Target Theory

Biochemical Pharmacology and Toxicology

In both pharmacology and toxicology, it is generally presumed that biological effects (which may be desirable or undesirable) occurs when a chemical interacts with a cellular target site.  Although there are a number of different ways that molecule may interact with a target, in a test tube, the mathematical description of the relationship between concentration and effect can usually be described with a relatively small set of alternative possibilities:

• Mass Action.  If the interaction is ionic and reversible, the ligand receptor interaction can be described with the same dissociation kinetic equation that is found in any introductory chemistry text.  That basic equation has been modified for biochemical applications with an additional parameter that relates chemical associations to enzyme activity .   The same equation is used in pharmacology, but what is called an enzyme substrate in biochemistry is called a ligand instead.
• Massive Action. There are some biochemical effects that are mediated by cooperative binding, which that multiple molecules are required to produce an effect means that there is an S-shaped (sigmoidal) curve with very little effect at low concentrations. With yet another additional parameter, the law of mass action can be adapted to describe this using the Hill equation.
• Irreversible Binding.  Although it is not common in pharmacology, another form of molecular interaction that underlies many toxicological effects is covalent, irreversible binding.  The mathematics for that interaction can also be found in a chemistry text book under the heading of first order kinetics, which results in an exponential relationship between concentration, time, and effect.
• Nonspecific target sites. There are also many generic toxicological effects, like oxidative damage, that really don’t have a specific target site.  Many of these effects occur from natural causes (e.g. oxygen), so any given molecule may add to damage to proteins or DNA that occurs without it.   Linear models that assume that the additional damage is directly proportional to concentration are often used for this.

So, without delving into either the mathematics or other many minor variations, here is a quick graphical view of the range of potential biochemical relationships between concentration and biochemical effect:

1. There is a wide variation in the relationship between what happens at high concentrations and what happens at low concentrations.  
2. In spite of all that variation, all the curves are all monotonic; as the concentration decreases, the effect decreases as well.   
3. All of these functions are approximately linear at low concentrations, but the difference in the linear slope is immense.

Dose-Response Relationships in Pharmacology and Toxicology

Biology is far more complicated than biochemistry.  That complexity is often divided into two categories:

• Pharmacokinetics.  What happens after the drug or chemical is ingested, but before it gets to the target.
• Pharmacodynamics.  What happens after the drug or chemical gets there.

Suffice it say, the relationship between dose and response may bear little relationship to what happens in a test tube.  In particular, homeostatic mechanisms make real dose-response relationships look more sigmoidal than would be expected from target theory alone.   While short-term toxicological effects are often like pharmacological effects, only with a higher dose, effects that take place over a long period of time often result from non-specific targets where receptor-ligand theory really doesn’t apply.

However, since the target interaction is at least part of the equation, giving at least some consideration  to the biochemical interaction at the target is worthwhile:

1. If the data are available to support it, a complex biological model can be used to characterize the dose response relationship.  While this is much more common in pharmacology than toxicology, models have been developed for especially important toxic agents like formaldehyde and anticholinergic pesticides.  
2. Knowing something about the biochemical interaction may affect the interpretation of what happens physiologically.   
3. Even if the target site is unidentified and the biochemical mechanism is unknown, the list of potential possible interactions serves to limit the range of interpretation that is plausible.  For example, a linear dose-response model is usually at least plausible, whereas a supralinear function where the effects get bigger as the dose gets smaller is not.  
4. It is generally not reasonable from a biochemical standpoint to suppose that pharmacological or toxicological effects are nonmonotonic.  If a dose-response relationship appears to be nonmonotonic, there are generally two good explanations:

• The appearance isn’t real.  This is the explanation of first resort when interpreting epidemiological data.  There are many times when association really doesn’t mean causation, and this is probably one of them.
• There is more than one biochemical effect.  This is in fact quite common; U-shaped “hormetic” dose response functions where a response goes down and then up can usually be explained this way.  Since two effects means two "causes", the inductive reasoning for the "up" part and the "down" part of a curve may be quite different by relying on different data for empirical support and different theory for theoretical support.

The Linear No Threshold Debate

Since biological variability can be eliminated in a test tube, biochemistry can measure very tiny effects.  Pharmacology and Toxicology must be content with measuring not-so-tiny effects.  With the exception of the ‘ordinarily render’ clause of 402(a)(1), Food Toxicology is inherently concerned with unmeasurable effects, so some speculation about what may happen at dose that have no consequence is unavoidable.  This speculation often results in a debate over whether or not there is a threshold of some sort, and if not, presuming that high to low dose extrapolation using a linear model is justified.  Biochemistry supports neither of these positions.  First, there is no biochemical mechanism for a threshold.  Second, even though it is reasonable to suppose that all dose-response functions are linear at low dose, it is not reasonable to presume linearity at all doses where the effect is unmeasurable. 

The alternative is this: Assume that the measurable effect ”high dose” portion of the curve has something to tell you.  If it looks linear at high doses, then a linear high-to-low dose extrapolation is usually very plausible.  If it is nonlinear at high doses, then using a plausible curve instead of a line is a mighty fine idea.  Sort of like Benchmark Dose modeling, except without the Benchmark Dose.  That wouldn’t be so crazy.

General Reference

Brunton, LL, Lazo JS, and Parker (2006).  Chapter 1: Pharmacokinetics and Pharmacodynamics: The Dynamics of Drug Absorption, Distribution, Action, and Elimination. Goodman & Gilman’s: The Pharmacological Basis of Therapeutics, 11^th Edition.  McGraw-Hill, New York.

Or the first chapter in any other edition.

Official Post Soundtrack

Blondie (1978).  One Way or Another.  In: Parallel Lines, Track 2.

Post Notes

Post Thesis #18.  Part of dose-response modeling thread.