PSA: on the use of allosteric vs linear scaling

[WSH]

image

As you can see, ketamine reduces depression at sub-anesthetic doses (10mg/kg) but not at anesthetic doses (80mg/kg).

You might say: "but 10mg/kg -> 750mg IM is anesthetic in a 75kg-human!"

I might reply: "but with allosteric scaling (using the factor 8x) 10mg/kg is 10mg/kg /8 *75kg = ~94mg IM which is perfectly sub-anesthetic, wheras 80mg/kg /8 *75kg = 750mg which is almost the exact usual anesthetic dose of ~600mg IM!"

 

[sekio]

Where does the factor 8 come from?

 

[WSH]

Where does the factor 8 come from?

I read it in a study and it makes it pretty easy because 75kg * 10mg/kg /8 = 94.75mg
Equally 75kj * 80mg/kg /8 = 1.5mg = 750mg
And 75kg * 1 mg/kg /8 = 9.375mg

so I can basically just drop the /kg and multiply by 10:
10mg/kg = ~100mg for a 75kg human (which is approximately my weight)
80mg/kg = ~800mg for 75kg
1mg/kg = ~10mg

which makes for an awesomely easy rule of thumb!

HOWEVER: you can't use it e.g. for MDMA, for which you guys should use linear scaling:
e.g. 1mg/kg -> 75mg for 75kg

 

[sekio]

I still don't understand, why 8 in particular? How is this number derived? Which study is this you are talking about?

Does this hold true for rats only, or mice as well? Rabbits? Dogs? Monkeys?

 

[aced126]

I still don't understand, why 8 in particular? How is this number derived? Which study is this you are talking about?

Does this hold true for rats only, or mice as well? Rabbits? Dogs? Monkeys?

https://en.wikipedia.org/wiki/Kleiber's_law

Metabolic rate goes as mass^0.75. Assuming metabolic rate is proportional to dose required, all these different scaling factors can be derived.

In general if we have 2 species, A and B, one with mass a and the other with mass b, and with b>a, the scaling factor required to convert the dose/mass ratio from the lighter species to the heavier species can be shown to be (b/a)^0.25 (ask if you want this expanded on).

As an example, a female Wistar rat might weigh 0.3kg, and a human might weigh 75kg. If a dose of 6 mg/kg is needed in a rat, then the approximate dose for a human would be 6*(75/0.3)^0.25 = ~24 mg/kg.

Obviously this is a rough approximation, and it gets even less valid when dealing with drugs with specific sorts of metabolic pathways, as specific enzymes are more likely to be expressed at ratios otherwise predicted by their metabolic rate in varying species.