# Translating from milligrams in the pill to Ki at the receptor

Many places (e.g. Wikipedia) report the action of a drug on the various receptors, transporters, ion channels, and the like in terms of the Ki(nM). (This is for drugs that act primarily through such channels). They really ought to, but usually don't, also tell you whether the mechanism is competitive, uncompetitive, noncompetitive, as these can affect the rate of binding by a factor of 2 (or more?). For purposes of this question, assume we are dealing with competitive binding.

Is there a way to go from drug dosage and these Ki values to the level of binding of particular receptor? For example, suppose we have 100% absorption (or we look at the pharmacokinetics for greater precision). If you know the molecular weight of a drug, and blood volume (average about 5 liters, though you should adjust for body weight) then you can calculate the concentration in nM. (I am guessing that I can neglect the volume of blood cells and leakage into the lymphatic system, though I may be wrong about this). Then I think you can just multiply by the Ki.

My goal is to draw a line between the interactions that matter and those that don't under standard dosage. More precisely, I am trying to compare receptor and transporter bindings for several drugs in the same drug class at the usual prescribed dosage for each. I observe that the range of reported Ki(nM) is often six orders of magnitude or greater. So even if you don't know the binding mechanism, one should still be able to divide the actions into those definitely present, often at near saturation, those that are only trivially present, and those in a range that might be affected by doubling or halving the dose. The difference in magnitude caused by different binding mechanisms should only matter for those in the middle ground.

However, I am not a pharmacist, biochemist, or doctor, and I am very aware that every step in the chain of logic above might be mistaken. This is about trying to think clearly about the effects of related drugs, and the information is not going to be used to set dosage for any animal or human. So I think it is OK for me to look for, and for you to offer, pretty good information that may not have 100% scientific validation.

• There are just too many unknowns in this to be able to estimate level of binding without a lot more information. You cannot assume 100% absorption. Where is the site of action? If it is brain then you have to consider transport across the blood/brain barrier. There may be preferential uptake into some tissues. You need information about the rate of uptake into the blood stream and metabolism too. Commented Jul 14, 2021 at 6:50
• Have you read further in the literature, eg a search for "drug binding ki receptor"? I hit for instance this right away: pubs.acs.org/doi/pdf/10.1021/acschemneuro.7b00185 Like Waylander, I think ignoring the"D" in ADME might get you bad results. OTOH for a highly soluble drug with few side-effects ignoring other targets might not be so bad (<- opinion). Commented Jul 14, 2021 at 12:28
• In vivo "target engagement" assays are notoriously complex, especially for non-covalent ligands. Your target might be intracellular. It might be partially expressed on the cell surface of an epithelial and thus exposed to the plasma, but there might be a second population of receptors/targets that are not at the cell surface, but e.g. on the mitochondrial surface. Those two populations might be exposed to different levels of ligand. Commented Jul 14, 2021 at 17:41
• Well, not exactly what I hoped to hear (but thanks, Buck Thorn!, This article is very helpful, & I'm working my way through it). I'm trying to compare about 15 antidepressents, focusing on non-transporter receptors. Antidepressants are differentially effective on various special populations, such as seniors, those with treatment-resistant depression, those with concommitant cognitive problems (which don't abate with depressed mood), to see if receptor bindings correlate to the variation. But I cann't begin to address these questions unless I know which receptors are bound. Commented Jul 14, 2021 at 22:10