By combining equations 1, 2, and 3 and assuming that the hydrostatic pressure difference across the membrane is equal to zero, the following coupled nonlinear equations describing the cell volume and amount of solute in the cell as functions of time can be applied:
Activation energies for parameters Lp and PCPA. The Arrhenius relationship was used to determine the temperature dependence of the parameters Lp and PCpa. The value of any parameter Pa (Lp or Pcpa) at any temperature T can be obtained by the following formula: where Ea is the activation energy for the process, expressed here in Kcal/mol, R is the universal gas constant, and T is the absolute temperature. The subscript “o” represents the values at a reference temperature T„. From equation 6b, data collected at different temperatures are plotted as ln[P„(Tj] vs. 1/T, a linear plot, (Arrhenius plot), and the slope is defined as:
from which Ea can be determined.
The electronic particle counter was interfaced to a microcomputer using a CSA-1 interface (The Great Canadian Computer Company, Edmonton, AB, Canada). Changes in cell volume were measured over time, as shown in Figure 1, and a commercial software package, MLAB (Civilized Software, Inc., Bethesda, MD), was used to solve equations 4 and 5 using the Gear method. flovent inhaler
The Marquard-Lev-enberg curve-fitting method , as implemented in MLAB, was used to fit the experimental data and determine the values of Lp and PCpa- A fixed value for Vb was used in the fitting calculation, and the reflection coefficient, ct, was assumed to be noninteracting and was calculated using the following equation:
TABLE 2. Definitions of major symbols used in equations.
|SymbcA||>1 Description surface area of cell||Units(Ш12||Valueparameter|
|e,i||Superscripts (e = external, i = internal to cell)||—||—|
|M%||osmolality of external permeating salts||Osmol/kg H20||0.290|
|M’„||osmolality of internal permeating salts||Osmol/kg H20||variable|
|PCPA||CPA permeability||cm/m in||parameter|
|R||universal gas constant||Kcal/mol/K||1.987 x 10-3|
|s,n||Subscripts (s = solute, n = nonpermeating salts)||—||—|
|V(t)||volume of cell||jim3||variable|
|Vb||osmotically inactive cell volume||jim3||parameter|
|vs||partial molar volume of solute DMSO Glycerol EC||liter/mol||0.0690.0710.054|
FIG. 1. Kinetic volume changes of boar sperm upon dilution of permeant solute. The sample was exposed to EC and allowed to equilibrate at room temperature. The sample was then abruptly diluted in an isos-motic solution without CPA, and the volume was measured over time.