Fides: Reliable trust-region optimization for parameter estimation of ordinary differential equation models

Ordinary differential equation (ODE) models are widely used to study biochemical reactions in cellular networks since they effectively describe the temporal evolution of these networks using mass action kinetics. The parameters of these models are rarely known a priori and must instead be estimated by calibration using experimental data. Optimization-based calibration of ODE models on is often challenging, even for low-dimensional problems. Multiple hypotheses have been advanced to explain why biochemical model calibration is challenging, including non-identifiability of model parameters, but there are few comprehensive studies that test these hypotheses, likely because tools for performing such studies are also lacking. Nonetheless, reliable model calibration is essential for uncertainty analysis, model comparison, and biological interpretation.We implemented an established trust-region method as a modular Python framework (fides) to enable systematic comparison of different approaches to ODE model calibration involving a variety of Hessian approximation schemes. We evaluated fides on a recently developed corpus of biologically realistic benchmark problems for which real experimental data are available. Unexpectedly, we observed high variability in optimizer performance among different implementations of the same mathematical instructions (algorithms). Analysis of possible sources of poor optimizer performance identified limitations in the widely used Gauss-Newton, BFGS and SR1 Hessian approximation schemes. We addressed these drawbacks with a novel hybrid Hessian approximation scheme that enhances optimizer performance and outperforms existing hybrid approaches. When applied to the corpus of test models, we found that fides was on average more reliable and efficient than existing methods using a variety of criteria. We expect fides to be broadly useful for ODE constrained optimization problems in biochemical models and to be a foundation for future methods development.Author summary: In cells, networks of biochemical reactions involving complex, time-dependent interactions among proteins and other biomolecules regulate diverse processes like signal transduction, cell division, and development. Precise understanding of the time-evolution of these networks requires the use of dynamical models, among which mass-action models based on ordinary differential equations are both powerful and tractable. However, for these models to capture the specifics of a particular cellular process, their parameters must be estimated by minimizing the difference between the simulation (of a dynamical variable such as a particular protein concentration) and experimental data (this is the process of model calibration). This is a difficult and computation-intensive process that has previously been tackled using a range of mathematical techniques whose strengths and weaknesses are not fully understood. In this manuscript, we describe a new software tool, fides, that makes rigorous comparison of calibration methods possible. Unexpectedly, we find that different software implementations of the same mathematical method vary in performance. Using fides, we analyze the causes of this variability, evaluate multiple improvements, and implement a set of generally useful methods and metrics for use in future modeling studies.