Abstract
Growth rate and yield are fundamental features of microbial growth. However, we lack a mechanistic and quantitative understanding of the rate-yield relationship. Studies pairing computational predictions with experiments have shown the importance of maintenance energy and proteome allocation in explaining rate-yield tradeoffs and overflow metabolism. Recently, adaptive evolution experiments of Escherichia coli reveal a phenotypic diversity beyond what has been explained using simple models of growth rate versus yield. Here, we identify a two-dimensional rate-yield tradeoff in adapted E. coli strains where the dimensions are (A) a tradeoff between growth rate and yield and (B) a tradeoff between substrate (glucose) uptake rate and growth yield. We employ a multi-scale modeling approach, combining a previously reported coarse-grained small-scale proteome allocation model with a fine-grained genome-scale model of metabolism and gene expression (ME-model), to develop a quantitative description of the full rate-yield relationship for E. coli K-12 MG1655. The multi-scale analysis resolves the complexity of ME-model which hindered its practical use in proteome complexity analysis, and provides a mechanistic explanation of the two-dimensional tradeoff. Further, the analysis identifies modifications to the P/O ratio and the flux allocation between glycolysis and pentose phosphate pathway (PPP) as potential mechanisms that enable the tradeoff between glucose uptake rate and growth yield. Thus, the rate-yield tradeoffs that govern microbial adaptation to new environments are more complex than previously reported, and they can be understood in mechanistic detail using a multi-scale modeling approach.
Highlights
Growth rate and yield are basic features of microbial life that are widely implicated in cell fitness, adaptation, and evolution [1]
We found that adaptive laboratory evolution (ALE) experiments of E. coli reveal a two-dimensional rate-yield tradeoff in adapted strains where the dimensions are (i) a tradeoff between growth rate and growth yield, previously reported by [5], and (ii) a tradeoff between substrate uptake rate and growth yield
Negative correlations between μ and Y are observed [5], and for E. coli, this can be explained by a tradeoff between metabolic efficiency and enzymatic efficiency that lead to decreasing Y at high μ [12, 13]
Summary
Growth rate and yield are basic features of microbial life that are widely implicated in cell fitness, adaptation, and evolution [1]. In the context of modeling the phenotypic relation between substrate uptake, metabolism, and biomass growth, there is a great interest in developing quantitative descriptions of the relationship between μ and Y. Negative correlations between μ and Y are observed [5], and for E. coli, this can be explained by a tradeoff between metabolic efficiency and enzymatic efficiency that lead to decreasing Y at high μ [12, 13]. [1] summarized these observations where positive μ–Y correlation at low μ and negative μ–Y correlation at high μ are different parts of a bell-shaped μ–Y curve (Fig 1A). Recent experiments suggest that adaptation to new environments can modify the bell-shaped μ–Y tradeoff [3, 14, 15]
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