From: STEVE HARDING <sczsteve@szn1.agric.nottingham.ac.uk>
  To  : rasmb@bbri.harvard.edu
  Date: Thu, 3 Jul 1997 09:05:37 GMT0BST

(Fwd) Re: hollow cylinders

Dear Julius
I agree with Allen Minton's reply to you re; the hollow bit doesnt 
matter re: the virial coefficient.  The cylinder is a limiting form 
of a general ellipsoid, the formulae worked out by Rallison & myself 
(J. Coll. Int. Sci. 1985, 103, 284-289).  It is available in the form 
of a PC programme COVOL which we are just about to lodge on the RASMB 
database.  It requires an estimate for the hydration of the 
macromolecule,  molecular weight and aspect ratio.  If charge 
contributions aren't adequately supressed you need to enter the charge(valency) Z
 (found by titrtaion - see e.g. Jeffrey 
et al, J.Phys.Chem 1977, 81, 776) and the ionic strength in mol/ml  
Like everything else, it assumes dilute solution behaviour  (i.e. the effects of 
simultaneous encounters between 3 or more particles are negligible), 
the particles are rigid and Brownian.

There is a similar programme already out (ELLIPS2 - should also be on 
the database by now) which works out 
the frictional ratio due to shape (we call the Perrin function P) for 
user specified semi-axial dimensions a,b,c (set b=c for a cylinder). 
along with a whole host of weird and wonderful functions.  The Garcia 
de la Torre routine SOLPRO does the same for bead models (i.e. you 
model your cylinder as a composite array of beads).. 
ELLIPS: Eur. Biophys. J. 25 (1997) 347
SOLPRO ibid, 361

Hope this helps
Steve Harding