Allosteric model of an ion pump.

We present a simple model of a free-energy transducer made of allosterically coupled two ratchet subsystems. Each of the subsystems transports particles from one particle reservoir to another. The coupling of the subsystems imposes correlated transitions of the potential profiles of the two subsystems. As a result, a downhill flux in one subsystem with higher chemical-potential difference drives an uphill flux in the other subsystem with lower chemical-potential difference. The direction of the driven flux inverts depending on the direction of the driving flux. The ratio between the fluxes conveyed by the two subsystems is variable and nonstoichiometric. By selecting appropriate parameters, the maximum ratio of the driven flux to driving flux and maximum free-energy transducing efficiency reaches some 90 and 40%, respectively. At a stalled state, the driven flux vanishes while the driving flux remains finite. The allosteric model enables explicit analysis of the timing between binding-unbinding of particles and transitions of potential profile. The behavior of the model is similar to but different from that of the alternate access model, which is a biochemical model for active transport proteins. Our model works also as a regulatory system. We suggest that the correlated transitions of the subsystems (subunits or domains) through allosteric interaction are the origin of the diverse functions of the protein machineries.