A model reduction method for biochemical reaction networks.

Shodhan Rao,Barbara M Bakker,Karen Van Eunen,Arjan Van Der Schaft,Bayu Jayawardhana

doi:10.1186/1752-0509-8-52

Shodhan Rao, Barbara M Bakker + Show 3 more

Open Access

https://doi.org/10.1186/1752-0509-8-52

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Abstract

BackgroundIn this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The method proceeds by a stepwise reduction in the number of complexes, defined as the left and right-hand sides of the reactions in the network. It is based on the Kron reduction of the weighted Laplacian matrix, which describes the graph structure of the complexes and reactions in the network. It does not rely on prior knowledge of the dynamic behaviour of the network and hence can be automated, as we demonstrate. The reduced network has fewer complexes, reactions, variables and parameters as compared to the original network, and yet the behaviour of a preselected set of significant metabolites in the reduced network resembles that of the original network. Moreover the reduced network largely retains the structure and kinetics of the original model.ResultsWe apply our method to a yeast glycolysis model and a rat liver fatty acid beta-oxidation model. When the number of state variables in the yeast model is reduced from 12 to 7, the difference between metabolite concentrations in the reduced and the full model, averaged over time and species, is only 8%. Likewise, when the number of state variables in the rat-liver beta-oxidation model is reduced from 42 to 29, the difference between the reduced model and the full model is 7.5%.ConclusionsThe method has improved our understanding of the dynamics of the two networks. We found that, contrary to the general disposition, the first few metabolites which were deleted from the network during our stepwise reduction approach, are not those with the shortest convergence times. It shows that our reduction approach performs differently from other approaches that are based on time-scale separation. The method can be used to facilitate fitting of the parameters or to embed a detailed model of interest in a more coarse-grained yet realistic environment.

Highlights

In this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics
There is a need for techniques that can reduce a given kinetic model of a biochemical reaction network to a simplified version that mimics the behaviour of the original model satisfactorily, but contains less differential equations and parameters
We describe a new model reduction method that reduces the number of reactions, metabolites and parameters, such that the dynamics of the metabolite concentrations of the reduced model are close to those of the original model

Summary

Introduction

In this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The application of singular perturbation, time-scale separation, quasi equilibrium and quasi steady state approaches to general enzyme-kinetic rate laws, such as Michaelis-Menten and ping-pong bi-bi is difficult and leads to complicated rate law expressions in the reduced models. Some of the time-scale separation techniques are either based on a priori experimental information or eigenvalues of the Jacobian corresponding to the model and are only locally effective Another recent approach for model reduction uses tropical geometry (see e.g., [14]), wherein the polynomial occuring in every rate equation is replaced by a monomial which is equal to the largest, in absolute value among the monomials that constitute the polynomial

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