At first glance, robots and proteins have little in common. Robots are commonly thought of as tools that perform tasks such as vacuuming the floor, while proteins play essential roles in many biochemical processes. However, the functionality of both robots and proteins is highly dependent on their motions. In order to study motions in these two divergent domains, the same underlying algorithmic framework can be applied. This method is derived from probabilistic roadmap methods (PRMs) originally developed for robotic motion planning. It builds a graph, or roadmap, where configurations are represented as vertices and transitions between configurations are edges. The contribution of this work is a set of intelligent methods applied to PRMs. These methods facilitate both the modeling and analysis of motions, and have enabled the study of complex and high-dimensional problems in both robotic and molecular domains. In order to efficiently study biologically relevant molecular folding behaviors we have developed new techniques based on Monte Carlo solution, master equation calculation, and non-linear dimensionality reduction to run simulations and analysis on the roadmap. The first method, Map-based master equation calculation (MME), extracts global properties of the folding landscape such as global folding rates. On the other hand, another method, Map-based Monte Carlo solution (MMC), can be used to extract microscopic features of the folding process. Also, the application of dimensionality reduction returns a lower-dimensional representation that still retains the principal features while facilitating both modeling and analysis of motion landscapes. A key contribution of our methods is the flexibility to study larger and more complex structures, e.g., 372 residue Alpha-1 antitrypsin and 200 nucleotide ColE1 RNAII. We also applied intelligent roadmap-based techniques to the area of robotic motion. These methods take advantage of unsupervised learning methods at all stages of the planning process and produces solutions in complex spaces with little cost and less manual intervention compared to other adaptive methods. Our results show that our methods have low overhead and that they out-perform two existing adaptive methods in all complex cases studied.

Protein folding is considered to be one of the grand challenge problems in biology. Protein folding refers to how a protein's amino acid sequence, under certain physiological conditions, folds into a stable close-packed three-dimensional structure known as the native state. There are two major problems in protein folding. One, usually called protein structure prediction, is to predict the structure of the protein's native state given only the amino acid sequence. Another important and strongly related problem, often called protein folding, is to study how the amino acid sequence dynamically transitions from an unstructured state to the native state. In this dissertation, we concentrate on the second problem. There are several approaches that have been applied to the protein folding problem, including molecular dynamics, Monte Carlo methods, statistical mechanical models, and lattice models. However, most of these approaches suffer from either overly-detailed simulations, requiring impractical computation times, or overly-simplified models, resulting in unrealistic solutions. In this work, we present a novel motion planning based framework for studying protein folding. We describe how it can be used to approximately map a protein's energy landscape, and then discuss how to find approximate folding pathways and kinetics on this approximate energy landscape. In particular, our technique can produce potential energy landscapes, free energy landscapes, and many folding pathways all from a single roadmap. The roadmap can be computed in a few hours on a desktop PC using a coarse potential energy function. In addition, our motion planning based approach is the first simulation method that enables the study of protein folding kinetics at a level of detail that is appropriate (i.e., not too detailed or too coarse) for capturing possible 2-state and 3-state folding kinetics that may coexist in one protein. Indeed, the unique ability of our method to produce large sets of unrelated folding pathways may potentially provide crucial insight into some aspects of folding kinetics that are not available to other theoretical techniques.