Proposed Feature in Targeted MD

From: Minh, David D. (
Date: Mon Jan 31 2011 - 13:12:38 CST

A minor change to targeted MD can make it possible to calculate
potentials of mean force in the region between two structures.

Right now, the code allows targeting toward one final structure, with
the potential given by the following equation,
U_{TMD} = \frac{1}{2} \frac{k}{N} [ RMS(t) - RMS^*(t) ]^2

It should be relatively easy to modify targeted MD and have the option
of targeting the transition between two structures. The potential
would be,
U_{TMD} = \frac{1}{2} \frac{k}{N} [ DRMS(t) - DRMS^*(t) ]^2,
with DRMS(t) = RMS_1(t) - RMS_2(t), and RMS_1 being the RMSD from
structure 1 and RMS_2 being the RMSD from structure 2, and DRMS^*(t)
being a time-dependent function. This bias was used in,
NK Banavali and B Roux. Free Energy Landscape of A-DNA to B-DNA
Conversion in Aqueous Solution. J. Am. Chem. Soc. 127(18), 6966-6876
K Arora and CL Brooks. Large-scale allosteric conformational
transitions of adenylate kinase appear to involve a population-shift
mechanism. PNAS 104(47), 18496-18501 (2007).
and probably other papers.

Using the theory described in,
G Hummer and A Szabo. Free energy reconstruction from nonequilibrium
single-molecule pulling experiments. PNAS 98(7), 3658-61 (2001).
one could calculate the PMF along the DRMS coordinate from a set of
TMD trajectories. The theory described in,
DDL Minh. Multidimensional Potentials of Mean Force from Biased
Experiments along a Single Coordinate. J. Phys. Chem. B 111,
4137-4140 (2007).
can be used to calculate the PMF along other coordinates, or 2D PMFs.
The theory in,
DDL Minh and AB Adib. Optimized Free Energies from Bidirectional
Single-Molecule Force Spectroscopy. Phys. Rev. Lett 100(18), 180602
DDL Minh and JD Chodera. Optimal estimators and asymptotic variances
for nonequilibrium path-ensemble averages. J. Chem. Phys. 131(13),
134110 (2009).
would be useful for combining data for the transition from structure 1
to structure 2 and the reverse process from structure 2 to structure 1.

Actually, it is possible to reconstruct PMFs with the current TMD
code, but I think the PMF between two structures would be more

I'd like to give this a try. Would any NAMD developers be interested
in making this modification? Any thoughts?

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