  In a conformational nonequilibrium steady state (cNESS), enzyme turnover is
modulated by the underlying conformational dynamics. Based on a discrete
kinetic network model, we use the integrated probability flux balance method to
derive the cNESS turnover rate for a conformation-modulated enzymatic reaction.
The traditional Michaelis-Menten (MM) rate equation is extended to a
generalized form, which includes non-MM corrections induced by conformational
population currents within combined cyclic kinetic loops. When conformational
detailed balance is satisfied, the turnover rate reduces to the MM functional
form, explaining its validity for many enzymatic systems. For the first time, a
one-to-one correspondence is established between non-MM terms and combined
cyclic loops with unbalanced conformational currents. Cooperativity resulting
from nonequilibrium conformational dynamics has been observed in enzymatic
reactions, and we provide a novel, rigorous means of predicting and
characterizing such behavior. Our generalized MM equation affords a systematic
approach for exploring cNESS enzyme kinetics.
