Ligand binding to biopolymers 

A wide variety of physiological processes are the reflection of ligand interactions with macromolecules, especially with proteins or nucleic acids. The most common are interactions between enzymes and their substrates and with other molecules that influence activity. In addition, there are interactions between hormones and hormone receptors, between small molecules and proteins involved in the active transport of the small molecules, between ions and both nucleic acids and proteins, etc. With this tool it's easy (hopefully) to analyse your experimental data of ligand interactions. Your data are fitted to appropriate equations using a MarquardtLevenberg algorithm. For a reference see 'Numerical recipes (Press, W.H., ed.) Cambridge Univ. Press'. Results are presented by several plots, f.e. by a Scatchard plot. 

The available methods for analysis are listed below. Choose the appropriate one. Each method requires different input data to be run. So each method has it's own form. In all forms you can find example data. For a simple test, paste the example data into the corresponding form on the left side. To get the results, simply press the "Submit button". For more detailed information press the "HELP button" given on each method page. 



The following is 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} 

Langmuir 
K and n*p_{0} are needed 



The following are two first order Langmuir adsorption isotherms with a fit of K_{1} and K_{2} (i.e. the binding constants) and n_{1}*p_{0,1} and n_{2}*p_{0,2} (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} 

Two Langmuirs  K_{1}, K_{2}, n*P_{0,1}, and n*P_{0,2} are needed  


The following is a Hill plot with  
l_{bound} = l_{max. bound}*l_{total}*K/(1+l_{total}*K)  
Hill (coefficient is 1)  K and L_{max} are needed  


The following is a Hill plot with  
l_{bound} = l_{max. bound}*l_{total}*a/(1+a) with a = K*l_{total}^{h}. 

Hill (coefficient is variable)  K, L_{max}, and Hill coefficient are needed  


The following is a first order Langmuir adsorption isotherm (identical to topic 1) but for which not concentrations but absorption or fluorescence changes are known.  
Langmuir with fluorescence detection  K, n*P_{0}, P_{0}, f_{free}, and f_{bound} are needed 
Institut für Physikalische Biologie (Department of Biophysics) Heinrich HeineUniversität Düsseldorf, Germany 

Mär. 10, 2011  
G. Steger / M. Labensky / A. Jäger 