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 kcat,C and SC/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 (kcat,C) and affinity (SC/O), resulting in present-day enzymes occupying distinct
regions of the plots in panels A and B.