Browsing by Subject "Reaction pathway"
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Item Atomically detailed simulation of the powerstroke in myosin II by milestoning(2019-08-13) Poole, Katelyn Elizabeth; Elber, Ron; Baiz, Carlos R; Johnson, Kenneth; Makarov, Dmitrii E; Ren, PengyuThe 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 calculationsItem Protein dynamics in sequence and conformational spaces(2016-08) Chen, Szu-Hua; Elber, Ron; Ren, Pengyu; Johnson, Kenneth A.; Ellington, Andrew; Makarov, Dmitrii E.Proteins are biological macromolecules that are involved in a wide range of cellular processes. The diverse functions of proteins are closely related to their dynamics and structures. Structures are frequently coded in a complex manner in the amino acid sequences. In this dissertation I discuss the dynamics of a special class of proteins through studies of their sequences and structures. These proteins are “switches,” which are made of highly similar sequences that fold to dramatically different structures. The existence of protein switches provides a great challenge to structure prediction algorithms as well as to our understanding of the process of protein structure evolution. To identify protein switches, we developed methods that assign switch sequences to structures with high accuracy. One method uses short MD simulations to enrich structural ensembles of protein switches in the neighborhood of their initial conformations for scoring by contact maps. The other method uses evolutionary profiles and contact maps of the wild-type proteins. Both methods were first tested against a series of experimentally engineered proteins in a switching system and then applied to examine a large number of computationally sampled protein switches for a particular pair of structures in sequence space. From the sampled switch sequences we found that making a point mutation near the N- and C-termini of the sequences is more likely to make the proteins switch between structures. To study the conformational change of a protein switch with a fixed sequence between two metastable states in conformational space, we proposed a new algorithm, named “Chain Growth”, to calculate reaction pathways. Unlike commonly used methods that require an initial guess of a path and minimize the energy of the path by local quenching, our method propagates the path in small segments and optimizes the whole path globally. These features avoid the problems of generating very distorted initial structures that other methods frequently encounter and allow more efficient minimization of the path. We provided computational examples of using Chain Growth to calculate the minimum energy path on the Müller potential energy surface as well as to the studies of conformational changes of alanine dipeptide and folding of tryptophan zipper.