Page 81 - The Toxicology of Fishes

Toxicokinetics in Fishes 61

relative solubility of the compound in the membrane and water. This coefficient may be difficult to
measure. Lipid–water partitioning is often used, therefore, as a surrogate for membrane–water partition-
ing. The relationship of these factors can be summarized using Fick’s law of diffusion:
Flux = ( DP mw )( 1 C 2 (3.1)
hC − )

2
where D is the diffusion coefficient (cm /sec), P is the membrane–water partition coefficient (unitless),
mw
h is the thickness of the diffusion path or membrane (cm), and C and C are toxicant concentrations
2
1
3
on each side of the membrane (mg/cm ). When collected together, D, P , and h define a permeability
mw
coefficient with units of cm/sec. For a unit area membrane, the rate of toxicant transfer across the
membrane (flux) has units of mg/sec/cm . Multiplication by the membrane surface area provides a
2
measure of total flux with units of mg/sec.
Flux that is directly proportional to the concentration gradient ([C – C ]/h) is first order and linear
1
2
and progresses by a fractional rate constant. Numerous factors may influence the concentration of
chemical available for diffusion, including external and internal pH partitioning phenomena, binding to
organic material in water, and plasma protein binding. Composite fractional rate constants take these
features into account for a given compound.
Empirical evidence suggests that non-ionized compounds diffuse more readily across membranes than
ionized forms. These observations have important implications for membrane flux of weak organic acids
and bases. If the non-ionized moiety has a lipid–water partition coefficient that favors membrane
penetration, it will tend to reach an equilibrium concentration on both sides of the membrane, while the
ionized form may be much more limited in its movements. As an approximation, therefore, the equilib-
rium concentration across the membrane will be based on the concentration of the non-ionized or
lipophilic form, with Fick’s law of diffusion applying only to this non-ionized form. The ratio of the
two ionization states is dependent on the dissociation constant (pK ) of the compound and the pH of
a
the surrounding media. This relationship is described by the Henderson–Hasselbach equation:
For weak organic acids: pH = pK + log (ionized/non-ionized) (3.2)
a
For weak organic bases: pH = pK + log (non-ionized/ionized) (3.3)
a
For a weak organic acid, a decrease of one pH unit results in a tenfold increase in the concentration
of the non-ionized form. Conversely, an increase of one pH unit results in a tenfold increase in the
concentration of the ionized form. Weak organic bases behave in the opposite manner; for example, a
weak organic acid (pK of 7) in moderately acidic water (pH of 5) would exist in a non-ionized/ionized
a
ratio of 100/1. For a weak organic base, the ratio would be 1/100. The effect of pH on the non-ionized/
ionized ratio can be extreme; thus, a pH change from 5 to 1 would change the non-ionized/ionized ratio
of a pK 7 organic acid from 100/1 to 1,000,000/1.
a
Differences in pH across biological membranes will cause the degree of ionization to differ on either
side of the membrane. The side with the greatest degree of ionization may have a much higher total
xenobiotic concentration because the equilibrium distribution of chemical is based on concentrations of
the diffusing non-ionized form (Figure 3.2). This phenomenon is referred to as ion trapping. The
theoretical equilibrium concentration ratio (R ) of a xenobiotic across a membrane with two sides, x
xy
and y, can be calculated as follows:

For weak organic acids : R xy = 1 + antilog( ( pH x − pK a) (3.4)
+
1antilog (pH y − pK a )
For weak organic bases : R xy = 1 + antilog( ( pK a − pH x) (3.5)
+
1antilog (pK a − pH y )
With respect to these relationships, fish present a number of interesting nuances that are not typically
encountered in mammals. While ion trapping in mammals is generally limited to internal membranes