Cooperative specific adsorption

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.

Potassium-sodium distribution in human lymphocytes: description by the association-induction hypothesis

Human lymphocytes were equilibrated for 48 hours over a wide range of external potassium levels, and their contents of potassium, sodium, and water determined. As external potassium rose from zero, cell potassium rose steeply in a sigmoidal fashion, reached half-saturation at 0.4 mM esternal potassium, and then saturated at 129 mmoles/kg cells. The saturable cell potassium exchanged mole-for-mole with sodium. Analysis of the saturable components by a statistical-mechanical adsorption model demonstrated a cooperative intraction between sites determining equilibrium potassium-sodium distribution. Superimposed upon the saturable fraction of cell potassium was a smaller one that was non-saturable with increasing external potassium to at least 64 mM, and that, when expressed as mmoles/liter cell water, existed in a ratio to external potassium of 0.6. The results strongly support the association-induction hypothesis, which predicts a small non-saturable component of ions determined by exclusion from oriented cell water and a cooperative interaction between sites throughout the cell that associate with potassium or sodium.