The point of maximum cell water volume excursion in case of presence of an impermeable solute.

A relativistic permeability model of cell osmotic response (Cryobiology 40:64-83; 41:366-367) is applied to a two-solute system with one impermeable solute. The use of the normalized water volume (w), and the amount of intracellular permeable solute (x), which is the product of the water volume and intracellular osmolality (y), as the main variables allowed us to obtain a homogeneous differential equation dx(Delta)/dw(Delta)=f(x(Delta)/w(Delta)), where w(Delta)=w-w(f), x(Delta)=x-x(f), and f refers to the final (equilibrium) values. The solution of this equation is an explicit function, w(Delta)=g(x(Delta)), which is given in the text. This approach allows us to obtain an analytical (exact) expression of the water volume at the moment of the maximum excursion (water extremum w(m)). Results are compared with numeration of basic osmotic equations and with approximation given in (Cryobiology 40:64-83). Assumption that, dw/dt approximately 0 gives good approximations of the kinetics of water and permeable CPA after the point of maximum volume excursion (the slow phase of osmotic response). Practical aspects of the relativistic permeability approach are also discussed.