Figure 2.

Scenarios that produce strong correlations between enzyme kinetic parameters. As the logs of the kinetic parameters are linearly related to energy barriers, linear energetic trade-offs should manifest as log–log correlations between kinetic parameters (power laws). Panel A describes a situation in which two kinetic parameters are inextricably linked by the enzyme mechanism, diagrammed here as negative coupling between k_cat,C and S_C/O as an example. These couplings take the form of “equality constraints” in which one parameter determines the other within measurement error. Correlation is expected as long as diverse enzymes are measured. In panel A, selection moves enzymes along the blue curve but cannot produce enzymes off the curve (gray) because they are not feasible. Panel B diagrams an alternative scenario in which the enzyme mechanism imposes an upper limit on two parameters (an inequality constraint). In the “selection within limits” scenario, effective selection is required for correlation to emerge because suboptimal enzymes (e.g., ancestral sequences) are feasible. In the examples plotted, different environmental CO₂ and O₂ concentrations should select for different combinations of rate (k_cat,C) and affinity (S_C/O), resulting in present-day enzymes occupying distinct regions of the plots in panels A and B.