While using our definition for a classical model above allows us to evaluate the energy of a given arrangement of atoms, and potentially to optimize the structure to a local minimum energy conformation when connected to an optimization algorithm, this approach has only limited scientific value. This is especially true when one wants to study a processive enzyme such as the cellulose hydrolysis enzyme CBH I. In such a situation, it is the dynamics of the system that are of interest to researchers trying to uncover its mode of action with the aim of ultimately improving its efficiency. Thus, to obtain such dynamical properties it is necessary to use the potential energy equation discussed above, and the corresponding gradients (or forces) to propagate the system through time. This is achieved by using dynamics methods that are collectively termed molecular dynamics (MD).

8.4.1 Dynamics methods

The workhorse of the MD methodologies and programs is the dynamics engine that treats the system as a classical mechanical system and integrates Newton’s equations of motion based on the force field that is applied. This amounts to initiating some velocities for the atoms, determining forces (the negative gradient of the potential), and then propagating the velocities and adjusting them for the forces one small step at a time. An analytical solution to Newton’s equations of motion for even a four-atom molecule using a typical all-atom force field does not exist and thus it is necessary to employ numerical techniques. Numerous numerical algorithms exist for solving the differential equations that arise from Newton’s equations of motion, two popular formulations being the predictor-corrector methods (47) and finite difference methods. The most commonly used are the finite difference methods and so the following discussion centers on these methods.