Theory of the statistics of kinetic transitions

PHYS 583

Irina Gopich, and Attila Szabo, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892
Single-molecule spectroscopy can monitor transitions between two microscopic states when these transitions are associated with the emission of photons. A general formalism is developed for obtaining the statistics of such transitions from a microscopic model when the dynamics is described by master or rate equations or their continuum analog, multidimensional reaction-diffusion equations. The focus is on the distribution of the number of transitions during a fixed observation time, the distribution of times between transitions, and the corresponding correlation functions. It is shown how these quantities are related to each other and how they can be explicitly calculated in a straightforward way. Our formalism reduces to renewal theory when the monitored transitions either go to or originate from a single state. The influence of dynamics slow compared with the time between monitored transitions is treated in a simple way, and the probability distributions are expressed in terms of Mandel-like formulas. The formalism is illustrated by a detailed analysis of the statistics of catalytic turnovers of enzymes.

Poster Session
7:30 PM-10:00 PM, Wednesday, 13 September 2006 Moscone Center -- Hall D, Poster

8:00 PM-10:00 PM, Monday, 11 September 2006 Moscone Center -- Hall D, Sci-Mix

Division of Physical Chemistry

The 232nd ACS National Meeting, San Francisco, CA, September 10-14, 2006