Calculation of binding isotherms for heterogeneous polymers

TLDR

Binding of small molecules to polymers is straightforward when sites are identical, but becomes complex when sites differ or interact, analogous to helix–coil transitions in heterogeneous polypeptides, especially for aperiodic sequences common in natural materials. The purpose of this paper is to demonstrate that such problems can be solved accurately using random‑number methods on a high‑speed digital computer. The matrix method of statistical mechanics, combined with random‑number simulations on a high‑speed computer, is employed to calculate equilibria for small‑molecule binding to heterogeneous polymers. The authors illustrate the method with a calculation and show it applies to binding of actinomycin, Hg⁺, and acridine dyes to DNA.

Abstract

Abstract The matrix method of statistical mechanics is used to calculate equilibria for the binding of small molecules to polymers. When there is only one kind of binding site the problem is simple; some examples are given for illustrative purposes. If, however, the binding sites are not all equivalent and the bound molecules interact or interfere with each other, the problem is no longer trivial, being formally analogous with calculation of the helix–coil transition equilibrium in a heterogeneous polypeptide. Particular difficulties arise when the sequence of binding sites is aperiodic; most naturally occurring materials fall in this class. The purpose of this paper is to point out that problems of this type are readily solved with good accuracy by use of random‐number methods on a high‐speed digital computer. One such calculation is presented for illustration. The methods developed are applicable to such systems as the binding of actinomycin, Hg – , and acridine dyes to DNA.