Inferring the dynamics of quasi-reaction systems via nonlinear local mean-field approximations

TL;DR

This paper introduces a nonlinear mean-field approximation method for quasi-reaction systems that improves parameter estimation accuracy and computational efficiency, especially with large time gaps and stiff biological data.

Contribution

It proposes an analytical first-order Taylor approximation for hazard rates, enabling explicit solutions and nonlinear predictions for generic quasi-reaction systems.

Findings

Enhanced kinetic rate estimation accuracy

Improved computational efficiency over existing methods

Robustness to system stiffness in biological applications

Abstract

In the modelling of stochastic phenomena, such as quasi-reaction systems, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive measurements is large. Local linear approximation approaches account for the stochasticity in the system but fail to capture the nonlinear nature of the underlying process. At the mean level, the dynamics of the system can be described by a system of ODEs, which have an explicit solution only for simple unitary systems. An analytical solution for generic quasi-reaction systems is proposed via a first order Taylor approximation of the hazard rate. This allows a nonlinear forward prediction of the future dynamics given the current state of the system. Predictions and corresponding observations are embedded in a nonlinear least-squares approach for parameter estimation. The performance of the algorithm is compared to existing SDE and ODE-based methods via a simulation study. Besides the increased computational efficiency of the approach, the results show an improvement in the kinetic rate estimation, particularly for data observed at large time intervals. Additionally, the availability of an explicit solution makes the method robust to stiffness, which is often present in biological systems. An illustration on Rhesus Macaque data shows the applicability of the approach to the study of cell differentiation.