Uptake is the transfer of a chemical from the environment into an organism. A toxic substance must pass through a cell membrane to enter the organism. This can occur naturally by several mechanisms, which were described in Section 4.1. Passive transport occurs whenever there is a concentration gradient across the membrane. The situation is illustrated in Figure 18.1.
The passive transport flux, Fpt [M • t-1 • L-2], can be modeled in a simplified way as being proportional to the concentration difference across the membrane by the diffusion coefficient, D, and inversely proportional to the membrane thickness, h:
The diffusion coefficient depends on the properties of the solute and of the membrane, but in general, it is inversely related to the square root of the molar mass of the diffusing species. Thus, small molecules diffuse faster. The concentrations at the faces of the plasma lipid membrane can be assumed to be in equilibrium with the aqueous phases in which they are in contact. Thus, C2 = KMC\ and C3 = KMC4, where KM is the partition coefficient between the membrane and the adjacent phases. Substituting these relations into
equation (18.9), we can express the flux in terms of the concentrations in the aqueous phases:
Thus, it can be seen that the partition coefficient has a direct impact on the rate of transport. Since the octanol-water partition coefficient is a model for the lipid-water system, compounds with a high KOW will be absorbed easily by passive transport. The constants in equation (18.10) can be lumped into a single parameter, the mass transfer coefficient, k:
The mass transfer coefficient is an inverse measure of the resistance posed by the membrane to movement of the substance. A similar equation can be used to describe the transfer between two phases in the absence of a membrane, such as from air to water or from blood plasma to a lipid phase. This is the film theory model of interphase mass transfer. The presence of two immiscible phases in contact with each other implies that they will be physicochemically different and have different affinities for the solute as described by the partition coefficient. The flux of solute can be described similar to equation (18.11), but modifying the concentration of one of the phases by the partition coefficient, so that the flux will be zero when the two phases are in equilibrium. For example, the model for transfer from an organic phase with concentration CO to an aqueous phase with concentration CW will be
In this case the mass transfer coefficient, k, will depend on the diffusion coefficients of the solute in the two phases, as well as other factors, such as the amount of mixing between the interface and the bulk fluid.
Other transport mechanisms were described in Section 4.1. These include filtration, facilitated diffusion, active transport, and endocytosis. Facilitated diffusion and active transport, which depend on a carrier in the membrane, have a maximum flux associated with saturation of the carrier. As a result, their dynamics can be described by a form of Michaelis-Menten kinetics.
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