The Ability of Flux Balance Analysis to Predict Evolution of Central Metabolism Scales with the Initial Distance to the Optimum
Open Access
- 20 June 2013
- journal article
- research article
- Published by Public Library of Science (PLoS) in PLoS Computational Biology
- Vol. 9 (6), e1003091
- https://doi.org/10.1371/journal.pcbi.1003091
Abstract
The most powerful genome-scale framework to model metabolism, flux balance analysis (FBA), is an evolutionary optimality model. It hypothesizes selection upon a proposed optimality criterion in order to predict the set of internal fluxes that would maximize fitness. Here we present a direct test of the optimality assumption underlying FBA by comparing the central metabolic fluxes predicted by multiple criteria to changes measurable by a 13C-labeling method for experimentally-evolved strains. We considered datasets for three Escherichia coli evolution experiments that varied in their length, consistency of environment, and initial optimality. For ten populations that were evolved for 50,000 generations in glucose minimal medium, we observed modest changes in relative fluxes that led to small, but significant decreases in optimality and increased the distance to the predicted optimal flux distribution. In contrast, seven populations evolved on the poor substrate lactate for 900 generations collectively became more optimal and had flux distributions that moved toward predictions. For three pairs of central metabolic knockouts evolved on glucose for 600–800 generations, there was a balance between cases where optimality and flux patterns moved toward or away from FBA predictions. Despite this variation in predictability of changes in central metabolism, two generalities emerged. First, improved growth largely derived from evolved increases in the rate of substrate use. Second, FBA predictions bore out well for the two experiments initiated with ancestors with relatively sub-optimal yield, whereas those begun already quite optimal tended to move somewhat away from predictions. These findings suggest that the tradeoff between rate and yield is surprisingly modest. The observed positive correlation between rate and yield when adaptation initiated further from the optimum resulted in the ability of FBA to use stoichiometric constraints to predict the evolution of metabolism despite selection for rate. The most common method of modeling genome-scale metabolism, flux balance analysis, involves using known stoichiometry to define feasible metabolic states and then choosing between these states by proposing that evolution has selected a metabolic flux that optimizes fitness. But does evolution optimize metabolism, and if so, what component of metabolism equates to fitness? We directly tested the underlying assumption of stoichiometric optimality by comparing predicted flux distributions with changes in fluxes that occurred following experimental evolution. Across three experiments ranging in length from a few hundred to fifty thousand generations, we found that substrate uptake – an input to the model – always increased, but supposed optimality criteria such as yield only increased sometimes. Despite this, there was a clear trend. Highly optimal ancestors evolved slightly lower yield in the course of increasing the overall rate, whereas more sub-optimal strains were able to increase both. These results suggest that flux balance analysis is capable of predicting either the initial metabolic behavior of strains or how they will evolve, but not both.Keywords
This publication has 45 references indexed in Scilit:
- The biomass objective functionCurrent Opinion in Microbiology, 2010
- Cross-species analysis traces adaptation of Rubisco toward optimality in a low-dimensional landscapeProceedings of the National Academy of Sciences of the United States of America, 2010
- Omic data from evolved E. coli are consistent with computed optimal growth from genome‐scale modelsMolecular Systems Biology, 2010
- Genome evolution and adaptation in a long-term experiment with Escherichia coliNature, 2009
- Diversity-based, model-guided construction of synthetic gene networks with predicted functionsNature Biotechnology, 2009
- Historical contingency and the evolution of a key innovation in an experimental population ofEscherichia coliProceedings of the National Academy of Sciences of the United States of America, 2008
- Metabolic flux elucidation for large-scale models using 13C labeled isotopesMetabolic Engineering, 2007
- Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coliMolecular Systems Biology, 2007
- A genome‐scale metabolic reconstruction for Escherichia coli K‐12 MG1655 that accounts for 1260 ORFs and thermodynamic informationMolecular Systems Biology, 2007
- Long-Term Experimental Evolution in Escherichia coli. I. Adaptation and Divergence During 2,000 GenerationsThe American Naturalist, 1991