AW: [RASMB] The INVEQ function

[Arthur Rowe]

Thanks, Titus!  I am sure that Origin will do the trick - as you will  
have noticed my suggestion is that people should 'paste in' the  
equation to whatever fitting program they are addicted to. Origin, as  
it is supplied with an XL-I/A, has an obvious head start. Does it  
support simple 1-click full error stats? (often called  
'boot-strapping'). The error surface associated with fitting the INVEQ  
function is a bit strange, valleys rather than nice depressions, so the  
error estimates given by Levenberg-Marquadt tend to be quite  
optimistic. My routine usage is 500 iterations, confidence level 67%,  
with binning and graphic every parameter of interest. Easy enough to do  
in Origin?

Kind regards

Arthur




On Feb 3, 2009, at 15:56, Titus M. Franzmann wrote:

> 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 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™ . . . . .
>
>
>   
> *********************************************************************** 
> ********
>  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
>   
> *********************************************************************** 
> ********
> _______________________________________________
> RASMB mailing list
> RASMB at rasmb.bbri.org
> http://rasmb.bbri.org/mailman/listinfo/rasmb
>
************************************************************************ 
*******
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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