Exact solutions of a two parameter flux model and cryobiological applications

Solute-solvent transmembrane flux models are used throughout biological sciences with applications in plant biology, cryobiology (transplantation and transfusion medicine), as well as circulatory and kidney physiology. Using a standard two parameter differential equation model of solute and solvent transmembrane flux described by Jacobs [The simultaneous measurement of cell permeability to water and to dissolved substances, J. Cell. Comp. Physiol. 2 (1932) 427-444], we determine the functions that describe the intracellular water volume and moles of intracellular solute for every time t and every set of initial conditions. Here, we provide several novel biophysical applications of this theory to important biological problems. These include using this result to calculate the value of cell volume excursion maxima and minima along with the time at which they occur, a novel result that is of significant relevance to the addition and removal of permeating solutes during cryopreservation. We also present a methodology that produces extremely accurate sum of squares estimates when fitting data for cellular permeability parameter values. Finally, we show that this theory allows a significant increase in both accuracy and speed of finite element methods for multicellular volume simulations, which has critical clinical biophysical applications in cryosurgical approaches to cancer treatment.