From animals to humans
This lesson shows how allometric scaling predicts human clearance from animal clearance, and where it fails. For linezolid, a prediction made after human values were published lay inside the reported range. For UCN-01, an extreme case, simple allometry predicted a clearance about 5,000 times too high, possibly in part because of strong binding to a human plasma protein.
Key points
- Allometric scaling predicts human clearance from animal clearance with a power equation.
- Simple allometry fits a line to clearance and body weight on logarithmic scales, often with an exponent close to 0.75.
- The rule of exponents corrects the fit for some exponents, and single-species scaling uses one animal and a fixed factor.
- Species differences in metabolism, transporters and binding limit the method.
- The prediction error was largest for drugs that the liver removes only to a small extent.
- For linezolid, a prediction made after human values were published lay inside the reported range.
- For UCN-01, an extreme case, simple allometry predicted a clearance about 5,000 times too high.
- The overprediction was possibly in part because of strong binding to a human plasma protein.
Worked example
Linezolid and UCN-01
Two published examples show that a prediction can lie inside the observed human range or be about 5,000 times too high. Linezolid is an antibiotic. In mice, rats and dogs, its clearance exponent was 0.66, in the range where the rule of exponents keeps simple allometry. The authors made the prediction after human values were published. It was 4.68 liters per hour, inside the reported range of 4 to 10.5 liters per hour, near its lower end. UCN-01 is an experimental anticancer drug. In experimental animals, it had a large volume of distribution and a rapid clearance. In the first trials in patients, both were extremely low: the clearance was 0.04 to 0.25 milliliters per hour per kilogram. In laboratory tests, UCN-01 bound strongly to human alpha-1-acid glycoprotein. The authors suggest that this binding could explain the human values, at least in part. Simple allometry predicted a human clearance about 5,000 times too high, and the rule of exponents about 1,750 times too high. The authors call this an extreme example of overprediction. In an early trial in 47 patients, strong binding to plasma proteins required a change in the dose steps and the schedule.Equations
- Y
- the property, for example clearance
- W
- the body weight
- a
- the coefficient, the value of Y at 1 kilogram
- b
- the exponent, which sets how fast Y changes with body weight
- Vd
- the volume of distribution
- CLhuman/kg
- human clearance per kilogram
- CLmonkey/kg
- the monkey clearance per kilogram
0:00Predicting human clearance from animals
Lesson 7.3 of our prediction module: from animals to humans. To help select the first dose in people, drug developers predict human clearance from studies in animals. Plasma is the liquid part of the blood. Clearance is the volume of plasma from which the body removes all of the drug per unit of time. The volume of distribution is the amount of drug in the body divided by the plasma concentration.
0:34Allometry and the power equation
Allometry is the study of how a property of an animal changes with its body size. Allometric scaling uses this relation to predict human values from animal values. The relation is a power equation: Y equals a times W to the power b. Y is the property, for example clearance, and W is the body weight. The coefficient, a, is the value of Y at 1 kilogram. The exponent, b, sets how fast Y changes with body weight. On logarithmic scales, the equation is a straight line with slope b.
1:19Exponents for clearance and volume
For clearance, the exponent is often close to 0.75. In published data for 115 compounds, clearance correlated with body weight for 91 of them. For these 91, the mean exponent was 0.74, with a range of 0.29 to 1.2. An exponent below 1 means that a larger species has a lower clearance per kilogram. For the volume of distribution, a review found an average exponent of about 0.8 to 0.9, with single values from minus 0.2 to 2.2.
2:07Simple allometry from several species
Allometric scaling of clearance has three parts: simple allometry, corrections and limits. The first is simple allometry from several species. Clearance is measured in each species after an intravenous dose, an injection into a vein. Clearance is plotted against body weight on logarithmic scales, and the fitted line is extended to a human body weight, such as 70 kilograms. A study of 12 compounds concluded that a reliable prediction of clearance needs three or more species.
2:48The rule of exponents and single-species scaling
The second is the correction of the fit. The rule of exponents chooses the correction from the exponent of the simple fit: it keeps simple allometry for 0.55 to 0.70. From 0.71 to 1.0, it multiplies each clearance by the maximum life span of the species, and above 1.0 by the brain weight. In species that live longer, liver enzymes often oxidize drugs more slowly. The human value of the fit is then divided by the human maximum life span or brain weight. Single-species scaling uses one animal and a fixed factor: a study of 102 drugs set human clearance per kilogram at 0.407 times the monkey value.
3:48The limits of allometric scaling
The third is the limits. Allometry assumes that body size alone sets the differences between species. Species also differ in the enzymes that metabolize drugs, and in transporters, membrane proteins that carry drugs into or out of cells. Binding to plasma proteins also differs, for example to albumin and alpha-1-acid glycoprotein.
4:19Accuracy for 81 small-molecule drugs
An analysis of 81 small-molecule drugs tested simple allometry from three or more species. For drugs that the kidneys excrete unchanged, the prediction was on average 1.8 times too high or too low. For drugs that the liver removes only to a small extent, it was on average 4.5 times too high or too low.
4:47Two examples: linezolid
Two published examples show that a prediction can lie inside the observed human range or be about 5,000 times too high. Linezolid is an antibiotic. In mice, rats and dogs, its clearance exponent was 0.66, in the range where the rule of exponents keeps simple allometry. The authors made the prediction after human values were published. It was 4.68 liters per hour, inside the reported range of 4 to 10.5 liters per hour, near its lower end.
5:31UCN-01
UCN-01 is an experimental anticancer drug. In experimental animals, it had a large volume of distribution and a rapid clearance. In the first trials in patients, both were extremely low: the clearance was 0.04 to 0.25 milliliters per hour per kilogram. In laboratory tests, UCN-01 bound strongly to human alpha-1-acid glycoprotein. The authors suggest that this binding could explain the human values, at least in part. Simple allometry predicted a human clearance about 5,000 times too high, and the rule of exponents about 1,750 times too high. The authors call this an extreme example of overprediction. In an early trial in 47 patients, strong binding to plasma proteins required a change in the dose steps and the schedule.
6:44Summary
In summary, allometric scaling predicts human clearance from animal clearance with a power equation. Simple allometry fits a line to clearance and body weight on logarithmic scales, often with an exponent close to 0.75. The rule of exponents corrects the fit for some exponents, and single-species scaling uses one animal and a fixed factor. Species differences in metabolism, transporters and binding limit the method. The prediction error was largest for drugs that the liver removes only to a small extent. For linezolid, a prediction made after human values were published lay inside the reported range. For UCN-01, an extreme case, simple allometry predicted a clearance about 5,000 times too high. The overprediction was possibly in part because of strong binding to a human plasma protein. This concludes lesson 7.3 on allometric scaling.
What is allometry?
What is the power equation of allometric scaling?
What exponent does clearance often have?
How does simple allometry predict human clearance?
What does the rule of exponents do?
What limits allometric scaling?
How accurate was simple allometry for 81 small-molecule drugs?
How close was the linezolid prediction, made after human values were published?
How far was the prediction for UCN-01, an extreme case, from the human clearance?
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Illustrations adapted from Servier Medical Art (smart.servier.com), CC BY 4.0. Structures drawn with RDKit.