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Constraints on reciprocal flux sensitivities in biochemical reaction networks.

ABSTRACT: We identify a connection between the structural features of mass-action networks and the robustness of their steady-state fluxes against rate constant variations. We find that in all positive steady states of so-called injective networks-networks that arise, for example, in metabolic and gene regulation contexts-there are certain firm bounds on the flux control coefficients. In particular, the control coefficient of the flux of a reaction, with respect to variation in its own rate constant, is delimited in a precise way. Moreover, for each pair of reactions, the flux of at least one of them must have a precisely delimited control coefficient with respect to variation in the rate constant of the other. The derived bounds can, however, be violated in noninjective networks, so for them a more pronounced lack of robustness could be exhibited. These results, which indicate a mechanism by which some degree of robustness is induced in the injective setting, also shed light on how robustness might evolve.

SUBMITTER: Shinar G

PROVIDER: S-EPMC3059583 | biostudies-literature | 2011 Mar

REPOSITORIES: biostudies-literature

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Constraints on reciprocal flux sensitivities in biochemical reaction networks.

Shinar Guy G Mayo Avi A Ji Haixia H Feinberg Martin M

Biophysical journal 20110301 6

We identify a connection between the structural features of mass-action networks and the robustness of their steady-state fluxes against rate constant variations. We find that in all positive steady states of so-called injective networks-networks that arise, for example, in metabolic and gene regulation contexts-there are certain firm bounds on the flux control coefficients. In particular, the control coefficient of the flux of a reaction, with respect to variation in its own rate constant, is d ...[more]

PMID: 21402019

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Project description:BACKGROUND: 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 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. RESULTS: We 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%. CONCLUSIONS: The 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.

Dataset Information

Constraints on reciprocal flux sensitivities in biochemical reaction networks.

Publications

Constraints on reciprocal flux sensitivities in biochemical reaction networks.

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