This thesis revolves around the comprehension of static and dynamic fluctuations in protein dihedrals and their correlation with protein function. We explore four distinct aspects that influence protein functionality:

(a) Establishing long-distance communication between residues. (b) Analyzing the electrostatically heterogeneous nature of protein surfaces. (c) Investigating changes in the conformational thermodynamics of proteins in varying environments. (d) Examining the equilibrium of forces that lead to protein aggregation.

The binding of ligands at distant sites is often integral to protein functionality. In this context, we propose an approach to investigate the causal connections between binding residues in a small protein known as ubiquitin (Ub). This approach is based on the analysis of time-dependent dihedral cross-correlation functions derived from microsecond-long, all-atom Molecular Dynamics (MD) simulations and mathematical modeling. Our findings reveal that the dihedrals of these functionally significant yet spatially distant residues exhibit substantial temporal correlations within biologically relevant time scales.

The distinct characteristics of hydrophilic residues result in the heterogeneous distribution of charges across the protein surface. We address whether this heterogeneity influences the movement of metal ions, which play crucial roles in protein functions. By analyzing the mean squared displacement and self-van Hove function of metal ions from microsecond-long, all-atom MD simulations, we observe that these ions undergo anomalous diffusion due to trapping at various sites. However, reducing the strength of trapping leads to a return to normal Fickian diffusive profiles.

Conformational fluctuations represent another factor capable of modulating protein functionality. In this regard, we calculate the changes in thermodynamic free energy and entropy of a bacterial protein, flagellin, within a lipid bilayer compared to an aqueous medium. We employ a histogram-based method to analyze equilibrium fluctuations of dihedral angles. Our observations suggest that the lipid bilayer provides greater conformational stability to flagellin compared to water, potentially playing a significant role in the immune responses triggered within host cells upon bacterial adhesion.

The self-assembly of misfolded proteins is a crucial aspect of neurodegenerative disorders. We investigate protein aggregation using a model system characterized by a charged core and a solvophobic surface. Through Monte Carlo (MC) simulations and mean-field analytical treatments, we demonstrate that hydrophobicity-mediated attraction primarily drives aggregation in this system. The stability of finite-sized clusters or aggregates is controlled by electrostatic repulsion.