9Plasma Protein Binding and Volume of Distribution:Determination, Prediction and Use in Early Drug DiscoveryFranco Lombardo, R. Scott Obach, and Nigel J. Waters

9.1Introduction: Importance of Plasma Protein Binding

The importance of plasma protein binding primarily resides in its impact onpharmacokinetic properties such as clearance and volume of distribution, as well aspotency and CNS penetration. However plasma protein binding is generally not, initself, a deciding factorwhen consideration is given to theadvancement of a compoundto further studies and development, nor does a change in plasma protein bindingmeanmuch from a clinical relevance perspective [1]. Plasma protein binding is rathera �modulator� or a �buffer� of the free drug concentration; and a nice treatment of thisaspect is offered by Trainor [2]. Also, as explained in the following sections, the valuesare generally reported as equilibrium values and they are determined in plasma withlittle or no consideration toward possible physiological variability of plasma proteincontent and the on/off rate. Thus, they represent �bulk� values and relevant examplesof apparent exceptions are presented in the following section, with caveatsmentionedin the section on the determination of plasma protein binding values. Onemore wordof caution in interpreting the results can be offered when dealing with highly protein-bound compounds. A small percent difference, for example, 3% difference between99% bound and 96% bound represents a fourfold difference in free fraction, while a3% difference between say 76% bound and 73% bound represents only a 1.1-folddifference in free fraction. And, of course, a value of 99.9% bound versus a value of99% bound represents a 10-fold difference, but measuring a value of >99% withconfidence is generally problematic.

9.2Impact of Plasma Protein Binding on PK, Exposure, Safety Margins, Potency Screensand Drug–Drug Interaction

According to the free drug hypothesis only the unbound drug is available to act atphysiological sites of action, whether it is the intended pharmacological target, oraction at an undesired site with potential toxicological consequences and a schematic

Hit and Lead Profiling. Edited by Bernard Faller and Laszlo UrbanCopyright � 2009 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-32331-9

j197

representation of the partition phenomena between plasma and target as well as non-target tissues is shown in Figure 9.1. In either case, assessing drug exposure as thearea under the plasma concentration–time curve (AUC) or maximal plasma concen-tration (Cmax), expressed in their free forms (i.e., unbound AUC, unbound Cmax)can be paramount. In pharmacodynamic studies of the azole antifungals, Andeset al. [3] using a mouse model of disseminated candidiasis, showed that the freeAUC-to-MIC (minimum inhibitory concentration) ratio was the pharmacokinetic–pharmacodynamic (PK-PD) parameter most predictive of efficacy for voriconazole.This correlated well with large clinical studies on voriconazole, where free drug AUCwas considered rather than total drug AUC [4]. Similar work on the fluoroquinoloneantibiotics has shown free AUC/MIC ratio to be a successful predictor of efficacy ina rat model of pneumococcal pneumonia, and in the case of moxifloxacin, thefree AUC/MIC was similar to that reported in human [5]. In clinical studies of thebcr-abl/c-kit inhibitor, imatinib, in patients with advanced gastrointestinal stromaltumors, hematotoxicity was assessed as percent absolute neutrophil count andpercent platelets. These parameters were correlated to the estimated AUC at steadystate, with correlations using unbound AUC being stronger than those to totalAUC [6]. In addition to assessing and understanding PK-PD and exposure–toxicity

D

T:D

T:D

T:D

T:D

T:D

T:D

T:D

T:D

T:D

D D R:D

Txp

T:DT:DT:D

D

P:DP:DP:D

P:DP:DP:D

D

D

D

D

D D

P:DP:DP:D

P:DP:DP:D

T:D

T:D

T:D

T:D

T:D

T:D

Target TissuePlasmaNon-Target Tissue

Figure 9.1 In this scheme, there are threecompartments represented, the central (plasma)compartment, the target compartment, and allother tissues compartment. The letters representthe following: D¼ drug, P¼ plasma protein,T¼non-specific tissue binding sites, R¼ targetreceptor, Txp¼ drug transporter. All bindinginteractions are reversible and the drug canreadily traverse the membranes that divide thevarious compartments. In the plasma, thescheme shows 12 drug molecules bound andfour free, indicating a value for fu of 0.25. The

drug can readily penetrate the non-target tissuesand there is binding capacity for the drug in thesetissues. The fu(tissue) value is 0.16, which islower than the plasma free fraction, but thefree concentration is still the same (4D). In thetarget tissue, there is also non-specific bindingcapacity as well binding to the target receptor.The fu(target tissue) is 0.33, but the free drugconcentration is lower (2D) due to activetransport from the tissue. If both target andnon-target tissues are included together, thefu(tissue) value would be 0.20 (6/30).

198j 9 Plasma Protein Binding and Volume of Distribution: Determination, Prediction

relationships, expressing AUC and Cmax in their free forms allows direct compoundcomparisons to bemade at the lead and candidate selection phases of drug discovery.There are cases where differences in plasma protein binding arising as a result of

inter-species variation or in numerous disease states, can affect the pharmacokineticsand pharmacodynamics of a drug. In Phase I clinical studies on the antitumor agent,UCN-01, the clearance and steady state distribution volume were markedly lowerthan that expected from studies in preclinical species. The percent unbound inhuman plasma at 1mg/mLwas<0.02% compared to 0.42, 1.75 and 1.17% in dog, ratand mouse respectively. Further studies illustrated UCN-01 binds to a single,saturable high-affinity binding site on human a1-acid glycoprotein (AAG), with anassociation constant (Ka) of 803� 106 L/mol [7]. This Ka is >10-fold higher than fortypical ligands such as dipyridamol, disopyramide and thioridazine (Ka 15.5� 106,1�106 and 63� 106 L/mol, respectively). As well as a cause of species variation,plasma proteins can lead to variation in clinical response. Albumin concentrations(physiologically around 40 g/L in humans) are known to vary in a number of diseasesand altered physiological states, including liver and renal disease, surgery, trauma,pneumonia and sepsis. In many cases, patients with burns, cirrhosis or nephroticsyndrome, may have plasma albumin concentrations as low as 20–30% of normal,down at �10 g/L. Hypoalbuminemia leads to an increase in free fraction andhas been observed with the NSAIDs, diflunisal, naproxen, phenylbutazone andsalicylate [8]. As an acute phase protein, plasma concentrations of AAG are known tobe increased in a number of pathologies, including trauma, inflammation, bacterialinfection andcancer, while the generally acceptedphysiological value is around0.75 g/L. It is thought to serve a protective function by binding toxic entities such as lectins,endotoxins and bacterial lipopolysaccharide, but in doing so also acts to lower freetherapeutic drug levels. The clinical pharmacokinetics of imatinib in cancerpatients has been shown to be dependent on the levels of circulating AAG. Theinter-individual variability in imatinib clearance was significantly reduced whennormalized for the plasma AAG concentration [6]. Comparable clinical findings havebeen presented on the anti-arrhythmic agent, pilsicainide, where patients withincreased levels of C-reactive protein and AAG exhibited lower clearance andincreased total plasma concentrations of pilsicainide [9].The impact of plasma protein binding on the extent of renal drug clearance has

been investigated in vitro and in vivo, althoughnot in parallel with the plethora ofworkin the area of drug transporters. The organic anion, p-aminohippurate, binds withlow affinity to serum albumin (Ka�2.3� 103 L/mol) and its renal clearance of�10mL/min/kg greatly exceeds that of the glomerular filtration rate (GFR, �1.8mL/min/kg) indicating efficient active tubular secretion. In contrast, ochratoxin A(OTA), a naturally occurring mycotoxin, binds with high affinity to serum albumin(Ka 5� 106 L/mol, more than 1000 times that of p-aminohippurate) leading to a renalclearance of only 0.002mL/min/kg. This occurs despite the fact OTA is a high affinitysubstrate of the organic anion transporters (OATs) expressed on the proximal tubularmembrane [10]. The importance of free drug concentrations in transporter-mediatedclearance has been investigated in vitro using ochratoxin A, estrone sulfate andmethotrexate. In both oocyte expression systems and theMDCK cell line transfected

9.2 Impact of Plasma Protein Binding on PK, Exposure, Safety margins, Potency Screens j199

with human OAT1, the presence of albumin (0.5% w/v, eightfold lower than in vivoconcentrations) essentially eliminated the uptake of OTA. This was confirmed usingOAT1 substrates, estrone-3-sulfate (ES) and methotrexate (MTX), that bind toalbumin with lower affinity (OTA> ES>MTX). Increasing albumin concentrationsto physiological levels did not inhibit the accumulation ofMTX in hOAT1-expressingoocytes, and is in agreement with in vivo data where the renal CL (�2.8mL/min/kg)exceeds GFR (human GFR�1.8mL/min/kg). Accumulation of ES in hOAT1-expres-sing oocytes was significantly inhibited by albumin concentrations >0.5% (w/v),correlating well with ES renal CL in vivo (�0.04mL/min/kg) indicating no activesecretion. The understanding of active drug transport in drug disposition hasexpanded greatly in recent years and the role of plasma protein binding may needto be carefully considered in extrapolation to the in vivo situation.The prediction of clinical CYP-mediated drug–drug interactions (DDI) from in

vitro data using models based on the ratio of inhibitor concentration [I] to theinhibition constant, Ki, also relies on assessment of fraction unbound in plasma andthere are many reports discussing the relative merits of total and unbound inhibitorconcentration [11–13].With respect to reversible CYP inhibition, the use of unboundhepatic inlet inhibitor concentration is considered most predictive whilst fortime-dependent CYP inhibition the unbound systemic Cmax appears to be morerelevant [14]. Although the use of different inhibitor concentrations dependingon the inhibitory mechanism requires further investigation, it is clear the free, asopposed to total, drug concentration is crucial.The consensuswith respect to plasmaprotein binding displacement interactions is

that they are of minor clinical significance ([15]; [1]). For two highly bound drugsproposed to cause a plasma protein binding displacement interaction, the pharma-cokinetic implications can be thought of as follows: (i) the displacer causes thevolume of distribution of the displaced drug to increase, as less displaced drug is inthe plasma comparedwith tissues, as the tissue:plasma equilibrium is re-established;(ii) any increase in free levels of the displaced drug is also available for drugelimination. Hence, any increase in pharmacological effect of the displaced drugis transient and cannot be sustained. Thus, the overall result of displacement is that itmay cause a minor transient increase in free drug concentration and effect, but themean steady-state free drug concentration will be unaltered. It is the interpretation oftotal drug concentrations when using therapeutic drug monitoring that can beaffected. An example of this type of interaction is seen when valproic acid andphenytoin are co-administered and the interpretation of total phenytoin concentra-tion is confounded by the increase in free fraction [16].Although PPB displacement has little clinical significance as amechanism of DDI

itself, it can confound the in vitro prediction ofmetabolicDDI such that an increase infree fraction of a drug by a displacer increases its hepatic clearance based on totalplasma drug concentration that, in turn, may mask a concomitant effect of thedisplacer as an enzyme inhibitor in decreasing drug clearance. One such example isthat of warfarin and gemfibrozil, where the expected increase in total warfarin AUC,as a result of gemfibrozil-mediatedCYP2C9 inhibition, is not observed. Interestingly,thismay be the case formany 2C9 interactions given the overlapping SARwith serum

200j 9 Plasma Protein Binding and Volume of Distribution: Determination, Prediction

albumin affinity. Hence, equations describing human serum albumin displacementare incorporated into quantitative DDI models like SimCyp [17]. Although PPBdisplacement for serum albumin is a rare event, it may be key for AAG, which iseasier to saturate and as an acute phase protein, exhibits variable expressiondependent on disease state, genetics and so on.The impact of plasma or serum drug binding on in vitro potency is a common

observation in drug discovery programs where addition of the plasma or serumfraction to the in vitro system expressing the target receptor/enzyme, renders adrop-off in activity. The presence of serum albumin (typically bovine or human) orwhole serum (e.g., fetal calf) lowers the free drug concentrations resulting in arightward shift in the IC50 or EC50 potency curve. This was recently demonstratedusing cocaine-induced sodium channel blockade in cardiac myocytes, where thepresence of a1-acid glycoprotein (AAG) reversed the action of cocaine in a dose-dependentmanner [18]. Similarly, the intracellular accumulation of theHIVproteaseinhibitors, saquinavir, ritonavir and indinavir, was shown to be reduced by thepresence of increasing concentrations of AAG in vitro, impacting on antiviral activityin vitro [19]. An important consideration with in vitro cell culture assays is the usualrequirement for 10% fetal calf serum in order to maintain cell viability, with culturestypically not being able to tolerate growth media containing >50% human serum.This leads to two incorrect assumptions that: (i) the absence of human serumrepresents a protein- or serum-free potency measure (despite 10% fetal calf serumbeing a component); (ii) the presence of 50% human serum (and 10% FCS)representing the full effect of serum binding [16].

9.3Methodologies for Measuring Plasma Protein Binding

There are a multitude of approaches applied to the measurement of plasma proteinbinding and several of them are presented in Table 9.1. They typically fall into threecategories: in vitro, in vivo and higher-throughput surrogate methods. In addition, anumber of analytical technologies are employed including, but not limited to,UVandfluorescence [20], nuclear magnetic resonance [21], circular dichroism [22] andsurface plasmon resonance [23] spectroscopy; but the focus here is on methodscurrently in widespread use throughout pharmaceutical R&D.In vitro assessment of plasma protein binding requires a technique capable of

separating free and bound drug for subsequent analysis and usually involves someform of ultrafiltration, ultracentrifugation or equilibrium dialysis. Ultrafiltrationforces the aqueous plasma component containing the free drug through a selective,semipermeablemembrane aided by vacuum,positive pressure or centrifugation. It isa simple, relatively rapid (15–45min) procedure that has been formatted into 96-wellplates [24–26]. This approach can suffer from compound adsorption issues to boththe device and filter, and protein leakage across the filter can lead to erroneousdeterminations of free fraction for highly bound compounds. Efforts have beenmadeto overcome some of the drawbacks associated with the ultrafiltration technique.

9.3 Methodologies for Measuring Plasma Protein Binding j201

Table9.1Su

mmaryof

approaches

toPP

Bdeterm

inationin

vitro.

Metho

dology

Advan

tages

Disadvantages

Reference

Ultrafi

ltration

Simple,

rapid,

96-wellform

at.

Adsorptionissues,p

rotein

leakage.

[24–27

]

Ultracen

trifugation

Minim

alnon

-specificbindingan

dosmotic

volumeshifts.

Largeplasmavolumes

requ

ired,lon

gassaytime,

issues

such

assedimen

-tation

,backdiffusion

andviscosity.

Poten

tial

forlip

oprotein

contamina-

tion

ofplasmawater

layer.

[28,

29]

Equ

ilibrium

Dialysis

Stan

dard

ED

High-through

put,96

-wellform

at.

Longincubation

time–compo

und

instability

andplasmadegradation.

Issues

ofpH

driftan

dosmotic

vol-

umeshifts

(can

becorrectedfor).

Mem

bran

eadsorption

/non

-specific

bindinga.

[30–32

]

Rapid

ED

Incubation

times

canbe

shorter–

minim

izingvolumeshifts.A

men

a-bletoau

tomation.H

ighthrough

put.

Mem

bran

eadsorption

/non

-specific

bindinga.

[36,

37]

Com

parative

ED

Relativebindingusefulforhighly

boundcompo

unds.

Mixingplasmatypescaninfluen

cebindingprop

erties.T

imeto

reach

equilibrium

canexceed

24h.

[38,

39]

202j 9 Plasma Protein Binding and Volume of Distribution: Determination, Prediction

Erythrocyte

distribu

tion

inplasmaan

dbu

ffer

Noneedformechan

ism

toseparate

boundan

dfree

drug–adsorption

issues

minim

ized.F

orhighlybo

und

compo

unds,analytical

precisionno

longeraprerequisite.

Lowthrough

put,morecomplex

as-

sayform

at.

[40]

PAMPA

Bindingconstan

tsob

tained

forpro-

tein

insolution

.Norequ

irem

entfor

massbalance

orequilibrium.

Bindingmeasuremen

tmadeon

proteinof

interestrather

than

whole

plasma.

[41]

HPLC

Rapid,sim

ple,

high-th

rough

put.

Bindingspecificity

ofim

mob

ilized

proteinassumed

tobe

sameas

insolution

.Non

-specificbindingan

dadsorption

issues.B

indingmea-

suremen

tmadeon

proteinof

inter-

estrather

than

who

leplasma.

[42–45

]

aIm

pactson

massbalance

butshou

ldnot

affect

concentrationratioifsystem

isat

equilibrium.

Table9.1(Contin

ued)

Metho

dology

Advan

tages

Disadvantages

Reference

9.3 Methodologies for Measuring Plasma Protein Binding j203

By utilizing two centrifugations and using the proteinaceous retentate from a controlplasma sample, it is possible to aid compound solubility and perturb non-specificbinding, as demonstrated for a series of corticosteroids [27]. Ultracentrifugation usescentrifugal forces in excess of 105 g in order to separate the aqueous phase fromproteinaceous material [28]. There is no membrane and so non-specific binding isminimized, with negligible potential for osmotic volume shifts. However, ultracen-trifugation uses large plasma volumes (�2mL/sample), can take 12–16 h andintroduces issues such as sedimentation, back-diffusion and viscosity. Anothermajor concern is the potential for lipoprotein contamination of the plasma waterlayer that is generated [29].Equilibriumdialysis has tended to be the �gold standard� inmost drugmetabolism

laboratories with a number of high throughput approaches being reported recent-ly [30–32]. In all cases, equilibrium dialysis comprises two chambers divided by aselective, semi-permeable membrane with a plasma �retentate� on one side and abuffer �dialysate� on the other. This system is then incubated over the course of hours(6–24 h) usually at a physiologically relevant temperature (37 �C) before the retentateand dialysate chambers are sampled and analyzed for drug concentrations. Longincubation times can confound the determination of fraction unbound values as aresult of compound instability or degradation of plasma components as reported, forexample, for quinidine [33]. The observation and impact of pH drift on proteinbinding over long incubation times has also been reported [34, 35]. Membraneadsorption and non-specific binding can impact on mass balance, but as long as thesystem is in equilibrium this does not affect the concentration ratio. With longequilibration times, the osmotic pressure of the plasma proteins can induce volumeshifts, driving the flow of fluid from the buffer chamber to the plasma side. Thedilution of the plasma by the net flow of buffer can alter binding properties in anunpredictable way by influencing factors such as ionic strength and pH. If retentateand dialysate volumes are measured post-incubation, the volume shift itself can beeasily corrected for using the Boudinot equation shown below.

fup ¼ 1�ðCplasma�CbufferÞ � ðV final

plasma=VinitialplasmaÞ

ðCplasma�CbufferÞ � ðV finalplasma=V

initialplasmaÞþCbuffer

As part of this, an important phenomenon is the Gibbs–Donnan effect wherecharged proteins held on the retentate side draw low molecular weight ions acrossthe membrane to achieve electroneutrality, leading to an uneven distribution ofsmall ions. This can be overcome by using isotonic phosphate buffers. Attempts toimprove the throughput and laborious nature of ED assays has included develop-ment of rapid equilibrium dialysis (RED) offering shorter experiment times andbeing amenable to automation. The dialysis cell format with an increased surfacearea to volume ratio enables potentially shorter equilibration times with minimalvolume shift [36]. A comparative analysis of the RED and standard ED approachesusing a diverse subset of compounds showed the value of this assay to increasethroughput and reduce experiment time without compromising data accuracy orrobustness [37].

204j 9 Plasma Protein Binding and Volume of Distribution: Determination, Prediction

A variant on the equilibrium dialysis protocol was recently reported. Comparativeequilibrium dialysis places plasma from two different sources (e.g., species, in-dividuals, etc.) on either side of the dialysis membrane. The total concentration atequilibriumon each side represents the ratio between the respective fu values, and assuch is a measure of the relative binding. This has been proposed for speciescomparisons and for highly bound compounds where determining the actual fu canbe complicated by analytical precision and sensitivity [38]. However, other groupshave shown it is likely that mixing plasma types changes the binding properties bymixing of low MW fractions. This was confirmed using dialyzed blank plasma in asubsequent ultrafiltration experiment. Due to this inherent problem and the time toreach equilibriumexceeding 24 h, the authors did not recommend this approach [39].For highly bound compounds with high lipophilicity and potential apparatusadsorption problems, Schuhmacher et al. [40] proposed measuring a plasma-freefraction based on distribution between erythrocytes and aqueous, proteinaceoussolutions. By performing incubations containing resuspended erythrocytes anddiluted plasma or buffer in glass tubes and without the need for a mechanismto separate plasma-free drug from plasma-bound drug, adsorption issues wereminimized. With this approach, plasma fu was calculated as the ratio of the partitioncoefficients of erythrocytes:plasma and erythrocytes:buffer, accounting for thehematocrit in both cases. This type of �biological dialysis� precludes the accuratemeasurement of low drug concentrations which are prone to error.A novel application of the parallel artificial membrane permeability assay (PAM-

PA) system to measuring protein binding constants was demonstrated recently [41].The apparent permeability of 11 test compounds was measured in the presence andabsence of human serum albumin in the donor compartment, and by solving thedifferential equations describing the kinetics ofmembrane permeability, membraneretention and protein binding, the authors were able to obtain the Kd. With theprotein in solution rather than immobilized andwithout the need formass balance orequilibrium conditions, this approach provides an attractive alternative to existingmethods with the potential to be applied to an array of other soluble proteins.Much work has been reported on the development and application of surrogate

systems to assess plasmaprotein binding. ChromatographicmethodologieswherebyHSA or AAG is chemically bonded to silica-based stationary phases were firstreported by Wainer and colleagues about 15–20 years ago [42, 43]. This approachmeasures a chromatographic retention factor (k0) which is directly related to theproportion ofmolecules in the stationary phase and in themobile phase, and so fromthis a percent bound value can be obtained describing the interaction between theimmobilized protein and test compound of interest. Although, typically a UVendpoint is employed making it a rapid and straightforward method, the underlyingassumption is that the chemically bonded protein retains the binding specificity andconformational mobility of the native protein. In addition, there is potential for non-specific binding and adsorption issues with the silica support and long retentiontimes. Reasonable correlations have been reported between HSA binding andliterature values, although this has not been the case in studies using immobilizedAAG [44, 45]. This is possibly a reflection of the fact this type of method is not truly

9.3 Methodologies for Measuring Plasma Protein Binding j205

representative of whole blood plasma, lacking the full complement of plasmaproteins and using high concentrations of organic solvent (up to 30% organic,depending on chemistry). The speed and simplicity offered by this approach has beensomewhat superseded by the increased throughput of standardized in vitromethodsutilizing whole plasma as detailed above. A variation on the HPLC methodology,TRANSIL technology, involves immobilization ofHSA onto the inert surface of silicabeads suspended in PBS buffer [46]. After compound addition andmixing, the beadsare separated by low speed centrifugation and the resultant supernatant is analyzedby UVorMS. Validation has been performed on a range of compounds but there arefew reported applications in the literature. Other similar approaches include gelfiltration which was applied historically to investigate a number of protein–ligandinteractions [47], and more recently solid phase microextraction (SPME) whichmeasures the partitioning of drug between plasma proteins and a SPME fiber [48].In a similar manner, charcoal has been used as a binding �sink�, so PPB can bemeasured as the time course of decline of the percent bound drug remaining inplasma while the free drug is removed by charcoal adsorption. This can prove usefulin alleviating some of the issues of non-specific binding observed with highlylipophilic compounds [49].Accurate determination of drug-free fraction in vivo is a complex undertaking but

has been achieved with some success using microdialysis. Based on the dialysisprinciple,microdialysis comprises a probe inserted into the tissue of interest throughwhich fluid is delivered. The probe is made up of a hollow fiber that is permeable towater and low MW molecules, and during the perfusion, molecular exchange bydiffusion occurs in both directions. Dialysate samples are then analyzed online bystandard techniques, such as LC–MS, with appropriate analyte separation by LC orCE. In pharmacokinetic studies, the major advantage over conventional bloodsampling is the collection of protein-free samples allowingmeasurement of unbounddrug concentrations. Microdialysis coupled with simultaneous blood sampling thenenables the in vivo determination of plasma protein binding, with each samplingtechnique giving a measure of free and total drug concentration, respectively.Microdialysis has been used to investigate the temporal profile and saturation ofprotein binding of irbesartan [50] as well as obtaining binding parameters for drugssuch as flurbiprofen [51], methotrexate [52] and valproate [53]. The use of thisapproach in pharmacokinetic and pharmacodynamic studies was nicely reviewed byH€ocht et al. [54], although due to issues of complexity and the availability of in vitroalternatives, themethod has not been reported to be applied to PPB determination indrug discovery.

9.4Physicochemical Determinants and In Silico Prediction of Plasma Protein Binding

The physicochemical determinants of plasma protein binding and the in silicoprediction of the latter have been examined by several authors [55–57] and generallyfound to coincidewith lipophilicity (generally expressed by logPoct or logDoct) and, for

206j 9 Plasma Protein Binding and Volume of Distribution: Determination, Prediction

acidic compounds, charge was also found to be important, considering the presenceof basic ionized residues in the binding sites of albumin. It is a common observationthat the vast majority of acidic compounds tend to be largely bound to albumin, inparticular, and to yield a correspondingly higher bound fraction relative to basic andneutral compounds although there are exceptions to this �rule�.Plasma protein binding typically shows a sigmoidal relationship when the data are

plotted against lipophilicity, as shown by van deWaterbeemd et al. [55] on a data set ofapproximately 150 compounds, comprising neutral, acidic and basic molecules. In amore recent analysis reported by Obach et al. [57] the sigmoidal trend was linearizedby transforming the fu data into the logarithm of the apparent affinity constant logKcalculated as log bound/free. The set of 554 compounds used shows that an increasein lipophilicity, expressed as calculated logP, correlateswith an increase in logK for allcharge classes (neutral, basic, acidic and zwitterionic molecules) and this parameter,together with charge, is essentially the only parameter for which a relationship withlogK exists. Charge is important as well, even for basic compounds, because the lattertend to bind to a1-acid glycoprotein due to electrostatic interactions with acidicresidues on the protein.Many attempts have been made at predicting plasma protein binding from

structures only, with a variety of statistical approaches and sizes of data set; and therecent work of Gleeson [56] as well as the review recently published by Egan [58],both citing several examples of prior work, are mentioned here as leading refer-ences. It should be noted, when considering in silico approaches and their perfor-mance that, while plasma protein binding is generally determined as an equilibri-um property, the binding process is not controlled by bulk properties alone, such aslipophilicity, and that, for example, structural differences may be importantdeterminants of binding, especially when considering the diverse binding sitespresent on albumin.The review article by Egan examines several predictive approaches, from fairly

simple ones, using only one variable and showing a sigmoidal relationship [55], toincreasingly more complex approaches where non-linear equations were success-fully used to predict percent protein binding for neutral, basic and zwitterioniccompounds across a set of 302 compounds, but where a similar attempt was used foracidic compounds the result was a poor fitting model [59].Gleeson [56] used plasma protein binding data in human and rat, encompassing

approximately 900 compounds for the human set and approximately 1500 com-pounds in rat, which were both split 75% (training set) to 25% (test set), yielding atraining set in human of 686 compounds. Like Obach et al. [57], he used the logKvalue (with K being a pseudo-equilibrium constant calculated as the ratio bound/free). Several parameters, including polar surface area, hydrogen-bond donor andacceptor indicators and estimation of their strength, as well as logD and logP and theextent of ionization, were calculated and a PLS approach used. Extensive statisticalvalidation and comparative workwere presented together withmodel limitations andwemention two of the conclusions reported by the author. One is that the model canbe used to rank compounds according to the criteria of whether they will be boundgreater than 99%. If a compound is predicted to be 95% bound, the author

9.4 Physicochemical Determinants and In Silico Prediction of Plasma Protein Binding j207

commented, it is highly likely that the actual value is<99% given the r2 and RMSE ofthe model, 0.56 and 0.55, respectively, with a 70% confidence that its range would be86.0–98.4% and a corresponding interval of the experimental value of 92.3–96.8%bound. Thus, the author concludes that, while the model may not be predictiveenough to predict subtle changes during lead optimization, it could be used to rankvirtual possibilities.We submit, however, that plasma protein binding is probably notamenable to use as a ranking tool and in a predictive fashion but, rather, it is aneminently experimental parameter that aids in rationalizing differences in totalversus intrinsic clearance and differences between in vitro versus in vivo potency. Or,in other words, it aids in understanding the composite nature of PK rather thanoffering basis to prioritize synthesis and choice of compounds. Second, the analysisof the model descriptors confirms that lipophilicity, size (molecular weight) andcharge type/extent of ionization are the key descriptor types, and the addition of anacidic group (or a decrease in its pKa) was found to increase binding while theaddition (or the increase in basic pKa) of a basic group was generally found to lead todecreased binding in line with other work and generally observed �rules� which werealso recently discussed by the same author [60].

9.5Volume of Distribution: General Considerations and Applicationsto Experimental Pharmacokinetics and Drug Design

The volume of distribution is a parameter that can be calculated from plasma drugconcentration versus timedata (expressed as area under the curve orAUC), accordingto the two equations shown below, for terminal or steady-state volume of distribution,respectively.

VDb ¼ DoseAUC � kel

VDss ¼ Dose �AUMC

AUC2

In these equations kel is the elimination rate constant and AUMC is the area underthe first moment curve. A treatment of the statistical moment analysis is of coursebeyond the scope of this chapter and those concepts may not be very intuitive, butAUMC could be thought of, in a simplified way, as a measure of the�concentration–time� average of the time–concentration profile and AUC as ameasure of the �concentration� average of the profile. Their ratio would yield MRT,ameasure of the �time average� of the profile termed in factmean residence time.Or,in other words, the time–concentration profile can be considered a statisticaldistribution curve and the AUC and MRT represent the �zero� and �first� momentwith the latter being calculated from the ratio of AUMC and AUC.By itself, volume of distribution does not provide any insight into mechanisms of

drug distribution, however it is a useful descriptive index of how well the drug

208j 9 Plasma Protein Binding and Volume of Distribution: Determination, Prediction

partitions away from the central plasma compartment. Volume of distribution isdependent on the extent of plasma binding and peripheral tissue binding, which aredependent on the binding capacity of each of these compartments and the affinity ofthe drug for specific plasma and tissue macromolecules and structures:

VD / fbðtissuesÞfbðplasmaÞ

¼ fuðplasmaÞfuðtissuesÞ

Clearly, the mechanistic contributors to the extent of plasma and tissue bindingarenumerous,andtheVDtermrepresentsa simplisticpictureofpotentiallyhundreds,maybe thousands, of individual tissue binding interactions. Despite this possiblecomplexity, there may be a few individual types of tissue binding that are mostlyresponsible for tissue partitioning, and as described elsewhere in this chapter, thisphenomena may be more related to non-specific interactions that are a function ofgross physicochemical properties of the drug than specific binding interactions.The larger the VD, the longer the t1/2, since the time it will take for the drug

to reemerge from the tissues can drive the t1/2 (or mean residence time if it is thesteady-state VD that is being considered). Thus, in medicinal chemistry drug designefforts, when faced with a predicted short half-life, there is temptation to drivetowards higher VD to gain a longer t1/2 (in essence, leveraging tissue binding as aninternal reservoir of drug that slowly re-enters the systemic circulation and becomesavailable to the pharmacological target).However, while there has been description ofsome limited successes using this approach (e.g., amlodipine vs felodipine [61]), thisis generally not a good strategy because:

1. Structural modifications needed to alter VD generally need to alter physicochem-ical properties (e.g., lipophilicity, charge, etc.) which in turn alter other pharma-cokinetic characteristics of the molecule and may not be tolerated by thepharmacophore of the target.

2. If intrinsic potency remains the same, the dosemust be greater in order to �fill thetissue reservoirs� and attain the same unbound efficacious concentration. Non-specific tissue capacity will take up a greater proportion of the dosed drug.

3. Many of the structural modifications that can lead to increased VD also lead toincreased rates of metabolism, hence clearance, and results in a zero-sum effecton half-life.

4. Very large VD values can be frequently associated with drugs that can exhibitphospholipidosis. It is important to note that this is not a cause and effectrelationship, but a general trend. Furthermore, drugs that exhibit high tissuebinding are difficult to remove by hemodialysis, in the event that a deleteriousevent, such as overdose, must be treated.

In order to increase the predicted human t1/2, it is a generally more successfulstrategy to design new molecules with the intent to decrease the free clearance.However, while designing new molecules to attain specific VD values may not be afruitful endeavor, the prediction of VD is still an important activity in drug design

9.5 General Considerations and Applications to Experimental Pharmacokinetics j209

because it is an important component of predicting t1/2 and mean residencetime (MRT):

t1=2 ¼0:693 �VDb

CLand MRT ¼ VDss

CL

in which VDb and VDss refer to terminal phase and steady-state VD values,respectively. (For drugs that exhibit multiphasic concentration vs time profiles, theMRTwill be a better indicator than t1/2 of the potential dosing frequency needed andexpected accumulation ratio that will occur with repeated administration.)

9.5.1Prediction of Human Volume of Distribution

Over the years, several types of methods were developed to predict human VD.BecauseVD is thought to bemoredependent of overall physicochemical properties ofdrugs contributing to non-specific binding rather than specific structural attributesresponsible for specific protein–ligand interactions, prediction of VD is moresuccessful than prediction of clearance. The methods vary in their accuracy andlabor needed to gather the needed input data; generally with an inverse relationshipbetween the accuracy and labor. Different approaches are applicable at various stagesduring drug design. In early efforts, when there are hundreds of compoundsbeing considered for a given therapeutic target receptor/enzyme, approaches mustbe simple and high throughput. Applications of in silico methods are probably bestin most cases at this stage, since compounds would not even need to be synthesizedto accomplish these predictions. As the number of compounds being consideredfor further development decreases, there is a greater need for increased confidence inthe VD prediction. Reliance on laboratory data increases at this later stage andmay include approaches that use in vitro data and/or pharmacokinetic data fromlaboratory animal species. These three types of VD prediction approaches aredescribed below and the reader is referred to a recent detailed discussion of thesemethods [62].

9.5.1.1 Prediction of Human Volume of Distribution from AnimalPharmacokinetic DataIf VD is trulymore dependent on non-specific interactions between drug and tissues,then the differences that could be observed across the species for the VD of a drug ismore a function of differences in body tissue compositions among animals versushumans than specific structural attributes of the drug. Drugs that exhibit high VD inanimals also exhibit high VD in humans; drugs that exhibit low VD in animals alsoexhibit lowVD inhumans. This logic, taken to an extreme, would suggest that theVDfor a set of drugs in humans should correlate to VD values for these same drugs in alaboratory animal species, such as rat. This is exactly the approach described byCaldwell et al. [63] in which a linear correlation was derived between human and ratVD values for a set of 144 drugs such that the VD measured in rat, uncorrected forbody weight, could merely be multiplied by 188 to obtain the human VD prediction.

210j 9 Plasma Protein Binding and Volume of Distribution: Determination, Prediction

Other investigators suggested the same approach but used the monkey as thelaboratory species [64].VD is a function of both tissue binding and plasma protein binding, and while the

formermay be comprised of amultiplicity of non-specific interactions dependent ongross physicochemical characteristics, the latter is generally a function of just a fewinteractions (i.e., binding to albumin,a1-acid glycoprotein, lipoproteins), albeit this isalso more driven by physicochemical characteristics rather than specific ligand–re-ceptor type interactions (see Section 9.4). Thus, it is possible to observe differences inplasma protein binding across species, although these differences are not usuallylarge. Nevertheless, in vitro measurements of plasma protein binding are fairlyeasy tomake and canbeused to correct humanVDpredictionsmade fromanimalVDdata. Such a correction is employed in two methods, one which only uses pharma-cokinetic data from dogs and one in which pharmacokinetic data from multipleanimal species are required [65]. In the dog–human VD proportionality approach,dog VD (per body weight) is measured and corrected to free VD by dividing by theunbound fraction in dog plasma. The free VD in dog is assumed to be equal to that inhuman, and the human VD is obtained by multiplying this value by the free fractionin human plasma. Thus, differences in plasma protein binding can be consideredin the prediction. In the othermethod, VD and plasma protein binding aremeasuredin multiple species, and used to make estimates of the fraction unbound in tissues( fu(tissue)) for each species using the Oie–Tozer equation which relates fu(plasma),fu(tissue), VDss and several physiological volumes [66]:

VDss ¼ VPð1þRE=IÞþ fuVPðVE=VP�RE=IÞþ VR fufut

The parametersVP,VE andRE/I are the plasma and extracellular fluid volumes andthe extravascular to intravascular protein (albumin) ratio, respectively. Their values inhuman, as an example, are 0.0436 and 0.151 L/kg, respectively, with aRE/I ratio of 1.4.VR is defined as the physical space into which the drug distributes minus theextracellular space and its value, in human, is taken as 0.380 L/kg. fu and fut aredefined as above.The fu(tissue) values are averaged for the species, this average is assumed to be the

value for human, inserted back into the Oie–Tozer equation and combined with themeasured value of fu(plasma) in human to obtain a predicted value for human VD.However, despite its increased complexity it does not offer additional accuracy overthe above mentioned dog–human proportionality method and may only be mostappropriate when plasma protein binding shows considerable inter-speciesvariability.Finally, no discussion of human pharmacokinetic predictions is complete without

a consideration of allometric scaling [67–69]. In general, allometry is the examinationof relationships between size and function and it has been applied to the prediction ofhuman pharmacokinetic parameters from animal pharmacokinetic parameters fordecades [70]. Allometry has been shown to work reasonably well for predictinghuman VD from animal VD data, probably because volumes of plasma and varioustissue across species are allometrically scaleable to body weight, a notion reinforced

9.5 General Considerations and Applications to Experimental Pharmacokinetics j211

by the frequent observation that the allometric exponent (�b� in the equation below)is typically unity for scaling VD:

VD ¼ a �Wb

in which a is the allometric coefficient andW is body weight for each species. The VDvalues measured in various species are plotted against their body weights (on alogarithmic scale), and the VD value for human is extrapolated from 70 kg. Themethod suffers fromaneed to generateVDvalues in potentiallymultiple species, andif the single species methods described above can work, the impetus for usingallometry may be diminished in the spirit of decreasing unneeded animalexperimentation.

9.5.1.2 Prediction of Human Volume of Distribution from In Vitro DataSince VD is a function of relative tissue and plasma binding, it follows that if thesemeasurements could be made in vitro, then the data could be used to predict VD.Furthermore, if tissue binding is driven by physicochemical properties, such aslipophilicity, then it also follows that physicochemical measurements could serve assurrogates for tissue binding propensity. In vitro tissue binding and physicochemicalmeasurements form the basis of in vitro approaches to predict human VD.In considering tissue binding and its role in VD, the identities of the most

important tissues must be known. Some tissues have a high binding affinity butlack a high capacity (e.g., binding of cationic drugs in melanin-containing structuresof the eye), while others have a high capacity because of their mass but affinity maynot be great (e.g., muscle, bone, skin, adipose). Thus, selection of which tissues toinclude in an in vitro tissue binding experiment andwhether to combine tissues is notwell established. Furthermore, there are practical limitations to conducting tissuebinding experiments: the tissuesmust be diluted in order tomake homogenates andmost investigators use animal tissues as surrogates for human tissues. Finally, thesemethods mostly rely upon developing correlations between tissue binding andVD [71, 72] and with one exception [73] do not mathematically scale the bindingdata using physiologically based pharmacokinetic modeling.Since tissue binding is likely related to physicochemical properties, other

investigators derivedmethods to predict human VD from such data [74–77]. Poulinand Thiel categorize tissues into two types: adipose and non-adipose. For the lattervalue, octanol:water partitioning is used as a surrogate while for adipose, olive oil:water partitioning is used. These values are combined with physiological constantsfor these tissue volumes, along with plasma and blood volumes, to predict humanVD. In the methods described by Lombardo et al. [75], Lombardo et al. [76] andHollosy et al. [77], HPLC methods are used as surrogates for physicochemicalmeasurements, and these are used in correlations to tissue binding. In the formermethod, the ElogD parameter (i.e., logD7.4 obtained by reverse phase HPLC) ismeasured, and together with the fraction unbound in plasma ( fu) and fractionionized ( fi) based on pKa, it is used to predict the fraction unbound in tissue ( fut)viaa multiple linear regression equation. The correlation derived between ElogD, fu, fiand fut from known drugs is used to predict tissue binding, and combined with

212j 9 Plasma Protein Binding and Volume of Distribution: Determination, Prediction

measured plasma binding to predict VD in human, for the compound of interest. Inthe latter method, albumin and phospholipid HPLC columns are used as surro-gates for plasma and tissue binding, respectively under the assumption that thesetwo entities are what give the greatest drive to plasma and tissue binding. The dataare correlated to human VD to show that these measurements can be made topredict VD for new compounds.

9.5.1.3 Prediction of Human Volume of Distribution from In Silico MethodsThe types of physicochemical parameters used in the in vitro prediction approachescan also be derived computationally, suggesting that purely in silico approaches arepossible for predicting VD. In an earlymethod, compoundswere separated by chargetype before deriving a relationship between a single computed physicochemicalparameter and humanVD [78], however themethod accuracywas not high enough tomerit its use in drug design efforts.Additional efforts at developing computational models for predicting human VD

were more successful and used more computed descriptors as well as severalstatistical approaches (e.g., partial least squares, neural networks, stepwise regres-sion, classification and regression trees, and random forest [79–82]). As expected,lipophilicity and charge type play an important role in these models. The generalapproach for model building has been to use large datasets of human VD data todevelop themodels and then to test themusing subsets of the data that were not usedinmodel building. It is important to note that the predictive accuracy of test sets fromthese models has now approached the accuracy of aforementioned methods that useanimal or in vitro data. The advantage is that no laboratory experimentation is needed,no compound needs to be synthesized and the VD prediction can be made from aproposed structure alone. In this way, medicinal chemists can query proposedcompounds and understand how various substituents can influence VD.

9.6Relationship Between Clearance, VDss and Plasma Protein Binding

As already alluded, VDandplasmaprotein binding are intrinsically linked, asVDss isa weighted mean ratio of tissue and plasma binding affinity, with VD corrected forspecies/individual differences in PPB (unbound VD) in many cases remainingconstant for a given compound. In addition, free fraction in plasma is a keydeterminant of clearance in vivo, together with intrinsic clearance (CLint); a measureof the efficiency of drug turnover or elimination not restricted by organ blood flow.A number of physiological models are applied to drug clearance, with the well stirredmodel being the most commonly used.

CLH ¼ QH � fu �CLintQH þ fu �CLint

From this model it is clear that, for example, highly bound drugs with high CLintcan exhibit low clearance. A commonmedicinal chemistry strategy to increase t1/2 is

9.6 Relationship Between Clearance, VDss and Plasma Protein Binding j213

to lower CL by modulating PPB towards higher binding. Although this tends toreduce CL, it also lowers VD to a similar extent, as plasma binding is increased, thushaving negligible effect on the t1/2.

9.7Summary and Conclusions

Throughout this chapter we discuss the importance of plasma protein binding andits relationship with clearance and volume of distribution. We also illustrateexperimental and computational methods for the determination of both plasmaprotein binding and volume of distribution, ranging from in vitro to in vivo to in silicoapproaches, andwe close this chapterwith some considerations along those lines.Onthe subject of physicochemical determinants and in silico or in vitro prediction wepoint out that there is a correlation between plasma protein binding and lipophilicityand that a correlation can be found between volume of distribution and lipophilicityas well. Charge, in contrast, modulates those relationships in a somewhat oppositeway, since negatively charged compounds tend to be more tightly bound to plasmaprotein (albumin) and tend to have lower volume of distribution as well as lowerclearance values, while the opposite is generally true for positively charged com-pounds. These are of course broad generalizations; and exceptions are known andhave been discussed.The prediction of volume of distribution, based on largely although not exclusively

passive diffusion phenomena, can be achieved with reasonable accuracy with in silicomethods, over and above available in vivo and in vitro methods, with obviousadvantages in terms of time, cost of synthesis and animal use. However, an accurateprediction of plasma protein binding, in the high range (e.g., �98% bound) is stilldifficult to achieve, and a small error in prediction (or determination) in the highrange yields a large error in terms of fold difference in free fraction, which isultimately what matters when evaluating the concentration of drug free to interactwith a receptor or enzyme. These errors in prediction are also rooted in the difficultyin obtaining very high accuracymeasurements, at least routinely. However, it may bepossible to confidently explore trends and classify molecules, depending on thepredicted value, on the basis of the likelihood that they have a very large (�98%bound) percent bound or not, as reported by Gleeson [56].We discuss, largely on the basis of the commentary by Benet and Hoener [1], the

fact that changes in plasma protein binding are seldom of clinical relevance sincemost drugs (whether high or low extraction ratio compounds) are administered orallyandmostly cleared by the liver.We also illustrate caveats regarding the use of volumeof distribution in trying to increase t1/2 citing, among other factors, the likelihood thatstructural modification leading to an increase in VD also leads to an increase inclearance and thus to a zero-sum effect, making this an �indirect� link between thetwo otherwise independent parameters.Finally, we note that plasma protein binding is generally determined on a

�retrospective� or �interpretation� basis, and it is seldom determined routinely, as

214j 9 Plasma Protein Binding and Volume of Distribution: Determination, Prediction

a primary parameter and/or in a screeningmode,while several other characterizationstudies are instead conducted on a given compound. The advent of fasterexperimental methods, and of course experience with the application of in silicomethods, may change this approach but it is doubtful that it will greatly impact thedecision-making process on the selection of a compound, as we alluded to inSection 9.4.

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