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 there are 2(n!)^{2} decoupled molecules to a generic binding polynomial. For molecules with more binding sites for the second ligand, we provide computational results.
Highlights
A ligand is a substance that binds to a target molecule to serve a given purpose
A common model for describing equilibrium and steady states of a ligand L binding to the sites of a target molecule M comes from the grand canonical ensemble of statistical mechanics (Ben-Naim 2001; Hill 1985; Schellman 1975; Wyman and Gill 1990)
The grand partition function, in our context known as the binding polynomial, arises as the denominator of the rational function describing the average number of occupied binding sites as a function of ligand activity
Summary
A ligand is a substance that binds to a target molecule to serve a given purpose. 1 where the variable Λ denotes the activity of the ligand in the environment, and a is a transformation of the binding energy depending on the temperature, which is usually assumed to be constant This equation is known as the (sigmoid) Henderson– Hasselbalch titration curve. For systems of molecules with n binding sites it generalizes to the Adair equation (Adair et al 1925; Stefan and Le Novère 2013): nanΛn + (n − 1)an−1Λn−1 + · · · + a1Λ anΛn + an−1Λn−1 + · · · + a1Λ + 1 In this model, the binding polynomial and its roots play an important role for the characterization of the binding behavior of the ligand to the target molecule (Briggs 1983, 1984, 1985; Connelly et al 1986), in particular in the context of cooperativity (Abeliovich 2016; Stefan 2017).
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