Mathematical Biology Seminar



Tuesday, 02/19/2019, at 4:10 - 5:00








(Bio)Molecular Machines, Markov Walks, and Single Molecule Tracking: Ion Channels, Enzymes, and Synthetic Polymers



James Brozik




Department of Chemistry, WSU










The operation of biological and synthetic molecular machines can be described through a diffusion process on a free energy surface that couples mechanics to fuel.  The framework of any potential energy surface starts with a complete description of the molecular machine’s state-space which takes into account all possible conformations and chemically distinct intermediates, no matter how rare those states maybe.  The underlying mechanism of a molecular machine can then be described in terms of the most probable paths the machine may take during a complete turn over cycle.  A discussion of how one can use single molecule tracking and direct observation to partly identify (bio)chemical states and the transitions between those states will be presented from a maximum likelihood perspective and include a critical look of at the intrinsic limitations of using single molecule fluorescence as a means to uncover molecular detail in a framework model.  Also discussed are some new constrained hidden Markov Models that can account for the intrinsic photophysical and photochemical stochastic transitions observed in single fluorescent probe molecules and used to extract estimates of elementary stochastic rate constants and fundamental thermodynamic values of the molecular machine being probed.  A special emphasis will be placed on the development of framework models for membrane proteins; the P2X1 receptor in particular.  A validation method will be briefly discussed as well as new efforts to make standardized probes for stochastic biophysics.