  A central question is how the conformational changes of proteins affect their
function and the inhibition of this function by drug molecules. Many enzymes
change from an open to a closed conformation upon binding of substrate or
inhibitor molecules. These conformational changes have been suggested to follow
an induced-fit mechanism in which the molecules first bind in the open
conformation in those cases where binding in the closed conformation appears to
be sterically obstructed such as for the HIV-1 protease. In this article, we
present a general model for the catalysis and inhibition of enzymes with
induced-fit binding mechanism. We derive general expressions that specify how
the overall catalytic rate of the enzymes depends on the rates for binding, for
the conformational changes, and for the chemical reaction. Based on these
expressions, we analyze the effect of mutations that mainly shift the
conformational equilibrium on catalysis and inhibition. If the overall
catalytic rate is limited by product unbinding, we find that mutations that
destabilize the closed conformation relative to the open conformation increase
the catalytic rate in the presence of inhibitors by a factor exp(ddG/RT) where
ddG is the mutation-induced shift of the free-energy difference between the
conformations. This increase in the catalytic rate due to changes in the
conformational equilibrium is independent of the inhibitor molecule and, thus,
may help to understand how non-active-site mutations can contribute to the
multi-drug-resistance that has been observed for the HIV-1 protease. A
comparison to experimental data for the non-active-site mutation L90M of the
HIV-1 protease indicates that the mutation slightly destabilizes the closed
conformation of the enzyme.
