Subject: large scale movements

From: Jean-Luc Verschelde <[email-masked]>
Date: Thu, 1 Dec 1994 11:36:38 +0100 (MET)

Hi all,

	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?

		Thanks,	

			Jean-Luc

---

From: [email-masked] (Hinsen Konrad)
Date: Thu, 1 Dec 94 17:21:50 -0500

Jean-Luc Verschelde wrote:

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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