Theoretical Study of High-Performance FrontalAnalysis: A Chromatographic Method forDetermination of Drug-Protein InteractionAkimasa Shibukawa* and Terumichi Nakagawa

Faculty of Pharmaceutical Sciences, Kyoto University, Sakyo-ku Kyoto, 606 Japan

High-performance frontal analysis (HPFA), a chromato-graphic method to determine unbound drug concentrationin drug-protein binding equilibrium, has been consid-ered on the basis of a theoretical plate model, where arapid equilibrium of drug-protein binding in the mobilephase in the interstices of packing materials and achromatographic partition equilibrium of the drug weretaken into account simultaneously. When a certain excessvolume of drug-protein mixed solution is injected directlyinto a HPFA column packed with a restricted-access typephase that excludes protein but retains drug in themicropores, the drug is eluted as a zonal peak with aplateau region. The elution profile can be well simulatedby the mass balance equation derived according to arelatively simple plate theory concept, which confirms thatthe drug concentration in the plateau range agrees withthe unbound drug concentration in the sample solution.The model was applied to the theoretical and systematicinvestigation of the dependence of the HPFA profile onseveral chromatographic conditions and the properties ofthe sample solution, such as injection volume of samplesolution, drug and protein concentrations in samplesolution, capacity factor of the drug, theoretical platenumber, and binding parameters. The smaller capacityfactor and the higher column efficiency lead to the largerplateau volume. The lower drug concentration, the higherprotein concentration, and the stronger binding constant,which give the lower unbound drug fraction, lead to thelarger plateau volume and allow frontal analysis with asmaller sample size.

Protein binding of a drug plays an important role in pharma-cokinetics and pharmacodynamics of drugs.1-3 Quantitativeinvestigation of drug-protein binding is essential for drugdevelopment and for determining a drug’s safety in clinical use.Equilibrium dialysis and ultrafiltration followed by HPLC analysishave been widely used for this purpose. However, these methodssuffer from undesirable adsorption of drug to the membrane,leakage of bound drug from the membrane, and long equilibrationtime. These troubles can be avoided by using chromatographicmethods such as gel filtration frontal analysis and the Hummeland Dreyer method.4 Recently, we developed a new chromato-graphic method, high-performance frontal analysis (HPFA).5-15

HPFA uses a restricted-access type HPLC column that size-excludes a large protein molecule but retains a small drugmolecule.16,17 When a drug-protein mixed solution is directlyinjected into this type of column, bound drug is released fromprotein in the mobile phase because protein binding is a reversibleand kinetically rapid process. When the injection volume exceedsa certain limit, an equilibrium zone is generated in the intersticesof packing materials near the top of the column. In this zone, adrug-protein binding equilibrium the same as that in the samplesolution is reproduced; i.e., the drug concentration in the mobilephase in the micropore becomes equal to the unbound drugconcentration in the sample solution. As a result, protein is elutedfirst, and then the drug is eluted as a trapezoidal peak having aplateau region. The plateau region reflects the zonal elution ofthe unbound drug. Consequently, the unbound drug concentra-tions in the drug-protein binding equilibrium can be determinedby measuring the drug concentration in the plateau region.6

HPFA has several unique features:(1) HPFA allows direct sample injection analysis with a simple

procedure.(2) HPFA is free from troubles such as drug adsorption on

membrane and leakage of bound drug from membrane, whichcause erroneous results in the conventional equilibrium dialysisand ultrafiltration methods.

(3) When the trapezoidal drug peak is well separated fromthe protein peak, the total drug concentration and the unbounddrug concentration are simultaneously determined from the peakarea and the plateau height, respectively.6

(4) The HPFA method can be easily incorporated into an on-line HPLC system. The unbound concentration of a chiral drug

(1) Meyer, M. C.; Guttman, D. E. J. Pharm. Sci. 1968, 57, 895-918.(2) Vallner, J. J. J. Pharm. Sci. 1977, 66, 447-465.(3) Kwong, T. C. Clin. Chem. Acta 1985, 151, 193-216.(4) Korpela, T. K.; Himanen, J.-P. In Aqueous Size-Exclusion Chromatography;

Dubin, P. L. Ed.; Elsevier: Amsterdam, 1988; Chapter 13.

(5) Shibukawa, A.; Nakagawa, T.; Nishimura, N.; Miyake, M.; Tanaka, H. Chem.Pharm. Bull. 1989, 37, 702-706.

(6) Shibukawa, A.; Nishimura, N.; Nomura, K.; Kuroda, Y.; Nakagawa, T. Chem.Pharm. Bull. 1990, 38, 443-447.

(7) Shibukawa, A.; Nagao, M.; Kuroda, Y.; Nakagawa, T. Anal. Chem. 1990,62, 712-716.

(8) Nishimura, N.; Shibukawa, A.; Nakagawa, T. Anal. Sci. 1990, 6, 355-359.(9) Shibukawa, A.; Terakita, A.; He, J.; Nakagawa, T. J. Pharm. Sci. 1992, 81,

710-715.(10) Terakita, A.; Shibukawa, A.; Nakagawa, T. Anal. Sci. 1993, 9, 229-232.(11) Shibukawa, A.; Nagao, M.; Terakita, A.; He, J.; Nakagawa, T. J. Liq.

Chromatogr. 1993, 16, 903-914.(12) Shibukawa, A.; Nakao, C.; Sawada, T.; Terakita, A.; Morokoshi, N.;

Nakagawa, T. J. Pharm. Sci. 1994, 83, 868-873.(13) Terakita, A.; Shibukawa, A.; Nakagawa, T. Anal. Sci. 1994, 10, 11-15.(14) Shibukawa, A.; Kadohara, M.; He, J.; Nishimura, M.; Maito, S.; Nakagawa,

T. J. Chromatogr. A 1995, 694, 81-89.(15) Shibukawa, A.; Sawada, T.; Nakao, C.; Izumi, T.; Nakagawa, T. J. Chromatogr.

A 1995, 697, 337-343.(16) Anderson, D. J. Anal. Chem. 1993, 65, 434R-443R.(17) Pinkerton, T. C. J. Chromatogr. 1991, 544, 13-23.

Anal. Chem. 1996, 68, 447-454

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can be determined stereoselectively by coupling a HPFA columnwith a chiral HPLC column.7,9,11,12,14

(5) Because of the “regulation effect”,12 the elution volume ofthe plateau region becomes larger than the initial injection volume.This effect serves to improve the detectability.

The HPFA profile depends on several chromatographic condi-tions, such as injection volume, capacity factor, theoretical platenumber, etc., and also on the properties of the sample solution,such as drug concentration, protein concentration, and theirbinding parameters. However, some of these factors have notbeen evaluated because of the practical difficulty in changing thesevalues arbitrarily. This paper aims to evaluate the effects of thesefactors upon the HPFA profile quantitatively on the basis of atheoretical plate model, where a rapid equilibrium of drug-proteinbinding in the interstices of packing materials and a chromato-graphic partition equilibrium of the drug are taken into accountsimultaneously.

THEORYFigure 1 illustrates the theoretical plate model used for the

simulation of a HPFA profile. The abbreviation v represents theinterstitial volume per plate, j is the ratio of pore volume tointerstitial volume, and k′ is the capacity factor of drug. U(m,h)and B(m,h) represent the unbound drug concentration and thebound drug concentration in the interstice of the hth plate at timem, respectively. In each theoretical plate, bound drug, unbounddrug, and protein in the interstice are in the state of bindingequilibrium. At the same time, the unbound drug is in the stateof partition equilibrium. The volume v of mobile phase in oneplate is transferred to the next plate per one unit time. Proteinand bound drug suffer size-exclusion effect and migrate (1 + j)times faster than an unretained small compound. Thus, wepostulate the following:

(a) Neither protein nor bound drug migrates into micropores.(b) Drug-protein binding and chromatographic partition

equilibria are established momentarily.(c) Drug is bound to protein at a single class of binding site;

the binding equation is given as K ) Cb/Cu(nCp - Cb), where Krepresents the binding constant, n is the number of binding sitesper protein molecule, Cb is the bound drug concentration, Cu isthe unbound drug concentration, and Cp is the total proteinconcentration.

(d) Diffusion of protein in the HPFA column is negligible.(e) Drug partitioning between mobile phase and stationary

phase is linear.Protein, bound drug, and unbound drug in the interstice are

transferred into the next plate per one unit time, and the drugsstagnant in the pore promptly reach simultaneous equilibria ofprotein binding and chromatographic partition. The followingmass balance equation then becomes valid:

From eq 1, U(m,h) and B(m,h) are described as

where

and

Cp is the protein concentration and K is the protein bindingconstant, defined as

where Cb and Cu are the bound and unbound drug concentrations,respectively, and n is the number of the binding sites per proteinmolecule. The whole drug concentration is described as the sumof U(m,h) and B(m,h).

The simulation of the HPFA profile and the calculation of theminimum injection volume required to obtain a plateau region(MIV)8 by using eqs 2 and 3 were performed in FORTRANlanguage using a personal computer equipped with an Intel 80486DX2 (66 MHz) CPU and an arithmetic coprocessor.

RESULTS AND DISCUSSIONSimulation of HPFA Profile. The upper chromatograms in

Figure 2 show, respectively, the HPFA elution profiles obtainedby injecting 5-40 µL portions of 200 µM warfarin (Wf)-550 µMhuman serum albumin (HSA) mixed solution.7 A Pinkertoncolumn (15 cm × 4.6 mm i.d.) was used as the HPFA column.The lower chromatograms are the simulations of the correspond-ing elution profiles of the drug calculated by using eqs 2 and 3.The binding parameters estimated from Scatchard analysis (K )1.96 × 105 M-1 and n ) 1.24)7 and the experimental values forchromatography (k′ ) 2.9; N (number of theoretical plates) )866; Vm (interstitial volume + pore volume) ) 1.50 mL; v ) 1.19µL; j ) 0.46; flow rate, 0.5 mL/min) were adopted. The Vm valueand the interstitial volume were calculated from the retention timesof unretained compound (glucose, detected by using a refractiveindex detector) and albumin, respectively. The pore volume (0.47mL), interstital volume (1.03 mL), and j value were in agreementwith the reported values (0.53 mL, 1.09 mL, and 0.49, respec-tively).18 As shown in the upper chromatograms, the Wf peakbroadens toward the HSA peak as the injection volume increases.When a 40 µL portion of the sample solution was injected, the Wf

(18) Cook, S. E.; Pinkerton, T. C. J. Chromatogr. 1986, 368, 233-248.

Figure 1. Plate theory model for HPFA.

vU(m - 1,h - 1) + vB(m - 1,h - 1) + vjU(m - 1,h) +v(1 + j)k′U(m - 1,h) ) vU(m,h) + vB(m,h) + vjU(m,h) +

v(1 + j)k′U(m,h) (1)

U(m,h) ) [-b + (b2 + 4ac)1/2]/2a (2)

B(m,h) ) nKCpU(m,h)/[1 + KU(m,h)] (3)

a ) K(1 + j)(1 + k′)

b ) (1 + j)(1 + k′) + nKCp - cK

c ) U(m - 1,h - 1) + B(m - 1,h - 1) +[j + (1 + j)k′]U(m - 1,h)

K ) Cb/Cu(nCp - Cb)

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peak attained the maximum height, and a plateau region appeared.The calculated chromatograms are in agreement with the ob-served chromatograms. The calculated Wf peak reaches theplateau level when the injection volume is more than 20 µL, whilethe observed Wf peak at 20 µL injection did not reach the plateaulevel. Sample diffusion in the injection loop is probably the reasonfor this disagreement. Introduction of the diffused sample portioncan be avoided by reswitching the injector valve (injector re-switching technique).9

The upper chromatograms in Figure 3 show the HPFA elutionprofiles of 50, 100, or 200 µM Wf-100, 300, or 550 µM HSA mixedsolution,7 and the lower chromatograms are the correspondingcalculated chromatograms. The binding parameters and thechromatographic parameters were the same as those in Figure2. The calculated chromatograms were in agreement with theobserved chromatograms. In the present simulation, the bindingat the low-affinity site on the HSA molecule is neglected. However,since this binding becomes significant in the case of 100 µM Wf-100 µM HSA mixed solution,7 the unbound drug concentration

(9.64 µM) is lower than the calculated Cu (12.3 µM). This is whythe observed peak height is lower than the calculated peak heightin Figure 3B.

As mentioned below, HPFA of the sample solution with higherunbound fraction needs a larger injection volume. Since theunbound drug fraction increases with the decrease in HSAconcentration, we changed the injection volume according to theHSA concentration (40 µL for the samples containing 550 µM HSA,60 µL for those containing 300 µM HSA, and 300 µL for thosecontaining 100 µM HSA). The MIV was calculated as 19 µL for200 µM-550 µM HSA mixed solution, 27 µL for 100 µM-300µM HSA, and 262 µL for 100 µM-100 µM HSA. The increase inthe calculated MIV against the decrease in the HSA concentrationis consistent with the above-mentioned selection of the injectionvolume.

The agreement of the simulation with the observed chromato-grams shown in Figures 2 and 3 supports the validity of thepresent model.

Figure 2. HPFA profile of 200 µMWf and 550 µM HSA (upper)7 and simulated Wf elution profile (lower). HPFA conditions: column, Pinkertoncolumn (15 cm × 4.6 mm i.d.); mobile phase, phosphate buffer (pH 7.4, I ) 0.17); flow rate, 0.5 mL/min; column temperature, 37 °C; detection,UV 308 nm; injection volume, 5-40 µL. Binding parameters:7 K ) 1.96 × 105 M-1, n ) 1.24. Column parameters: N ) 866, v ) 1.19 µL,j ) 0.46, k′ ) 2.9.

Figure 3. HPFA profile of Wf-HSA mixed solution (upper)7 and simulated Wf elution profile (lower). Sample: (A) 50 µM Wf-100 µM HSA,(B) 100 µM Wf-100 µM HSA, (C) 50 µM Wf-300 µM HSA, (D) 100 µM Wf-300 µM HSA, (E) 50 µM Wf-550 µM HSA, (F) 100 µM Wf-550µM HSA, (G) 200 µM Wf-550 µM HSA. Injection volume: (A,B) 300 µL; (C,D) 60 µL; (E-G) 40 µL. The absorbance units for the full rangeof A and B were 4 times larger than those of C-G. Other HPLC conditions are as in Figure 2.

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Effect of Chromatographic Conditions and Sample Prop-erties on the HPFA Profile. Figure 4 shows the effect of sampleinjection volume on simulated HPFA profile. The sample contains550 µM total protein, which is the physiological plasma concentra-tion of human albumin, and 10 µM total drug. The chromato-graphic parameters used in this simulation (Vm ) 1.50 mL, j )0.5, N ) 900) are similar to those in Figures 2 and 3. The bindingparameters are K ) 1 × 105 M-1 and n ) 1. The unbound drugconcentration is calculated as 0.182 µM. Similarly to Figure 2,the drug peak broadens forward as the injection volume increases.When the injection volume is more than 40 µL, the peak heightreaches a maximum level. The plateau height remains constantregardless of the injection volume, and the drug concentration inthe plateau region is 0.182 µM, which agrees with the unbounddrug concentration in the sample solution. This result confirmsthe principle of HPFA method; that is, the unbound drug can bedetermined by measuring the drug concentration in the plateauregion.

When the injection volume is 160 µL, the front of the plateauregion overlaps completely with the protein peak. The increasein drug concentration around the retention time of 1 min is dueto the bound drug in the overlapping zone. However, when theinjection volume is less than 60 µL, the plateau region does notoverlap with the protein peak. The integration of the zonal peakarea agrees with the total amounts (bound + unbound) of theinjected drug. This means that, when the drug peak is wellseparated from the protein peak, the total drug concentration andthe unbound drug concentration can be determined simulta-neously from the peak area and the plateau height, respectively.

Table 1 shows the dependence of the elution volume in theplateau region (plateau volume) on the number of theoreticalplates (N) and the capacity factor (k′). The injection volume is40 µL, and the other conditions are the same as in Figure 4. Theplateau volume increases with N. For example, for k′ ) 3, theplateau volume increases from 476 µL to 1.29 mL with the increasein N from 500 to 2000. This is because the larger N leads to less

broadening of the eluted zone. In contrast, as the capacity factorbecomes larger, the drug peak suffers more broadening, resultingin a decrease in the plateau volume. For example, in the case ofN ) 1000, the plateau volume decreased from 1.26 mL to 594 µLwith the increase in capacity factor from 1 to 5. The calculatedchromatograms for this example are shown in Figure 5. In thecase of N ) 500 and k′ ) 5, an injection volume of 40 µL is notenough to obtain the plateau region.

When the j value in Figure 5 was changed from 0.5 to 0.35 or0.65, almost no change was observed in the chromatograms, aswell as in the plateau volume, except that bound drug was elutedfaster in the case of the larger j value (the elution times of bounddrug were 1.1, 1.0, and 0.9 min for j ) 0.35, 0.5, and 0.65,respectively). This indicates that the j value does not have asignificant influence on HPFA analysis.

Figure 6 shows the effect of total drug concentration on thesimulated HPFA profile. The chromatographic conditions and theproperties of sample solution are the same as in Figure 4, exceptfor the injection volume (50 µL) and the total drug concentration(1, 10, and 100 µM for samples A, B, and C, respectively). Forconvenience, the ratio of the drug concentration in the eluent tothe unbound drug concentration in the sample solution (0.0179,0.182, and 2.16 µM for samples A, B, and C, respectively) wasplotted vertically. This ratio in the plateau region is unity for every

Table 1. Effect of Capacity Factor (k′) and Number ofTheoretical Plates (N) on Plateau Volume (mL)a

N

k′ 500 1000 1500 2000

1 0.924 1.26 1.41 1.513 0.476 0.948 1.16 1.295 0 0.594 0.877 1.05

a Sample conditions: Ct ) 10 µM, Cp ) 550 µM, K ) 1 × 105 M-1,n ) 1. Injection volume, 40 µL. Other conditions are as in Figure 4.

Figure 4. Effect of injection volume on the simulated HPFA profile. Cp ) 550 µM, Ct ) 10 µM, K ) 1 × 105 M-1, n ) 1; Vm ) 1.5 mL, j )0.5, N ) 900, k′ ) 4; flow rate, 1 mL/min; injection volume, 2.2-160 µL.

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sample, which implies that the drug concentration in the plateauregion agrees with the unbound drug concentration. In everycase, the integration of the drug amount in the eluent agreescompletely with the injected amount of the total (bound +unbound) drug. The plateau volume decreases as the unbounddrug fraction increases. Samples A and B have almost the sameunbound fraction (1.79% and 1.82% for samples A and B, respec-tively) and give almost the same plateau volume. In contrast,sample C, with a larger unbound drug fraction (2.16%), gives anarrower plateau range.

Figure 7 shows the effect of protein concentration in the samplesolution. The chromatographic conditions and the properties ofsample solution are the same as in Figure 4, except for injectionvolume (160 µL) and protein concentration (0, 100, 300, and 550µM for samples A, B, C, and D, respectively). When the samplesolution contains no protein (sample A), the drug is eluted as asharp peak. In contrast, the existence of protein produces theplateau region, and the drug concentration in the plateau regionagrees with the unbound drug concentration in the samplesolution (0.990, 0.333, and 0.182 µM for samples B, C, and D,

Figure 5. Effect of capacity factor on the simulated HPFA profile. Cp ) 550 µM, Ct ) 10 µM, K ) 1 × 105 M-1, n ) 1; Vm ) 1.5 mL, j ) 0.5,N ) 1000; flow rate, 1 mL/min; injection volume, 40 µL. Capacity factor (k′): (A) 1, (B) 3, and (C) 5.

Figure 6. Effect of total drug concentration on the simulated HPFA profile. Ct ) (A) 1, (B) 10, and (C) 100 µM; Cp ) 550 µM, K ) 1 × 105

M-1, n ) 1; Vm ) 1.5 mL, j ) 0.5, N ) 900, k′ ) 4; flow rate, 1 mL/min; injection volume, 50 µL. The ratio of drug concentration in the eluentto the unbound drug concentration (C/Cu) is plotted vertically.

Analytical Chemistry, Vol. 68, No. 3, February 1, 1996 451

respectively). The plateau region becomes broader with decreas-ing bound drug fraction.

Figure 8 shows the effect of binding constant (K) on thesimulated HPFA profile. The chromatographic conditions and theproperties of the sample solution are the same as in Figure 4,except for injection volume (450 µL) and binding constant (5 ×103, 1 × 104, and 1 × 105 M-1 for samples A, B, and C,respectively). An increase in binding constant accompanies adecrease in the unbound drug concentration (Cu ) 2.69, 1.56, and0.182 µM when K ) 5 × 103, 1 × 104, and 1 × 105 M-1,respectively), resulting in a decrease in the plateau height. As inFigure 7, the plateau becomes narrower with an increase in theunbound drug fraction (1.82%, 15.6%, and 26.9% for samples C, B,and A, respectively).

Effect of Drug Concentration and Binding Constant on theMIV. The appearance of a plateau region is essential for HPFA,and the injection volume should be large enough to obtain thisregion. Figure 9 shows the effects of total drug concentration(Ct) and binding constant (K) upon the MIV, where the MIV isplotted against the unbound drug fraction. In line A, Ct is variedbetween 10 and 550 µM, while K remains constant (1 × 105 M-1).

In line B, K is varied between 1 × 105 and 1 × 104 M-1, while Ct

remains constant (10 µM). The capacity factor is 3. Other sampleproperties and chromatographic conditions are the same as inFigure 4. Both lines indicate an almost linear relation betweenthe MIV and the unbound drug fraction. This relation coincideswith the above-mentioned result that the plateau becomes nar-rower with an increase in the unbound drug fraction. This canbe explained as follows. Frontal analysis has two fundamentalrequirements. One is the difference in mobility between drugand protein, which is attained by the size-exclusion effect of therestricted-access type phase. The other is generation of the samebinding equilibrium as in the sample solution. In size-exclusionmode, this requirement is satisfied only when the drug concentra-tion in the micropores is equal to the unbound drug concentrationin the sample solution; otherwise, the drug-protein bindingequilibrium in the interstices is disturbed. Thus, HPFA needsextra sample injection volume to fill the micropores with theunbound drug solution, and the larger extra injection volume isnecessary for the sample with a higher unbound drug fraction.This is why the MIV increases with increasing unbound drugfraction.

Figure 7. Effect of total protein concentration on the simulated HPFA profile. Cp ) (A) 0, (B) 100, (C) 300, and (D) 550 µM; Ct ) 10 µM, K) 1 × 105 M-1, n ) 1; Vm ) 1.5 mL, j ) 0.5, N ) 900, k′ ) 4; flow rate, 1 mL/min; injection volume, 160 µL.

Figure 8. Effect of binding constant on the simulated HPFA profile. K ) (A) 5 × 103, (B) 1 × 104, and (C) 1 × 105 M-1; Cp ) 550 µM, Ct )10 µM, n ) 1; Vm ) 1.5 mL, j ) 0.5, N ) 900, k′ ) 4; flow rate, 1 mL/min; injection volume, 450 µL.

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Figure 10 compares the simulated HPFA profiles of two samplesolutions with the same unbound drug fraction (5%) but differentbinding constants and different total drug concentrations (Ct )380 µM, K ) 1 × 105 M-1 for sample A; Ct ) 10 µM, K ) 3.5 ×104 M-1 for sample B). The injection volume is 180 µL, and otherconditions are the same as in Figure 9. The HPFA profiles weredrawn by plotting vertically the ratio of the drug concentration inthe eluent to the unbound drug concentration in the samplesolution. While the drug with lower affinity is eluted almost as arectangular peak, the drug with higher affinity is eluted as a much

broader peak with a narrower plateau range. As a result, thesample with the stronger binding constant requires a larger MIVthan the sample with the same unbound drug fraction but aweaker binding constant. This is why line A becomes steeperthan line B in Figure 9.

MIV for Scatchard Analysis. The binding parameters ofdrug-protein interaction are usually estimated by Scatchardanalysis based on r/Cu ) nK - Kr, where r ) Cb/Cp. Scatchardanalysis requires analyses of a series of sample solutions withdifferent unbound drug concentrations. When HPFA is applied

Figure 9. Dependence of the MIV on the unbound drug fraction in the cases of (A) constant K and (B) constant Ct. Sample: (A) Cp ) 550µM, Ct ) 10-550 µM, K ) 1 × 105 M-1; (B) Cp ) 550 µM, Ct ) 10 µM, K ) 1 × 105-1 × 104 M-1. Vm ) 1.5 mL, j ) 0.5, N ) 900, k′ ) 3;flow rate, 1 mL/min.

Figure 10. Comparison of simulated HPFA profiles for samples containing the same unbound drug fraction. Sample: (A) Cp ) 550 µM, Ct

) 380 µM, K ) 1 × 105 M-1; (B) Cp ) 550 µM, Ct ) 10 µM, K ) 3.5 × 104 M-1. Injection volume, 180 µL. Other conditions are as in Figure9. Unbound drug concentration: (A) 19.1 and (B) 0.502 µM.

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for this purpose, the injection volume should be larger than theMIV of the sample with the highest unbound drug fraction. Thepresent model is useful for preliminary selection of the injectionvolume.

In cases with strong protein binding, such as K ) 1 × 105

M-1 and n ) 1, the MIV for the sample containing 550 µM totalprotein and 528 µM total drug is calculated as 371 µL under thechromatographic conditions given in Figure 9. The unbound drugconcentration in this sample is 58.4 µM, and the r value, which isplotted on the abscissa of the Scatchard plot, is 0.85. This meansthat a series of sample solutions containing up to 58.4 µM unbounddrug can be analyzed with an injection volume of 371 µL, andthese samples cover up to 85% of the Scatchard plot. This rangeis wide enough to allow estimation of the binding parameters withgood accuracy. Therefore, in this case, the injection volume canbe selected as 371 µL. Of course, a slightly larger injection volumeis necessary to obtain a clear plateau region in actual analyses.For example, the injection volumes in Figure 2 were larger than

the MIV values by 20-30 µL, which serves to obtain a clearplateau region.

Another calculation indicates that, when the binding param-eters are K ) 1 × 104 M-1 and n ) 1, which is categorized as amoderate protein binding, the MIV for the sample containing 550µM total protein and 1034 µM total drug is 778 µL. The r valuefor this sample is 0.85. This means that a 778 µL sample injectionvolume is required to cover up to 85% of the Scatchard plots. Theseresults indicate that HPFA is useful for the analysis of strongprotein binding, because it allows the use of a small sample sizein the binding assay.

Received for review March 31, 1995. Accepted November22, 1995.X

AC950318N

X Abstract published in Advance ACS Abstracts, January 1, 1996.

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