Quantum Diffusive Dynamics of Macromolecular Transitions

We study the role of quantum fluctuations of atomic nuclei in the real-time dynamics of non-equilibrium macro-molecular transitions. To this goal we introduce an extension of the Dominant Reaction Pathways (DRP) formalism, in which the quantum corrections to the classical overdamped Langevin dynamics are rigorously taken into account to order h^2 . We first illustrate our approach in simple cases, and compare with the results of the instanton theory. Then we apply our method to study the C7_eq to C7_ax transition of alanine dipeptide. We find that the inclusion of quantum fluctuations can significantly modify the reaction mechanism for peptides. For example, the energy difference which is overcome along the most probable pathway is reduced by as much as 50%.Comment: Final version, to appear in the Journal of Chemical Physic

Single-Sweep Methods for Free Energy Calculations

A simple, efficient, and accurate method is proposed to map multi-dimensional free energy landscapes. The method combines the temperature-accelerated molecular dynamics (TAMD) proposed in [Maragliano & Vanden-Eijnden, Chem. Phys. Lett. 426, 168 (2006)] with a variational reconstruction method using radial-basis functions for the representation of the free energy. TAMD is used to rapidly sweep through the important regions of the free energy landscape and compute the gradient of the free energy locally at points in these regions. The variational method is then used to reconstruct the free energy globally from the mean force at these points. The algorithmic aspects of the single-sweep method are explained in detail, and the method is tested on simple examples, compared to metadynamics, and finally used to compute the free energy of the solvated alanine dipeptide in two and four dihedral angles

Making the best of a bad situation: a multiscale approach to free energy calculation

Many enhanced sampling techniques rely on the identification of a number of collective variables that describe all the slow modes of the system. By constructing a bias potential in this reduced space one is then able to sample efficiently and reconstruct the free energy landscape. In methods like metadynamics, the quality of these collective variables plays a key role in convergence efficiency. Unfortunately in many systems of interest it is not possible to identify an optimal collective variable, and one must deal with the non-ideal situation of a system in which some slow modes are not accelerated. We propose a two-step approach in which, by taking into account the residual multiscale nature of the problem, one is able to significantly speed up convergence. To do so, we combine an exploratory metadynamics run with an optimization of the free energy difference between metastable states, based on the recently proposed variationally enhanced sampling method. This new method is well parallelizable and is especially suited for complex systems, because of its simplicity and clear underlying physical picture

Atomically detailed simulation of the powerstroke in myosin II by milestoning

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

Characterizing the switching transitions of an adsorbed peptide by mapping the potential energy surface

Peptide adsorption occurs across technology, medicine, and nature. The functions of adsorbed peptides are related to their conformation. In the past, molecular simulation methods such as molecular dynamics have been used to determine key conformations of adsorbed peptides. However, the transitions between these conformations often occur too slowly to be modeled reliably by such methods. This means such transitions are less well understood. In the study reported here, discrete path sampling is used for the first time to study the potential energy surface of an adsorbed peptide (polyalanine) and the transition pathways between various stable adsorbed conformations that have been identified in prior work by two of the authors [Mijajlovic, M.; Biggs, M. J. J. Phys. Chem. C 2007, 111, 15839−15847]. Mechanisms for the switching of adsorbed polyalanine between the stable conformations are elucidated along with the energetics of these switches