Enhanced sampling and free energy methods

In addition to using analysis methods to look for scientifically relevant information in molecular dynamics trajectories it is also possible to increase the sampling rate, or force a reaction event to occur. Such approaches are termed enhanced sampling methods and if used carefully can be used to test a number of hypotheses about reaction mechanisms.

Restraints. Restraining potentials are used to keep a system within a defined region of con­figuration space. Most restraints take the form of a harmonic potential placed on some defined quantity such as distance between two atoms, distance between two parts of a molecule, radius of gyration, or root mean square distance (RMSD) from some reference state. When restraints are used, the states of the system are sampled for configurations that are near the minimum of the restraining potential. NOE distances, from Nuclear Mag­netic Resonance experiments, can be used as restraints to refine structures by exploring configurations but keeping within the defined NMR structural information. Structural changes can be followed or initiated by slowly changing restraining potentials from an initial state to a final state, thus achieving a change that might never occur with a simple MD simulation. Ensemble averages can be extracted from the biased runs to calculate thermodynamic properties, so simulations using restraints are not only exploratory but also for collecting data in state space that are rarely or never visited in normal MD runs. Steered MD. This term refers to forcing MD simulations to follow a trajectory that is biased by a force or biasing potential much like a restraint but with many variations and not necessarily related to a well-defined potential. One clear example is modeling an Atomic Force Microscopy experiment using either a constant pulling force or constant pulling velocity where one end of a molecule is fixed while the other end is pulled in a particular direction. Another example is targeted MD (TMD) (61) in which a final structure is the target and a force is applied to the system, such as a force on the RMSD from the final structure or the Euclidean distance of some atoms from some target, until the target is reached. These methods rarely provide accurate or precise energetic or thermodynamic data, but the approximate data is very useful for probing unknown pathways and providing insight into designing more accurate simulations of the processes or structures of interest. The method of Jarzynski (62, 63) can be used with these methods to gain ensemble statistics if a large number of pulling or targeted simulations are performed, but often this method is no less computationally demanding than the slower sampling methods due to the sheer number of trajectories that must be run. In a very practical sense, this method is very useful to bring a system to a structural state of interest, for which there

is no crystal or NMR structure, such as docking a ligand into a site allowing the nearly natural reconfiguration of the receptor in the process.

Nudged elastic band. The nudged elastic band (NEB) method provides a method for locating low energy transition pathways in biological systems. In NEB (64, 65), the minimum en­ergy path for a conformational change is quantified with a series of images of the molecule describing the path. The images at the endpoints remain fixed in space while each image in-between is connected to its immediate neighbors by “springs” along the pathway that act to keep each image from sliding down the energy landscape onto adjacent images. By running simulated annealing, followed by quenched MD, it is possible to freeze out these images equally spaced along a low energy reaction pathway. The advantage of the NEB method over traditional transition path sampling calculations is that it does not require an initial hypothesis for the pathway. Such simulations, when coupled with QM/MM approaches to allow for bond breaking and formation, will likely prove extremely useful in studying the catalytic action of cellulases acting on cellulose substrates. In particular, such approaches may offer insights into the processive nature of such enzymes.