Symmetry based mechanism for hand-over-hand molecular motors

Dynamics of a polymer in a Brownian ratchet

We have used Brownian dynamics simulations to study the dynamics of a bead-and-spring polymer subject to a flashing ratchet potential. To elucidate the role of hydrodynamic (HD) interactions, simulations were carried out for the cases where HD interactions are present and when they are absent. The average speed of the polymer and its conformational properties were examined upon variation in the polymer length, N, and the ratchet spatial period, L. Two distinct dynamical regimes were evident. In the low-N/high-L regime, the velocity decreases with increasing N, and center-of-mass diffusion is a key part of the motional mechanism. By contrast, in the high-N /low-L regime, the velocity is insensitive to variation in N, and motion is achieved via the coupling of internal modes to the cycling of the ratchet potential. The location of the regimes is correlated with the average conformational state of the polymer. Incorporating HD interactions increases the average polymer velocity for all polymer lengths and ratchet spatial periods considered. The dynamical behavior of polymers in the low-N/high-L regime can be understood using simple a theoretical model that yields quantitatively reasonable predictions of the polymer velocity.

Thermodynamics and kinetics of molecular motors

Molecular motors are first and foremost molecules, governed by the laws of chemistry rather than of mechanics. The dynamical behavior of motors based on chemical principles can be described as a random walk on a network of states. A key insight is that any molecular motor in solution explores all possible motions and configurations at thermodynamic equilibrium. By using input energy and chemical design to prevent motion that is not wanted, what is left behind is the motion that is desired. This review is focused on two-headed motors such as kinesin and Myosin V that move on a polymeric track. By use of microscopic reversibility, it is shown that the ratio between the number of forward steps and the number of backward steps in any sufficiently long time period does not directly depend on the mechanical properties of the linker between the two heads. Instead, this ratio is governed by the relative chemical specificity of the heads in the front-versus-rear position for the fuel, adenosine triphosphate and its products, adenosine diphosphate and inorganic phosphate. These insights have been key factors in the design of biologically inspired synthetic molecular walkers constructed out of DNA or out of small organic molecules.