Optimizing rotary processes in synthetic molecular motors.

We deal with the issue of quantifying and optimizing the rotation dynamics of synthetic molecular motors. For this purpose, the continuous four-stage rotation behavior of a typical light-activated molecular motor was measured in detail. All reaction constants were determined empirically. Next, we developed a Markov model that describes the full motor dynamics mathematically. We derived expressions for a set of characteristic quantities, i.e., the average rate of quarter rotations or "velocity," V, the spread in the average number of quarter rotations, D, and the dimensionless Péclet number, Pe = V/D. Furthermore, we determined the rate of full, four-step rotations (Omega(eff)), from which we derived another dimensionless quantity, the "rotational excess," r.e. This quantity, defined as the relative difference between total forward (Omega(+)) and backward (Omega(-)) full rotations, is a good measure of the unidirectionality of the rotation process. Our model provides a pragmatic tool to optimize motor performance. We demonstrate this by calculating V, D, Pe, Omega(eff), and r.e. for different rates of thermal versus photochemical energy input. We find that for a given light intensity, an optimal temperature range exists in which the motor exhibits excellent efficiency and unidirectional behavior, above or below which motor performance decreases.