Follow-up study on hydrogen mass repartitioning (HMR) schemes?

[jchodera]

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:

1. 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)
2. 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!

[kyleabeauchamp]

I found an interesting paper with Huafeng and Ed Harder (http://scitation.aip.org/content/aip/journal/jcp/115/5/10.1063/1.1385159 ; PDF available by google search for paper title) where they showed that slightly different ways to do the PME real vs reciprocal space breakdown can lead to longer outer step timesteps.

I can't really comment on the technical merit or the implementation difficulty, but this will probably be worth discussing with Peter at some point---the authors claim up to a 50% speedup.

[jchodera]

This paper by Grubmüller and Tavan evaluating MTS methods may also be relevant: http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1096-987X(199810)19:13%3C1534::AID-JCC10%3E3.0.CO;2-I/abstract

And this recent paper suggests HMR isn't needed to achieve 5 fs timesteps---just clever MTS methods with clever constraint methods: http://onlinelibrary.wiley.com/doi/10.1002/jcc.23899/full

[jchodera]

Maybe we can collect paper PDFs into a zotero collection?

[jchodera]

Actually, I already have some subcollections on Zotero under "choderalab > Molecular dynamics integration". Will add these there.

[jchodera]

Scratch that---I can't get at the Harder/Xu/berne paper through MSK. Can you add that?

[kyleabeauchamp]

http://www.columbia.edu/cu/chemistry/groups/berne/papers/jcp_115_2348_2001.pdf

[jchodera]

The Berne paper is interesting!

This could be tested most easily by simply implementing Eq. 13 as two CustomNonbondedForce forces, one $+\Delta$ and another $-\Delta$, assigned to separate force groups. One would be added to the direct space electrostatics force group and the other to the reciprocal space electrostatics force group.

Should this prove effective at allowing us to increase the outer timestep by removing some rapidly varying components from the reciprocal space force group, we could likely convince OpenMM to add a CustomPMEForce or CustomReciprocalSpaceForce that would make it easier to specify which expressions should be used in direct and reciprocal space.

[jchodera]

This nice paper from Roux, Dinner, and Weare just came out and uses a multiple timestep method plus Metropolization: http://dx.doi.org/10.1021/acs.jctc.5b00706

They quantify the "error work" instead of the nonequilibrium free energy.

[kyleabeauchamp]

Can someone email me the paper? I don't think I have access.