🚀 go-pugleaf

In article <richard.657852606@fafnir.la.locus.com> richard@locus.com (Richard M. Mathews) writes:
>tom@stl.stc.co.uk (Tom Thomson) writes:
>>The interesting thing is how much space they take up, not how big
>>they are:  it's not as if they were closely and rigidly packed so
>>that the space they take depends on their size.   Even with BIG
>>molecules in solution, the average radius is SMALL compared with
>>the mean free path.
>The space occupied by small molecules and radicals in solution
>cannot be anywhere near the space occupied by a DNA molecule.

     This is certainly true.  You are both focussing on the wrong aspect of
the problem however.  It is not the size of the molecules that matters,
but their area of contact with the membrane.
     Consider a simple ion in solution.  It can cover an area of the
membrane roughly proportional to the square of its radius.  Now consider a
big ugly polymer.  In order to even guesstimate how much of the membrane it can
cover, we need to know its conformation in solution.  Suppose it is
hydrophobic and "balls up".  Even if it is a big molecule, the point of
contact will be (to the lowest order approximation) a single atom.  It
therefore doesn't obscure any more of the surface than the simple ion.
Suppose now that the thing loves water and stretches out into a long
string.  To figure out how much of the surface it covers, you have to
work out in detail the statistics of such chains in water.  (This is
related to the problem of computing boundary visits in self-avoiding
random walks of finite length.)  By far the likeliest thing for
reasonably short chains however is that if one end touches the membrane,
no other point will (again, contact area goes roughly as the square of
one atomic radius).  For longer chains, we have a significant
probability that the membrane will be touched in more than one place by
a single molecule.  This explains why significant deviations from the
ideal p~c law are observed with polymers at moderate concentrations.

				Marc R. Roussel
                                mroussel@alchemy.chem.utoronto.ca