  Interactions between a protein and a ligand are often accompanied by a
redistribution of the population of thermally accessible conformations. This
dynamic response of the protein's functional energy landscape enables a protein
to modulate binding affinities and control binding sensitivity to ligand
concentration. In this paper, we investigate the structural origins of binding
affinity and allosteric cooperativity of binding two calcium ions to each
domain of calmodulin (CaM) through simulations of a simple coarse-grained
model. In this model, the protein's conformational transitions between open and
closed conformational ensembles are simulated explicitly and ligand binding and
unbinding is treated implicitly within the Grand Canonical Ensemble. Ligand
binding is cooperative because the binding sites are coupled through a shift in
the dominant conformational ensemble upon binding. The classic
Monod-Wyman-Changeux model of allostery with appropriate binding free energy to
the open and closed ensembles accurately describes the simulated binding
thermodynamics. The simulations predict that the two domains of CaM have
distinct binding affinity and cooperativity. In particular, C-terminal domain
binds calcium with higher affinity and greater cooperativity than the
N-terminal domain. From a structural point of view, the affinity of an
individual binding loop depends sensitively on the loop's structural
compatibility with the ligand in the bound ensemble, as well as the
conformational flexibility of the binding site in the unbound ensemble.
