AW: [RASMB] The INVEQ function

Titus M. Franzmann tmfr at umich.edu
Tue Feb 3 07:56:50 PST 2009


Origin from OriginLab is a comprehensive fitting and layout program for
windows that can handle this and other equations with minor modifications
(e.g. setting the "var" to "double"). It uses an Origin specified C source
code and supports other programming features, such as X-Function, LabTalk,
Labview, scripting etc. Though a license is also expensive. 

Best wishes

Titus

 

Von: rasmb-bounces at server1.bbri.org [mailto:rasmb-bounces at server1.bbri.org]
Im Auftrag von Arthur Rowe
Gesendet: Tuesday, February 03, 2009 10:40 AM
An: RASMB
Betreff: [RASMB] The INVEQ function

 

This function for fitting monomer-dimer equilibria with both thermodynamic
(BM) and mass interaction parameters (Ka) floated is simple in the extreme.
Yet it makes no concessions to the art of approximation: it may have only a
single second virial term (BM) for both monomer and dimer, but it is trivial
to expand the function to cover separate coefficients for monomer and for
dimer, or to incorporate a third virial term (CM). Equally, there is a
simple mod to make it fit heterologous (equimolar) interaction, so long as
the 2 sigma values are not too disparate (say from 3:1 to 1:3).

But let's start with the basic INVEQ function, inveq5a. Which deals with the
situation when BM(1) = BM(2) is an adequate approximation, which it often
is:

function inveq5a(c_reference,sigma,r_reference,BM,Ka,E:real);

description
'fits non-ideal single solute data using the inverse equation',
'float baseline offset E, BM, Ka and c_reference. Set r_initial & sigma
inactive';

var
aq,b,c,alpha,sigmaw:real;

begin

aq:=2*Ka*(x+E);
b:=-(4*Ka*(x+E)+1);
c:=2*Ka*(x+E);

alpha:=(-1)*(b+((b*b-4*aq*c)^0.5))/(2*aq);

sigmaw:=sigma*(alpha*2 + (1-alpha));

y:=((ln((x+E)/(c_reference+E))+0.5*(sigmaw/(1+2*BM*(x+E)))*r_reference^2)/(0
.5*(sigmaw/(1+2*BM*(x+E)))))^0.5;

end;

Yes, that's it. I am not sure that I could justify a major SEMINAR on it's
application! Of course what you get out in the way of ease of use does
depend a bit on what you paste this function into. I use pro FitT on Mac
OS-X, which has loads of lovely features, lovingly incorporated by the
mathematical physicists and engineers who are it's authors and principal
users. You need to be a MATLAB** user, I think, to get anything similar
under Windows. BUT: someone who is a Grafit user - a nice but not at all
sophisticated Windows package - had no problems feeding the above algorithm
in, and it ran just fine, albeit with a much simpler GUI and none of the
fancy full statistics you can do as routine in pro FitT.

Final comment: I cannot of course guarantee that there are no fitting
engines out there which will gum up when presented with the above function.
But why should they - it is not a transcendental equation, and the only
really horrible parameter correlation is between sigma and E, and you fix
that by fixing E. 

Regards to all

Arthur

**but a single copy of MATLAB will set you back more than the total cost of
a Mac Mini + KB + mouse + display + single copy of pro FitT. AND you will
have to learn MATLAB programming. But you will end up with what it take to
get a decent GUI, and full capabilities for multi-algorithm fitting and
advanced error stats. Just like in pro FitT . . . . . 


****************************************************************************
***
Arthur J Rowe
Professor of Biomolecular Technology / Director NCMH Business Centre
School of Biosciences
University of Nottingham
Sutton Bonington
Leics LE12 5RD

TEL: 0115 9516156
FAX: 0115 0516157
****************************************************************************
***

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