Kinetic models for mechanoenzymes: Structural aspects under large loads

Abstract

A broad class of chemical kinetic model for mechanoenzymes is analyzed theoretically in order to uncover structural aspects of the underlying free-energy landscape that determine the behavior under large resisting and assisting loads, specifically the turnover rate or, for a translocatory motor protein, the mean velocity, say, V. A systematic graphical reduction algorithm is presented that provides explicit analytical expressions for mean occupation times in individual biomechanochemical states, for the splitting or backward/forward fractions, for the overall mean dwell time, and for the turnover rate. Application to the previously studied N-state sequential and (N alpha,N beta)-parallel-chain models provides explicit structural criteria (independent of the zero-load transition rates) that determine whether mid /V/ diverges to large values or, conversely, exhibits extrema and converges to a vanishing value as the externally imposed load grows. Closed-form analytical extensions accommodate side-chain and looped side-chain reaction sequences in the enzymatic cycle. A general divided-pathway model is analyzed in detail.