Putting the free drug principle into practice to calculate brain penetrance and other PK/PD parameters
September 11th, 2025 By John Widen
I was reading an article gearing up to write about a drug target.
However, that will have to wait because while I was reading,
I was reminded of an issue that has been a problem in scientific literature for a long time.
That issue is ignoring the “free drug hypothesis” when interpreting pharmacokinetic (PK) and pharmacodynamic (PD) data.
The free drug hypothesis shouldn’t really be called a hypothesis anymore (although, it does have a nice ring to it).
At this point, free drug concentrations are definitively relevant to the accurate interpretation of PK/PD parameters.
Hence, I will refer to the “free drug hypothesis” as the “free drug principle” as proposed in
this article written in 2021.
Free concentration measurements are particularly important when evaluating brain penetrance of small molecules and
several recent articles I have come across ignore the free drug principle when doing so.
Therefore, I’m going to focus on how to calculate and report unbound corrected
values and brain penetrance in rodent models for this article.
I have seen more awareness of the free drug principle very recently but maybe that is due to the
Baader–Meinhof phenomenon.
But when reviewing publications regarding drug discovery, many fall short of proper PK/PD analysis
taking free drug concentrations into account. Regardless, a couple months ago
Drug Hunter hosted Dennis Smith,
a DMPK/ADMET expert with over 35 years of experience in drug discovery, for a webinar going over important
concepts of the free drug principle. I would highly recommend anyone in drug discovery or an adjacent field
to check it out. If you are going to publish a paper with any reported in vitro or in vivo
data, please look through the literature and/or consult with a DMPK expert to ensure the free drug
principle is being used in your analysis. A
perspective published in the Journal of Medicinal Chemistry
(also co-authored by Dennis Smith) this year covers free drug concepts but much of the focus is dedicated to
explaining why optimizing for protein binding of a small molecule is a bad idea.
I actually find some of the explanations presented in this perspective confusing.
For instance, one of the key concepts of the free drug principle is quoted as:
Unbound concentrations in vivo are not determined by the extent of plasma or tissue binding;
instead, plasma and tissue binding determine the concentrations of bound drug.
I really think the authors should have workshopped this sentence a little bit.
I have read it at least one hundred times and still squint my eyes and scratch my head.
It is explained a little bit better in the Drug Hunter Webinar mentioned above, but not by much.
I interpret this confusing sentence to mean that free (unbound) concentration is not dependent
on protein binding because protein binding can be exhausted at higher concentrations.
Put another way, total concentration (Ct) is not linearly proportional to dose,
especially at higher doses, when protein binding becomes exhausted.
Maybe I'm off the mark on my interpretation, but the main point of the concept quoted above is
that optimizing for protein binding (referred to as fu) is futile.
After reading sentences like the one quoted above, it is no wonder people have a difficult time adopting the free drug principle.
The concepts of the free drug principle are relatively simple.
Free Drug Principle
- Only free (unbound) drug can act on the protein target of interest. This makes sense conceptually because if the molecule is bound to something,
how would it then engage a different protein. Molecules cannot be two places at once.
- At equilibrium, free drug concentration in plasma equals that of the concentration in tissue.
This is true the majority of the time for all tissues except for the brain, due to the blood-brain barrier (BBB).
I will describe this in more detail below.
If nothing else, just remember not to use Ct or uncorrected clearance (CL) to interpret PK/PD parameters.
Learning the concepts of the free drug principle is important but for this article I’m more interested in how these concepts are actually used in drug discovery.
In practice, Ct is what is measured in vivo.
Plasma or tissue is processed and injected into an LC-MS/MS to determine concentration.
They are total concentrations because solvent is used to dissolve compound and denature protein.
The process pulls all of the bound molecule away from any proteins.
Why is it done this way? There are two very good reasons: 1.)
Measuring free fraction directly is very challenging because processing steps of biological tissue for measurement
changes the equilibrium (i.e. dilution, solvent, separation). Total concentration is much easier,
cheaper, and faster using LC-MS/MS methods.
2.) Free fractions can be very small. Especially, with highly bound compounds.
Therefore, measuring total concentrations are easier and more reliable.
The total concentration values that are directly measured from tissues are then corrected by
multiplying by an in vitro measurement of protein binding (fu).
Protein binding is a unitless number between 0 to 1. It is a fraction of compound bound
to something like protein and free in solution, hence, free fraction (fraction unbound: fu).
I know the majority of people hate math.
I actually like math and was good at it once upon a time (humble brag).
I promise I will not show a bunch of equations and derivations in this article to make a point.
However, I’ll let all of you math haters in on a little secret.
All protein binding corrections are simple multiplication or division by an fu value.
That is it! There are no integrals, exponentials, or derivatives.
For instance, total concentration (Ct) x free fraction (fu) = free (unbound) concentration (Cu).
You have most of the free drug principle covered if you remember that simple equation.
For correction of clearance values (CL), you just divide by fu to get unbound clearance (CLu).
That’s the second equation. There are no unit changes, unbound and total values have the exact same units because fu is unitless. Those two equations cover the majority of situations scientists run into.
I’m going to give a third equation and kind of break my promise I just made above.
But I swear it is simple. It’s to correct potency values.
Let’s say you have a cell-based assay that contains 10% FBS (fetal bovine serum).
FBS contains proteins in it, which small molecules can non-specifically bind to.
Any assay with FBS or a similar supplement should be corrected with the free fraction.
To adjust the IC50 value you measure the compound’s fu in 10% FBS,
which is a simple equilibrium assay that many CRO’s can do on the cheap.
Then you multiple them! That’s it. That gives you the corrected unbound IC50 value (IC50,u).
This value is important for determining the concentration required to cover the target in vivo.
Now, not every compound needs to have the IC50 corrected by free fraction.
When comparing uncorrected IC50 values of compounds within a series,
we are making an assumption that the free fraction will not change so much between close analogues.
This isn’t always a perfect assumption but it is good enough to make decisions on compounds to synthesize.
It is always good practice to spot check the best compounds to make sure there isn’t anything unexpected.
There is more nuance but I’ll stop there. Maybe, I’ll cover this in more detail in another blog post.
That is a bit of a crash course on free drug principles and how to put it into practice. Reporting corrected parameters accounting for free drug concentrations for assays, PK, and PK/PD experiments will bring SO MUCH value to your publications. If you run animal experiments, I would highly recommend splurging the extra ~$200 or so to get free fraction measurements to bring meaning to your data. Total, bound concentrations and uncorrected clearance values are pretty meaningless when comparing across molecules.
To summarize everything I just wrote into three equations:
- Cu = Ct x fu
- unbound concentration = total concentration x free fraction
- CLu = CL / fu
- Unbound clearance = clearance / free fraction
- ICxx,u = ICxx x fu
- Unbound potency = potency x free fraction
(I put xx for ICxx because often times people want to cover the target above the IC50 value.
For instance, IC95, which is just taking the IC50 multiplied by 19.)
Okay. Let’s discuss how the free drug principle applies to evaluation of brain penetrance in rodents.
This is probably the most common area where publications fall short.
I do appreciate that these days more labs are at least running PK experiments to evaluate their top compounds.
Even ten years ago, labs would just ignore anything to do with PK,
report an ‘efficacy’ study and boom, the compound worked, everything is fine,
nothing to see here. Maybe they ran PK experiments in the background
and didn’t report the data. But, that brings down the value of reporting
any efficacy data to nearly zero. Labs are still falling short on reporting meaningful
data for brain penetrance by only reporting total concentration values and using those
in calculations instead of unbound concentrations.
Here is a nice article with details about calculating
brain penetrance.
The reason to evaluate brain penetrance is because of the blood-brain barrier (BBB).
The BBB is composed of specialized endothelial cells that form tight junctions and express efflux
pumps (mostly Pgp, P-glycoprotein) around the vasculature through the brain to exclude large,
polar molecules from entering the brain. It is a protective barrier to keep the precious hardware intact.
Tissue within the brain is also very fatty due to myelin and other membranes protecting neurons.
Therefore, the tissue has different non-specific binding than plasma.
The BBB and different properties of the brain need to be accounted for when evaluating concentration
of a molecule in the brain. That is the short version of why determining brain penetrance using unbound concentrations
for molecules is necessary and important for CNS-focused drug targets.
Even for non-CNS related programs, knowing the brain penetrance is important.
If the target of interest is important only in the periphery,
restricting your small molecule from the brain would reduce potential off-target effects.
Brain penetrance is an important consideration in every drug discovery program!
I’ll start with the experimental setup of the PK experiment to evaluate brain penetrance.
There are a variety of different ways to get to the same answer.
Depending on budget and information needed to make a decision, the experimental setup can vary.
I’m going to describe a general in vivo brain PK experiment that I am familiar with.
An initial brain PK experiment requires a cohort of mice or rats, typically three for each set.
The compounds can be run in a cassette or individually.
Cassettes combine 3-4 compounds into one injection to save the rodents and money.
For example, if you run three compounds individually in three rodents each and measure three brain concentration time points,
that is 27 rodents total. Each brain timepoint requires mice to be sacrificed. Kind of a lot.
Alternatively, you can dissolve all of the compounds into one formulation at the same concentration
and inject all three compounds at once into nine rodents total to obtain three time points for three molecules.
Not so many rodents. People have different beliefs about cassettes.
I’m not going to get into that. I’m just giving it here as an option to ask your DMPK expert about.
There are certain requirements for cassettes including large enough differences in exact mass
for LC-MS/MS detection since the compounds would all have to be detected separately from the same samples.
For simplicity, we are going to evaluate one molecule for CNS penetrance in rats.
The compound is typically injected I.V. at low concentration (1-10 mg/kg).
The dose depends on the limit of detection, time points to be measured, and elimination rates.
The next important aspect of a PK experiment is time points.
You typically want measurements once steady-state of clearance and distribution is reached.
For I.V. injections, this is typically very rapid and occurs within 15 minutes.
Steady-state is after the initial spike in concentration is observed and the concentration levels off.
You don’t really need to know the exact details, just remember to collect plasma and brain at 2-3
time points after steady-state is reached. Sometimes, compounds can be kinetically slow to equilibrate but that is why taking multiple
measurements at different time points is best practice. The time points that I am familiar with are 30, 60,
and 120 minutes post injection. There are other nuances to the experiment including collecting CSF (cerebral spinal fluid)
and plasma out to 24 hours to obtain clearance and half-life values. CSF collection is typically
conducted alongside brain collection for comparison. There are some debates about
the usefulness of CSF measurements as well. I’m in the faction that thinks it is a
useful measurement as a sanity check. I will save this discussion for a future blog post (I smell a blog series coming!).
Keep in mind that for every brain measurement time point, three mice will be sacrificed.
So, nine rodents will be required for the experiment I just described.
Also, keep in mind that it is helpful to run a general I.V.
PK experiment prior to a brain PK study to ensure that the compounds have a reasonable clearance and half-life.
If you are unsure about the general PK, the clearance could be high and the compound could be eliminated before your time points.
Therefore, no useful data will be required. I’ll stop there. Consult a DMPK expert for more details before executing these experiments.
Now we have measurements of total brain and plasma concentrations at three time points from the brain PK study.
Because we are implementing the free drug principle, we also measured the free fraction (fu)
of the molecule in plasma and brain matrix to correct the total concentrations into free concentrations as discussed above.
This is where the very common mistake occurs. Most publications report the ratio of total brain-to-plasma
for evaluation of brain penetrance (Cb,t/Cp,t). To truly understand the free
fraction in the brain and the extent of brain penetrance these values have to be corrected for protein binding.
This does involve more math but only simple multiplication. The ratio for brain-to-plasma using free concentrations is commonly
called either Bu/pu (phonetically Bee-You to Pea-You) or Kp,uu (phonetically Kay-Pea-You-You).
These two abbreviations are the same thing. Kp,uu is more common in the literature.
Think of it as an equilibrium between unbound plasma and unbound tissue. Technically, Kp,uu can
be used to describe partitioning between any tissue and plasma. If it is brain, the abbreviation should be
Kp,uu,brain, but most referr to the ratio as Kp,uu.
Okay. So, instead of reporting the ratio of total concentrations take both total concentration values
from the brain and plasma and multiply them by the free fraction values obtained. The simple equations are below:
- Pu = Pt x fp,u
- Unbound plasma concentration = total plasma concentration x free fraction in plasma
- and
- Bu = Bt x fb,u
- Unbound brain concentration = total brain concentration x free fraction in brain
- Brain penetrance ratio = Bu / Pu
These equations should look very familiar because they are the exact same as the first equation discussed above.
You correct the total concentration for each compartment with the corresponding free fraction
and then divide the brain number by the plasma number. Then, you’re done! Now, we can evaluate the
brain penetrance of the molecule in the rodent experiment! You measure three time points because you
want to make sure the Bu/Pu values do not change much over time.
In other words, to ensure the measurements are at steady-state.
One short cut for this experiment is to take one time point,
but you run the risk of not knowing if the measurements were done under equilibrium conditions.
I sound like a broken record, but consult a DMPK expert to decide what is best for your situation.
Let’s discuss the interpretation of Bu/Pu values and
why it is important to correct for free fraction instead of using total concentrations.
In Fig. 1 below, there are three molecules that were evaluated in a brain PK experiment.
These compounds come from real-world examples of molecules. It is not uncommon to have free
fraction differences between brain and plasma to be 3 to 5-fold different,
but even a 2-fold difference in free fractions can change the interpretation of the data
as seen with compound B. Compound B has a total brain-to-plasma ratio of 0.2, which is low.
But, when it is corrected with the free fraction values the Bu/Pu is now 0.5, which is good!
Generally speaking, the cutoff value for a compound having reasonable brain penetrance is 0.3.
The cutoff comes from
this paper that evaluates brain penetrance of 34 drugs.
For compound A, if the total brain-to-plasma ratio is used, one might determine that the compound is brain penetrant.
However, using the protein binding corrected values results in a Bu/Pu of 0.1,
which is considered to be peripherally restricted. The closer the free fractions are between brain and
plasma results in the total and unbound concentrations being similar as observed with Compound C.
These three examples demonstrate that even small changes in free fraction can have a drastic effect
on the interpretation of brain penetrance. Remember to correct for protein binding!
Now there may be a situation where the brain penetrance is poor (Bu/Pu < 0.3),
but the concentration required to cover IC95,u of your protein target in the brain can be achieved anyways.
That is perfectly fine. It is still good to know that you have room for improvement.
Additionally, compounds that are substrates for Pgp are actively effluxed and may affect the
drug concentrations at longer time points. Having a brain penalty can complicate the interpretation of PD experiments.
In summary, obtaining free fraction values for FBS, plasma, or brain matrix is
relatively inexpensive compared to rodent PK experiments. If you are spending ~$5k on an in vivo experiment,
I highly recommend spending the extra $200 or so to correct for free drug concentrations.
The calculations are simple multiplication and division. For the older folks reading this,
it is easier than balancing a check book. For younger people, it is like calculating 20% gratuity at a restaurant.
I did gloss over some details that I may go over as part of a series. But, hopefully, this crash course
provides enough information to make some simple calculations to interpret data correctly and encourage
readers to approach a DMPK expert to help evaluate PK/PD data.
Correction: A previous version of this article states that IC95 can be calculated by multiplying
IC50 by 9.5. That is incorrect. An approximate IC95 is obtained by multiplying IC50 by 19.
Unbound concentrations in vivo are not determined by the extent of plasma or tissue binding; instead, plasma and tissue binding determine the concentrations of bound drug.
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