Graphical Analysis of Ligand Binding Systems
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Simple ligand binding systems are all related by similar mathematical equations.  Depending on how these equations are rearranged, one can analyze the ligand binding system using the following graphical formats
Yd = 1-Ya where Yd = the dissociation fraction;  Ya = the association fraction; [H+] = [L], the equilibrium concentration of ligand ; [Ac-] = [R], the equilibrium concentration of receptor without ligand bound; [HAc] = [RL], the equilibrium concentration of receptor with ligand bound.
Y vs. X Y vs. X Y vs. X  
 
Rectangular Hyperbolic Plot
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 Yd or Ya vs. [H+] (linear scale)
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pH Saturation Plot
Ya vs. pH
 Scatchard Plot
r / [L] vs. r 
r = n * Ya = the average number of ligand molecules bound to a receptor with r ligand binding sites		 Roll mouse over links at left to view static images below of different acetic acid titration plots, or click on the links to open dynamic popup charts.
Log Saturation Plot
Yd vs. [H+] (log scale)
Base Titration Plot
pH vs. Yd		 Hill Plot
log (Ya / Yd ) vs. log [L]
pH Saturation Plot
Yd vs. pH
Henderson-Hasselbalch Plot
pH vs. log (Yd/Ya)
= log (Yd/(1-Yd))
 Rectangular Hyperbolic Michaelis-Menten Plot
Vo / Vmax vs. [S]
Vmax = the initial reaction velocity
Vo/ Vmax is mathematically equivalent to Ya 
© Duane W. Sears
Revised: September 30, 2010