[RASMB] The INVEQ function

[Arthur Rowe]

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 Fit™  
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  Fit™.

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 Fit™.  
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 Fit™  
. . . . .


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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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