Convex Representation of Metabolic Networks with Michaelis-Menten Kinetics

by Josh Taylor, Alain Rapaport & Denis Dochain

Polyhedral models of metabolic networks are computationally tractable and provide insight into cellular functions. For example, flux balance analysis is a linear program in which reaction fluxes are optimized over polyhedral mass-balance constraints. In this paper, we augment the standard polyhedral model of a metabolic network with a new, second-order cone representation of the Michaelis-Menten kinetics. This enables us to explicitly model metabolite concentrations without losing tractability. We formulate conic flux balance analysis, a second-order cone program in which reaction fluxes are maximized while metabolite concentrations are minimized. While not as tractable as linear programming, second-order cone programs with hundreds of thousands of variables can be solved in seconds to minutes using modern solvers like Gurobi and MOSEK. In addition to predicting both fluxes and concentrations, we can use conic duality to compute sensitivities to kinetic parameters, i.e., maximum reaction rates and Michaelis constants. We also incorporate the second-order cone representation of the Michaelis-Menten kinetics into dynamic flux balance analysis and minimal cut set analysis. These tools provide new, tractable ways to analyze reaction fluxes and metabolite concentrations in metabolic networks. The Python code for each tool is available at https://urldefense.com/v3/__https://github.com/JAT38/conic-metabolic__;!!NVzLfOphnbDXSw!CB8YzXwI0ErdeBFcgljtFA36uhpf2ATRf6MEgYTiLhceaAzDS6gF7M5m047C62AYZH8xjVWlPanu7H7qQcsSzjBGP_RJ4rc$