Binding affinity (Ki) confusion

[tennisall]

Hi guys,
Im an academic psychiatrist and try to better understand the properties of psychiatric drugs I prescribe by studying their Ki values for different receptor targets.

I'm confused about a few of things and hoping for some helpful replies:
1) Since Ki is expressed as a drug concentration (mM or nM), isn't it true that we don't know whether a drug is actually meaningfully hitting that receptor target (other than clinical observation for side effects, for example) unless we measure plasma concentrations to see if it's reasonability near the Ki? There's also huge individual variability in plasma concentrations of psychiatric drugs that fluctuates markedly over the course of a 24 hour period.

2) Do labs typically report the plasma concentration of drugs to include the protein bound component, or just the free (unbound) component?

3) All receptor targets (e.g. 5-HTT, 5HT2A, 5HT2C) are assayed individually in human and animal models to determine their respective Kis. Lets suppose there is a drug whos Ki is 1.0mM for 5-HTT, 10mM for 5, HT2A, and 100mM for 5HT2C. Isn't it likely that in reality, that this drug would need to reach a plasma concentration substantially greater than 100mM to meaningfully effect all three receptors, since the drug has three binding options (rather than one in experimental assays)?

4) Related, we say things in psychiatry like, "mirtazapine is basically an antihistamine only at 7.5mg." How do we honestly know it's not hitting all these other receptors too, even those with Kis in the 100s? It doesn't seem necessarily true to me that low doses of a psychiatric drug should always bind only to its lowest Ki receptor targets, because a lot of other things go into deciding a drugs dosage range.

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[ridethecliche]

Have you gone back and looked at college level lectures for michaelis-menten kinetics? That might be a good starting point.

Just because you're not at vmax concentration doesn't mean you're not getting good receptor modulation. Vmax is the point at which the relationship becomes asymptotic. Re: mirtazapine. We say that because the levels required to get more meaningful activation of the other receptor types hasn't been reached. Yes of course we're hitting all the other receptors, but if the affinity is minimal and dissociation is more likely than activation then why does it really matter? Everything hits everything at some level, but if its not meaningful then does it really matter other than for a thought experiment like this?

You said you're an academic psychiatrist. If you have access to the resources, I'd reach out to basic science colleagues and see if someone in biochem research looking at modeling this stuff has office hours that you can come and attend. This is relatively upper level biochem stuff though so I'd brush up on it first if it's been a while.

 

[aim-agm]

Hi guys,
Im an academic psychiatrist and try to better understand the properties of psychiatric drugs I prescribe by studying their Ki values for different receptor targets.

I'm confused about a few of things and hoping for some helpful replies:
1) Since Ki is expressed as a drug concentration (mM or nM), isn't it true that we don't know whether a drug is actually meaningfully hitting that receptor target (other than clinical observation for side effects, for example) unless we measure plasma concentrations to see if it's reasonability near the Ki? There's also huge individual variability in plasma concentrations of psychiatric drugs that fluctuates markedly over the course of a 24 hour period.

2) Do labs typically report the plasma concentration of drugs to include the protein bound component, or just the free (unbound) component?

3) All receptor targets (e.g. 5-HTT, 5HT2A, 5HT2C) are assayed individually in human and animal models to determine their respective Kis. Lets suppose there is a drug whos Ki is 1.0mM for 5-HTT, 10mM for 5, HT2A, and 100mM for 5HT2C. Isn't it likely that in reality, that this drug would need to reach a plasma concentration substantially greater than 100mM to meaningfully effect all three receptors, since the drug has three binding options (rather than one in experimental assays)?

4) Related, we say things in psychiatry like, "mirtazapine is basically an antihistamine only at 7.5mg." How do we honestly know it's not hitting all these other receptors too, even those with Kis in the 100s? It doesn't seem necessarily true to me that low doses of a psychiatric drug should always bind only to its lowest Ki receptor targets, because a lot of other things go into deciding a drugs dosage range.

Re 1) Yes. In an individual patient you can't, but you can make good predictions based on the pharmicokinetic studies. It's also more complicated because for most of our drugs it's the intrasynaptic concentration that matters, which is much harder to determine. Some drugs are more predictable and consistent between people though.

Re 2) This probably varies by assay/drug and a bit by lab whether they are reporting free or total values.

Re 3) No.

Re 4) It binds to every target at an affinity determined by its Ki, but % occupancy matters enormously, e.g. you need >20% H1 occupancy to be sedating, >80% (IIRC) SERT occupancy to have effect on depression, etc. Mirtazapine 1 nM, assuming H1 ki is 1 nm and A2 is 20 nm, will occupy 50% of H1 receptors which is clinically significant, but <5% of A2 receptors which isn't. You also need to factor that it is competing with the endogenous neurotransmitter to have an effect; for A2 you need a lot more mirtazapine in the synapse than norepinephrine to change receptor activation/inhibition because NE has (IIRC) ~20x higher affinity.

 

[clausewitz2]

There seems to be a bit of a confusion in your initial post, OP. Ki is definitely expressed as a concentration, but it's the concentration needed to achieve 50% occupancy of the receptor. While obviously the overall concentration of the drug matter, unless you think there is substantial nonlinearity in binding affinity for some reason varying with concentration, the Ki will tell you how much of a given amount of a drug is going to bind to a particular receptor relative to other potential targets. That is to say, if Ki1 is 0.5 and Ki2 is 1.0 (assuming no other targets and no competing ligands) then at any concentrations below saturation, whatever the concentration of the molecule much more will end up bound to Receptor 1 than Receptor 2.

So in your example number 3, at, say, 3.0 mM concentration, the vast majority of the molecule is going to end up bound to 5-HTT with a small amount left over bound to 5HT2A and miniscule number of molecules bound to 5HT2C. The drug is going to fill up its high affinity binding options to the point of saturation before reaching an equilibrium where meaningful amounts are bound to the lower affinity targets. Does that clarify things?

 

[jbomba]

There seems to be a bit of a confusion in your initial post, OP. Ki is definitely expressed as a concentration, but it's the concentration needed to achieve 50% occupancy of the receptor. While obviously the overall concentration of the drug matter, unless you think there is substantial nonlinearity in binding affinity for some reason varying with concentration, the Ki will tell you how much of a given amount of a drug is going to bind to a particular receptor relative to other potential targets. That is to say, if Ki1 is 0.5 and Ki2 is 1.0 (assuming no other targets and no competing ligands) then at any concentrations below saturation, whatever the concentration of the molecule much more will end up bound to Receptor 1 than Receptor 2.

So in your example number 3, at, say, 3.0 mM concentration, the vast majority of the molecule is going to end up bound to 5-HTT with a small amount left over bound to 5HT2A and miniscule number of molecules bound to 5HT2C. The drug is going to fill up its high affinity binding options to the point of saturation before reaching an equilibrium where meaningful amounts are bound to the lower affinity targets. Does that clarify things?

In that example, 3 mM concentration of drug...

Once the highest affinity receptor is at 50% occupancy, what determines how much of the drug starts filling the second highest affinity receptor at a meaningful level vs. continuing to fill the highest affinity receptor above that 50% occupancy level?

 

[FlowRate]

In that example, 3 mM concentration of drug...

Once the highest affinity receptor is at 50% occupancy, what determines how much of the drug starts filling the second highest affinity receptor at a meaningful level vs. continuing to fill the highest affinity receptor above that 50% occupancy level?

These links should get you started on familiarization with the sort of terms and math involved in being able to make any sort of useful sense of Ki values beyond the more qualitative "probably binds to this vs that at a given concentration." I used to have a better understanding of this stuff when I was using it on a regular basis as a chemical engineering student but I'm way too rusty at this point. I don't think you can make practical use of Ki values alone as that doesn't necessarily directly translate to what you're actually interested in (Effect at a given concentration.)

https://www.sciencesnail.com/science/the-difference-between-ki-kd-ic50-and-ec50-values

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5355565/

http://websites.umich.edu/~elements/6e/09chap/pdf/CD_Ch07Receptors.pdf

https://www.frontiersin.org/articles/10.3389/fphar.2019.00605/full

 

[clausewitz2]

In that example, 3 mM concentration of drug...

Once the highest affinity receptor is at 50% occupancy, what determines how much of the drug starts filling the second highest affinity receptor at a meaningful level vs. continuing to fill the highest affinity receptor above that 50% occupancy level?

Depends on your model of the occupancy function. 50% is picked as an arbitrary reference point for comparison. If it's strictly linear and there's an order of magnitude difference between them then the answer can be approximated as essentially all of the first receptor being occupied prior to filling the second highest affinity receptor in equilibrium

That's a lot of probably false assumptions though

 

[Psychresy]

Depends on your model of the occupancy function. 50% is picked as an arbitrary reference point for comparison. If it's strictly linear and there's an order of magnitude difference between them then the answer can be approximated as essentially all of the first receptor being occupied prior to filling the second highest affinity receptor in equilibrium

That's a lot of probably false assumptions though

This stuff is interesting no doubt, but if I don't take the time to learn it super in depth am I short changing myself/my patients?

 

[FlowRate]

Depends on your model of the occupancy function. 50% is picked as an arbitrary reference point for comparison. If it's strictly linear and there's an order of magnitude difference between them then the answer can be approximated as essentially all of the first receptor being occupied prior to filling the second highest affinity receptor in equilibrium

That's a lot of probably false assumptions though

A qualitative understanding of equilibrium processes that I developed back when I was actually doing quantitative work on this stuff was that it's very rarely "all" anything. So there's probably some minor effect on binding sites with less affinity even before you saturate the high affinity sites. Unfortunately I can't remember the math well enough to try and prove that, so certainly open to being told I'm wrong.

 

[clausewitz2]

A qualitative understanding of equilibrium processes that I developed back when I was actually doing quantitative work on this stuff was that it's very rarely "all" anything. So there's probably some minor effect on binding sites with less affinity even before you saturate the high affinity sites. Unfortunately I can't remember the math well enough to try and prove that, so certainly open to being told I'm wrong.

Yeah I was very much doing physicist math, aka " A >> B, therefore set B = 0"

 

[clausewitz2]

This stuff is interesting no doubt, but if I don't take the time to learn it super in depth am I short changing myself/my patients?

I think it can be useful for thinking about some issues but binding affinities are very far from the only major factor determining effectiveness ( i.e. what patients care about) and in some circumstances aren't even especially major.

 

[FlowRate]

Thanks to curiosity sparked by this thread, I just asked my clinical psych pharmacist about good resources for pharmacodynamic reference texts and will follow-up if we find something good (she's going to reach out to a broader network of clinical psych pharmacists.) Also curious if anyone here knows of any good centralized resources for effect vs dose (concentration) of meds?

 

[NickNaylor]

This stuff is interesting no doubt, but if I don't take the time to learn it super in depth am I short changing myself/my patients?

I don't think it is strictly necessary. However, it does provide you with at least a basic understanding of why medications have the effects they have, moving you to a more sophisticated understanding beyond "magic." Understanding in a gross sense a drug's binding affinities for clinically relevant receptors is useful information, I think, though maybe not super clinically useful. It can help you understand, for example, why quetiapine at low doses is basically just sedating and unlikely to have any meaningful impact on mood or psychotic symptoms. Is not knowing that "short-changing" anyone? I don't know, I guess not, but given that a psychiatrist is supposed to be an expert as it relates to the use of psychotropic medications, it seems like it would be useful to understand as much as you can about them.

Knowing specific binding affinities doesn't affect how I dose medications - there's more that goes into that decision-making than Ki. But it does help me understand side effects which can be very useful when counseling patients.

 

[Sikrouf]

Thanks to curiosity sparked by this thread, I just asked my clinical psych pharmacist about good resources for pharmacodynamic reference texts and will follow-up if we find something good (she's going to reach out to a broader network of clinical psych pharmacists.) Also curious if anyone here knows of any good centralized resources for effect vs dose (concentration) of meds?

Please let us know