The AMBER folks have just put out an article on their approach to HMR.
They compute a number of equilibrium static physical properties (phi/psi distribution, rotamer populations, pKas, RMSD distributions, etc.) and a kinetic property (rotamer transition rates) to show that the static properties are mostly undisturbed despite the timestep increase for HMR calculations.
Interestingly, they omitted some simple-to-compute properties that may be especially sensitive to timestep, such as liquid densities, enthalpies of vaporization, and pressures at fixed volume.
There are two follow-up questions we could easily tackle using tools in openmmtools
:
- They don't actually concretely show that sampling is faster by computing correlation times (though Fig 14 is suggestive evidence it speeds up convergence of pKa calculations)
- They don't have some figure of merit that allows a comparison between different timesteps or HMR schemes to allow someone to compare which is "better" or even "acceptable".
Issue #1 is simple to fix---we could just compute integrated autocorrelation functions to directly show that phase space really is sampled more quickly despite the mass repartitioning.
Issue #2 also has a ready solution, using Eq. 6 of this work; see results for flexible and rigid waterboxes plotted in Fig 2:
http://dx.doi.org/10.1103/PhysRevX.3.011007
This number---the steady state nonequilibrium free energy---is essentially a measure of how far the system is driven from the desired equilibrium distribution for any symplectic integration scheme we sandwich inside a VVVR integrator (such as VV, VV with HMR, MTS, etc.).
I even have scripts for this sitting around that could be adapted to use openmmtools.integrators
and openmmtools.testsystems
if this was of interest for putting out a paper on approaches to HMR.
I actually wonder (given previous suggestions from @kyleabeauchamp) if HMR + MTS would work even better. And using Metropolization (e.g. MTS GHMC + HMR) might be a no-brainer if we ever get the speed issues with CustomIntegrator
figured out.
Also, I'm thrilled to see Bennett's paper on HMR get a shout-out!