From: John Philo <jphilo@mailway.com>
  To  : Borries Demeler <demeler@bioc09.v19.uthscsa.edu>
  Date: Wed, 26 Apr 2000 11:47:54 -0700

RE: variation of local lnks

A few comments/thoughts on this issue:

Certainly allowing the association constants to differ for each cell/channel
and comparing that to a normal global fit can be a useful means of detecting
heterogeneity. However, you need to keep in mind that this will ALWAYS give
a better fit since you have added so many new fitting parameters, so one
would expect a drop in variance even when there are no incompetent species
or other sources of heterogeneity.

In principle one can use statistical measures to judge the significance of
the drop in variance seen when using individual rather than global
association constants. However, those statistical measures assume the noise
is random, which is not true, so those statistical measures may be
misleading.

Certainly my experience is that even for really clean, stable, simple
proteins, when you globally analyze 12-18 data sets there are always at
least a few of them where the residuals are clearly non-random (presumably
due to systematic errors). While floating all the association constants
indeed may clean that up, it doesn't necessarily mean that you have real
sample heterogeneity.

In addition to the trends with loading concentration mentioned by Emory,
another trend to look for in the fitted individual association constants is
some systematic variation with rotor speed. If you have incompetent monomer,
that will tend to get enriched at higher rotor speeds (i.e. more of the
competent associated species are lost in the unobservable region at the cell
base), whereas some irreversible aggregation on top of a reversible
association will give the opposite trend.

With regard to Borries questions about modeling these sorts of things, in my
version of NONLIN I have incorporated a model with incompetent monomer plus
a single association step for the competent monomer (unfortunately not
enough associations to handle Borries' system). In principle that approach
works, but I have used it very little, and it is hard to say to what extent
it is possible to recover 'correct' association constants for the competent
part since there are no appropriate real systems I know of for testing this.

One issue in how to approach modeling such systems is whether to assume that
the fraction of incompetent material is constant across all cells. That
assumption makes some conceptual sense, and would greatly reduce the number
of extra fitting parameters. However, even if this assumption is actually
true across the whole cell, it won't be exactly true across the regions that
are included in your fitting. Hence in my implementation I fit the
concentration of the incompetent monomer for each data set.

I also wanted to mention that the equilibrium simulator in the Beckman
Origin software does allow for inclusion of incompetent monomer and/or
contaminants such as aggregates. It will write out the simulations as XL
data files (with noise too) so you can read them in and fit them with NONLIN
to see how these things will alter your results. A highly useful exercise if
you really want to see what can and can't be done!

Lastly, if anyone can suggest a good model system where the association
constants are well known and for which you can deliberately generate
incompetent species, that would certainly be a useful tool for addressing
these issues.

John Philo
Alliance Protein Laboratories
www.ap-lab.com

-----Original Message-----
From: Borries Demeler [demeler@bioc09.v19.uthscsa.edu]">mailto:demeler@bioc09.v19.uthscsa.edu]
Sent: Wednesday, April 26, 2000 10:39 AM
To: rasmb@alpha.bbri.org
Subject: Re: variation of local lnks


More to the point:

The protein I am investigating is heme containing, although a small
population lost the heme group. When I track the association at around
400nm (where heme absorbs) I get a perfect dimer-tetramer-octamer system,
when looking at it at 280, 230 and 207 where also the non-heme containing
subpopulation absorbs, I see this presence of incompetent material.
Clearly, Nonlin is not capable of extracting this information, so I need
to know what models people have used to describe such (apparently frequent)
phenomena. In my case it looks like the heme-containing subpopulation
doesn't produce incompetent species, only the non-heme containing stuff.
This in itself is very interesting biologically in my case.
However I would like to quantify this effect for the monomer-dimer
assoc. constant. However, only at 207 is the conc. low enough for me to
see monomer, but both populations absorb so I can't separate them.
The proper model/software should be able to extract the k2 for the
"competent" species. Has anybody written something like this?

First the question of which assoc. state is incompetent? Does anybody
have experience in telling which one is (OK, I can simulate, but I'd
rather not)? PAGE is not conclusive.  Next, on first glance it seems
that it should be possible to formulate a global model. Any suggestions?

Thanks so much for any pointers, -Borries

>
> Borries and others; We have frequently run into this situation.  Do you
> notice that there is a trend in the values of lnK, in that they increase
> in a positive direction as loading concentration decreases? If so, that
> is probably due to the presence of incompetent species, not only monomer.
> Irreversible species can be any size--but usually we have found that
> they are at the high end.  Of course it could also be an impurity with a
> MW not related to any of the species that you are trying to fit.
> The best fitting procedure is to solve your
> model so that you are fitting globally all but the last step of the
> association sequence.  Then let that step be fit globally followed by
> letting that step be fit locally.  Then compare rms and systematic errors.
> There are attempts being made to get info re: the species that is
incompetent
> and what fractional concentration is present.  Yujia Xu, Dave's last
student
> has a dissertation devoted to this which I hope will be published soon.
> You could play around with it in a similar way by simulating various
mixtures
> of incompetent species, and seeing what Nonlin will do. Hope this helps.
>                                                         Emory
>