A combined model reduction algorithm for controlled biochemical systems

Thomas J Snowden,Marcus J Tindall,Piet H Van Der Graaf

doi:10.1186/s12918-017-0397-1

Abstract

BackgroundSystems Biology continues to produce increasingly large models of complex biochemical reaction networks. In applications requiring, for example, parameter estimation, the use of agent-based modelling approaches, or real-time simulation, this growing model complexity can present a significant hurdle. Often, however, not all portions of a model are of equal interest in a given setting. In such situations methods of model reduction offer one possible approach for addressing the issue of complexity by seeking to eliminate those portions of a pathway that can be shown to have the least effect upon the properties of interest.MethodsIn this paper a model reduction algorithm bringing together the complementary aspects of proper lumping and empirical balanced truncation is presented. Additional contributions include the development of a criterion for the selection of state-variable elimination via conservation analysis and use of an ‘averaged’ lumping inverse. This combined algorithm is highly automatable and of particular applicability in the context of ‘controlled’ biochemical networks.ResultsThe algorithm is demonstrated here via application to two examples; an 11 dimensional model of bacterial chemotaxis in Escherichia coli and a 99 dimensional model of extracellular regulatory kinase activation (ERK) mediated via the epidermal growth factor (EGF) and nerve growth factor (NGF) receptor pathways. In the case of the chemotaxis model the algorithm was able to reduce the model to 2 state-variables producing a maximal relative error between the dynamics of the original and reduced models of only 2.8% whilst yielding a 26 fold speed up in simulation time. For the ERK activation model the algorithm was able to reduce the system to 7 state-variables, incurring a maximal relative error of 4.8%, and producing an approximately 10 fold speed up in the rate of simulation. Indices of controllability and observability are additionally developed and demonstrated throughout the paper. These provide insight into the relative importance of individual reactants in mediating a biochemical system’s input-output response even for highly complex networks.ConclusionsThrough application, this paper demonstrates that combined model reduction methods can produce a significant simplification of complex Systems Biology models whilst retaining a high degree of predictive accuracy. In particular, it is shown that by combining the methods of proper lumping and empirical balanced truncation it is often possible to produce more accurate reductions than can be obtained by the use of either method in isolation.

Highlights

Systems Biology continues to produce increasingly large models of complex biochemical reaction networks
We demonstrate the algorithm via application to two examples: an 11 dimensional model of bacterial chemotactic signalling in Escherichia coli [47] and a 99 dimensional model of extracellular signal-regulated kinase (ERK) phosphorylation mediated via the epidermal growth factor (EGF) and nerve growth factor (NGF) receptor pathways [48]
Results and discussion two examples are employed to demonstrate the application of the combined model reduction algorithm, the enhancements made to the base methods, and the calculation of the indices of controllability and observability

Summary

Introduction

Systems Biology continues to produce increasingly large models of complex biochemical reaction networks. The BioModels Database, which acts as an open repository for Systems Biology models, saw the number of models it stores increase approximately ten-fold between 2005 and 2010, with the average number of reactions per model having nearly tripled in the same period [1] This increase in complexity, in the number of species or reactions modelled by each system, has become a defining characteristic of research in this area. Such systems are typically developed by bringing together biochemical and physiological knowledge to inform highly detailed mechanistic models of biological networks (e.g. signalling pathways, protein-protein interactions, and genetic cascades). Complexity of this form is often associated with the ‘curse of dimensionality’, whereby the data that can be obtained for such systems in practice are sparse relative to the volume of the state and parameter spaces

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