Efficient computation of steady states in large-scale ODE models of biochemical reaction networks

Abstract

In systems and computational biology, ordinary differential equations are used for the mechanistic modelling of biochemical networks. These models can easily have hundreds of states and parameters. Typically most parameters are unknown and estimated by fitting model output to observation. During parameter estimation the model needs to be solved repeatedly, sometimes millions of times. This can then be a computational bottleneck, and limits the employment of such models.In many situations the experimental data provides information about the steady state of the biochemical reaction network. In such cases one only needs to obtain the equilibrium state for a given set of model parameters. In this paper we exploit this fact and solve the steady state problem directly rather than integrating the ODE forward in time until steady state is reached. We use Newton’s method - like some previous studies - and develop several improvements to achieve robust convergence. To address the reliance of Newtons method on good initial guesses, we propose a continuation method. We show that the method works robustly in this setting and achieves a speed up of up to 100 compared to using ODE solves.