Advances of experimental and computing technology have profoundly changed the field of biophysics. On the experimental side, recent developments in nanotechnology have allowed scientists to follow biological processes on single-molecule basis, providing scientists with powerful means of studying many biophysical processes that were inaccessible just a decade ago. This new frontier also raises significant statistical challenges. It calls upon an urgent need for stochastic modeling, because many classical models derived from oversimplified assumption are no longer valid for single-molecule experiments. Parallel to the experimental progress, the rapid advance of computing resources and Monte Carlo methods also offers great potential for biophysical studies, because in most biophysical experiments inference on the underlying stochastic dynamics is complicated by latent processes, and many biophysical problems are computing intensive. The proposal consists of three projects: (A) Constructing stochastic models that account for the subdiffusion phenomenon in single-molecule biophysics, where the goal is to provide models that are not only physically meaningful, but also capable of explaining the subdiffusion phenomenon that eludes classical diffusion models. (B) Developing data augmentation tools to handle latent processes in biophysical experiments, where the goal is to use the data augmentation techniques to augment the hidden processes so as to efficiently infer from the experimental data the biophysical properties of interest. (C) Developing more efficient Monte Carlo method for computing intensive biophysics problems, where the goal is to construct new Monte Carlo methods capable of sampling complicated distributions, and apply the new method to study the HP protein folding problem.
Technology advances have profoundly changed the society and science in the recent decades. The field of biophysics benefits from these advances in particular, as the technology advances have allowed scientists to study many biological processes that were inaccessible just a decade ago. These advances also raise significant challenges for statistics, because the unprecedented amount of data brought by the new technology requires critical statistical analysis. While the United States leads the world in both statistics and biophysics research, future prominence depends on innovations in both fields and the interdisciplinary collaborations between them. The research in this proposal aims at developing new statistical models and inference tools that can be directly applied to biophysics studies and will lead to new insight about the physics of complex biological processes. The development of statistics and biophysics not only presents many interdisciplinary research opportunities, but also attracts many bright students in mathematical, biological and physical sciences. The proposed research is integrated with the principal investigator's educational activities at both the graduate and undergraduate level. It seeks to meet high academic standards, while providing graduate training that will prepare students for interdisciplinary research careers.
