Panel A shows a state-transition diagram that includes arrows labeled with transition rates k plus, k minus, and k plus. Panel B shows the assumed effects of coupling in a transition-rate theory formulation. It includes three curves: a curve representing Gibbs free energy along the transition path of a channel gating independently, a second curve modified by coupling to an open channel, and a third curve representing a shifted version of the modified energy profile. Panel C shows a diagram illustrating how the two native kinetic transition rates, k minus and k plus, are modified by interaction with an open channel. Panel D shows a diagram illustrating the requirement for microscopic reversibility, displaying the relationship K1 multiplied by K4 equals K2 multiplied by K3.
Gating of independent and allosterically coupled identical channels. (A) The transitions of two channels gating independently. (B) Assumed effects of coupling, in a transition rate theory formulation. The curve in green depicts Gibbs free energy along the transition path of a channel gating independently. In red is the curve modified by coupling to an open channel. In grey is a shifted version of the modified curve, corresponding to a shifted definition of energies, which simplifies the algebra and clarifies the allosteric effects without altering the physics (see note in text). (C) How the two “native” kinetic transition rates, and , are modified by the interaction with an open channel. (D) Illustrates a requirement for microscopic reversibility, namely , the implications of which are developed in Box 1.