Introduction to Systems Biology for Mathematical Programmers

Constraint-based optimization, such as flux balance analysis (FBA), has become a standard systems-biology computational method to study cellular metabolisms that are assumed to be in a steady state of optimal growth. The methods are based on optimization while assuming (i) equilibrium of a linear system of ordinary differential equations, and (ii) deterministic data. However, the steady-state assumption is biologically imperfect, and several key stoichiometric coefficients are experimentally inferred from situations of inherent variation. We propose an approach that explicitly acknowledges heterogeneity and conducts a robust analysis of metabolic pathways (RAMP). The basic assumption of steady state is relaxed, and we model the innate heterogeneity of cells probabilistically. Our mathematical study of the stochastic problem shows that FBA is a limiting case of our RAMP method. Moreover, RAMP has the properties that: A) metabolic states are (Lipschitz) continuous with regards to the probabilistic modeling parameters, B) convergent metabolic states are solutions to the deterministic FBA paradigm as the stochastic elements dissipate, and C) RAMP can identify biologically tolerable diversity of a metabolic network in an optimized culture. We benchmark RAMP against traditional FBA on genome-scale metabolic reconstructed models of E. coli, calculating essential genes and comparing with experimental flux data.

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Metabolic Networks and Modern Research Problems in Operations Research

Brooks¹,

Holder²

2017

The Operations Research Revolution

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Introduction to Systems Biology for Mathematical Programmers

Cited by 3 publications

References 45 publications

A Simplex Approach to Solving Robust Metabolic Models with Low-Dimensional Uncertainty

A Simplex Approach to Solving Robust Metabolic Models with Low-Dimensional Uncertainty

Robust Analysis of Fluxes in Genome-Scale Metabolic Pathways

Metabolic Networks and Modern Research Problems in Operations Research

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