[RASMB] time to reach equilibrium

[John Correia]

Any discussion of time to equilibrium should of course reference the
original paper by vanHolde & Baldwin  1958 J Phys Chem 62: 734-743 where
an equation was given that predicts the time for simple systems.

The question of failure to reach equilibrium cannot easily be separated
from irreversible processes like denatureation/aggregation possibly
involving disufides.  In my experience aggregation during the runs is
the primary reason for failure in reaching a true equilibrium.  This
assignment must be combined with fitting efforts - can the data be
globally fit to a descrete model or are separate K's for each loading
concentration required.  

Often lower temperature helps to achive an approach to equilibrium that
is interpretatble but clearly involves aggregtaion events - see S.S.
Rosenfeld, J.J. CORREIA, J. Xing, B. Rener and H.C. Cheung (1996)
"Structural Studies of Kinesin-Nucleotide Intermediates", J. Biol.
Chem., 271: 30212-30221 - in this case sed vel was invaluable in the
final assignments.

If disulfides are a problem that reducants help and in limited cases
stronger reductants like TCEP help more - see J.J. CORREIA, B.M. Chacko,
S.S. Lam and K. Lin. (2001)  "Sedimentation Studies Reveal a Direct Role
of Phosphorylation in Smad3:Smad4 Homo- and Hetero-Trimerization."
Biochemistry, 40, 1473-1482.  The problem is as mention earlier
disulfides often shuffle and reductants just increase the rate of this
process without removing the aggregation.  For Smads they work pretty
good - but not perfectly (see paper above & manuscript in prep).

A final assignment of the cause of the problem requires fitting models
that take into account the nature of the aggregates - cell to cell
variation makes unique assignments difficult.  This was discussed in a
book chapter by Yphantis & co-workers years ago - D.A Yphantis, J.J.
CORREIA, M.L. Johnson and G.-M. Wu (1978).  "Detection of  
Heterogeneity in Self-Associating Systems," in "Physical Aspects of
Protein Interactions," N. Catsimpoolas, ed., Elsevier, pp. 275-303.  A
down loadable version is on my web page under links of interest.  A
reinvestigation of this will appear in Biophys Chem soon.

The suggestion that kinetics of association or that polymerization in
general is the problem with slow equilibrium achievement is not in my
opinion correct.  I am aware of systems like TMV capsid or some tubulin
or actin assembly systems that might exhibit slow kinetics, but the
problem is the mechanism of assembly, indefinite processes that
re-equilibrate slowly due to cascades of assembly/disassembly.  the
microscopic events are fast.  In general simple systems like
monomer-dimer or 1-3 or 1-2-4 will "never" exhibit this problem.  If
examples in the liturature exist I would like to hear about them?  I
would guess that just like sed vel, if the time constant for
re-equilibration is less than about 100 secs then the boundary will
reflect equilibrium behavior. - Refer to Cann & Kegeles references from
60's & 70's to assess this.

Another issue I am not sure has been extensively investiagted is that
is there is appreciable monomer around, the sed equil system will
equilibrate fast due to the rapid radial diffusion of the momomer, with
the equilibrium at each radial posistion occuring quickly by mass
action.  The equil work by RC Williams on sickle cell hemoglobin
demonstrated this (I need to search for this ref but its early 70's I
think.).





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 Dr. John J. "Jack" Correia
 Department of Biochemistry
 University of Mississippi Medical Center
 2500 North State Street
 Jackson, MS  39216
 (601) 984-1522                                 
 fax (601) 984-1501                             
 email address: jcorreia at biochem.umsmed.edu     
 homepage location: http://biochemistry.umc.edu/correia.html
 dept homepage location:    http://biochemistry.umc.edu/
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