This form is an experimental service of the Biophysics Department (Institut für Physikalische Biologie; Heinrich HeineUniversität Düsseldorf).

The Langmuir server calculates the binding
constant(s) for following reaction(s):
P + n·L<==> C
with


Following evaluations are possible:

 a simple first order Langmuir adsorption isotherm with a fit of K (i.e. the binding constant) and n·p_{0} (i.e. the total concentration of binding places). Besides the fitted parameters following plots are produced:
 a plot titled 'Langmuir': l_{bound} vs. l_{total}
 a plot titled 'Langmuir': l_{bound} vs. log(l_{free})
 a plot titled 'Scatchard': l_{bound}/l_{free} vs. l_{bound}
 two first order Langmuir adsorption isotherms with a fit of K_{1} and K_{2} (i.e. the binding constants) and n_{1}·p_{1,0} and n_{2}·p_{2,0} (i.e. the concentrations of binding places). Both equilibria are independent of each other!
Besides the fitted parameters following plots are produced:
 a plot titled 'Langmuir': l_{bound} vs. l_{total}
 a plot titled 'Langmuir': l_{bound} vs. log(l_{free})
 a plot titled 'Scatchard': l_{bound}/l_{free} vs. l_{bound}
 a Hill plot with
l_{bound} = l_{max. bound}*l_{total}*K/(1+l_{total}*K)
Besides the fitted parameters l_{max. bound} and K, a plot is produced with title 'Hill'.
 a Hill plot with
l_{bound} = l_{max. bound}*a/(1+a)
with a = K*l_{total}^{h}. Besides the fitted parameters l_{max. bound},
h (i.e. the Hill coefficient) and K, a plot is produced with title 'Hill n'.


How is it done ?

All fits are based on the same mathematics, a MarquardtLevenberg algorithm. For reference see 'Numerical recipes' (Press, W.H., ed.) Cambridge Univ. Press.

Graphics output to your browser is done in GIF format; the output is also available in PostScript or numeric format.

Graphics output is produced via Chris Pugmire's GLE (graphics language editor) in PostScript® format. Conversion into GIF® format is done via ghostscript and ppmtogif.


Tips and tricks

 You have to guess starting values for all parameters. In case the program aborts with an error message like
'GAUSSJ: Singular Matrix'
choose better/more accurate starting values.
 Start the fitting procedure with the most simple method; i.e., use 'Langmuir' prior to 'Two Langmuirs'
 Repeat the fitting procedure with results from the last fit; this helps sometimes to improve the result.
 Try different starting values for the parameters. If this results always in similar or identical values this gives some confidence not to be trapped in a local minimum but not the global optimum of the solution.
