Subject: Protein Hydration and Spectral Density Functions.

From: Chuck Watts <[email-masked]>
Date: Fri, 3 Jan 1997 13:09:01 -0600 (CST)

Dear  CCL:

	I have a small queation for you that is not completely
computational in nature although it does pertain to the investigation of
biomolecular dynamics using NMR and I know that many NMR spectroscopists
subscribe to this list. I was recently reading the papers

Otting, G.; Liepinsh, E.; Wutrich, K. (1991) "Protein Hydration in Aqueous
Solution" Science 254, 974-980.

and

Kubinec, M. G.; Wemmer, D. E. (1992) "NMR Evidence for DNA Bound Water in
Solution" JACS 114, 8739-8740.

In these papers combined NOESY and ROESY experiments are used
to measure the lifetimes of waters bound to BPTI and DNA  as interpreted
by a Random Diffusion model.  The model consists of a protein molecule
with a radius rp, a proton spin displaced from the protein center by pp, and a
rotational correlation time of tp, a water molecule with a radius rw, a
proton spin displaced from the water center by pw, and a rotational
correlation time of tw, the protein and water are related to each other
via the diffusion coefficient D which can then be translated into a
correlation time for the interaction using the Einstein-Smoluchowski
relation.  The NOE and ROE rates dependency on the spectral density
function are then given as

	k(NOE) = 6J(2wo) - J(0)

	k(ROE) = 3J(wo) + 2J(0)

and it is stated that the spectral density is related to the rate
processes that govern the modulation of the dipole-dipole coupling of the
system.  My question is as follows, I can easily find the generic
treatment of the spectral density function that relates its dependency on
a single correlation time with the assumption of isotropic tumbling, how
is the spectral density function used in these studies different from this
and how specifically did they generate the NOE/ROE vs. 1/D curves for
this paper given the data above.
	Sorry, I know this pobably isn'y a short queation but I thought
someone on the list might have some insight as to the solution.

Best Wishes,

Charles R. Watts                      ************************************
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