The structure of glass has been the subject of many studies, however some

details remained to be resolved. With the advancement of microscopic

imaging techniques and the successful synthesis of two-dimensional materials,

images of two-dimensional glasses (bilayers of silica) are now available,

confirming that this glass structure closely follows the continuous random

network model. These images provide complete in-plane structural information

such as ring correlations, and intermediate range order and with computer

refinement contain indirect information such as angular distributions, and

tilting.

This dissertation reports the first work that integrates the actual atomic

coordinates obtained from such images with structural refinement to enhance

the extracted information from the experimental data.

The correlations in the ring structure of silica bilayers are studied

and it is shown that short-range and intermediate-range order exist in such networks.

Special boundary conditions for finite experimental samples are designed so atoms

in the bulk sense they are part of an infinite network.

It is shown that bilayers consist of two identical layers separated by a

symmetry plane and the tilted tetrahedra, two examples of

added value through the structural refinement.

Finally, the low-temperature properties of glasses in two dimensions

are studied. This dissertation presents a new approach to find possible

two-level systems in silica bilayers employing the tools of rigidity theory

in isostatic systems.

In a typical living cell, millions to billions of proteins—nanomachines that fluctuate and cycle among many conformational states—convert available free energy into mechanochemical work. A fundamental goal of biophysics is to ascertain how 3D protein structures encode specific functions, such as catalyzing chemical reactions or transporting nutrients into a cell. Protein dynamics span femtosecond timescales (i.e., covalent bond oscillations) to large conformational transition timescales in, and beyond, the millisecond regime (e.g., glucose transport across a phospholipid bilayer). Actual transition events are fast but rare, occurring orders of magnitude faster than typical metastable equilibrium waiting times. Equilibrium molecular dynamics (EqMD) can capture atomistic detail and solute-solvent interactions, but even microseconds of sampling attainable nowadays still falls orders of magnitude short of transition timescales, especially for large systems, rendering observations of such "rare events" difficult or effectively impossible.

Advanced path-sampling methods exploit reduced physical models or biasing to produce plausible transitions while balancing accuracy and efficiency, but quantifying their accuracy relative to other numerical and experimental data has been challenging. Indeed, new horizons in elucidating protein function necessitate that present methodologies be revised to more seamlessly and quantitatively integrate a spectrum of methods, both numerical and experimental. In this dissertation, experimental and computational methods are put into perspective using the enzyme adenylate kinase (AdK) as an illustrative example. We introduce Path Similarity Analysis (PSA)—an integrative computational framework developed to quantify transition path similarity. PSA not only reliably distinguished AdK transitions by the originating method, but also traced pathway differences between two methods back to charge-charge interactions (neglected by the stereochemical model, but not the all-atom force field) in several conserved salt bridges. Cryo-electron microscopy maps of the transporter Bor1p are directly incorporated into EqMD simulations using MD flexible fitting to produce viable structural models and infer a plausible transport mechanism. Conforming to the theme of integration, a short compendium of an exploratory project—developing a hybrid atomistic-continuum method—is presented, including initial results and a novel fluctuating hydrodynamics model and corresponding numerical code.

The continuous random network (CRN) model of network glasses is widely accepted as a model for materials such as vitreous silica and amorphous silicon. Although it

has been more than eighty years since the proposal of the CRN, there has not been conclusive experimental evidence of the structure of glasses and amorphous

materials. This has now changed with the advent of two-dimensional amorphous materials. Now, not only the distribution of rings but the actual atomic ring

structure can be imaged in real space, allowing for greater charicterization of these types of networks. This dissertation reports the first work done

on the modelling of amorphous graphene and vitreous silica bilayers. Models of amorphous graphene have been created using a Monte Carlo bond-switching method

and MD method. Vitreous silica bilayers have been constructed using models of amorphous graphene and the ring statistics of silica bilayers has been studied.

This thesis explores a wide array of topics related to the protein folding problem, ranging from the folding mechanism, ab initio structure prediction and protein design, to the mechanism of protein functional evolution, using multi-scale approaches. To investigate the role of native topology on folding mechanism, the native topology is dissected into non-local and local contacts. The number of non-local contacts and non-local contact orders are both negatively correlated with folding rates, suggesting that the non-local contacts dominate the barrier-crossing process. However, local contact orders show positive correlation with folding rates, indicating the role of a diffusive search in the denatured basin. Additionally, the folding rate distribution of E. coli and Yeast proteomes are predicted from native topology. The distribution is fitted well by a diffusion-drift population model and also directly compared with experimentally measured half life. The results indicate that proteome folding kinetics is limited by protein half life. The crucial role of local contacts in protein folding is further explored by the simulations of WW domains using Zipping and Assembly Method. The correct formation of N-terminal β-turn turns out important for the folding of WW domains. A classification model based on contact probabilities of five critical local contacts is constructed to predict the foldability of WW domains with 81% accuracy. By introducing mutations to stabilize those critical local contacts, a new protein design approach is developed to re-design the unfoldable WW domains and make them foldable. After folding, proteins exhibit inherent conformational dynamics to be functional. Using molecular dynamics simulations in conjunction with Perturbation Response Scanning, it is demonstrated that the divergence of functions can occur through the modification of conformational dynamics within existing fold for β-lactmases and GFP-like proteins: i) the modern TEM-1 lactamase shows a comparatively rigid active-site region, likely reflecting adaptation for efficient degradation of a specific substrate, while the resurrected ancient lactamases indicate enhanced active-site flexibility, which likely allows for the binding and subsequent degradation of different antibiotic molecules; ii) the chromophore and attached peptides of photocoversion-competent GFP-like protein exhibits higher flexibility than the photocoversion-incompetent one, consistent with the evolution of photocoversion capacity.

Proteins are a fundamental unit in biology. Although proteins have been extensively studied, there is still much to investigate. The mechanism by which proteins fold into their native state, how evolution shapes structural dynamics, and the dynamic mechanisms of many diseases are not well understood. In this thesis, protein folding is explored using a multi-scale modeling method including (i) geometric constraint based simulations that efficiently search for native like topologies and (ii) reservoir replica exchange molecular dynamics, which identify the low free energy structures and refines these structures toward the native conformation. A test set of eight proteins and three ancestral steroid receptor proteins are folded to 2.7Å all-atom RMSD from their experimental crystal structures. Protein evolution and disease associated mutations (DAMs) are most commonly studied by in silico multiple sequence alignment methods. Here, however, the structural dynamics are incorporated to give insight into the evolution of three ancestral proteins and the mechanism of several diseases in human ferritin protein. The differences in conformational dynamics of these evolutionary related, functionally diverged ancestral steroid receptor proteins are investigated by obtaining the most collective motion through essential dynamics. Strikingly, this analysis shows that evolutionary diverged proteins of the same family do not share the same dynamic subspace. Rather, those sharing the same function are simultaneously clustered together and distant from those functionally diverged homologs. This dynamics analysis also identifies 77% of mutations (functional and permissive) necessary to evolve new function. In silico methods for prediction of DAMs rely on differences in evolution rate due to purifying selection and therefore the accuracy of DAM prediction decreases at fast and slow evolvable sites. Here, we investigate structural dynamics through computing the contribution of each residue to the biologically relevant fluctuations and from this define a metric: the dynamic stability index (DSI). Using DSI we study the mechanism for three diseases observed in the human ferritin protein. The T30I and R40G DAMs show a loss of dynamic stability at the C-terminus helix and nearby regulatory loop, agreeing with experimental results implicating the same regulatory loop as a cause in cataracts syndrome.