Abstract
There are several studies of small molecule binding by biopolymers which use “Scatchard‐type” plots to determine the intrinsic binding constant (k) and pairwise interaction energy between bound sites (S). “Scatchard‐type” refers to the plot ln (r/m(n – r)) versus r in this text whereas “Scatchard plot” conventionally refers to the plot r/m versus r. The quantities r, n, and m are, respectively, the average bound ligand/site, ligand/site at saturation, and concentration of free ligand. Although these plots result from approximate solutions to the problem of binding small molecules on a general three‐dimensional lattice, they are often used to represent binding isotherms in linear systems for which the solutions are known exactly. A critical examination regarding the applicability of “Scatchard‐type” analysis to systems with a large number of binding sites is presented herein.
Both experimental and simulated binding data are analyzed by “Scatchard‐type” and exact nearest neighbor plots (θ versus ln m, where θ = r/n). Numerical determination of k and S for the two theoretical approaches differ greatly in highly cooperative systems although their theoretical equivalence (interconversion) is demonstrated. A modified Scatchard theory, which correctly counts the degenerate energy states, is presented which reconciles this discrepancy. The “Scatchard‐type” plot for the modified theory in the highly cooperative limit is mathematically equivalent to the form ln (r/n – r) + p, where p contains all the molecular information and locates the r/n = 1/2 point. Contrary to the original theory, the r dependence in the “Scatchard‐type” representation is devoid of molecular interpretation and is characterized by curvature in the low and high‐binding regions with a (maximum) slope of 4 at r/n = 1/2. The modified theory is shown to reproduce accurately the poly(cytidylic acid)‐guanosine data of Sarocchi et al. and to account for the maxima exhibited in the conventional Scatchard plots.