Protein structure and motion plays an essential role in nearly all forms of life. Understanding both protein folding and protein conformational change can bring deeper insight to many biochemical processes and even into some devastating diseases thought to be the result of protein misfolding. Experimental methods are currently unable to capture detailed, large-scale motions. Traditional computational approaches (e.g., molecular dynamics and Monte Carlo simulations) are too expensive to simulate time periods long enough for anything but small peptide fragments. This research aims to model such molecular movement using a motion framework originally developed for robotic applications called the Probabilistic Roadmap Method. The Probabilistic Roadmap Method builds a graph, or roadmap, to model the connectivity of the movable object?s valid motion space. We previously applied this methodology to study protein folding and obtained promising results for several small proteins. Here, we extend our existing protein folding framework to handle larger proteins and to study a broader range of motion problems. We present a methodology for incrementally constructing roadmaps until they satisfy a set of evaluation criteria. We show the generality of this scheme by providing evaluation criteria for two types of motion problems: protein folding and protein transitions. Incremental Map Generation eliminates the burden of selecting a sampling density which in practice is highly sensitive to the protein under study and difficult to select. We also generalize the roadmap construction process to be biased towards multiple conformations of interest thereby allowing it to model transitions, i.e., motions between multiple known conformations, instead of just folding to a single known conformation. We provide evidence that this generalized motion framework models large-scale conformational change more realistically than competing methods. We use rigidity theory to increase the efficiency of roadmap construction by introducing a new sampling scheme and new distance metrics. It is only with these rigidity-based techniques that we were able to detect subtle folding differences between a set of structurally similar proteins. We also use it to study several problems related to protein motion including distinguishing secondary structure formation order, modeling hydrogen exchange, and folding core identification. We compare our results to both experimental data and other computational methods.

Proteins are dynamic molecules involved in virtually every chemical process in our bodies. Understanding how they flex and bend provides fundamental insights to their functions. At the atomic level, protein motion cannot be observed using existing experimental methods. To gain insights into these motions, simulation methods are used. However such simulations are computationally expensive. Rigidity analysis is a fast, alternative graph-based method to molecular simulations, that gives information about the flexibility properties of molecules modeled as mechanical structures. Due to the lack of convenient tools for curating protein data, the usefulness of rigidity analysis has been demonstrated on only a handful of proteins to infer several of their biophysical properties. Previous studies also relied on heuristics to determine which choice of modeling options of important stabilizing interactions allowed for extracting relevant biological observations from rigidity analysis results. Thus there is no agreed-upon choice of modeling of stabilizing interactions that is validated with experimental data. In this thesis we make progress towards large-scale validation of protein flexibility using rigidity analysis. We have developed the KINARI software to test the predictive power of using rigidity analysis to infer biophysical properties of proteins. We develop new tools for curating protein data files and for generating biological functional forms and crystal lattices of molecules. We show that rigidity analysis of these biological assemblies provides structural and functional information that would be missed if only the unprocessed data of protein structures were analyzed. To provide a proof-of-concept that rigidity analysis can be used to perform fast evaluation of in silico mutations that may not be easy to perform in vitro, we have developed KINARI-Mutagen. Finally, we perform a systematic study in which we vary how hydrogen bonds and hydrophobic interactions are modeled when constructing a mechanical framework of a protein. We propose a general method to evaluate how varying the modeling of these important inter-atomic interactions affects the degree to which rigidity parameters correlate with experimental stability data.

Cancer is a global epidemic; over 1.5 million new cancer diagnoses and greater than 600,000 deaths due to cancer are estimated to occur in the United States within the year 2015 alone. Approximately two-thirds of patients with bone metastases will experience pain, pathological fractures, spinal cord or nerve root compression, paralysis, impaired mobility, bone marrow infiltration and hypercalcemia of malignancy. We induced bone metastases through inoculation of rat femurs with MDA-MB-231 human breast cancer cells in order to compare the effectiveness of various treatment modalities, disease progression and recovery through the use of imaging methods in current clinical practice. CTRA provides highly accurate monitoring of metastases progression and treatment through both Ibandronate and Paclitaxel therapies. Using computed tomography (QCT)-based analysis to calculate the load bearing capacity of bone infiltrated with metastatic breast carcinoma, fracture risk threshold was predicted using Computed Topography Rigidity Analysis (CTRA) with 100% sensitivity and 90% specificity. The results of this study further validate that there is an existing gap between clinical guidelines and physician’s recommendations. This inconsistency necessitates that the decision making process for the selection of surgical or non-surgical treatment must be narrowed by more advanced prognostic tools such as CTRA.