Tweetorial: Clearance vs. Intrinsic Clearance
12 November 2021
It never ceases to amaze me how many things in medicinal chemistry, and pharmacology more generally, boil down to the free drug hypothesis. Ultimately, in vivo, everything boils down to the free drug hypothesis. This topic is no exception.
There’s tremendous confusion out there, even among some seasoned medicinal chemists, about a proper framing of in vivo clearance. The key takeaway for this tweetorial is that in vivo clearance is a total drug parameter, and therefore can be misleading (like all total drug parameters) when not properly corrected for the unbound fraction. Intrinsic clearance is the simplest measure of unbound drug clearance, and the well-stirred model allows us to relate these two things to one another.
A proper understanding of the free drug hypothesis and its intersection with clearance and other topics was not part of my early upbringing as a medicinal chemist in the pharmaceutical industry nearly 20 years ago. It was much more poorly understood among medicinal chemists generally back then than it is today. This is one area where the DMPK experts have firmly put their foot down in the intervening two decades, and chemists have mostly (but not entirely) listened. For me, I had to pull myself up the hard way and teach myself all of this stuff at an embarrassingly late point in my career. When I look back at some of my earlier publications, I cringe at the lack of understanding that my colleagues and I possessed. You can even find a paper (which I won’t go out of my way to reference) where I’m a coauthor and a stated goal was to reduce plasma protein binding, which is a cardinal sin.
Anyway, hopefully my pain is your gain. Here’s the entire thread for posterity.
Time for another pharmacology tweetorial, this time about the distinction between clearance and intrinsic clearance. And also a cautionary tale about how we’re so often misled by over-focus on the former. 1/
References first. A key one for this discussion is this 1977 paper from Pang and Rowland, which describes the well-stirred model of clearance in considerable detail. (Not the first paper on the model, but maybe the most thorough.) 2/
It’s also worth pointing out that this discussion will relate back to the free drug hypothesis quite a bit, so a review of this earlier tweetorial is also valuable. 3/
Keith Hornberger @KRHornberger
Final preliminary: math alert. Usual small bucket of high school algebra ahead. If you’ve managed it for the other tweetorials, this one should be a breeze too. 4/
Let’s begin with some definitions. Systemic clearance (Cl), whether measured in blood or plasma, reflects the apparent volume of blood or plasma from which drug is removed per unit time (e.g. mL/min). It’s often normalized to body weight, in units like mL/min/kg. 5/
Hepatic clearance (Cl_h) reflects the proportion of Cl that is done by the liver. In cases where clearance is predominantly hepatic, Cl ≈ Cl_h is an okay assumption. We’re going to roll with that assumption for the purposes of this discussion. 6/
Intrinsic clearance (Cl_int), meanwhile, reflects the basic, underlying ability of metabolizing enzymes in the liver to remove drug from the body when not constrained by anything else -- pure enzyme kinetics. However… there are always constraints. 7/
One constraint is the rate of perfusion of the metabolizing organ. It should make intuitive sense that a drug can’t be cleared faster than the circulatory system can push it into the liver. This is reflected by the parameter hepatic blood flow (Qh). 8/
The other constraint is courtesy of our old friend the free drug hypothesis. Just as only free drug can act on the target of interest, only free drug can be metabolized by metabolic enzymes. If it’s bound e.g. to plasma proteins, it’s protected from metabolism. 9/
As a consequence of this latter constraint, the unbound fraction (fu) is also going to make an appearance. We’re further going to have to distinguish between the unbound fraction in plasma (fu,p) and blood (fu,b) in this case. Stay tuned for why. 10/
So to quickly state the difference between Cl and Cl_int: Cl is a measurement of total drug clearance, which reflects the constraints above. Cl_int is a measurement of free drug clearance in the absence of constraints. 11/
That’s great and all, but it leaves questions: 1) How do we relate Cl and Cl_int to each other? 2) How do I experimentally measure these things? 3) Why do I care about the difference between the two? The rest of the post will answer these questions. 12/
The most common model used to relate Cl and Cl_int is the well-stirred model. Sparing you the derivation, which can be found in the reference, here’s the equation. 13/
Graphically, here’s an example plot of Cl_h vs. Cl_int for a fixed value of Qh (90 mL/min/kg, typical for a mouse) and fu,b = 0.10 (randomly selected). Both a linear and a semilog plot are shown. Takeaway: it’s not a linear relationship. 14/
With equations like this, it’s useful to consider limiting examples. In the extreme case where Qh >> fu,b * Cl_int, the equation collapses as follows. 15/
This is the “low clearance” regime where the drug clearance is limited by how fast the metabolic enzymes can work (Cl_int) and how much free drug is available for the enzymes to work on (fu,b). 16/
This is the “high clearance” regime where the metabolic enzymes are so efficient at removing drug that clearance is now limited by hepatic blood flow (Qh). Remember, a drug can’t be metabolized any faster than the circulatory system can pump it into the liver! 18/
Now let’s transition to experimental measurement. Beginning with Qh, this is a fairly well-measured (semi) constant in numerous preclinical species and humans. Consult Table III in this paper for some values. 19/
The well-stirred model uses the unbound fraction in blood (fu,b) rather than plasma (fu,p). Why? Because the rest of the equation, specifically Qh, is expressed in terms of liver *blood* flow rather than plasma flow. 20/
This creates an experimental complication as it’s more common to measure plasma protein binding (PPB) to get fu,p than to measure blood binding to get fu,b. Fortunately, the two can be related via the free drug hypothesis, using the equation below. 21/
So fu,b can be determined by measuring PPB (to get fu,p) and blood/plasma partitioning (to get Cp/Cb), both of which are pretty common in vitro ADME experiments. 22/
In many cases Cp/Cb is close to 1 and it doesn’t matter so much, but this isn’t always true. Particularly for highly distributed compounds (high Vss), blood cells can be considered a “tissue” that drug distributes into, and Cp/Cb can be <<1. 23/
Cl_h: as stated previously, for compounds that are predominantly cleared hepatically, as a first approximation, Cl_h ≈ systemic Cl from an IV PK experiment. Note that this should be a blood clearance, and it’s more typical to have measured plasma clearance. 24/
Once again, the free drug hypothesis allows us to infer blood clearance (Cl_b) from plasma clearance (Cl_p) via the following equation. A measurement of blood/plasma ratio allows the necessary conversion to be made. 25/
Cl_int: this can be estimated from an in vitro metabolic stability study, typically using either microsomes or hepatocytes. Both have pros and cons. 26/
(Brief aside: metabolic reactions can broadly be divided into Phase I (oxidation, reduction, hydrolysis) and Phase II (bioconjugation) reactions. The goal of all metabolism is basically to increase polarity, which promotes eventual excretion.) 27/
Microsomes are a cell-free ER preparation, and thus free of complications from media serum or compound permeability. But they don’t have a full complement of Phase II enzymes, and the ones they do have won’t contribute unless the appropriate cofactors are added. 28/
Hepatocytes are intact cells and thus have the full complement of metabolizing enzymes -- helpful to capture Phase II processes. But if there’s serum in the media or the compounds have poor permeability, this can perturb the measurements. 29/
Now for the exciting collection of caveats and exceptions! We’ve assumed throughout that compounds are cleared hepatically. If your compound is cleared through other mechanisms (exclusively or partially), e.g. renal, the assumption of Cl ≈ Cl_h breaks down. 30/
The well-stirred model also assumes: 1) the free drug hypothesis is in effect; 2) the liver is uniformly perfused with free drug (also meaning permeability isn’t limiting); 3) linear metabolism kinetics. On 2), have you seen a liver? They’re not exactly uniform-looking. 31/
There’s another model, the parallel tube model, which assumes a concentration gradient of drug in the liver that declines from input to output point. It’s also reviewed in the reference in post 2 above, so you can compare and contrast. 32/
To close out this tweetorial, we’re now left with the most important question: who cares about any of this? 33/
A common use of the model is estimation of in vivo clearance. Animal PK studies, while significantly cheaper than they used to be, are still ~an order of magnitude more expensive than in vitro microsome or hepatocyte assays for rodents, and more for higher species. 34/
Put an in vitro measurement of Cl_int together with PPB data and a blood/plasma ratio, and you have enough information to estimate an in vivo clearance, either in blood or plasma. 35/
If that estimate holds up generally for many compounds in a series, the series can be said to have an in vitro-in vivo correlation (IVIVC). This can be a powerful way to prioritize compounds for PK studies, and is a common feature of drug discovery screening cascades. 36/
It’s also possible to run this in reverse: use the in vivo clearance data to calculate intrinsic clearance. This can be helpful as one does not always have an IVIVC, and total PK parameters influenced by fu (like clearance) are not great optimization parameters. 37/
Whether one determines Cl_int or just calculates e.g. unbound Cl as Cl_u = Cl_p / fu,p parameters free of the influence of fu are the ones to optimize. As previously discussed in this thread, fu is not an optimization parameter; it’s just a feature. 38/
Keith Hornberger @KRHornberger
(Aside: math lovers may note that Cl_u = Cl_p / fu,p rearranged as Cl_p = fu,p * Cl_u is in the same form as the well-stirred model “low clearance” regime when Qh >> fu * Cl_int. If in that regime and Cl_h ≈ Cl_b ≈ Cl_p, Cl_u can be a good approximation for Cl_int… 39/
...Even savvy chemists frequently assume this approximation is always the case. In reality, things are a little more complicated than that and some attention should be paid to make sure all the necessary assumptions are true.) 40/
To close, consider this tale of two compounds. We’ll do this just with clearances to make it easier. Compound A has mouse IV Cl = 50 mL/min/kg and fu = 0.10. Compound B has mouse iv Cl = 10 mL/min/kg and fu = 0.01. Which is “better”? 41/
