Leonard Pattenden wrote:
[...]
> > Len, to be the devil's advocate, how many molecules of HIV protease do
> > you think migt be in the budding HIV virion? Just wondering if our
> > concept of pH and ionic strength is at all applicable to similar
> > biological objects.
[...]
>> I am not sure I follow you here.
Let me explain on an example involving the HIV Vif protein:
Camaur D., Trono D.
Journal of Virology. 70(9):6106-11, 1996 Sep.
"Characterization of human immunodeficiency
virus type 1 Vif particle incorporation."
In this paper they found that each HIV particle contains between 7 and
20 /molecules/ of the Vif protein. The main point is, the number of Vif
/molecules/ per viral particle is in single to double digits.
Let's assume that this is the case also for the protease. I think we
can visualize the viral particle as densely packed, semi-solid body with
very little or no solvent inside (think of what it's like inside a
ribosome, for example: very little room for solvent). Somewhere inside
that gelatinous environment, we have /one/ molecule of the viral RNA and
probably just /a few/ molecules (between 7 and 20, in the case of Vif)
of other functional proteins. Now, in this situation the mass-action
law for (bio)chemical kinetics simply does not apply.
The mass action law, talking about "rate constants" and "equilibrium
constants", is /probabilistic/ in nature and not only that: it is based
on the assumption that the chemical system is composed of /very many/
particles ("law of large numbers"). If you run an assay of the protease
at [E] = 1.0 nM in 1.0 mL, you still have 10^(-9) x 10^(-3) x 6 x
10^(+23) = 6 x 10^(+11) or 600,000,000,000 HIV protease molecules in a
test tube. This is a statistical ensemble, so mass-action law applies.
However, if you have 6 molecules instead of 600 billion molecules, the
notion of "rate constant" or "equilibrium constant" is in principle not
applicable, because the HIV protease kinetics inside the virion (as
opposed to in the test tube or even in the cytoplasm of the infected
T-cell) does not follow the "law of large numbers".
[One of my former colleagues teaching pharmaceutical bacteriology always
had his students consider the "pH" inside E. Coli: I forgot the numbers,
but the point is, there seems to be so little water inside each
bacterium that the number of individual protons H(+), or hydronium ions
H3O(+), is extremely low, to the point that the whole notion of "pH"
barely makes sense. I must admit, though, I haven't done the math
myself.]
Eletrophysiologists know about this problem, because they use mechanical
devices ("patch clamps") on ion channels where there might be only
several hundreds of biomolecules responding to physiological events
(change in electric potential; change in ion concentrations). For these
situations, where we can't even use the notion rate constants or
equilibrium constants [also because the biomolecules are firmly embedded
in membranes], people developed a kinetic theory based on something
called "Markov chains" in statistics.
In my post, I was just asking whether the HIV virion, with its 7-20
molecules of the Vif protein (and possibly also a similarly low number
of protease molecules!?), and probably very little water, might not be a
good candidate for talking about HIV protease inhibition in a whole
different way. This "new way" would have to be based on the Markov
Chain statistics, instead of what Guldberg and Waage came up in the
1870's [theirs are actually very interesting papers, by the way] and
what is now know as "mass action kinetics".
-- Petr
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Petr Kuzmic, Ph.D. * BioKin, Ltd. * Consulting & Software Development
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