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Dear colleagues,
How to calculate the fraction unbound (fu) in a plasma protein binding
assay?
The plasma protein binding of a drug can be experimentatlly assessed by
incubating the drug with diluted plasma (e.g. 10% plasmain PBS). The
fraction unbound in 10% plasma is measured, whereafter the fraction
unbound in 100% plasma is calculated according to the following formula:
fu (10% plasma)
fu (100% plasma) = ----------------------
10 - 9*fu (10% plasma)
For drugs that bind strongly to plasma protein this formula is very
suitable, reproducible plasma protein binding can be measured because
nearly all of the 10% plasma protein is bound.
For drugs that are medium or low plasma protein binders this is not the
case, in an incubation with 10% plasma only a small amount of drug is
bound, the difference of the fraction unbound compared to control (no
plasma) is so small that we reproducible measurement is not possible.
To tackle this point we want to increase the amount of plasma in our
incubation to for instance 50%.
Now, our problem is that we don't know how to change our formula (the
above one) to be suitable to calculate fu in 100% plasma from a 50%
plasma incubation.
Does anyone know which formula we should use?
Of course we will look forward to any response on the subject for which
we thank you in advance!
Sylvia Lemstra
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The following message was posted to: PharmPK
Let me give it a try.
If 50% plasma is used, fu (100% plasma) should be calculated as follows
fu (50% plasma)
fu (100% plasma) = ----------------------
2 - fu (50% plasma)
The following is the derivation.
At equalibrium, [D]+[P]=[DP], where D is drug, P is protein and DP is
the
complex.
Assuming Kd is the equalibrim constant,
Kd=[DP]/([D]*[P])
Since [Dtotal]=[D]+[DP] (assuming 1:1 binding), [DP]=[Dtotal]-[D].
Then Kd=([Dtotal]-[D])/([D]*[P]) (1)
Define fu=[D]/[Dtotal]
Then dividing both the numerator and denominator of (1) by [Dtotal],
we get Kd=(1-fu)/(fu*[P])
Since only a very small percentage of total protein is bound by drugs,
[Ptotal]approx=[P].
Then Kd=(1-fu)/(fu*[Ptotal])
Define f' as the unbound fraction at another Ptotal, say [Ptotal]'.
Then (1-fu)/(fu*[Ptotal])=(1-f')/(f'*[Ptotal]') (Kd is independent of
the
concentration of protein).
If [Ptotal]=10% and [Ptotal]'=100%,
f'=fu/(10-9*fu).
If [Ptotal]=50% and [Ptotal]'=100%,
f'=fu/(2-fu).
Any comment is welcome.
Yaning Wang
Department of Pharmaceutics
College of Pharmacy
University of Florida
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The following message was posted to: PharmPK
Dear Yaning and Dave,
Thanks a lot for the derivation.....
Now it looks much simpler that our tries, we feel a little stupid, but
happy indeed.
Best regards,
sylvia
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The following message was posted to: PharmPK
You may try this procedure:
Spike your serum with the drug to different concentrations within the
expected range (Ct1..Ctn).
Incubate at 37 deg. For 1 hour.
Centrifuge to a maximal speed using filtration tubes (AMICON cutoff
10,000).
Measure the drug concentration in the protein-free filtrate (Cf).
%binding = Cf*100/Ct.
In a case the Cf is below the minimal quantitative concentration, use a
mixture of radiolabeled/unlabeled drug (label the hydrogen or the carbon
but don't insert labeled iodine because you don't want to change the
molecular structure). Be aware to the "absorption background" on the
tube wall and filter.
Shlomo
Shlomo Almog PhD
Head, Clinical Pharmacology and Toxicology Laboratory
Sheba Medical Center, Tel-Hashomer, Israel.
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