Molecular Aggregation Equilibria. Comparison of Finite Lattice and Weighted Random Mixing Predictions

Molecular aggregation equilibria
are described using finite lattice
and mean field theoretical modeling strategies, both built upon a
random mixture reference system. The resulting predictions are compared
with each other for systems in which each aggregate consists of a
central solute molecule whose first coordination shell can accommodate
multiple bound ligands. Solute–ligand (direct) and ligand–ligand
(cooperative) interactions are found to influence aggregate size distributions
in qualitatively different ways, as direct interactions produce a
shape-invariant transformation of the aggregate size distribution,
whereas cooperative interactions can lead to a vapor–liquid-like
transformation. When half the ligand binding sites are filled, the
corresponding aggregate size distributions are invariably unimodal
in the absence of cooperative interactions, but when the latter interactions
are attractive, the distributions are predicted to be bimodal below
and unimodal above a critical temperature. Mean field and finite lattice
predictions are found to be in globally good agreement with each other,
except under near-critical conditions, and even there, the predicted
average aggregate sizes and equilibrium constants are remarkably similar.
Potential applications of these theoretical predictions to the analysis
of experimental and molecular dynamics aggregation results are discussed.