Statistics and Related Topics in Single-Molecule Biophysics

Since the universal acceptance of atoms and molecules as the fundamental constituents of matter in the early-twentieth century, molecular physics, chemistry, and molecular biology have all experienced major theoretical breakthroughs. Although researchers had to wait until the 1970s to see individual biological macromolecules one at a time in action, the field of single-molecule biophysics has witnessed extensive growth in both experiments and theory since then. A distinct feature of single-molecule biophysics is that the motions and interactions of molecules as well as the transformation of molecular species are necessarily described in the language of stochastic processes, whether one investigates equilibrium or far-from-equilibrium living behavior. For laboratory measurements following a biological process, analysis of experimental data obtained by sampling individual participating molecules over time naturally calls for the inference of stochastic processes. The theoretical and experimental developments of single-molecule biophysics thus present interesting questions and unique opportunities for applied statisticians and probabilists. In this article, we review some important statistical developments in connection to single-molecule biophysics, emphasizing the application of stochastic-process theory and the statistical questions arising from modeling and analyzing experimental data.