Benchmarking of numerical integration methods for ODE models of biological systems

Yannik Schälte,Philipp Städter,Jan Hasenauer,Paul L Stapor,Leonard Schmiester

doi:10.1038/s41598-021-82196-2

Yannik Schälte, Philipp Städter + Show 3 more

Open Access

https://doi.org/10.1038/s41598-021-82196-2

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Abstract

Ordinary differential equation (ODE) models are a key tool to understand complex mechanisms in systems biology. These models are studied using various approaches, including stability and bifurcation analysis, but most frequently by numerical simulations. The number of required simulations is often large, e.g., when unknown parameters need to be inferred. This renders efficient and reliable numerical integration methods essential. However, these methods depend on various hyperparameters, which strongly impact the ODE solution. Despite this, and although hundreds of published ODE models are freely available in public databases, a thorough study that quantifies the impact of hyperparameters on the ODE solver in terms of accuracy and computation time is still missing. In this manuscript, we investigate which choices of algorithms and hyperparameters are generally favorable when dealing with ODE models arising from biological processes. To ensure a representative evaluation, we considered 142 published models. Our study provides evidence that most ODEs in computational biology are stiff, and we give guidelines for the choice of algorithms and hyperparameters. We anticipate that our results will help researchers in systems biology to choose appropriate numerical methods when dealing with ODE models.

Highlights

Systems biology aims at understanding and predicting the behavior of complex biological processes through mathematical models[1]
To analyze combinations of algorithms and hyperparameters, we considered the Ordinary differential equation (ODE) solvers from the SUNDIALS package CVODES9,16, which implement implicit multi-step methods for numerically solving an initial value problem, i.e., an ODE with initial conditions and offer a variety of hyperparameters
We collected a set of 142 benchmark ODE models collected from publications and used them to carry out a comprehensive study on the most essential hyperparameters of numerical ODE solvers

Summary

Introduction

Systems biology aims at understanding and predicting the behavior of complex biological processes through mathematical models[1]. Ordinary differential equations (ODEs) are widely used to gain a holistic understanding of the behaviour of such systems[2] These ODE models are often derived from biochemical reaction networks and stored/exchanged using the Systems Biology Markup Language (SBML)[3] or Cell Markup Language (CellML)[4]. We established a benchmark collection of 142 models from the two freely accessible databases BioModels[5,15] and JWS Online[6], which covers a broad range of different properties These models were simulated using various ODE solver algorithms implemented in the ODE solver toolboxes C VODES16 from the SUNDIALS suite[9] and the ODEPACK package[17], which are possibly the most widely used software package to integrate ODEs in systems biology. By analyzing the computation time and the failure rate, we derived guidelines for the tuning of ODE solvers in systems biology, which facilitate fast and reliable simulation of the corresponding ODE systems

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