problem of optimal simultaneous estimation of inputs and parameters from noisy data. After presenting a general statement of the inverse optimal control problem, and discussing special cases of interest, we outline numerical strategies which are scalable and robust. Results: We discuss the existence, relevance and implications of identifiability issues in the above problems. We present a robust computational approach based on regularized cost functions and the use of suitable direct numerical methods based on the control-vector parameterization approach. To avoid convergence to local solutions, we make use of hybrid global-local methods. We illustrate the performance and capabilities of this approach with several challenging case studies, including simulated and real data. We pay particular attention to the computational scalability of our approach (with the objective of considering large numbers of inputs and states). We provide a software implementation of both the methods and the case studies.