Molecular Mechanics (Part 2: Nonbonded Interactions)

My last post dealt with interactions between atoms that were separated by a small number of chemical bonds.  This post deals with the interactions between the atoms that are not connected by chemical bonds -- the nonbonded interactions.

Standard fixed-charge force fields typically have a nonbonded potential that accounts for interactions between partial atomic charges and van der Waals interactions that model dispersion interactions.  Because it is computationally efficient, the Lennard-Jones equation is often used to model van der Waals interactions.  The equations for these interactions are shown below:

$$ U_{elec} = \frac 1 2 \sum _ {i=1} ^ N \sum _ {j=1} ^ N \frac 1 {4 \pi \epsilon_0} \frac {q_i q_j} r $$
$$ U_{vdW} = \frac 1 2 \sum_{i=1}^N \sum_{i=1}^N 4 \epsilon_{i,j} \left[ \left( \frac {\sigma} r \right) ^ {12} - \left( \frac {\sigma} r \right) ^ 6 \right] $$

This part of the calculation is by far the most expensive, as interactions between all pairs of particles must be computed.  When trying to model systems in the condensed phase, we need to include the effect of the bulk solvent environment on our system of interest, meaning that we need to somehow account for $\approx 10^{23}$ water molecules!  Since modern hardware is limited to simulating $\approx 10^6$ atoms, we need to have some way of simplifying our model.

The two broad families of methods that researchers typically employ to simulate aqueous environments is to: a) model the solvent implicitly as a continuum dielectric using, for example, the Generalized Born (GB) model and b) construct a periodic unit cell with a small amount of solvent surrounding the solute and tessellate that unit cell in all directions to approximate a bulk solution.

What sets OpenMM apart from other software packages here is, once again, its extreme customizability and flexibility.  Using its Custom GB forces for example, you can rapidly prototype new implicit solvent models to improve the treatment of solvent effects on biomolecules.  All you need is an equation and a set of atomic parameters, and OpenMM will do the rest, letting you test your new models efficiently using the power of GPUs in minutes.