A yield-cost tradeoff governs Escherichia coli's decision between fermentation and respiration in carbon-limited growth

Abstract

Many microbial systems are known to actively reshape their proteomes in response to changes in growth conditions induced e.g. by nutritional stress or antibiotics. Part of the re-allocation accounts for the fact that, as the growth rate is limited by targeting specific metabolic activities, cells simply respond by fine-tuning their proteome to invest more resources into the limiting activity (i.e. by synthesizing more proteins devoted to it). However, this is often accompanied by an overall re-organization of metabolism, aimed at improving the growth yield under limitation by re-wiring resource through different pathways. While both effects impact proteome composition, the latter underlies a more complex systemic response to stress. By focusing on E. coli's 'acetate switch', we use mathematical modeling and a re-analysis of empirical data to show that the transition from a predominantly fermentative to a predominantly respirative metabolism in carbon-limited growth results from the trade-off between maximizing the growth yield and minimizing its costs in terms of required the proteome share. In particular, E. coli's metabolic phenotypes appear to be Pareto-optimal for these objective functions over a broad range of dilutions.The physiology of cell growth can nowadays be experimentally probed in exponentially growing bacteria both at bulk (see e.g. the bacterial growth laws detailed in [1][2][3]) and at single cell resolution [4][5][6][7]. Refining the picture developed since the 1950s [8,9], recent studies have shown that changes in growth conditions are accompanied by a massive re-organization of the cellular proteome, whereby resources are re-distributed among protein classes (e.g. transporters, metabolic enzymes, ribosome-affiliated proteins, etc.) so as to achieve optimal growth performance [10]. This in turn underlies significant modifications in cellular energetics to cope with the increasing metabolic burden of fast growth [11][12][13].E. coli's 'acetate switch' is a major manifestation of the existence of a complex interplay between metabolism and gene expression. Slowly growing E. coli cells tend to operate close to the theoretical limit of maximum biomass yield [14,15]. Fast-growing cells, instead, typically show lower yields, together with the excretion of carbon equivalents such as acetate [13]. One can argue that, in the latter regime, cells optimize enzyme usage, i.e. they minimize the protein costs associated to growth, while at slow growth they try to use nutrients as efficiently as possible [13]. As one crosses over from one regime to the other, E. coli's growth physiology appears to be determined to a significant extent by the trade-off between growth and its biosynthetic costs. Interestingly, a similar overflow scenario appears in other cell types in proliferating regimes (see e.g. the Crabtree effect in yeast [16,17] or the Warburg effect in cancer cells [18][19][20]).Several phenomenological models have tackled the issue of how metabolism and gene expression coordinate to optimize growth in ...

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