Maximum directionality and systematic classification of molecular motors

Track-walking molecular motors are widely used in living cells for transport purposes, and artificial mimics are being vigorously pursued in engineered molecular systems. The defining character for a motor is its intrinsic capability to utilize energy input to rectify a sustained directional motion out of stochastic thermal motion. The energy injection can be coupled to a motor's mechanical steps in different ways, leading to different motor mechanisms. We derive here a formulation for maximum motor performance in terms of a new quantity called directionality based on a general representation of the track-walking motors. Compared to performance measures like velocity and processivity, directionality is a cleaner and more robust indicator of the rectification mechanism that amounts to a motor's inner design/working principles. Meaningful and distinctly different upper limits of directionality were found to exist for a wide variety of experimentally demonstrated and theoretically proposed motors and their biological counterparts. The maximum directionality provides a conceptual framework by which all of these different motors were quantitatively compared and systematically classified according to their mechanistic advancement. The results yield a series of guidelines for artificial motor development, and expose important evolutionary traits of biomotors.