Reduction of dynamical biochemical reactions networks in computational biology.

O Radulescu,V Noel,A N Gorban,A Zinovyev

doi:10.3389/fgene.2012.00131

O Radulescu, V Noel + Show 2 more

Open Access

https://doi.org/10.3389/fgene.2012.00131

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Abstract

Biochemical networks are used in computational biology, to model mechanistic details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multiscaleness, an important property of these networks, can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler models, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state (QSS) and quasi-equilibrium approximations (QE), and provide practical recipes for model reduction of linear and non-linear networks. We also discuss the application of model reduction to the problem of parameter identification, via backward pruning machine learning techniques.

Highlights

During the last decades, biologists have identified a wealth of molecular components and regulatory mechanisms underlying the control of cell functions
Extensive effort has been dedicated to adapting the main ideas used for model reduction of deterministic models, namely exact lumping, invariant manifolds (IM), quasi-steady state (QSS), quasi-equilibrium approximations (QE), and averaging, to the case of stochastic models
Gene transcription and translation can be represented as one step and one constant in a phenomenological model, but can consist of several steps such as initiation, transcription of mRNA leading region, ribosome binding, translation, folding, maturation, etc., in a complex model. Not all of these steps are important for the network functioning and not all parameters are identifiable from the observed quantities

Summary

INTRODUCTION

Biologists have identified a wealth of molecular components and regulatory mechanisms underlying the control of cell functions. Stochastic simulation algorithm (SSA, Gillespie, 1976, 1977) can be very expensive in computer time when applied to large unreduced models, precluding model analysis and identification For this reason, extensive effort has been dedicated to adapting the main ideas used for model reduction of deterministic models, namely exact lumping, IM, QSS, QE, and averaging, to the case of stochastic models. (Erban et al, 2006) propose diffusion approximations for slow/fast stochastic networks, in which the drift and diffusion parameters were obtained numerically These parameters were derived directly from the master equation of stochastic networks with species in small and large copy numbers (Radulescu et al, 2012).

DETERMINISTIC DYNAMICAL NETWORKS

MULTI-SCALE REDUCTION OF MONOMOLECULAR REACTION NETWORKS

MODEL REDUCTION AND MODEL IDENTIFICATION

CONCLUSION

Gluing cycles and restoring cycle exit reactions

Restoring cycles