Guy Brown asked:
>Why is it that if a reaction has a second order rate constant of anything
>from 10^7 to 10^12 (s^-1) it is described as "diffusion controlled"?
>Surely if collisions can occur at 10^12 then a rate constant of 10^7 can
>not be diffusion controlled. Presumably steric factors are invoked: the
>molecules collide without reacting. But how can we distinguish steric
>factors from the "binding" of the substrate by the enzyme? How low could a
>rate constant go and still be diffusion controlled?
Guy is right that the term diffusion-controlled is often used in a sloppy
hand-waving way. Certainly, the magnitude of the rate constant doesn't by
itself establish whether the process is diffusion-controlled, because the
rate at which molecules diffuse depends on lots of things: molecular mass,
shape, flexibility of the molecule, not to mention temperature, viscosity
etc. of the medium. In general, small molecules diffuse faster than large
ones, and are less affected by viscosity, especially that part of the
viscosity that can be attributed to the presence of dissolved
macromolecules. For a bimolecular collision it's nice if both molecules can
diffuse rapidly, but the essential is that at least one them can. Thus a
reaction between a small molecule and a large one resembles a reaction
between two small molecules more than one between two large ones.
Guy's upper limit of 10^12 M^-1 s^-1 (he writes s^-1 but I assume he means
M^-1 s^-1 for a second-order rate constant) seems very high. The highest
numbers usually seen in the literature are around 10^10 M^-1 s^-1, but some
authorities reckon even this is too high by a factor of 10 or 100. Thus the
range of values that are commonly described as diffusion controlled is not
as wide as 5 orders of magnitude. Nonetheless, the dependence on the
identities of the molecules concerned means that one reaction with a rate
constant of 10^6 M^-1 s^-1 could be diffusion controlled whereas another
with 10^8 M^-1 s^-1 whereas another might not be. I don't think there is
any inconsistency about allowing this as a possibility.
We also need to be cautious about using "diffusion controlled" as a synonym
for "fast" or for "non-rate-limiting". A diffusion-controlled process need
not be particularly fast, and can be rate-limiting, as Jencks has
described. (I can't give a reference for this last point: it comes from a
lecture by Jencks that I heard years ago, but I'm sure he must refer to the
idea in his published work).
The details of Guy's question get us into details that I don't think the
experts agree about, so I'll refrain from putting my oar in. I have not
followed the carbonic anhydrase literature in recent years, so I don't know
if the argument continues, but in the past there was a lot of discussion
about how this enzyme could catalyse a reaction that went 10 or 100 times
faster than any reasonable estimate of the collision rate with the active
site. One popular idea was that the anomaly disappeared if one treated that
whole enzyme molecule as "active" rather than just a region approximately
the size of a bicarbonate ion (effectively assuming thereby that once a
bicarbonate ion struck the enzyme molecule anywhere on its surface surface
diffusion would then bring it to the active site). There was an article by
T. Li and K. Chou in Scientia Sinica 19, 117-136 (1976) about this, and
I've seen other Chinese work much more recently that seems rather similar.
On the other hand there is apparently a large buffer effect in the carbonic
anhydrase reaction, i.e. if you carefully adjust the pH by titration
without adding a buffer the reaction is far slower than it is in an
ordinary buffer. If I understand it rightly this has been interpreted to
mean that bicarbonate is brought to the active site with the help of buffer
catalysis without necessarily needing surface diffusion. This goes pretty
well to the limit of my knowledge of this, but I think that the recent
carbonic anhydrase literature would be a good place for anyone interested
in this to start looking.
If Guy really does mean s^-1 as his unit then he is of course talking about
first-order rate constants, which are *not* limited by diffusion (at least,
not in the sense commonly used by biochemists) but by other things like
bond vibration frequencies.
================================================================
Athel Cornish-Bowden
Laboratoire de Chimie Bacterienne, Centre National de la Recherche
Scientifique, 31 chemin Joseph-Aiguier, B.P. 71, 13402 Marseille Cedex 20,
France
Phone: + 33 491 16 41 38; fax: + 33 491 71 89 14
****Email: If you have had trouble with my alternative address at
bigfoot.com, please use athel at ibsm.cnrs-mrs.fr instead. Even if you have
not had problems I intend to phase out the bigfoot address (though without
cancelling it, so if it has worked before it should continue to do so)
Home page: http://ir2lcb.cnrs-mrs.fr/lcbpage/athel/homepage.htm
