Phenotypic fluctuation rendered by a single genotype and evolutionary rate

Do proteins with larger fluctuations in their functions show higher rates of their evolutions? To gain some insight on the question, we conducted an in vitro experimental evolution where a mutant of green fluorescence protein (GFP) with random sequence at its N terminus was subjected to ten cycles of random mutagenesis and selection based on the fluorescence expressed by host Escherichia coli cell. The evolution rate was defined as the fluorescence increase from the parental clone to the selected clone at each generation and the fluctuation was defined as the variance in green fluorescence among the host cells of the parental clone at each generation. The analysis of the relationship between the evolution rate and the fluctuation based on fluctuation–dissipation theorem in statistical physics shows that the gene or encoded protein rendering a larger fluctuation of the fluorescence shows a larger evolution rate, i.e., positive correlation between fluctuation and molecular evolution rate