Modeling genome-wide enzyme evolution predicts strong epistasis underlying catalytic turnover rates

Systems biology describes cellular phenotypes as properties that emerge from the complex interactions of individual system components. Little is known about how these interactions have affected the evolution of metabolic enzymes. Here, we combine genome-scale metabolic modeling with population genetics models to simulate the evolution of enzyme turnover numbers (k_cats) from a theoretical ancestor with inefficient enzymes. This systems view of biochemical evolution reveals strong epistatic interactions between metabolic genes that shape evolutionary trajectories and influence the magnitude of evolved k_cats. Diminishing returns epistasis prevents enzymes from developing higher k_cats in all reactions and keeps the organism far from the potential fitness optimum. Multifunctional enzymes cause synergistic epistasis that slows down adaptation. The resulting fitness landscape allows k_cat evolution to be convergent. Predicted k_cat parameters show a significant correlation with experimental data, validating our modeling approach. Our analysis reveals how evolutionary forces shape modern k_cats and the whole of metabolism.