Protein interactions with the environment are crucial for proper function, butinteraction mechanisms are not always understood. In G protein-coupled receptors (GPCRs), cholesterol modulates the function in some, but not all, GPCRs. Coarse grained molecular dynamics was used to determine a set of contact events for each residue and fit to a biexponential to determine the time scale of the long contacts observed in simulation. Several residues of interest were indicated in CCK1 R near Y140, which is known to render CCK1 R insensitive to cholesterol when mutated to alanine. A difference in the overall residence time between CCK1 R and its cholesterol insensitive homologue CCK2 R was also observed, indicating the ability to predict relative cholesterol binding for homologous proteins. Occasionally large errors and poor fits to the data were observed, so several improvements were made, including generalizing the model to include K exponential components. The sets of residence times in the improved method were analyzed using Bayesian nonparametrics, which allowed for error estimations and the classification of contact events to the individual components. Ten residues in three GPCRs bound to cholesterol in experimental structures had large tau. Slightly longer overall interaction time for the cholesterol sensitive CB1 R over its insensitive homologue CB2 R was also observed. The interactions between the cystic fibrosis transmembrane conductance regulator (CFTR) and GlyH-101, an open-channel blocker, were analyzed using molecular dynamics. The results showed the bromine in GlyH-101 was in constant contact with F337, which is just inside the extracellular gate. The simulations also showed an insertion of GlyH-101 between TM1 and TM6 deeper than the starting binding pose. Once inserted deeper between TMs 1 and 6, the number of persistent contacts also increased. This proposed binding pose may help in future investigations of CFTR and help determine an open-channel structure for the protein, which in turn may help in the development of treatments for various medical conditions. Overall, the use of molecular dynamics and state of the art analysis tools can be useful in the study of membrane proteins and eventuallyin the development of treatments for ailments stemming from their atypical function.

The properties of materials depend heavily on the spatial distribution and connectivity of their constituent parts. This applies equally to materials such as diamond and glasses as it does to biomolecules that are the product of billions of years of evolution. In science, insight is often gained through simple models with characteristics that are the result of the few features that have purposely been retained. Common to all research within in this thesis is the use of network-based models to describe the properties of materials. This work begins with the description of a technique for decoupling boundary effects from intrinsic properties of nanomaterials that maps the atomic distribution of nanomaterials of diverse shape and size but common atomic geometry onto a universal curve. This is followed by an investigation of correlated density fluctuations in the large length scale limit in amorphous materials through the analysis of large continuous random network models. The difficulty of estimating this limit from finite models is overcome by the development of a technique that uses the variance in the number of atoms in finite subregions to perform the extrapolation to large length scales. The technique is applied to models of amorphous silicon and vitreous silica and compared with results from recent experiments. The latter part this work applies network-based models to biological systems. The first application models force-induced protein unfolding as crack propagation on a constraint network consisting of interactions such as hydrogen bonds that cross-link and stabilize a folded polypeptide chain. Unfolding pathways generated by the model are compared with molecular dynamics simulation and experiment for a diverse set of proteins, demonstrating that the model is able to capture not only native state behavior but also partially unfolded intermediates far from the native state. This study concludes with the extension of the latter model in the development of an efficient algorithm for predicting protein structure through the flexible fitting of atomic models to low-resolution cryo-electron microscopy data. By optimizing the fit to synthetic data through directed sampling and context-dependent constraint removal, predictions are made with accuracies within the expected variability of the native state.