Regulation of signaling pathways in the cell often involves multidomain allosteric enzymes that are able to adopt alternate active or inactive conformations in response to specific stimuli. It is therefore of great interest to elucidate the energetic and structural determinants that govern the conformational plasticity of these proteins. In this study, free-energy computations have been used to address this fundamental question, focusing on one important family of signaling enzymes, the Src tyrosine kinases. Inactivation of these enzymes depends on the formation of an assembly comprising a tandem of SH3 and SH2 modules alongside a catalytic domain. Activation results from the release of the SH3 and SH2 domains, which are then believed to be structurally uncoupled by virtue of a flexible peptide link. In contrast to this view, this analysis shows that inactivation depends critically on the intrinsic propensity of the SH3-SH2 tandem to adopt conformations that are conducive to the assembled inactive state, even when no interactions with the rest of the kinase are possible. This funneling of the available conformational space is encoded within the SH3-SH2 connector, which appears to have evolved to modulate the flexibility of the tandem in solution. To further substantiate this notion, we show how constitutively activating mutations in the SH3-SH2 connector shift the assembly equilibrium toward the disassembled, active state. Based on a similar analysis of several constructs of the kinase complex, we propose that assembly is characterized by the progressive optimization of the protein's conformational energy, with little or no energetic frustration.