[RASMB] time to reach equilibrium

[John Correia]

Allen

If the system is at equilibrium when you start then velocity and
probably equilibrium gets you the right answer (see Stafford paper in
Methods).  

But the system you are describing is actually a kinetically mediated
system where nucleation is unfavorable and thus the # of polymers is
limiting.  This occurs in microtubule assembly and thin filament
assembly.  My allusion to TMV capsid the other day is very relavant
here.  In that case temperature is extremely important and if you
overshoot re-equilibration takes days/weeks.  The tubulin and actin
systems are more complicated because they also exhibit GTP hydrolysis
(ie. non-equilibrium system) and polymer annealing reactions.  The
opinion has been expressed that the annealing system never reaches
equilibrium unless there is a single infinitely long polymer.

For vinca alkaloid induced spirals a slow nucleation step does not
exist, & thus the sytem is not kinetically mediated.  Re-equilibration
upon dilution for example is slow because many, many endwise
dissociation events occurs to reach the new equilibrium state.  But the
sytem also exhibits breaks in the middle of each spiral polymer (all the
bonds are identical!) and thus probably both growth and disassmbly can
occur by an annealing mechanism too.  (see S. Lobert, B. Vulevic and
J.J. CORREIA, (1996) "Interaction of Vinca Alkaloids  with Tubulin: A
Comparison of Vinblastine, Vincristine and Vinorelbine",  Biochemistry,
35, 6806-6814. for stopped flow data)

Nonetheless, couple this to tubulin instability and you understand why
we primarily (exclusively?) use sed velocity for this system.



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 Dr. John J. "Jack" Correia
 Department of Biochemistry
 University of Mississippi Medical Center
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>>> "Allen P. Minton" <minton at helix.nih.gov> 06/09/03 05:16AM >>>
Let me put in my two cents' worth on the issue of equilibration time
for
proteins undergoing indefinite polymerization (a la actin, tubulin). 
It
was recognized some time ago (I think originally by Oosawa and
Asakura,
and Damien Hall and I have recently studied this in some detail) that
reversible (as opposed to irreversible) polymerization takes place in
two
fairly distinct time domains.  The fast phase is the incorporation of
monomer into polymer.  The slow phase is the redistribution of
protomers
between polymers to achieve the final equilibrium distribution of
polymer
lengths.  The redistribution phase is essentially entirely
entropy-driven
and may require orders-of-magnitude longer time than it takes to
achieve
the initial polymerization.  Note that the slow phase, while not
significantly changing the amount of polymer, will change the mass
distribution, and hence the weight-average-molar mass, and hence the
concentration gradient in the centrifuge.  Caveat experimentor!