Decoupled molecules with binding polynomials of bidegree (n,2)

TL;DR

This paper investigates the number of decoupled molecules with specific binding properties, establishing a formula for systems with two ligand types and providing computational insights for more complex cases.

Contribution

It derives a formula for the count of decoupled molecules with a bidegree (n,2) binding polynomial, advancing understanding of molecular decoupling in ligand-binding systems.

Findings

For systems with (n,2) binding sites, there are 2(n!)^2 decoupled molecules.

Computational results for molecules with more than 2 binding sites for the second ligand.

The study provides a mathematical framework for analyzing molecular decoupling.

Abstract

We present a result on the number of decoupled molecules for systems binding two different types of ligands. In the case of $n$ and $2$ binding sites respectively, we show that, generically, there are $2(n!)^{2}$ decoupled molecules with the same binding polynomial. For molecules with more binding sites for the second ligand, we provide computational results.