Allosteric transition and binding of small molecule effectors causes curvature change in central β-sheets of selected enzymes

A quantitative description of allosteric transition remains a significant science challenge. Many allosteric enzymes contain a central beta-sheet in their catalytic domain. When an allosteric protein undergoes the transition between T (tense) and R (relaxed) allosteric states, this central beta-sheet undergoes a conformational change. A traditional method of measuring this change, the root mean square deviation (RMSD), appears to be inadequate to describe such changes in meaningful quantitative manner. We designed a novel quantitative method to demonstrate this conformational transition by measuring the change in curvature of the central beta-sheet when enzymes transition between allosteric states. The curvature was established by calculating the semiaxes of a 3-D hyperboloid fitted by least squares to the C-alpha atomic positions of the beta-sheet. The two enzymes selected for this study, fructose 1,6-bisphosphatase (FBPase) from pig kidney and aspartate carbamoyltransferase (ATCase) from E. coli, showed while transitioning between the allosteric states (T a double dagger R) a notable change in beta-sheet curvature (similar to 5%) that results in a large lateral shift at the sheet's edge, which is necessary to convey the signal. The results suggest that the beta-sheet participates in storing elastic energy associated with the transition. Establishing a tentative link between the energetics of the beta-sheet in different allosteric states provides a more objective basis for the naming convention of allosteric states (tense or relaxed), and provides insight into the hysteretic nature of the transition. The approach presented here allows for a better understanding of the internal dynamics of allosteric enzymes by defining the domains that directly participate in the transition.