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Dear Group,
Could any one explain under what circumstances protein binding of
ligands (high and low affinity) is non-saturable? I appreciate if you
can provide associated equations.
Thanks,
Kasiram.
[Have a look at http://www.boomer.org/manual/ch04.html#4d parameter
type 31-33 for saturable protein binding equations, lower
concentrations lead to non-saturable protein binding. Large volume of
distribution could mean lower concentrations - db]
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Dear Kasiram,
every binding is saturable. However, this is not relevant when the
concentration of binding sites is much higher than the concentration
of ligands. If a drug binds only to a single binding site of serum
albumin the availabel binding capacity in plasma is around 0.6 mM.
That means the fraction unbound of this drug will be constant at
plasma concentrations of the drug between 0 and approximately 0.05 mM
were it slowly starts increase (this is more or less true for high
and low affinity binding). For drugs binding to other proteins (e.g.
alpha 1 acid glycoprotein) the binding capacity is much smaller and
more variable.
Equations you can find in the below references:
Karlsson R (1994) Real-time competitive kinetic analysis of
interactions between low-molecular-weight ligands in solution and
surface-immobilized receptors. Anal.Biochem.; 221 (1):142-51.
Rich RL, Day YS, Morton TA, et al (2001) High-resolution and high-
throughput protocols for measuring drug/human serum albumin
interactions using BIACORE. Anal.Biochem.; 296 (2):197-207.
Regards,
Markus
Markus Weiss, PhD
ED/DMPK/ADME/ADE
Novartis Pharma AG, Werk Klybeck
WKL-135.4.83
CH-4002 Basel
Switzerland
Phone: +41 61 69 61075
Fax: +41 61 69 65146
Email : markus.weiss.-a-.novartis.com
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Kasiram,
It is a misconception to state that protein binding is "non-
saturable", and perhaps you mean to say "unsaturated".
For extent of binding of ligands to proteins, that can be modeled
according to the michaelis-menten expression for rate of enzyme
metabolism; the similiar function relating amount bound to substrate
concentration (with parameters: Protein total, and Kd ) reveals the
answer...
that the protein is relatively unsaturated, IF the concentration of
substrate accessible to the enzyme active site is below the Km (i.e.,
concentration at 50% of saturation -- a measure of binding affinity).
Hope that helps,
Shawn D. Spencer, Ph.D., R.Ph.
Assistant Professor of Biopharmaceutics and Pharmacokinetics
College of Pharmacy and Pharmaceutical Sciences
Florida A&M University
Tallahassee, FL 32311
shawn.spencer.aaa.famu.edu
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The following message was posted to: PharmPK
Dear Markus,
Thanks for your response. I was wondering what effect increasing protein
concentration would have on ligand binding. Can we expect linear binding
(non-saturable) under these conditions as binding sites will always be
greater than ligands?
Inputs from the group are much appreciated.
Kasiram
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Dear Kasirma,
in a situation were the concentration of binding sites is mucher
higher than the concentration of ligands - e.g. a drug at a
concentration in the range 0-50 uM bound to serum albumin (approx.
600 uM) - a change of the number of the availble bindinge sites (say
a drop to 300 uM in hepatic impaired patientes) would roughly double
the free fraction (fu); a doubling of available binding sites (e.g.
two binding sites on albumin with he same affintiy rather that 1)
would reduce it by 50%. Fu would be (almost) independent of the drug
concentration as long as it stays small compared to the binding site
concentration. It would be dependent on the affinty (Kd) and the
number of available binding sites. Was that what you meant?
Regards,
Markus
Markus Weiss, PhD
ED/DMPK/ADME/ADE
Novartis Pharma AG, Werk Klybeck
WKL-135.4.83
CH-4002 Basel
Switzerland
Phone: +41 61 69 61075
Fax: +41 61 69 65146
Email : markus.weiss.-at-.novartis.com
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The following message was posted to: PharmPK
Dear Markus,
Yes, partly that's what I meant. What I am specifically interested in is
the binding model to be used to explain the binding of a ligand to a
binding site under increasing concentrations of protein.
I know that there are three basic models for explaining protein binding
data viz. Linear (neither protein nor ligand depletes), Protein
depletion (saturation of binding sites) and Ligand depletion. Obviously
the binding data at increasing protein concentration ideally fits to the
ligand depletion model. However, what does it mean when the same data
fits to other models?
Is it because that linear binding phase exists in all cases (although
brief and dependent on affinity) as a result the data in this region
fits to all the three models?
I appreciate inputs from group on this.
Thanks,
Kasiram
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The following message was posted to: PharmPK
Dear Kasiram,
what kind of fittness function do you use for analysis of
mathematical model quality? If you use
classical measures like R2, F etc. you probably could not detect
overfitting. If that is true you
could not differentiate between underlying mechanisms. I think that
you could try crossvalidation or
bootstrap statistics. Resampling statistics measures could better
detect overfitting. Moreover, if
you have (or you can produce) a lot of points I suggest you to try
multiple leave-many-out
validation (multiple(100x) random splitting of complete set of
datapoints into training (80%) and
test set (20%)). Average R2 (experimental values against predicted
values) will efficiently eliminate
inappropriate models.
Hope this helps.
Zeljko Debeljak, PhD student
Osijek Clinical Hospital,
CROATIA
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Drug binding to protein binding is normally dealt with by linear
approximations, assuming an excess of binding sites. Conversely,
binding to receptors (or other targets) is dealt with using another
approximation, that of insignificant numbers of receptors compared
with moles of drug molecules added, such that the hyperbolic
Michaelis-Menten or Langmuir equations can be used.
In reality neither is strictly correct. Depending upon circumstances
a drug may go from being in excess of binding sites, to the binding
sites being in excess of the drug as it clears out. A binding site
can be on a protein or could be partition into a lipidic environment.
The latter of course we normally consider to have infinite capacity
relative to the dose of drug given, but this does not have to be true.
One path I have used whenever I am confused is to go back to the
fundamentals, write out the binding equations, which are second order
reactions, implement them as differentials and play with various
parameter estimates for binding contants, rate of supply and half-
lives of both drug and binding site(s).
;Drug + site <=> complex, assuming 1:1 binding
d/dt(drug) = InputDrugRate -CLdrug/Vdrug*drug -kon*drug*site
+koff*complex
d/dt(site) = InputSiteRate -ke*site -kon*drug*site
+koff*complex
d/dt(complex) = -kecomplex*complex +kon*drug*site -
koff*complex
Certain assumptions will also have to be made about the half-life of
the drug-site complex. Parameters can come from the literature, such
as albumin having a half-life of about 17 days, and is present at 40
mg/mL (at baseline). Then the rate of supply must be
Baseline*ke=40*0.04 or approx 1.6 mg/mL per day. Multiply by the Vss
and one gets the actual rate of production in mg/d. Molecular weight
is 68 kDa to convert to molar to use with the binding equations.
By simulation one will see the effects of changing either the binding
site levels and/or the drug levels. It can be very revealing,
especially if the drug is given at a molar dose which is in the same
range as the molar concentrations of binding sites. This is often the
case with biotech products, for example monoclonal antibodies, and
can give rise to interesting nonlinearities and dependencies on
target kinetics, but the underlying theory should hold for all
binding reactions.
Have fun.
Best regards, Phil.
Modelling & Simulation
Novartis Pharmaceuticals AG
CH-4002 Basel
Switzerland
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