Optimizing rotary processes in synthetic molecular motors

Abstract

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 Pé clet number, Pe ‫؍‬ V/D. Furthermore, we determined the rate of full, four-step rotations (⍀ eff), from which we derived another dimensionless quantity, the ''rotational excess,'' r.e. This quantity, defined as the relative difference between total forward (⍀ ؉) and backward (⍀؊) 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, ⍀ 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. Markov model ͉ unidirectional rotation

Allocating dissipation across a molecular machine cycle to maximize flux

“…Several other studies have argued that to maintain a high flux, large free energy increases should be broken up into smaller pieces, with no individual free energy change too large [11][12][13]. Even in synthetic molecular motors, it is thought that similar forward rates are optimal (to avoid 'traffic jams') [15]. We find an unequal optimal dissipation allocation occurs when: the nonequilibrium steady-state flux is maximized ; optimization is subject to fixed total dissipation budget per cycle ; the ratio of forward and reverse rate constants varies exponentially, not linearly, with dissipation (Eq.…”

“…Theoretical studies have found that under a variety of criteria, an even allocation of dissipation across all transitions in a machine cycle is optimal [6][7][8][9][10][11][12][13][14][15]. However, many models parametrized to experimental biomolecular machine dynamics contain effectively irreversible transitions [16][17][18][19][20][21][22], suggesting that some transitions dissipate a large amount of free energy compared to the 'reversible' transitions in the same cycle.…”

Light-Induced Translation of Motorized Molecules on a Surface

“…The proposed mechanism is therefore in concert with the well-studied unidirectional rotation of the Feringa motor, which we use. [11][12][13][14] For the azimuthal orientation of the molecules on the surface a preference of the 'wheel-wheel axle' at multiples of 60° relative to the Cu(111) surface is found (Fig. 5a), reflecting arrangement with the underlying crystal directions.…”

“…8 Several synthetic molecular motors have been synthesized, 2,9,10 including a molecular motor developed by Feringa and co-workers that rotates at a frequency in the MHz regime. [11][12][13][14] For ultimate control of molecular machines it is essential that the motor exhibits only one sense of rotation, resulting in unidirectional translation of the molecular machine on a surface, thus only forward and no backward motion, in contrast to random motion in all directions. 2 For synthetic molecular machines to contribute to the vision of nanotechnology by transporting molecular species and cargo on surfaces, the motion of…”

An effective description of a periodic one-dimensional hopping model

“…Actually, in many cases, such basic quantities are the only ones that can be measured directly in experiments. Recent discussion about a modified one-dimensional hopping model indicates that the method in the paper is good in more general hopping models, in which the particle in state i has more than two choices (states i − 1 and i + 1) to jump out of its present state [27]. …”