**From:** Axel Kohlmeyer (*akohlmey_at_cmm.chem.upenn.edu*)

**Date:** Wed Jun 03 2009 - 17:53:53 CDT

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On Wed, 2009-06-03 at 17:49 -0400, Stephen Hicks wrote:

*> Hi,
*

hi stephen,

*> I'm attempting to measure the diffusion constant of a more or less
*

*> spherical protein, the C-terminal domain of HIV capsid protein 1AUM.
*

*> It has 70 amino acids and I estimate the radius to be about a=1.3nm.
*

*> At 310K I estimate the viscosity of water to be anywhere from
*

*> eta=.25cP to .7cP (dependent on the model - I understand TIP3P is much
*

*> lower than experiment). So I ran NVT simulations in a large TIP3P
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*> water box (10nm to a side) with a 0.8fs timestep (langevin thermostat,
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*> rigid bonds) and measured D as follows:
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*>
*

*> D = <(x(t+t')-x(t'))^2>/6t
*

*>
*

*> where x is the (3-vector) position of the protein and the <..> are
*

*> averaging over times t'. For the t part, I calculate the average as a
*

*> function of t and fit the part near zero to a line to compute the
*

*> slope, which is my diffusion constant. But when I do this, my result
*

*> is always on the order of about 3e-7 cm^2/s, while I expect, using
*

actually, it might be better to use the time derivative of your

expression or fit a straight line to the large time part (last

third or so) of your MSD vs. time data. you definitely don't want

to fit so that D(0)=0, because the einstein relation only holds

for large t. have a look at, e.g. page 10 and beyond in.

http://www.theochem.ruhr-uni-bochum.de/~axel.kohlmeyer/files/talk-trieste2004-water.pdf

you also have to factor in system size effects. there should be

a paper by gerhard hummer deriving an estimate formula for that,

but i forgot exactly where.

cheers,

axel.

*> Einstein/Stokes, that
*

*>
*

*> D = kT/(6*pi*eta*a) ~ 2.5e-6 cm^2/s (using .7cP) or 7e-6 cm^2/s (using .25cP).
*

*>
*

*> So at best (using the experimental viscosity rather than the TIP3P
*

*> viscosity) I'm off by nearly an order of magnitude. I've done this at
*

*> different box sizes (4.3nm sides) and gotten the same D, so I'm
*

*> confident that it's not a finite-size effect. I also tried another
*

*> approach, applying a constant force of F=1.093kcal/mol*A =
*

*> (6*pi*.25cP*1.3nm)*12m/s in the +x direction, distributed evenly (by
*

*> mass) among all the atoms in the protein (i.e. F_i = F * m_i/m_total),
*

*> and found that the protein was drifting with a velocity of about
*

*> 0.8m/s - again about an order of magnitude too small!
*

*>
*

*> (On the other hand, I've integrated a box with nothing but water and
*

*> got more or less the correct experimental self-diffusion constant,
*

*> 3.5e-5 cm^2/s -- which may be only a factor of 2-3 too small if TIP3P
*

*> self-diffusion is supposed to be larger than experiment, but then my
*

*> protein results are off even more, by the same factor. I've also
*

*> tried to use TIP4P but so far I haven't been able to get NAMD to run
*

*> properly with it)
*

*>
*

*> I've seen a variety of papers that claim to measure the translational
*

*> diffusion of proteins with MD, so my question is, is there any known
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*> effect that would be throwing off my results? Why can't I reproduce
*

*> reasonable numbers here? Am I missing something in my integration, or
*

*> my water, or the way I'm measuring?
*

*>
*

*> Any help is greatly appreciated!
*

*> Steve Hicks
*

*> Ph.D. Candidate, Henley Group
*

*> Laboratory of Atomic and Solid State Physics
*

*> Cornell University
*

-- ======================================================================= Axel Kohlmeyer akohlmey_at_cmm.chem.upenn.edu http://www.cmm.upenn.edu Center for Molecular Modeling -- University of Pennsylvania Department of Chemistry, 231 S.34th Street, Philadelphia, PA 19104-6323 tel: 1-215-898-1582, fax: 1-215-573-6233, office-tel: 1-215-898-5425 ======================================================================= If you make something idiot-proof, the universe creates a better idiot.

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