CCL: Brownian Dynamics

 Jean-Luc Verschelde wrote:
 	   I want to simulate the large scale movements of the lid
 	   on horse pancreatic lipase . Therefore I need a brownian
 	   dynamics algorithm .
 	   Where can I find this algorithm and do you agree that this
 	   algorithm is the best for this problem?
 The classical reference for Brownian Dynamics is
   D.L. Ermak and J.A. McCammon
   Brownian Dynamics with hydrodynamic interactions
   J. Chem. Phys. 69, 1352 (1978)
 Since I don't know anything about the system you want to study,
 I can't give a "yes" or "no" about the suitability of this
 method for you. However, I can give some general considerations:
 - One condition is that the molecule you are studying is much
   larger than the molecules of the solvent around it. This is
   necessary to treat the solvent as a continuous liquid. It turns
   out that empirically this assumption is valid for much smaller
   molecules than one would expect, so this is probably not a
   problem for you.
 - The second condition is that the velocity of your molecule
   relaxes on a faster timescale than the one on which it
   moves. The relaxation time is the quotient of the mass
   of your molecule and its friction coefficient in the
   solvent. If you know these values and the typical timescale
   of observable motion, you can easily verify this condition.
   If it is not fulfilled, but the first one is, you can still
   use Langevin dynamics.
 - The Brownian Dynamics algorithm derived by Ermak & McCammon
   covers only translational motion. If you want to study
   molecules that do not have (approximately) spherical
   symmetry, you must also consider rotational motion. It is
   certainly possible to derive a similar equation of motion
   for rotation, but as far as I know this has not been done.
 - If the Peclet number for your system, defined as UL/D, where
   U is the typical velocity (on the long time scale), L is
   the size of your molecule (or whatever part of it that
   moves), and D is the corresponding diffusion coefficient,
   is much larger than 1, then the random displacements and
   the derivative of the diffusion matrix can be neglected
   compared to the influence of other forces. In this case,
   called Stokesian Dynamics, both translational and
   rotational equations of motion are available. It is also
   much cheaper.
 - The paper by Ermak & McCammon uses a very simple approximation
   to describe hydrodynamic interactions. In addition to being
   inaccurate, it has also a more fundamental problem (the
   diffusion matrix is not always positive definite). Better
   calculation schemes are available, but much more expensive
   in terms of CPU time.
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