Despite a wealth of structural and biochemical studies on the functional cycle of the <i>E. coli</i> chaperonins GroEL and GroES, no model proposed to date accounts for all the effects seen experimentally by the various allosteric ligands: ATP, ADP, SP, GroES, and K+. The work in this dissertation explores the various allosteric transitions in the GroEL reaction cycle and offers a refined model for nested cooperativity that successfully accounts for the effects of these ligands. Initial studies take advantage of a single ring variant, termed SR1, to examine the allosteric properties of GroEL in the absence of complicating interactions arising from negative cooperativity. Initial rates of ATP hydrolysis by GroEL and SR1 as a function of ATP concentration were fit to an equation that makes no arbitrary assumptions. A novel role for K+ and SP is proposed, which suggests they help regulate the negative cooperativity and control the timing of the chaperonin cycle. The kinetics of association of GroES to the trans ring of the asymmetric complex were also studied, using stopped flow fluorescence energy transfer (FRET), revealing that conditions which accelerate dissociation of the cis ligands also accelerate association to the trans ring. This, along with previous work obtained by our lab, suggests that the allosteric signal transmitted between the rings for cis ligand release is the binding of ATP to the T state of the trans ring. A mechanism for the formation of symmetrical particles, termed "footballs," is suggested.