A two-parameter model of cell membrane permeability for multisolute systems.

A two-parameter model of cell osmotic response (F. W. Kleinhans, 1998, Cryobiology 37, 271-289) is expanded for multisolute systems. The cell water volume W and intracellular osmolalities of N solutes are related as W[1 + L(p)RTSigma(N)(i=1)(M(i)/P(i))] = W(0)[1 + L(p)RTSigma(N)(i=1)(M(0)i)/P(i))], where M(i) is the intracellular osmolality of the ith solute (i = 1 ellipsis N), P(i) is the membrane permeability of the ith solute, L(p) is the membrane hydraulic conductivity, R is the gas constant, T is the absolute temperature, and the subscript "0" denotes the initial values at time zero. The above formula allows calculating the final (equilibrium) volume when all entities are permeable. Simple algebraic expressions for calculation of the number and magnitude of transient maximum volume excursions are presented. These simple expressions can all be calculated by hand on a pocket calculator. Practical examples of one-, two-, and three-solute systems are discussed. Special attention has been given to situations when systems contain an impermeable component. All formulas are simple to use for optimization of variety of cryobiological protocols. Application of the theory for optimization of addition and dilution of a permeable cryoprotectant is also discussed.