Figure 19.4 (a) Linear relationship for toxicity (the inverse of LD50); (b) effect of mixture fraction (1) directly on LD5q.

This can be rearranged to the following equation, which can be used to predict the additive LD50M:

LD50,m LD50,A LD50,b

Figure 19.4b shows an example of how LD50M will vary with 1A according to equation (19.18).

It is common to multiply equation (19.19) by LD50M to obtain Marking and Dawson's (1975) equation for additive toxicity. The result is defined as S, the sum of toxic action, and will equal 1.0 for additive toxicity:

LD50;A LD50;B

If the LD50M measured equals that computed by equation (19.19) (or S = 1.0), one can conclude that the toxicity is additive.

Example 19.2 If compound A has an LC50 of 100 mg/L, and compound B has an LC50 of 10 mg/L, what would the additive model predict for the LC50;M of a 75 : 25 mixture of the two? Answer

That is, a mixture of 23.1 mg/L A and 7.7 mg/L B will be expected to cause 50% mortality.

More than two toxic substances: Equations (19.19) and (19.20) can be applied to any number of toxins simply by adding similar terms. The sum of the 1's must be 1.0. Thus, a more general form of equation (19.19), which applies to n different toxic substances, is

Example 19.3 What would be the expected ECi° and associated individual concentrations, according to the additive model, of a mixture consisting of 10% A, 20% B, and 70% C? (All percentages are by weight.) The EC10 values for the three compounds individually are 10, 15, and 80 mg/L, respectively.


EC1°'M = 0.1/10 + 0.2/15 + 0.7/80 = 3L17mg/L dA = (0.10)(31.17) = 3.12mg/L dB = (0.20)(31.17) =6.23 mg/L dC = (0.70)(31.17) = 21.82 mg/L

Many organophosphate pesticides are additive toxins. This is because they have similar properties and act by a very similar mechanism—covalent bonding with acetylcholines-terase.

19.4.1 Nonadditive Interactions

If LD50M measured in the laboratory is less than that computed by equation (19.19) (or S < 1.0), the two toxins interact in a positive way. This is called synergistic interaction, also called "more than additive.'' Another type of positive interaction is when A is essentially nontoxic by itself but causes an increase in the toxicity of B when present. This is called potentiation (although this term is sometimes also used in the literature to indicate synergistic interaction).

Unfortunately for the additive model, synergistic interactions are common, as is to be expected, especially for an effect such as lethality. This is because, even if the two toxins have completely independent effects, one may sicken the organisms, making them more vulnerable to the effect of the other. The models of equations (19.19) or (19.21) could be extended to nonlinear interactions by adding terms involving products of toxicities and fitting the coefficients by regression. However, data on mixture toxicity are hard to come by. Furthermore, they may not be consistent at different effect levels. That is, if there is positive interaction between the LD50s of two compounds, it is not necessarily true that there will be positive interaction to a similar extent, or at all, in their LD0j values, let alone at the 10~6 risk level.

In an exception to what was noted about organophosphate interactions above, malathion interacts synergistically with some other organophosphates, as much as 50 times as strong in combination. As Rachel Carson put it in Silent Spring: "1/100 of the lethal dose of each compound may be fatal when the two are combined.''

Ethanol and carbon tetrachloride have a synergistic effect on the liver, and tobacco smoke and asbestos interact in lung cancer. In the latter case the interaction was defined differently from that above. It was observed that asbestos workers who did not smoke experienced a fivefold increase in their risk of lung cancer, and cigarette smokers who did not work with asbestos had an 11-fold increase. However, asbestos workers who smoked experienced a 55-fold increase in lung cancer rate. Thus, the interaction here is defined in terms of additivity of risk instead of additivity of toxicity. An example of poten-tiation is isopropanol, which does not harm the liver by itself but greatly increases the toxicity of carbon tetrachloride.

Positive interactions can be caused by a number of mechanisms, including:

• By interfering with an enzyme that detoxifies other compound

• By affecting absorption, blood transport, or excretion

• By reacting to form a more toxic substance (e.g., nitrites and some amines react in the stomach to form carcinogenic nitrosomines)

• Induction of biotransformation enzymes

If two toxins interact, resulting in a measured toxic effect less than that predicted by the additive model, this is a negative, or antagonistic, interaction, also called "less than additive.'' Antagonistic interactions are detected when the LD50 value of a mixture is greater than predicted by equations (19.19) or (19.21), or S > 1.0. Some antidotes take advantage of antagonistic interactions. Mechanisms causing negative interactions include:

• Chemical reactions, such as complexation between EDTA and heavy metals

• Inhibition of bioactivation (e.g., toluene competitively inhibits the enzymes that biotransform benzene)

• Two toxins produce opposite effects, such as central nervous system depressants and stimulants

• Competition for the same receptor

• Induction of detoxification enzymes

Enzyme induction was mentioned above as a mechanism of both positive and negative interactions. The cytochrome P450 enzymes are a common target of induction. Benzene can interact positively with other solvents by inducing cytochrome P450.

Example 19.4 Doudoroff (1952) measured the 8-hour LC50 of zinc and copper to fathead minnows (Pimephales promelas), obtaining LC50;zinc = 8 mg/L and LC50;copper = 0.2mg/L. He then tested a mixture with a fixed 1.0 mg/L zinc and varied the copper concentration to obtain the LC50;M . This was found to occur at a copper concentration of 0.025 mg/L. What kind of interaction is this? Answer

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