Na+/H+ antiporters are vital membrane proteins for cell homeostasis, transporting Na+ ions in exchange for H+ across the lipid bilayer. In humans, dysfunction of these transporters are implicated in hypertension, heart failure, epilepsy, and autism, making them well-established drug targets. Although experimental structures for bacterial homologs of the human Na+/H+ have been obtained, the detailed mechanism for ion transport is still not well-understood. The most well-studied of these transporters, Escherichia coli NhaA, known to transport 2 H+ for every Na+ extruded, was recently shown to bind H+ and Na+ at the same binding site, for which the two ion species compete. Using molecular dynamics simulations, the work presented in this dissertation shows that Na+ binding disrupts a previously-unidentified salt bridge between two conserved residues, suggesting that one of these residues, Lys300, may participate directly in transport of H+. This work also demonstrates that the conformational change required for ion translocation in a homolog of NhaA, Thermus thermophilus NapA, thought by some to involve only small helical movements at the ion binding site, is a large-scale, rigid-body movement of the core domain relative to the dimerization domain. This elevator-like transport mechanism translates a bound Na+ up to 10 Å across the membrane. These findings constitute a major shift in the prevailing thought on the mechanism of these transporters, and serve as an exciting launchpad for new developments toward understanding that mechanism in detail.

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.

Human islet amyloid polypeptide (hIAPP), also known as amylin, is a 37-residue intrinsically disordered hormone involved in glucose regulation and gastric emptying. The aggregation of hIAPP into amyloid fibrils is believed to play a causal role in type 2 diabetes. To date, not much is known about the monomeric state of hIAPP or how it undergoes an irreversible transformation from disordered peptide to insoluble aggregate. IAPP contains a highly conserved disulfide bond that restricts hIAPP(1-8) into a short ring-like structure: N_loop. Removal or chemical reduction of N_loop not only prevents cell response upon binding to the CGRP receptor, but also alters the mass per length distribution of hIAPP fibers and the kinetics of fibril formation. The mechanism by which N_loop affects hIAPP aggregation is not yet understood, but is important for rationalizing kinetics and developing potential inhibitors. By measuring end-to-end contact formation rates, Vaiana et al. showed that N_loop induces collapsed states in IAPP monomers, implying attractive interactions between N_loop and other regions of the disordered polypeptide chain . We show that in addition to being involved in intra-protein interactions, the N_loop is involved in inter-protein interactions, which lead to the formation of extremely long and stable β-turn fibers. These non-amyloid fibers are present in the 10 μM concentration range, under the same solution conditions in which hIAPP forms amyloid fibers. We discuss the effect of peptide cyclization on both intra- and inter-protein interactions, and its possible implications for aggregation. Our findings indicate a potential role of N_loop-N_loop interactions in hIAPP aggregation, which has not previously been explored. Though our findings suggest that N_loop plays an important role in the pathway of amyloid formation, other naturally occurring IAPP variants that contain this structural feature are incapable of forming amyloids. For example, hIAPP readily forms amyloid fibrils in vitro, whereas the rat variant (rIAPP), differing by six amino acids, does not. In addition to being highly soluble, rIAPP is an effective inhibitor of hIAPP fibril formation . Both of these properties have been attributed to rIAPP's three proline residues: A25P, S28P and S29P. Single proline mutants of hIAPP have also been shown to kinetically inhibit hIAPP fibril formation. Because of their intrinsic dihedral angle preferences, prolines are expected to affect conformational ensembles of intrinsically disordered proteins. The specific effect of proline substitutions on IAPP structure and dynamics has not yet been explored, as the detection of such properties is experimentally challenging due to the low molecular weight, fast reconfiguration times, and very low solubility of IAPP peptides. High-resolution techniques able to measure tertiary contact formations are needed to address this issue. We employ a nanosecond laser spectroscopy technique to measure end-to-end contact formation rates in IAPP mutants. We explore the proline substitutions in IAPP and quantify their effects in terms of intrinsic chain stiffness. We find that the three proline mutations found in rIAPP increase chain stiffness. Interestingly, we also find that residue R18 plays an important role in rIAPP's unique chain stiffness and, together with the proline residues, is a determinant for its non-amyloidogenic properties. We discuss the implications of our findings on the role of prolines in IDPs.

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.