  We propose a model of mass-conserving heterogeneous nucleation to describe
the dynamics of ligand-receptor binding in closed cellular compartments. When
the ligand dissociation rate is small, competition among receptors for free
ligands gives rise to two very different long-time ligand-receptor cluster size
distributions. Cluster sizes first plateau to a long-lived, initial-condition
dependent, "metastable" distribution, and coarsen only much later to a
qualitatively different equilibrium one. Surprisingly, we also find parameters
for which a very special subset of clusters have equal metastable and
equilibrium sizes, appearing to equilibrate much faster than the rest. Our
results provide a quantitative framework for ligand binding kinetics and
suggest a mechanism by which different clusters can approach their equilibrium
sizes in unexpected ways.
