Abstract
Nearest-neighbor cooperative binding of a ligand covering n sites and binding with equilibrium constant K and cooperativity factor ω to a large molecule with m binding sites (m ⪢ n / gw) can be approximately described by a Gaussian distribution P(q — qmax), where q is the number of ligands bound and qmax the most probable value of q. The variance of the Gaussian is equal to the derivative dqmax/d ln(L), where L is the free ligand concentration. This variance, σ2, is a complicated function of qmax. However, in the limits of very large cooperativity, ω ⪢ 1, very large anticooperativity, ω ⪡ 1, or noncooperativity, ω = 1, simpler expressions for σ2 can be given. For qmax = m/(n + 1), where the most probable number of bound ligands equals the number of free binding sites, σ2 has a particularly simple form: σ2 = 2mω/(n + 1)3. The Gaussian and the infinite lattice approximations for the average number of ligands bound are good approximations only if σ is much smaller than the number of binding sites. The variance may therefore provide an easy check on the validity of the infinite lattice approximation, which is commonly used to analyze experimental binding data.