# PharmPK Discussion - Unbound fraction calculation

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• On 7 Jul 2003 at 14:52:29, Maria.Kissel.at.4sc.com sent the message
`Dear colleagues,How to calculate the fraction unbound (fu) in a plasma protein bindingassay?The plasma protein binding of a drug can be experimentatlly assessed byincubating the drug with diluted plasma (e.g. 10% plasmain PBS). Thefraction unbound in 10% plasma is measured, whereafter the fractionunbound 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 verysuitable, reproducible plasma protein binding can be measured becausenearly all of the 10% plasma protein is bound.For drugs that are medium or low plasma protein binders this is not thecase, in an incubation with 10% plasma only a small amount of drug isbound, the difference of the fraction unbound compared to control (noplasma) is so small that we reproducible measurement is not possible.To tackle this point we want to increase the amount of plasma in ourincubation to for instance 50%.Now, our problem is that we don't know how to change our formula (theabove 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 whichwe thank you in advance!Sylvia Lemstra`
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• On 10 Jul 2003 at 15:55:59, "Yaning Wang" (yaning.-a-.ufl.edu) sent the message
`The following message was posted to: PharmPKLet 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 isthecomplex.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 oftheconcentration 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 WangDepartment of PharmaceuticsCollege of PharmacyUniversity of Florida`
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• On 11 Jul 2003 at 09:46:21, Sylvia.Lemstra.at.4sc.com sent the message
`The following message was posted to: PharmPKDear Yaning and Dave,Thanks a lot for the derivation.....Now it looks much simpler that our tries, we feel a little stupid, buthappy indeed.Best regards,sylvia`
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• On 11 Jul 2003 at 14:20:25, "Dr. Shlomo Almog" (salmog99.at.netvision.net.il) sent the message
`The following message was posted to: PharmPKYou may try this procedure:Spike your serum with the drug to different concentrations within theexpected range (Ct1..Ctn).Incubate at 37 deg. For 1 hour.Centrifuge to a maximal speed using filtration tubes (AMICON cutoff10,000).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 amixture of radiolabeled/unlabeled drug (label the hydrogen or the carbonbut don't insert labeled iodine because you don't want to change themolecular structure). Be aware to the "absorption background" on thetube wall and filter.ShlomoShlomo Almog  PhDHead, Clinical Pharmacology and Toxicology LaboratorySheba Medical Center, Tel-Hashomer, Israel.`
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