[RASMB] Sedimentation equilibrium question

Arthur Rowe arthur.rowe at nottingham.ac.uk
Thu Mar 29 08:28:25 PDT 2007


Greetings, everyone

Jo makes a point (below) which is in fact a general one. Assuming your
software allows it (and I know that Jo and I both use pro Fit, which makes
it easy) then every time you fix a parameter in a fit you should at least
give thought to constraining that value within error bounds. Unless it is
something like a radial value, where error can be taken as nil.

For a protein, the vbar value is indeed critical in evaluating sigma. Errors
in solvent density you can pretty much forget about, so final error in the
(1 - vbar* rho) term ought to be about 3 times greater than the uncertainty
in (usually computed via SEDNTERP) vbar value you use. I would reckon that
±1% in sigma would be OK for most cases.

That may sound a bit optimistic. But we need to bear in mind that if you do
have a system of some polydispersity, then the sigma value tends to be
significantly correlated with the (floated) baseline (E) value. So - whilst
I would 'give thought' to floating, I am not sure it would always be very
positive thought. There is a danger that shoving in one extra parameter into
a fit one may merely permit that fit to take advantage of the elbow room
given by data error to seek out an optimal chi-squared/whatever.

Arthur


Dear Sarah,

If I may chip in again, Arthur is basically correct - one usually knows
the actual monomer mass very accurately from sequence - but there is
still the problem of the v-bar to use for the residual mass correcting
for Archimedian buoyancy [i.e. M(1 - v-bar*rho)], which is why it is
usual to float the mass, at least within bounds.
One can also get interesting problems, such as one protein I worked on
which appeared as a dimerising, non-ideal dimer - which would never
dissociate (under non-denaturing conditions) to monomer.  It was a
couple of years later that my colleagues solved the crystal structure
and showed that it was a coiled-coil dimer, which would snap together on
synthesis and not dissociate again!

Jo

Arthur Rowe wrote:
> Hi Sarah
>
> There are lots of good suggestion coming your way - so I will not
> duplicate. But one little point does occur to me. You sound to be
> floating the (reduced) molecular weight of your protein. Assuming that
> what you have is a chemically pure system (i.e. there is only one
> covalently bound entity present (you say it is 84 kDa, purified) then
> you should be /fixing/ this parameter for the monomeric species,
> whatever mode of analysis you use.
>
> Oh, and one little thing more. There are dangers in the "try every
> model you can think of, select the one which has best
> residuals/whatever as being _correct_" approach. It has long been
> appreciated that simple theory shows that if you keep on doing this,
> then you will always, eventually, come up with something that looks
> good. Doesn't mean it's right, though. The famous example of this is
> the search (a few years back) for ways of predicting earthquakes -
> which eventually came up* with a statistically good correlation
> between occurrence of terrestrial earthquakes and the phases of a moon
> of the planet Uranus!
>
> Kind regards
>
> Arthur
> *the authors /did/ report this with tongue firmly in cheek, I should add.
> -
> *************************
> Arthur Rowe
> Lab at Sutton Bonington
> tel: +44 115 951 6156
> fax: +44 115 951 6157
> *************************
>
>
>     *From: *Tom Laue <tml at cisunix.unh.edu>
>     *Organization: *CAMIS-UNH
>     *Reply-To: *Tom.Laue at unh.edu
>     *Date: *Thu, 29 Mar 2007 09:06:47 -0400
>     *To: *Sarah Siegel <ssiegel at scripps.edu>
>     *Cc: *rasmb at server1.bbri.org
>     *Subject: *Re: [RASMB] Sedimentation equilibrium question
>
>
>     Hi Sarah-
>     Have you done sedimentation velocity analysis of your samples?
>     What does
>     it show with respect to the concentration dependence of the g(s)
>     patterns? This sort of analysis will tell you whether it is
>     worthwhile
>     doing equilibrium sedimentation by: 1) showing whether there is
>     aggregate, 2) showing if there is significant mass action
>     association/dissociation in the concentration range where you are
>     working and 3) making sure there are no smaller species.
>     With respect to the equilibrium analysis- fit the individual data
>     sets
>     first to a simple model (average molar masses as a function of
>     concentration).Essentially doing what Jo and Ariel suggested.
>     There are
>     several programs to help with this: Sedanal has Biospin built into
>     it,
>     MStar, Segal. The trick with any of these analyses is making sure the
>     signal is equal to the concentration, and it is the presence of any
>     baseline offset (i.e. zero signal does not equal zero concentration)
>     that is the usual concern. For absorbance data, the baseline offset
>     usually is small and can be determined experimentally by pelleting
>     your
>     material (or at least making sure some data are acquired at a rotor
>     speed where the meniscus region is entirely depleted of protein).
>     Interference optics are tougher to deal with since the baseline
>     offset
>     may change with rotor speed (due to window stresses). You may use
>     HeteroAnalysis, fitting to an ideal single component and fit for the
>     baseline offset. In this latter case, M will be between the weight
>     and
>     z- average, typically closer to the latter.
>     See if the individual data sets reveal systematic behavior with
>     respect
>     to concentration and rotor speed. If the M increases with
>     concentration
>     (I would suggest acquiring data over a wider initial concentration
>     range), then you have a mass action association, plus you have
>     some idea
>     (within a decade) of the monomer concentration range where the mass
>     action association is important to protein behavior. If M decreases
>     significantly with increasing rotor speed, you probably have
>     irreversible aggregate (but you would know this clearly from velocity
>     analysis).
>     Best wishes,
>     Tom
>
>     Sarah Siegel wrote:
>     > Hi Everyone,
>     >
>     > I am a beginner in the world of AUC and I'm having a lot of trouble
>     > fitting sedimentation equilibrium data.  I was hoping someone could
>     > help me figure out if my problem is in the way I'm fitting or
>     the way
>     > I set up my experiment.  I did attend last spring's AUC workshop at
>     > UConn, but this is my first time really running an equilibrium
>     > experiment.  The system I have is an 84 kDa purified protein
>     that may
>     > be in equilibrium with dimer, possibly also some larger species.
>      I am
>     > trying to get an idea of what the dominant species present are.
>      I ran
>     > two samples, at 1.0 and 0.5 mg/mL, collecting interference data
>     at a
>     > range of speeds from 8,000 rpm to 20,000 rpm.  I watched the
>     approach
>     > to equilibrium using Match in HeteroAnalysis.  I have been using
>     > HeteroAnalysis to try to fit the data globally.  I have tried
>     fitting
>     > to several models, including ideal and nonideal systems,
>     > monomer-dimer, monomer-trimer, monomer-tetramer, and several three
>     > species equilibria.  So far the best fit I have has rms
>     deviations of
>     > 0.027 using a nonideal model, however this fit also tells me the
>     > molecular weight of the protein is 138 kDa, which is larger than
>     > monomer and smaller than dimer, and the residuals do not have a
>     random
>     > pattern.  Does anyone have any ideas about another way I should be
>     > fitting this, or other data I should collect?  Thanks for your help!
>     >
>     > Sarah
>     >
>     > Sarah Siegel
>     > Graduate Student
>     > The Scripps Research Institute
>     > La Jolla, CA
>     > _______________________________________________
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>     > RASMB at rasmb.bbri.org
>     > http://rasmb.bbri.org/mailman/listinfo/rasmb
>     >
>
>     -- 
>     Department of Biochemistry and Molecular Biology
>     University of New Hampshire
>     Durham, NH 03824-3544
>     Phone: 603-862-2459
>     FAX:   603-862-0031
>     E-mail: Tom.Laue at unh.edu
>     www.bitc.unh.edu
>     www.camis.unh.edu
>
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Hills Road, Cambridge, CB2 2QH, UK.
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