A cooperative transition theory applied to the kinetics of ionic exchanges in cells.

Manifestations of a cooperative interaction between ion-adsorbing sites in cells include steep, sigmoidal equilibrium adsorption isotherms of K+ and Na+, critical temperature transitions of net exchanges of Na+ for K+, and the allosteric nature of the effects of ligands on cellular K+ and Na+. Cooperative ionic adsorption is described by a one-dimensional Ising model. The experimentally-determined equilibrium parameters permit prediction of the kinetics of exchange of K+ for Na+ (the approach to equilibrium) by stochastic or hydrodynamic solutions of a time-dependent Ising model. Studies of the rates of self-exchange of adsorbed ions reveal properties of the cooperatively interacting adsorption sites and their dependence on temperature and chemical potential. High rates of isotopic exchanges of K+ and Na+ occur near the transition point. This is explained by the hypothesis of an increase in susceptibility of the ensemble to slight variations of microK or microNA near the phase transition, which leads to an increase in microscopic fluctuations within the ensemble. It is suggested that the isotopic ion exchange experiment may be a means to explore the microscopic states of the ensemble and their transition probabilities.