The solution of the boundary-value problems for the simulation of transitions of protein conformations
Wednesday, December 5, 2007 - 11:15am - 12:15pm
Under certain kinetic or thermodynamic conditions, proteins make conformational transitions, resulting in significant functional variations. Such dynamic properties can be studied through molecular dynamics simulation. However, in contrast to conventional dynamics simulation protocols where an initial-value problem is solved, the simulation of transitions of protein conformations can be done by solving a boundary-value problem, with the beginning and ending states of the protein as the boundary conditions. While a boundary-value problem is more difficult to solve in general, it provides a more realistic model for the study of protein conformational transitions and has certain computational advantages as well, especially for large scale simulations. Here we study the solution of the boundary-value problems for the simulation of transitions of protein conformations using a standard class of numerical methods called the multiple shooting methods. We describe the methods and discuss the issues related to their implementations for our specific applications, including the definition of the boundary conditions, the formation of the initial trajectories, and the convergence of the solutions. We present the results from using the multiple shooting methods for the study of conformational transitions of a small molecular cluster and an alanine dipeptide, and show the potential extension of the methods to larger biomolecular systems.