Chapter 9 - Biomolecular structure and dynamics

Abstract

It is well established that not only the “average” or “equilibrium” structure of a protein molecule but also the dynamics around this structure is important for its function. This chapter highlights the essential mathematics concerning some selected and widely used computational techniques to investigate biomolecular structure and dynamics. One important area is protein structure comparison – the root mean square deviation is a metric that indicates the similarity between molecular conformations or, in general, between two ordered sets of points. The potential energy of a complex biomolecular system can be calculated as a function of its atomic coordinates. Many simulation strategies require prior minimization of energy and identification of the stable conformation. Molecular dynamics (MD) simulations predict the movement of each atom in a molecular system, such as a protein. Based on physical laws governing interatomic interaction, the technique has been widely used in physics, chemistry, and biological sciences. Nonetheless, its application is restricted to relatively short time scales. In many circumstances, a more feasible alternative is normal mode analysis (NMA). MD uses a realistic force field to solve the equations of motion approximately. In contrast, NMA finds the exact solutions but uses a simplified force field.