Guaranteed error bounds for structured complexity reduction of biochemical networks

Journal of Theoretical Biology
Thomas P Prescott, Antonis Papachristodoulou

Abstract

Biological systems are typically modelled by nonlinear differential equations. In an effort to produce high fidelity representations of the underlying phenomena, these models are usually of high dimension and involve multiple temporal and spatial scales. However, this complexity and associated stiffness makes numerical simulation difficult and mathematical analysis impossible. In order to understand the functionality of these systems, these models are usually approximated by lower dimensional descriptions. These can be analysed and simulated more easily, and the reduced description also simplifies the parameter space of the model. This model reduction inevitably introduces error: the accuracy of the conclusions one makes about the system, based on reduced models, depends heavily on the error introduced in the reduction process. In this paper we propose a method to calculate the error associated with a model reduction algorithm, using ideas from dynamical systems. We first define an error system, whose output is the error between observables of the original and reduced systems. We then use convex optimisation techniques in order to find approximations to the error as a function of the initial conditions. In particular, we use th...Continue Reading

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Citations

Apr 16, 2014·Journal of Theoretical Biology·Thomas P Prescott, Antonis Papachristodoulou
May 2, 2015·PLoS Computational Biology·Thomas P PrescottAntonis Papachristodoulou
Aug 1, 2016·Journal of Theoretical Biology·G IacobelliC Mocenni
Feb 15, 2017·BMC Systems Biology·Thomas J SnowdenMarcus J Tindall
Jun 29, 2017·Bulletin of Mathematical Biology·Thomas J SnowdenMarcus J Tindall
Mar 28, 2018·Journal of Pharmacokinetics and Pharmacodynamics·Thomas J SnowdenMarcus J Tindall
Jun 28, 2021·European Journal of Pharmaceutical Sciences : Official Journal of the European Federation for Pharmaceutical Sciences·Michelle PrzedborskiMohammad Kohandel
Aug 13, 2021·Biological cybernetics·Alberto PadoanRodolphe Sepulchre

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