We continued our study of the general dynamic properties of a Brownian particle in a fluctuating periodic ratchet potential. Specifically, we obtained a general rule relating the generation of direction reversal (the direction of the particle can be reversed by varying the frequency of the fluctuation) and the geometry of the ratchets in a two-state model. If the potential in each period is shaped like a regular ratchet with two-straight arms, direction reversal is not possible. If one of the linear arms is kinked or replaced by a continuous nonlinear function, then direction reversal is possible. The results are useful in designing devices for separating proteins or other small particles based on the size and the charge of the particle and the viscosity of the medium (work by Chen, Yan, Rubin, and Miura). We also started working on the mechanisms of regulation of muscle contraction by calcium. In 1980, Hill, Eisenberg, and Green (PNAS 77, 3186-90 (1980)) proposed a cooperative model in which the actin monomers covered by a tropomyosin-troponin complex can exist in two states, one active and the other inactive. The equilibrium between the two states is controlled by the concentration of the calcium in solution. The model is able to simulate the equilibrium binding of S1 (subfragment 1 of a trypsin digested myosin molecule) to actin in the presence and absence of calcium. Recently, a three-state model including a blocked state in the kinetic scheme has been proposed by Geeves and colleagues based on the kinetics of the binding reactions. In this study, we examined whether the two-state model of Hill, Eisenberg, and Green can simulate the kinetics of binding of S1 to regulated actin or not. Preminary results showed that the experimentally obtained kinetic curves can be simulated qualitatively by the two-state model, without adding the blocked state to the scheme. Thus, the calcium regulation of muscle contraction may not require that actin exists in three state (work by Chen, Yan, Chalovich).Another project in which we have made some progress is the molecular dynamics study of the conformation of kinesin (a microtubule-based molecular motor) in solution bound with different nucleotides. The main purpose is to investigate whether the fluctuations of movement of the residues in the linker region (the region linking the coil-coiled stem to the head (or the motor) part of the kinesin) are different with different bound nucleotides. Due to the long computer times needed, the calculations are slow. However, we have found that the fluctuations are large when ADP is bound and small when ATP is bound or without a nucleotide. The results suggest that the dynamics of motion in the linker region may play an important role in the directional movement of kinesin molecules on microtubule (work by Yan and Chen) - motility, fluctuation, myosin, actin, microtubule, muscle, kinesin, Brownian motion
