Design of a minimal, allosteric, and ATPase-like machine using mechanical linkages.

ATPases cyclically convert chemical energy in the form of ATP gradients into directed motion inside cells. To function, ATPases rely on allosteric communication between at least two binding sites-an internal signaling mechanism that is not well understood. Here, we model an ATPase-like machine by using a system of mechanical linkages to recreate negative allosteric coupling between two binding sites and generate cycles in which the sites alternate occupancy. The ATPase analog has two mechanical degrees of freedom and two discretized binding sites: one for the ATP, Pi and ADP analogs, and one for an allosteric effector analog. The geometry of the ATPase analog allows stepwise binding reactions at each site to capture the two degrees of freedom in a mutually exclusive way. Consequently, the enzyme interconverts between multiple rigid and partially rigid forms, such that neither site can be fully bound when both sites are occupied. Two mechanisms work together to generate an enzymatic cycle: one, in which the tighter-binding ATP analog can bind and displace the effector from the enzyme; and a second, in which flexibility introduced by splitting the ATP analog into two pieces (catalysis) allows the effector to rebind and displace the products (ADP analog). We show that cleavage (forward catalysis) and ligation (reverse catalysis) alter the rigidity of the enzyme complex equivalently to binding and dissociation, respectively, but must do so more slowly for effective cycling to take place. Simple designs for synthetic systems that mimic ATPase monomers can be derived from this work.