Thermodynamics of adsorption (Seelig, 2000). Quantitation of biochemical concepts is often a useful tool, and so the determination of air-water, Kaw, or lipid-water, Klw, partition coefficients for a panel of Pgp substrates was used to gain further understanding of Pgp mechanisms. The thermodynamics of adsorption is given by the Gibbs adsorption isotherm:

dg = - RT/(NaAs) d ln C = -RTGd lnC = -dp

g represents the surface tension of the buffer at the air-water interface and p is the difference in adsorption upon the addition of Pgp substrate. C is the concentration of the amphiphile, RT is the surface energy, Na Avogadro's number, As surface area for the amphiphile, and G the excess surface concentration. As long as the excess surface concentration value is constant, a plot of p vs. ln C results in a straight line.

A derivative form of this equation is the Szyszkowski equation:

p = RTG ln (1 + KC)

K = 55.5Kaw, accounting for the molar concentration of water. Fitting this equation to the p/C curve as determined by the Gibbs equation provides a means to analyze the Kaw value.

Thermodynamics of amphilicity (Seelig, 2000). The thermodynamics of amphiphilicity (Gam) was determined by taking the difference between the standard free energy of partition (Gaw) and the free energy of micelle formation (Gmic).

DDGam = DGaw - DGmic

DGaw = -RT ln (55.5Kaw)

DGmic = RT ln (CMC/55.5)

Pgp and Michaelis-Menten kinetics (Seelig, 2000) Kaw was determined for each of the 11 compounds tested, and linear plots of logKaw vs. log(1/Km), the Michaelis-Menten constant (previously determined) were developed. In turn, using the equations of enzyme kinetics, an interesting feature of Pgp binding was determined.

T + Sm TSm ATPase activations

Sm is the concentration of substrate in the membrane, T is the transporter]

[Sm] = Klw[Saq]

V = k2[T] [Saq]/[Saq] + Km

k2[T] = Vmax

using these equations, the velocity can be rewritten in terms of [Sm]

V = Vmax[Sm]/[Sm] + (Km x Klw)

with a low substrate concentration, this term becomes

V = Vmax [Sm]/ (Km x Klw)

Using the substitution that Km x Klw @ 1, and Kaw @ Klw this equation reduces to

V = Vmax [Sm]

From this equation comes a very important conclusion in the kinetic analysis of Pgp: the rate-limiting step in the process of Pgp substrate binding is membrane partitioning.