Global relationships in fluctuation and response in adaptive evolution

Cells generally change their internal state to adapt to an environmental change, and accordingly evolve in response to the new conditions. This process involves phenotypic changes that occur over several different time scales, ranging from faster environmental adaptation without a corresponding change in the genomic sequence to slower evolutionary dynamics involving genetic mutations and subsequent selection. In this regard, a question arises as to whether there are any relationships between such phenotypic changes over the different time scales at which adaptive evolution occurs. In this study, we analyzed simulated adaptive evolution in a simple cell model, and found that proportionality between concentration changes in adaptation and evolution over all components, and the proportion coefficients were closely linked to the change in the growth rate of a cell. Furthermore, we demonstrated that the phenotypic variances in component concentrations due to (non-genetic) noise and genomic alternations are proportional across all components. These global relationships in cellular states were also supported by phenomenological theory and transcriptome analysis of laboratory evolution in {\it Escherichia coli}. These findings provide a basis for the development of a quantitative theory of plasticity and robustness, and to determine the general restriction of phenotypic changes imposed by evolution.