Robust Analysis of Fluxes in Genome-Scale Metabolic Pathways.
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.
Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, IN, USA.
Michael
M
MacGillivray
Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, IN, USA.
Amy
A
Ko
Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, IN, USA.
Emily
E
Gruber
Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, IN, USA.
Miranda
M
Sawyer
Department of Biotechnology, NTNU - Norwegian University of Science and Technology, Trondheim, Norway. eivind.almaas@ntnu.no.|K.G. Jebsen Center for Genetic Epidemiology, Department of Public Health and General Practice, NTNU - Norwegian University of Science and Technology, Trondheim, Norway. eivind.almaas@ntnu.no.
Eivind
0000-0002-9125-326X
E
Almaas
Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, IN, USA. holder@rose-hulman.edu.
Allen
A
Holder
D004926:Escherichia coli / Q000235:genetics* / Q000378:metabolism*; D064688:Metabolic Flux Analysis; D053858:Metabolic Networks and Pathways; D008962:Models, Theoretical; D049490:Systems Biology / Q000379:methods*