A revised 2p model for membrane transport; fitting bovine embryo permeability coefficients

Modelling membrane transport of CPA and water can help optimize cryopreservation methods. We may assume that the rate of change of intracellular osmolality, dMi/dt, resulting from transmembrane transport, i.e. the rate of dissipation of the driving force, or the work performed per unit time, is proportional to the magnitude of that driving force. The existing 2-parameter (2P) formalism is not ‘symmetrical’, as it appears to apply above assumption to the description for the solute flux, but not to that for the water flux. We propose a symmetrical 2P formalism, in which both the change of intracellular osmolality resulting from the flux of solute (dMi(sol)/dt·Vwi(t)) and the change resulting from the flux of water (dMi/dt(wtr)) are proportional to the magnitude of the respective driving force. Thus, for solute flux we use dMi(sol)/dt·Vwi = −PsA(Msi−Mso) (superscripts i and o denote intra- and extracellular space), from which we derive the underlying change of moles of solute dnsi/dt = −dm/dM·PsA(Msi−Mso). Herein, dm/dM is the reciprocal of the derivative of the (polynomial) function that gives M at each value of m. The description of dnsi/dt (rather than ‘dNsi/dt’) allows calculation of dVsi/dt by multiplying with the partial molar volume. For water flux, dMi/dt(wtr) is also taken proportional to its driving force, i.e. to −RT(Mi−Mo), from which we derive that dVwi/dt = dm/dM·LpART(Mi−Mo). Here, as an example, we used published values of m and M for binary glycerol/water solutions to fit measured osmotic volume excursions of a bovine morula exposed to 5 vol% glycerol with the two mentioned models, or with a model assuming Raoult’s law (i.e. m = M). These three models differ only a few percent in the estimates for Lp and Ps but can have appreciable differences in predicting potential osmotic injury in vitrification protocols.