Overcoming stability limitations in biomolecular dynamics. I. Combining
force splitting via extrapolation with Langevin dynamics in LN
We present an efficient new method termed LN for propagating biomolecular
dynamics according to the Langevin equation that arose fortuitously upon
analysis of the range of harmonic validity of our normal-mode scheme LIN.
LN combines force linearization with force splitting techniques and disposes
of LIN's computationally intensive minimization (anharmonic correction)
component. Unlike the competitive multiple-timestepping (MTS) schemes today-formulated
to be symplectic and time-reversible-LN merges the slow and fast forces
via extrapolation rather than "impulses;" the Langevin heat bath prevents
systematic energy drifts. This combination succeeds in achieving more significant
speedups than these MTS methods which are limited by resonance artifacts
to an outer timestep less than some integer multiple of half the period
of the fastest motion (around 4-5 fs for biomolecules). We show that LN
achieves very good agreement with small timestep solutions of the Langevin
equation in terms of thermodynamics (energy means and variances), geometry,
and dynamics (spectral densities) for two proteins in vacuum and a large
water system. Significantly the frequency of updating the slow forces extends
to 48 fs or more, resulting in speedup factors exceeding 10. The implementation
of LN in any program that employs force-splitting computations is straightforward,
with only partial second-derivative information required, as well as sparse
Hessian/vector multiplication routines. The linearization part of LN could
even be replaced by direct evaluation of the fast components. The application
of LN to biomolecular dynamics is well suited for configurational sampling,
thermodynamic and structural questions.
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