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.