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Wednesday, January 31, 2001
4:15 p.m., Bldg 380-Room 383-N
Eric Darve
Center for Turbulence Research, Stanford
Advanced
numerical methods for bio-molecular simulations
Abstract
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We investigate the behavior of complex molecular systems over long periods
of time. The best example is the problem of protein folding where given
the chemical formula of a protein we calculate its native folded state.
The simulation of the folding process is an extremely difficult problem
due to the extremely large computational expense. While the oscillations
of the atoms are on the order of 10 fs (10^-14 sec), protein are known
to fold only after a few micro seconds (10^-6 sec) or milli seconds. The
difficulty of such simulations is an obstacle for many other applications
such as transmission of nervous signals to transport of ions and nutrients
across membranes, etc. These time scales can only be attained if new numerical
methods which will reduce the computational expense by orders of magnitude
are developed.
In collaboration with Prof. Andrew Pohorille at NASA Ames, we attacked
the problem on three fronts. The first technique is a new long range force
method based on multigrids. Compared to other existing fast methods (FMM,
P^3 M), it yields a reduced number of floating operations and better parallelization
properties. The second project regards energy barriers which cause proteins
to fold on such long time scales. We devised a new technique to scale
these energy barriers. This will allow to reduce by an order of magnitude
the total number of time steps required to reach the native folded state.
Finally we are in the early stages of the development of a new multiple
time stepping method. Classical methods allow to update the long-range
forces every 5 time steps and become unstable or inaccurate if long range
forces are updated less often. The objective of this new method is to
have the ability of updating the long-range forces every 20 time steps
only.
Papers related to these topics:
A. Brandt and A. A. Lubrecht, ``Multilevel Matrix Multiplication and Fast
Solution of Integral Equations'', J. Comput. Phys., Vol. 90, pp. 348-370,
1990.
B. Garc'ia-Archilla, J. M. Sanz-Serna and R. D. Skeel, ``Long-Time-Step
Methods for Oscillatory Differential Equations,'' SIAM J. Sci. Comput.,
Vol. 20, pp. 930-963, 1998.
E. Darve, M. A. Wilson and A. Pohorille, ``Calculating Free Energies Using
a Scaled-force Molecular Dynamics,'' to appear in Mol. Sim.
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