Enforcing ensemble averages in molecular dynamics simulations using the Maximum Entropy principle

Molecular dynamics (MD) simulations in explicit solvent are nowadays a fundamental tool used to complement experimental investigations in biomolecular modeling. Typical molecular dynamics simulations are usually limited to the microseconds timescale, although milliseconds timescales can be achieved with ad-hoc machines. To overcome timescale limitations, over the years several enhanced sampling techniques have been developed, allowing to sample events that would require a much longer time in order to spontaneously happen. Simulations length is only one of the two factors contributing to simulations accuracy. The second important factor is the ability of the employed potential energy function, also called force field, to correctly describe the physics of the simulated system. The continuous refinement of enhanced sampling techniques, together with the constant growth of computing power, made the force field the major responsible of simulations inaccuracy. It is then necessary to always validate molecular simulations against experiments when possible. The usual procedure consists in performing a simulation and computing some observable for which an experimental value has been already measured. If the calculated and experimental values are compatible, the simulation can be trusted and other observables can be estimated in order to make genuine predictions. If the discrepancy between calculated and experimental values is significant, one is forced to make a step back and perform a new simulation with a refined force field. For instance, current force fields still exhibit visible limitations in the study of protein-protein interactions, in the structural characterization of protein unfolded states, in the simulation of the conformational dynamics of unstructured RNAs, and in the blind prediction of RNA structural motifs. Force fields improvement is a very challenging task with many groups involved in this “undertaking”. In fact, many correlated parameters should be adjusted, and modifications of one of them could easily lead to unpredictable effects on all the others. Furthermore, it is not guaranteed that the employed potential energy functional form is sufficient to describe the real energy function of the system. As a consequence, an emerging strategy is to restrain the simulations in order to enforce the agreement with experimental data. It must be noticed that experimental knowledge is usually already encoded in the simulation of complex systems (e.g., a short simulation starting from an experimental structure will then be biased toward it). If properly combined with simulations, experiments can be a valuable alternative to quantum chemistry based force-field refinement. Moreover, it must be noticed that usually quantum chemistry calculations are performed on short fragments while experiments are usually performed on much longer molecules. Particular care should be taken when interpreting bulk experiments that measure averages over a large number of copies of the same molecule. These experiments are valuable in the characterization of dynamical molecules, where heterogeneous structures might be mixed and contribute with different weights to the experimental observation. In such cases, a proper combination of them with molecular simulations can allow to construct a high-resolution picture of molecular structure and dynamics.