Designing Free Energy Surfaces That Match Experimental Data with Metadynamics

Creating models that are consistent with experimental data is essential in molecular modeling. This is often done by iteratively tuning the molecular force field of a simulation to match experimental data. An alternative method is to bias a simulation, leading to a hybrid model composed of the original force field and biasing terms. We previously introduced such a method called experiment directed simulation (EDS). EDS minimally biases simulations to match average values. In this work, we introduce a new method called experiment directed metadynamics (EDM) that creates minimal biases for matching entire free energy surfaces such as radial distribution functions and phi/psi angle free energies. It is also possible with EDM to create a tunable mixture of the experimental data and free energy of the unbiased ensemble with explicit ratios. EDM can be proven to be convergent, and we also present proof, via a maximum entropy argument, that the final bias is minimal and unique. Examples of its use are given in the construction of ensembles that follow a desired free energy. The example systems studied include a Lennard-Jones fluid made to match a radial distribution function, an atomistic model augmented with bioinformatics data, and a three-component electrolyte solution where ab initio simulation data is used to improve a classical empirical model.