Diminishing returns and tradeoffs constrain the laboratory optimization of an enzyme

Optimization processes, such as evolution, are constrained by diminishing returns - the closer the optimum, the smaller the benefit per mutation, and by tradeoffs - improvement of one property at the cost of others. However, the magnitude and molecular basis of these parameters, and their effect on evolutionary transitions, remain unknown. Here we pursue a complete functional transition of an enzyme with a >10⁹-fold change in the enzyme's selectivity using laboratory evolution. We observed strong diminishing returns, with the initial mutations conferring >25-fold higher improvements than later ones, and asymmetric tradeoffs whereby the gain/loss ratio of the new/old activity decreased 400-fold from the beginning of the trajectory to its end. We describe the molecular basis for these phenomena and suggest they have an important role in shaping natural proteins. These findings also suggest that the catalytic efficiency and specificity of many natural enzymes may be far from their optimum.