Delete if easily shocked by maths

Dima Klenchin klenchin at
Mon Sep 10 22:40:03 EST 2001

In article , klenchin at (Dima Klenchin) wrote:
>Michael Witty <mw132 at> wrote:
>>Dear All,
>>         one of the reasons I took up biology was that I would never have
>>to do any mathematics.  Sadly my careers advisor was economical with the
>>truth and I have a really difficult one.  BUT maybe one of you has been
>>here before.  Here is the problem:
>>One set of chromatography beads has 0.1mm diameter beads.
>>The other has 1mm diameter beads (approximately).
>>What is the difference in surface area (which could bind protein) for,
>>let us say, 10ml of each of the beads?
>>All this is so I have a rough idea about how much bigger to make the
>>column with coarser beads.
>>Formulae about the surface area of spheres don't seem to help.  I know
>>because I have tried and retired with a headache.
>Simple. There are two cases, depending on what type your beads are. 
>In both: if N spheres of diameter A fit in a given column diameter, then 
>N/10 beads  of diameter 10A fit there. The column is 3D entity, therefore
>we are talking about volumes, meaning three dimensions. Therefore, 
>where 1 big sphere fits, 1000 10X smaller spheres fit (e.g., 10e3).   
>1. Beads are non-porous (e.g. resins). Then binding surface to be 
>concerned with is strictly spheres area. Area ~ R^2 => 10X larger
>sphere means 100X larger surface area. 

>Thus we have that the same
>column volume occupied by bigger beads will have 1000X beads
>with each 100X larger surface. 

Umm, this is horribly written. The above sentense shuld read: 
.. the same column volume occupied by 10X larger beads will have 
1000X _less number of_ beads, with each having 100X larger surface. 

>Thus, the column has to be 1000/100=10
>times bigger to have the same capacity. 
>2. Beads are highly porous (e.g. conventional macromolecular matrix
>based on cellulose, dextrane, agarose or PAAG). Then the binding depends
>on total volume occupied by beads. Volume ~ R^3. Then you have 1000
>less beads, each 1000X smaller volume. Therefore, the the column 
>capacity is independent on bead size! 
>        (This is, of cource, first approximation and idealization, but it
>gives you right idea - when dealing with macroporous sorbents, 
>don't be bothered too much with particle size if capacity is your
>concern. Other things like resolution and back pressure, OTOH, 
>crucially depend on size). 
>        - Dima

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