This long-term interdisciplinary training program will utilize mathematical modeling and computational techniques to obtain a theoretical framework for a complete qualitative and quantitative analysis and interpretation of newly available data on the molecular motor protein - myosin - and its potential to generate force and displacement. The program will draw on the superb computational facilities and the unusually large constellation of molecular muscle physiologists at the University of Vermont. Realistic mathematical model mechanisms, based upon current biochemical, structural and mechanical knowledge of the myosin motor protein obtained from both optical trapping and in vitro motility assays, and their refinements as they apply to the dynamics of actomyosin interaction will be employed. We will emphasize both deterministic and contemporary stochastic approaches in training our students and postdoctoral research associates who wish to specialize in molecular mechanical studies as well as the art mathematical modeling in the biological sciences. 

A potential benefit of this mathematical modeling project is to use the empirical facts surrounding the actomyosin interaction to propose testable model mechanisms that will predict most of myosin's mechanical and biochemical properties, without which any characterization of myosin molecule will be suspect. The modeling efforts, analyses and hypotheses testing such as we propose to conduct can be of vital importance, providing potentially the only way to fully understand and interpret data from numerous experimental protocols. The models may also apply to other molecular motors (e.g. kinesin, dynein, RNA polymerase). In fact, signaling proteins, such as G-proteins, share a remarkable homology to the catalytic domain of myosin so we can have cross fertilization.

The approach to these problems will be as follows: first, the relevant experimental data, some of which are available from our collaborators, will be analyzed to provide guidance in the formulation of both mechanical and chemomechanical models for actomyosin interaction. Next, the governing equations will be analyzed to develop a qualitative understanding of the models and their parametric sensitivity. The Huxley-Hill formalism will be revisited, together with an investigation into Brownian dynamics and continuum electrostatic models.

Modal superposition methods will be used to uncouple systems of Langevin differential equations emanating from the Brownian dynamics modeling approach, and perturbation methods will be used to derive explicit analytical approximations for both white and colored noise--induced stationary fluctuations.
Finally, the necessary finite difference and finite element numerical techniques for solving the model equations will be developed, and the numerical simulations involved will be done. Fluctuation analytical methods will include windowed mean variance analysis, discrete Fourier transform, and wavelet transform techniques.

Once developed and validated, the models will form the basis for a complete description of the evolving complex micro-interactions in the overall framework of muscular contraction studies. Thus, the results from this project will not only be useful to biotechnological researchers studying molecular motor proteins at the nanotechnological level but also be eminently suitable for the training of graduate students and postdoctoral researchers. This training grant will result in the creation of a coordinated curriculum that will include a formal course, workshop series, and a regular seminar series that will train prospective graduate students and postdocs in mathematical methods applied to a broad spectrum of molecular muscle research. Also, we will vigorously recruit underrepresented groups as trainees for the program and we will create a series of summer mentorships to nurture strong candidates for other graduate programs that utilize quantitative approaches.