Laboratory Evolution Reveals a Two-Dimensional Rate-Yield Tradeoff in Microbial Metabolism

Growth rate (µ) and yield (Y) are fundamental features of microbial growth. However, we lack a mechanistic and quantitative understanding of the µ–Y 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 a simple µ–Y relationship. Here, we identify a two-dimensional µ–Y tradeoff in adapted E. coli strains where the dimensions are (A) a tradeoff between µ and Y and (B) a tradeoff between substrate uptake rate (q_glc) and Y. We employ a multi-scale modeling approach, combining a previously reported small-scale proteome allocation model with a genome-scale model of metabolism and gene expression (ME-model), to develop a quantitative description of this two dimensional µ–Y relationship using data for E. coli K-12 MG1655. The analysis provides a mechanistic explanation of the two-dimensional µ–Y tradeoff. Furthermore, the analysis identifies modifications to the P/O ratio as a potential mechanism that enables the q_glc-Y tradeoff. Thus, the µ–Y 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.