The activity of many proteins, including metabolic enzymes, molecular machines, and ion channels, is often regulated by conformational changes that are induced or stabilized by ligand binding. In cases of multimeric proteins, such allosteric regulation has often been described by the concerted Monod-Wyman-Changeux and sequential Koshland-Némethy-Filmer classic models of cooperativity. Despite the important functional implications of the mechanism of cooperativity, it has been impossible in many cases to distinguish between these various allosteric models using ensemble measurements of ligand binding in bulk protein solutions. Here, we demonstrate that structural MS offers a way to break this impasse by providing the full distribution of ligand-bound states of a protein complex. Given this distribution, it is possible to determine all the binding constants of a ligand to a highly multimeric cooperative system, and thereby infer its allosteric mechanism. Our approach to the dissection of allosteric mechanisms relies on advances in MS--which provide the required resolution of ligand-bound states--and in data analysis. We validated our approach using the well-characterized Escherichia coli chaperone GroEL, a double-heptameric ring containing 14 ATP binding sites, which has become a paradigm for molecular machines. The values of the 14 binding constants of ATP to GroEL were determined, and the ATP-loading pathway of the chaperone was characterized. The methodology and analyses presented here are directly applicable to numerous other cooperative systems and are therefore expected to promote further research on allosteric systems.