[RASMB] NONLIN

Thu May 9 08:35:00 PDT 2002

Dear all,
Though not intending to jump into this, I feel compelled to reply to
Michael's e-mail. I agree that a better manual would be helpful, but this
would be a substantial undertaking. Nonlinear least squares curve fitting
requires a great deal of practice, in addition to some understanding of the
fundamental tasks being performed by the program. Both need to be addressed,
and a manual can only address half of the needs.

Michael's assertion that manipulation of the data somehow improves its
accuracy is incorrect: the information content of a signal may not be
increased by manipulation. The omega function (or other similar forms) is a
suitable means for analyzing data, but it does not (and cannot) increase the
information content. The parameters which are explicit in NONLIN are tucked
in (and assumed known) in the omega analysis. It does provide a model
independent means of visualizing a system, and that is very useful. However,
the extraction of parameters from the analysis requires the use of models,
and the error estimates on those parameters may or may not be accurate.

The tone of Michael's message is most unfortunate, and I hope that more
light and less heat will be forthcoming.
Tom Laue

University of New Hampshire
46 College Road
Rudman 379
Durham, NH 03824-3544
Phone: 603-862-2459
FAX:   603-862-0031
www.bitc.unh.edu
www.camis.unh.edu

 -----Original Message-----
From: 	rasmb-admin at rasmb-email.bbri.org
[mailto:rasmb-admin at rasmb-email.bbri.org]  On Behalf Of mmorris
Sent:	Thursday, May 09, 2002 1:19 AM
To:	RASMB
Subject:	Re: [RASMB] NONLIN

 << File: michael.morris.vcf >> I've nearly always found (and this will
raise cheers from many and groans from many)
that NONLIN is a complete pain.

As Jack states initial guesses matter, particularly for NONLIN because the
problem (as
many will know and which I think I have right) lies in a combination of
things: Highly
precise data (because it is essentially 'unmanipulated' from the raw data),
an almost
inevitably imposed systematic error from one or more sources (e.g., baseline
correction, convection, Wiener skewing, others unknown), the exponential
nature of the
function to be fitted, and the number of parameters that can be floated at
one time
(including, e.g., baseline offsets) leading to high cross correlations.

It's a potent mix, frequently resulting in initial guesses blowing out of
the water by
not converging or converging to something dumb.

The strategy, as many have stated, is clearly to fix as many parameters as
you can and
then let them float at some point, with which I have always been
uncomfortable and
which often, for me, doesn't get me far in terms of getting back sensible
parameter
values and errors.

The single exception for me has been single ideal/nonideal species fits for
which I
have found NONLIN works well. For everything else I use the Omega function
analysis,
which almost inevitably and blissfully converges to sensible answers
rapidly. Yes, it
has some limitations but not the frustrations.

Having said that: (i) The use of NONLIN would definitely benefit from a
decent manual.
(ii) I have not compared NONLIN to other NONLIN-like programs, which may,
for whatever
reasons (e.g., the nonlinear regression algorithm used) prove more
tractable.

Time now for the authors of those programs to sales-pitch their product.

Yours, Michael

John Correia wrote:

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>
> Nonlin is a nonlinear least squares fitter which means mathematically
> that the guesses matter - ie. they don't in linear least squares because
> there is a finite tractable solution when you only have the diagonal
> elements in the matrix - so if you guess zero for a parameter in NLLS -
> it depends upon the function - then NLLS often crashes - & if you guess
> a value far from the minima then the program has no gradient to work
> with to find the minima in rms.  So it gets stuck.
>
> So you guessed lnK = 0 and you got that back because it had nowhere to
> go!  As Neil suggested guess values near LnK = 1 or so.  If the progam
> gets up above LnK = 20 the same thing happens - it makes A0 very very
> small and you have to reset the parameters to values near the correct
> values.
>
> Initially fix delta to zero & sigma to the "known" value of MW & see
> what happens with a simple model.  Maybe initially just fit each channel
> separately to sigma or MW to see how good/bad the data looks.
>
> As to units I cannot speak for the Beckman version but typically Nonlin
> fits to the units of the data so if you have an XLA its Abs units and
> the Ka for a dimerization is abs-1 units.  for trimerization the units
> are abs-2, etc  This has been described in many of my papers as well as
> papers by others and the formula for various models have been described
> & listed.  This has also been discussed on the rasmb numerous times, so
> all I can suggest is learn how to derive the correct conversion & teach
> everybody you can to do the same.
>
> K2 (abs-1) = [abs2]/[abs1]*[abs1]
>
> now substitute beers law where [abs] = [molar conc] * extinction *
> length, cancel terms & rearrange
>
> note length is typically 1.2 cm and you usually calculate extinction at
> 280 nm from say sednterp or amino acid composition, for example.   Note
> further that the extinction for dimer = 2*extinction for monomers
> approximately - in one paper I propagated the error caused by mistakes
> in extinction coefficients, for example ignoring ATP bound, and in free
> energy units its not very big.  When you rearrange you want to replace
> or solve for
>
> K2 (M-1) = [M2]/[M1]*[M1] or the molar definition of a dimerization
> constant in terms of K2 (abs-1) * extinction & length terms.  The
> correct final equation is:
>
> K1 (M-1) = K2 (abs-1) * extinction * L / 2
>
> for trimer or tetramer you get similar equation devided by 3 or 4 where
> extinction & length are squared or cubed, etc etc etc
>
> Finally here are sed equil references from my work & all I can suggest
> is you read more about this in primary sources.  Now if I'm incorrect &
> the Beckman program converts to LnK (M-1) please tell me but to do that
> you must enter the extinction somewhere in the routine ???
>
> J.J. CORREIA, S.P. Gilbert, M.L. Moyer and K.A. Johnson  (1995)
> "Sedimentation Studies on The Kinesin Head Domain Constructs K401, K366
> and K341."  Biochemistry, 34, 4898-4907.
>
> 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.
>
> PPSS:  I mentioned propagating error and since Nonlin gives confidence
> limits about LnK but you undoubtedly want K and deltaG you must
> propagate those errors in LnK to the linear forms - now you're into
> statistics and a book like Bevington's Data Reduction and Error Analysis
> for the Physical Sciences & another topic.
>
> Hope this helps........
>
> -------------------------------------------------------------------
>  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
> -------------------------------------------------------------------
>
>
>
> >>> Daryl Bosco <bosco at brandeis.edu> 05/08/02 08:07AM >>>
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> The older archived RASMB emails can be found at:
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>
> Hello
>
> I have recently started using NONLIN in an effort to calculate Kd's
> for
> a self associating system (comparing WT and mutants).
>
> I first used the Beckman/ Origins software to calculate a Ka in
> absorbance units which I converted to a Kd.  I then went to NONLIN and
> found that the Ka in absorbance units (I assume that is what I am
> calculating) is many orders of magnitude off.  I assume this is
> because
> I am not experienced with the program and how it is working.
>
> First question:
>
> Can anyone tell me explicitly where I may find a comprehensive manual
> for NONLIN?  I have been on the web and found useful material
> (including
> past emails to RASMB), but not a manual.  For example, I was not able
> to
> find how to plot the residuals under the plot menu.  (?)
>
> Second more detailed question (for those who have the time):
>
> I set up the NONLIN fitting procedure according to the instructions
> for
> self association in the README file that accompanied NONLIN.  First I
> read in 8 files (one speed, one detected wavelength, 8
> concentrations).
> Set the value for LnK2 to 0 (allow to converge).  Delta y is 0 (b/c
> this
> is absorbance), LnA refers to the lowest concentration and so I set
> this
> to -12 (for 7 uM)--allow to converge.  Set sigma to 0.8 (calculated
> with
> SEDNTERP) and allow to converge.  Do not put anything in for
> concentration and speed factors b/c only one speed used here and one
> wavelength detected.  LnK2 is calculated by NONLIN as -13.  I assume
> this means the Ka in absorbance is 3.1 e-6 (in Beckman I get Ka in
> absorbance of 0.151).  I know the accuracy will improve by using
> another
> speed, but I am first trying to get a handle on the program and hope
> to
> get something that is reasonable (Ka of 3.1 e-6 is not reasonable).
> If
> the more experienced NONLIN user can already see a fatal error in my
> fitting approach, would you please let me know?
>
> Your responses are greatly appreciated, thank you
>
> Daryl Bosco
>
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