Bio-molecules and proteins are building blocks of life as is known, and understanding

their dynamics and functions are necessary to better understand life and improve its

quality. While ergodicity and fluctuation dissipation theorem (FDT) are fundamental

and crucial concepts regarding study of dynamics of systems in equilibrium, biological

function is not possible in equilibrium.

In this work, dynamical and orientational structural crossovers in low-temperature

glycerol are investigated. A sudden and notable increase in the orientational Kirk-

wood factor and the dielectric constant is observed, which appears in the same range

of temperatures that dynamic crossover of translational and rotational dynamics oc-

cur.

Theory and electrochemistry of cytochrome c is also investigated. The seeming

discrepancy in reorganization energies of protein electron transfer produced by atom-

istic simulations and those reported by protein electrochemistry (which are smaller)

is resolved. It is proposed in this thesis that ergodicity breaking results in an effective

reorganization energy (0.57 eV) consistent with experiment.

Ergodicity breaking also affects the iron displacement in heme proteins. A model

for dynamical transition of atomic displacements in proteins is provided. Different

temperatures for rotational and translational crossovers of water molecules are re-

ported, which all are ergodicity breaking transitions depending on the corresponding

observation windows. The comparison with Mössbauer spectroscopy is presented.

Biological function at low temperatures and its termination is also investigated in

this research. Here, it is proposed that ergodicity breaking gives rise to the violation

of the FDT, and this violation is maintained in the entire range of physiological

temperatures for cytochrome c. Below the crossover temperature, the protein returns

to the FDT, which leads to a sudden jump in the activation barrier for electron

itransfer.

Finally the interaction of charges in dielectric materials is discussed. It is shown

that the potential of mean force between ions in polar liquids becomes oscillatory at

short distances.

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.