Advanced Importance Sampling for Complex Soft/Biological System

Abstract

Importance sampling is widely applied to understand physical, chemical properties and mechanical processes in various scientific fields. Importance sampling introduces well-designed weight functions to gather useful information from collections of configurations of molecular systems. In this thesis, I develop an advanced importance sampling that uses clustering and non-Boltzmann distribution sampling, and compare its merits with conventional methods. Advanced importance-sampling methods effectively explore a whole configurational space, in which the free energy landscape has several local minima, and approximately identify important conformations from large simulation data. Thus I unveil the key interactions and mechanisms of complex soft systems and biological systems to explore unknown aspects of life processes. For real implementations, I apply the method to two important complex soft/biological systems (i.e., neurofilament brush (NB) and water molecules), and extract information about global configurational change. NBs domains are categorized into three types according to molecular weight: high (NF-H), medium (NF-M) and low (NF-L). We study the large-scale interactions between the projection domains in various conditions of monovalent salt in the presence of phosphorylation. In practical implementations, grand canonical Monte Carlo simulations are applied to a coarse-grained neurofilament brush model. We model a neurofilament as a uniformly-charged cylindrical backbone with tethered flexible projection tails. We introduce importance coordinates, average distances between amino acid (AA) residues and tethered surface, to quantitatively and intuitively describe the brush structure. We measure its typical looping and back-folding conformation to explain the conformal change under hyperphosphorylation. To obtain more-detailed insight, I apply metastable state analysis, which is a form of advanced importance sampling, by combining principal component analysis (PCA) and the density-based spatial clustering of applications with noise (DBSCAN) algorithm. By using this method, I depict novel major metastable states at different physical environments. Although water has crucial functions in biological systems, its physically and chemically anomalous behaviors, including its very complicated phase boundaries, are still not clearly understood. Numerical study is difficult because of thermodynamic instability during phase transition, which causes a sparsity of sampling in the transition (phase-change) zone. Here, I use the advanced importance sampling technique to study the vapor-liquid phase transition of water. To understand the microstructural mechanism and the nucleation process, the intermediate states during transition must be sampled efficiently. In this thesis I perform generalized canonical ensemble replica exchange molecular dynamics (gceREMD) simulations with an advanced importance sampling method, to extract novel micro-structure of the transient states for water droplets or gas bubbles near the vapor-liquid transition. I analyzed morphological changes of the interfaces between vapor and liquid under various pressures. The nucleation process differed greatly depending on the system pressure. At low pressure, the main liquid nucleus shape is approximately spherical and its dynamical process is well described by classical nucleation theory (CNT). However, CNT does not hold near the critical point in which a major liquid droplet already in a ramified shape formed even before the spinodal due to its small free energy cost for surface fluctuation. We provide quantitative comparisons of the order parameters that are related to variations of the interface shape under different system pressures.