Ligand UDF Library

TableCurve 2D ships with LIGAND.UDL, a UDF library containing six implicit ligand binding models. This library offers implicit fits for a single ligand with 1, 2, and 3 binding sites, both with and without non-specific binding. The library also contains the explicit solutions for the single site case.

These are the models developed by Feldman (Henry A. Feldman, Mathematical Theory of Complex Ligand Binding Systems at Equilibrium: Some Methods for Parameter Fitting, Analytical Biochemistry, vol. 48, p317-338, 1972), and offered in the NIH Ligand software by Munson (Peter J. Munson and David Rodbard, LIGAND: A .Versatile Computerized Approach for Characterization of Ligand Binding Systems, Analytical Biochemistry, vol. 107, p220-239, 1980).

The first and second UDFs are for the single site model. Y is the Bound/Total ratio, X is the base 10 log of the Total, A0 is the affinity K, A1 is the binding capacity R, and A2 is the non-specific binding N for the first UDF:

F1=10^X

F2=((A0*A1/(1+A0*(F1-Y*F1))+A2)*(F1-Y*F1))/F1-Y

Y=IMPLICIT(F2,YMIN,YMAX,1E-8)

The third and fourth UDFs are for the two site model. Y is the Bound/Total ratio, X is the base 10 log of the Total, A0 is the affinity K1, A1 is the binding capacity R1, A2 is the affinity K2, A3 is the binding capacity R2,and A4 is the non-specific binding N for the third UDF:

F1=10^X

F2=((A0*A1/(1+A0*(F1-Y*F1))+A2*A3/(1+A2*(F1-Y*F1))+A4)*(F1-Y*F1))/F1-Y

Y=IMPLICIT(F2,YMIN,YMAX,1E-8)

The fifth and sixth UDFs are for the three site model. Y is the Bound/Total ratio, X is the base 10 log of the Total, A0 is the affinity K1, A1 is the binding capacity R1, A2 is the affinity K2, A3 is the binding capacity R2, A4 is the affinity K3, A5 is the binding capacity R3, and A6 is the non-specific binding N for the fifth UDF:

F1=10^X

F2=((A0*A1/(1+A0*(F1-Y*F1))+A2*A3/(1+A2*(F1-Y*F1))+A4*A5/(1+A4*(F1-Y*F1))+A6)*(F1-Y*F1))/F1-Y

Y=IMPLICIT(F2,YMIN,YMAX,1E-8)

The seventh UDF is identical to the first except that an explicit solution is used for an appreciably faster fit:

F1=10^X

Y=(A0*A1+A2+2*A0*A2*F1+1+A0*F1-SQRT(2*A2+2*A0*F1+1+A0*A0*(-2*A1*F1+A1*A1+F1*F1)+2*A0*A1+2*A0*A1*A2+A2*A2+2*A0*A2*F1))/(2*A0*F1*(A2+1))

The eighth UDF is identical to the second except that again an explicit solution is utilized:

F1=10^X

Y=(A0*A1+1+A0*F1-SQRT(2*A0*F1+1+A0*A0*(-2*A1*F1+A1*A1+F1*F1)+2*A0*A1))/(2*A0*F1)

The formulas used for the estimates are general ones. Adjustments should be made with the UDF Adjust procedure to insure successful fitting. This is especially true of the multiple site models.

For these UDFs, the models fit B/T vs. base 10 log of T. If your data consists of B/T vs. T, you can either apply an X=LOG(X) calculation to the data prior to fitting, or you can change the F1=10^X statements to F1=X within the individual UDFs.