The interaction between actin and myosin II plays an important role in a variety of cellular functions. In particular, myosin II is involved in muscle contraction, which is attributed to the sliding of thin filament actin past the thick myosin II filaments. Past studies on the structure of myosin have linked severe pathologies to defects in myosin, making it important to understand the mechanism of the system. In this dissertation I will discuss a study in which we focus our analysis on the powerstroke of the myosin II cross bridge cycle. To do this, we use an algorithm called Milestoning which partitions the dynamics into a sequence of trajectories between “milestones” along the reaction coordinate. The structure of myosin II bound to actin in the rigor state was used as a starting point, and a structure for the bound prepowerstroke state was developed using existing published structures for the unbound prepowerstroke state as well as experimental data gathered about the movement of myosin II during the powerstroke. With both the beginning and final states of the powerstroke, we can interpolate between these structures to build intermediate states along the pathway. We generate two approximate reaction paths using a chain minimization approach and targeted molecular dynamics (TMD). The all-atom intermediate structures along the pathway of the powerstroke were developed to be used in further simulations. Milestoning allows for the computation of kinetics and thermodynamics between the smaller partitions along the reaction coordinate to gain further insight into the kinetics of the myosin II powerstroke. This work will lead to a significant improvement in our understanding of the complete powerstroke mechanism, which will in turn facilitate future research on the effects of structural defects in myosin II on powerstroke function and muscle contraction. At present, due to problems in the model of the rigor state that was developed by others we are unable to obtain reliable comparison between our studies and experiment. The second research topic that I will discuss in this dissertation is a study that combines two computational techniques, umbrella sampling and locally enhanced sampling (LES). LES allows for enhanced sampling of a small subset of a system by running simulations using multiple copies of the region of interest. Since the small part does not add significantly to the computational costs, multiplying the local part increases statistics. The LES Hamiltonian, H [subscript LES], is a mean field approximation. Therefore, the weight of the configurations must be corrected to obtain the exact answer by exp(-β(H-H [subscript LES])). The exponential weight may have a wide distribution that impacts efficiency. In combination with umbrella sampling, the umbrella potential ensures that the exponent is close to one and the weight of all LES configurations is significant, while still retaining the computational advantages of LES. For illustration, we compute the free energy of alanine dipeptide with the Ψ angle for a coarse variable using a single copy and two LES copies. The resulting free energy profiles evaluate whether the addition of an umbrella potential to LES improves the accuracy of free energy calculationsChemistr
