[RASMB] NONLIN

Wed May 8 19:36:00 PDT 2002

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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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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