Determination of drug-plasma protein binding kinetics and equilibria by chromatographic profiling: Exemplification of the method using L-tryptophan and albumin

Article abstract of DOI:10.1021/ac010643c

Drug-plasma protein binding may greatly influence the bioavailability and metabolism of a plasma-borne drug, the bound form being partially protected from the metabolic fate of the unbound drug. Traditionally, equilibrium values (e.g., percentage binding) for drug-protein binding have been measured to rationalize in vivo phenomena. However, such studies overlook the influence of kinetics. A rapid method of simultaneously determining kinetic rate constants and equilibrium constants from chromatographic profiles has been developed, based on the use of immobilized protein columns and HPLC. By measuring the chromatographic profiles (the position and width) of a retained and an unretained compound one can directly determine both the rate and equilibrium constants. Results are presented for the binding of L-tryptophan to human serum albumin to exemplify the method. The association equilibrium constant (K_a) and the association and dissociation rate constants (k_a and k_d, respectively) were thereby measured in an aqueous pH 7.4 environment at 37 °C as 0.84 10⁴ M^-1, 5.8 10⁴ M^-1 s^-1, and 6.9 s^-1, respectively. These compare favorably with previously published results. The described method may be used in quantitative structure-property relationship based rational drug discovery or for the rationalization of drug pharmacokinetics.

Full text of DOI:10.1021/ac010643c

Anal. Chem. 2002, 74, 446-452
Determination of Drug-Plasma Protein Binding
Kinetics and Equilibria by Chromatographic
Profiling: Exemplification of the Method Using
L-Tryptophan and Albumin
Ann M. Talbert,† George E. Tranter,*,† Elaine Holmes,† and Peter L. Francis‡
Biological Chemistry, Biomedical Sciences Division, Imperial College of Science, Technology and Medicine, Exhibition Road,
London SW7 2AZ, U.K., and Glaxo Smith Kline Medicines Research Centre, Gunnels Wood Road, Stevenage,
Hertfordshire, SG1 2NY, U.K.
It is frequently assumed that the free and bound forms of the
drug exist in a permanent state of equilibrium, such that the
concentration of free drug is constantly and instantaneously
maintained at a value determined by the equilibrium binding
constant. This has led to the argument that plasma binding does
not directly influence metabolism or renal tubular excretion.2
However, this may be an inaccurate assumption under certain
circumstances: where the kinetics of the dissociation process are
significantly slower than the uptake of a strongly bound drug by
the surrounding tissues, the equilibrium assumption will not be
valid. Likewise, where dissociation of bound drug is slow, drug-
protein binding may partially protect a drug from metabolism;3
only if the kinetics are sufficiently rapid is the free drug level
maintained constant during passage through a tissue by dissocia-
tion of protein-bound material. Thus, a strong binding equilibrium
alone does not in itself determine the consequences of plasma
binding; the kinetics of binding can act as a major determining
factor. The terms restrictive and permissive (nonrestrictive) have
been used to describe binding that reduces availability and that
does not affect availability respectively.4 Strongly bound drug
molecules that have slow dissociation kinetics would be anticipated
to exhibit restrictive behavior.
Serum albumin is the major extracellular protein of human
plasma, accounting for 60% of total plasma protein content, having
a concentration of 34-50 g L-1 (500-750 µM).5 It is also present
in extravascular fluid. Human serum albumin (HSA) is of particular
interest in terms of its drug binding properties. The ability of
albumin to bind a wide variety of ligands allows it to perform a
considerable role in the transport, distribution, and metabolism
of both endogenous and exogenous compounds.4 Furthermore,
it is involved in the transfer of many of these compounds across
organ/ circulatory interfaces such as are found in the liver,
intestine, kidney, and brain. HSA circulates throughout the body
about once every minute, but of this minute spends only 1-3 s in
Drug-plasma protein binding may greatly influence the
bioavailability and metabolism of a plasma-borne drug,
the bound form being partially protected from the meta-
bolic fate of the unbound drug. Traditionally, equilibrium
values (e.g., percentage binding) for drug-protein binding
have been measured to rationalize in vivo phenomena.
However, such studies overlook the influence of kinetics.
A rapid method of simultaneously determining kinetic rate
constants and equilibrium constants from chromato-
graphic profiles has been developed, based on the use of
immobilized protein columns and HP LC. By measuring
the chromatographic profiles (the position and width) of
a retained and an unretained compound one can directly
determine both the rate and equilibrium constants. Re-
sults are presented for the binding of L-tryptophan to
human serum albumin to exemplify the method. The
association equilibrium constant (Ka) and the association
and dissociation rate constants (ka and kd, respectively)
were thereby measured in an aqueous pH 7 .4 environ-
ment at 3 7 °C as 0 .8 4 1 0 4 M-1 , 5 .8 1 0 4 M-1 s-1 , and
6.9 s-1, respectively. These compare favorably with previ-
ously published results. The described method may be
used in quantitative structure-property relationship-
based rational drug discovery or for the rationalization of
drug pharmacokinetics.
Many drugs exist in vivo largely bound to albumin or other
plasma proteins. Plasma proteins provide a depot for drugs with
poor aqueous solubility, maintain buffered free drug levels, and
assist drug distribution. There can be further consequences of
plasma protein binding, for instance, in the observed hypoglycemic
action of fatty acid acylated insulins1 (the observed duration of
hypoglycemic action in animals after subcutaneous injection is
correlated with their albumin binding affinities).
(2) Benet, L. Z.; Kroetz, D. L.; Sheiner, L. B. In Goodman and Gilman’s The
Pharmacological Basis of Therapeutics, 9th ed.; Hardman, J. G., Gilman, A.
G., Limbird, L. E., Eds.; McGraw-Hill: New York, 1996; p 10.
(3) Mu¨ ller, W. E.; Wollert, U. Pharmacology 1 9 7 9 , 19, 59-67.
(4) Herve´, F.; Urien, S.; Albengres, E.; Duche´, J-C.; Tillement, J.-P. Clin.
Pharmacokin. 1 9 9 4 , 26, 44-58.
* Corresponding author: (fax) 44 (0)20 7594 3066; (e-mail) g.tranter@ic.ac.uk.
† Imperial College of Science, Technology and Medicine.
‡ Glaxo Smith Kline Medicines Research Centre.
(1) Markussen, J.; Havelund, S.; Kurtzhals, P.; Andersen, A. S.; Halstrom, J.;
Hasselager, E.; Larsen, U. D.; Ribel, U.; Schaffer, L.; Vad, K.; Jonassen, I.
Diabetologia 1 9 9 6 , 39, 281-288.
(5) Guyton, A. C. Textbook of Medical Physiology, 9th ed.; W.B Saunders:
Philadelphia, 1996; pp 161-164.
446 Analytical Chemistry, Vol. 74, No. 2, January 15, 2002
10.1021/ac010643c CCC: $22.00 © 2002 American Chemical Society
Published on Web 12/12/2001

any particular capillary where it can exchange transported
substances with the neighboring cells.5
and dissociation has typically involved time-consuming stopped-
flow spectroscopic techniques.11 Chromatographic methods for
determining rate constants have been developed, but have
required multiple measurements at various flow rates.12 While all
these approaches can give accurate results, they are inappropriate
for the study of the larger number of compounds often considered
in modern drug discovery within a practical time span. To this
end, a method of rapidly determining the kinetic rate constants,
together with the corresponding equilibrium constants, from
chromatographic profiles has been developed, the application of
which we exemplify here.
Although serum albumin is a major drug binding protein, other
plasma proteins may bind drug molecules to a very significant
extent. One such protein is R1-acid glycoprotein (R1-AGP). This
is an “acute-phase” protein: levels of R1-AGP are increased in
disease states. It is of particular importance in the binding of basic
drugs. In contrast to HSA, which has a number of binding sites
at which specific binding of drugs occur, the high-affinity binding
of most drugs to R1-AGP is mediated by only one common binding
function.6 The kinetics of drug binding to R1-AGP will be the
subject of a future publication.
Chromatography has traditionally been used as a separative
technique. However, it may also be used to investigate the
distribution properties per se of an analyte. An example of this is
in the chromatographic determination of partition coefficients,13
which provides a rapid alternative to traditional methods, e.g.,
shake flask, for high-throughput work. The present work is based
on the use of immobilized protein columns, although the principles
apply to any stationary phase. Both the position and shape of a
chromatographic peak for an eluted ligand are used to determine
the equilibrium constant and the association and dissociation rate
constants. In essence, the retention time is characteristic of the
equilibrium constant for association, with the shape of the peak
containing information about the kinetics. The analysis is based
on the concept of chromatographic peaks as probability distribu-
tion functions, a concept first proposed by Giddings and Eyring.14
Giddings and Eyring published their statistical approach to
describe molecular migration in chromatography in 1955. They
treated the chromatographic process as a Poisson distribution
process and the chromatographic peak as the probability density
function for the elution of a solute as a function of time (in all of
the following, it is assumed that the detection method is linear
with concentration). Denizot and Delaage further developed this
statistical approach to the analysis of peak shapes in 1975.15 They
applied it to affinity chromatography, a technique traditionally used
for the separation of macromolecules. They also generalized the
approach, to take into account other forms of dispersion such as
diffusion.
Traditionally, equilibrium values (e.g., percentage binding) for
drug-protein binding have been measured to rationalize in vivo
phenomena. However, such studies overlook the strong influence
of kinetics in dynamic systems such as living organisms; it is not
just the equilibrium constant of binding that is important but the
rates of association and dissociation of a drug to and from a
protein. Some drug molecules undergo rapid dissociation from
plasma proteins. Therefore, even if they have an apparently high
percentage of binding they are not effectively protected from
metabolism or excretion. Conversely, those compounds that
undergo slow dissociation may not be able to exert their
therapeutic effect before being removed from the site of action
by the flow of blood. Hepatic clearance and passage of a drug
across the blood-brain barrier are two examples of processes
that respond to differences in the rate constants.7,8
The association of a drug (D) with a protein (P) to form a
complex (DP) and the reverse dissociation can be represented
as
ka
D + P y
\
k z DP
(1)
d
where ka and kd are the association and dissociation rate constants,
respectively. The corresponding association equilibrium constant
(Ka) is the ratio of the two rate constants:
In the Giddings and Eyring model each molecule is assumed
to have a constant probability of binding per unit time, pa, given
by the product of the association rate constant and the concentra-
tion of binding sites, i.e., ka[binding site]. Likewise, the complex
is presumed to have a constant probability per unit time of
dissociating, pd, given by the dissociation rate constant, kd. The
assumption is made that there is a single mode of binding, the
consequences of which will be considered further in the discussion
section below. Comparison of the behavior of a chromatographi-
cally retained compound with one that is unretained allows the
determination of these probabilities and thence the rate constants.
Each molecule is assumed to spend the same time, t0, in the
mobile phase and to move in the mobile phase with constant
velocity. Differences in retention time are accounted for by
Ka ) ka/ kd
(2)
Thus, different compounds may have the same equilibrium
constant, and hence percentage binding, but substantially differ
in the rates of association and dissociation, perhaps by orders of
magnitude, their ratio only remaining consistent. The determina-
tion of these kinetic rates is therefore important in elucidating
pharmacokinetics.
Historically, the primary methods of determining equilibrium
binding constants have involved dialysis, ultracentrifugation, or
direct spectroscopic methodology,9 although more recently chro-
matographic methods have been successfully employed.10 Like-
wise, the determination of kinetic rate constants for association
(6) Mu¨ ller, W. E.; Rick, S.; Brunner, F. In Protein Binding and Drug Transport;
Tillement, J.-P., Lindenlaub, E., Eds.; Symposia Medica Hoechst, 20; F. K.
Schattauer Verlag: Stuttgart, 1985; pp 29-41.
(11) Eccleston, J. F. In Spectrophotometry and Spectrofluorimetry: a practical
approach; Harris, D. A., Bashford C. L., Eds.; IRL Press Ltd.: Oxford, 1987;
pp 137-164.
(7) Weisiger, R. Proc. Nat. Acad. Sci. U.S.A. 1 9 8 5 , 82, 1563-1567.
(8) Robinson, P.; Rapoport, S. Am. J. Physiol. 1 9 8 6 , 251, R1212-R1220.
(9) Windzor, D. J.; Sawyer, W. H. Quantitative Characterization of Ligand
Binding; Wiley-Liss Inc.: New York, 1995; pp 12-61.
(12) Yang, J.; Hage, D. S. J. Chromatogr., A 1 9 9 7 , 766, 15-25.
(13) Lambert, W. J. J. Chromatogr., A 1 9 9 3 , 656, 469-484.
(14) Giddings, J. C.; Eyring H. J. Phys. Chem. 1 9 5 5 , 59, 416-421.
(15) Denizot, F. C.; Delaage, M. A. Proc. Natl. Acad. Sci. U.S.A. 1 9 7 5 , 72, 4840-
4843.
(10) Oravcova, J.; Bohs, B.; Lindner W. J. Chromatogr., B 1 9 9 6 , 677, 1-28.
Analytical Chemistry, Vol. 74, No. 2, January 15, 2002 447

differences in the time spent bound to the stationary phase. Each
solute molecule is eluted when it has covered a distance equal to
the column length or, equivalently, spent a time t0 in the mobile
phase within the column. It was demonstrated that the probability
p dt of having a retention time between tR and tR + dt for any n
(the number of bindings) is expressed by14,15
(pat0)n exp[-pat0](pdt)n-1 exp[-pdt]pd dt
∞
p dt )
(3)
∑
n!(n - 1)!
n)1
where the symbols tR and t0 represent the time at which a retained
and an unretained molecule elute and t ) tR - t0. This equation
essentially represents the shape of a chromatogram for the
retained compound.14
The shape of a chromatographic peak may be completely
characterized by its moments.16 The zero and first moments give
the area and mean (center of gravity), respectively. The second,
third, and fourth moments (if taken around the mean) are
measures of the peak’s width, asymmetry, and flattening, respec-
tively. Denizot and Delaage subsequently derived expressions for
the moments of the distribution described by eq 3 and considered
other sources of dispersion, such as diffusion and differences in
the flow rate of the solvent within the column. They therefore
viewed t0 as a random variable, as is t, rather than as a constant.
It follows from Denizot and Delaage that
Figure 1. Illustration of the parameters employed for an unretained
(E[t0], σ0) and retained (E[tR], σR) compound in the chromatographic
profiling analysis of DMSO and L-tryptophan, respectively. The two
chromatograms were obtained from separate injections, and the
DMSO chromatogram has been multiplied 3-fold for illustrative
purposes.
equilibrium constant can be determined as the ratio of the rate
constants:
ka (E[tR] - E[t0])
Ka )
)
(8)
pa
kd
E[t0][receptor]
mean time of retained peak ) E[tR] ) E[t0] 1 +
(4)
(
)
pd
Note that, in contrast to the individual rate constants, the
equilibrium constant is independent of the peak width and is
determined solely by the mean retention times.
and
Thus, by measuring the chromatographic profiles of a retained
and an unretained compound, one can directly determine ka, kd,
and Ka (assuming the receptor loading of the stationary phase in
known). To ensure the kinetics are measurable, it is necessary
to employ flow rates sufficiently fast that equilibrium on the
column cannot be established, whereupon peak broadening
through kinetic effects occur. Furthermore, by judicious choice
of temperature and mobile-phase composition, the conditions
employed may be tailored to simulate those found in vivo. Here
we illustrate the technique by determining the binding charac-
2
2p
pa
2
2
variance of retained peak ) σR
)
aE[t0] + 1 +
σ0
2
(
)
pd
pd
(5)
where E[tR] and E[t0] are the mean times of the chromatographic
peak of a retained and an unretained compound, respectively.
Likewise σR2 and σ02 are the respective peak variances, these being
a measure of the width of a peak (i.e., not of the error in its
position), for example, as depicted in Figure 1.
teristics of L-tryptophan, an archetypal plasma binding probe, using
Equations 4 and 5 can be solved with respect to pa and pd:
dimethyl sulfoxide (DMSO) as the unretained t0 reference.
While the measured dissociation rate constant is independent
of the protein concentration, the equilibrium constant and the
association rate constant are dependent on this value. Therefore,
measurement of the total accessible HSA concentration is re-
quired. This was performed by frontal analysis17 (FA) using
2E[t0](E[tR] - E[t0])2
σR (E[t0])2 - σ0 (E[tR])2
pa ) ka[receptor] )
(6)
(7)
2
2
2(E[t0])2(E[tR] - E[t0])
σR (E[t0])2 - E σ0 (E[tR])2
pd ) kd )
L-tryptophan and DMSO.
2
2
EXPERIMENTAL SECTION
Ultrapure grade -tryptophan and HPLC grade DMSO were
obtained from Sigma Aldrich Co. Ltd. AnalaR grade sodium
dihydrogen orthophosphate monohydrate, disodium hydrogen
L
where [receptor] is the molar concentration of receptor sites in
the volume of mobile phase within the column. Consequently, the
(16) Grushka, E., Myers, M. N.; Schettler, P. D.; Giddings, J. C. Anal. Chem.
1 9 6 9 , 41, 889-892.
(17) Loun, B.; Hage, D. S. J. Chromatogr.-Biomed. Appl. 1 9 9 2 , 579 (2), 225-
235.
448 Analytical Chemistry, Vol. 74, No. 2, January 15, 2002

Table 1. Kinetic and Equilibrium Results Obtained by Chromatographic Profiling for the Binding of L-Tryptophan to
HSA and Literature Results for Comparison
T
Ka
ka
kd
%
td1/ 2
(s)
(°C)
pH
7.4
7.4
(104 M-1
)
(104 M-1 s-1
)
(s-1
)
boundg
Current Work
5.8 ( 0.03
chromatographic
profiling
(3.5 mL/ min)
frontal analysis
37
37
0.836 ( 0.002
0.93 ( 0.01
6.9 ( 0.03
85.0
0.100 ( 0.001
86.3
94.2
Literature
Yang and Hagea
Yang and Hagea
McMenamyb
McMenamyb
McMenamyc
Lagercrantzd
37
37
37
37
2
7.0
7.4
7.6
7.0
7.6
7.4
2.4 ( 0.3
14
6.0
3e
0.116
5e
1.3
0.5
2f
20e
89.8
77.1
93.1
88.1
rt?
1.1
a
Reference 12. b Reference 18. c Reference 19. d Reference 20. e Read from graphical results, kinetic and equilibrium constants inconsistent in
original paper. f Read from graphical results. g Calculated for [HSA] ) 6.75 × 10-4 M.
orthophosphate dihydrate, and HPLC grade water for buffer
preparation were obtained from Merck Ltd.
functional form was found to fit the data to within the noise level
in all circumstances of this study. Full error analysis was
performed using standard propagation of errors formulas.
A Hewlett-Packard 1090 HPLC system with diode array
detection was used. All chromatography was performed isocrati-
cally at 37 °C using an aqueous 50 mM phosphate buffer (pH
7.4) mobile phase. Analytical immobilized HSA columns, 50 ×
4.6 mm, were obtained from Thermo Hypersil-Keystone. When
not in use, the column was stored at 4 °C in an aqueous solution
of 0.01% sodium azide to prevent bacterial growth. The flow rate
used was 3.5 mL min-1, which was confirmed by volumetric
collection of eluant. Five-microliter injections of either a 100 µM
RESULTS AND DISCUSSION
A representative chromatogram of DMSO (the t0 marker) and
L-tryptophan is presented in Figure 1, and the kinetic rate
constants and association equilibrium constant, as determined in
this study, are presented in Table 1. In addition, the derived
dissociation half-life (td1/ 2) and in vivo percentage bound (% bound)
are tabulated. For comparison, previously reported results from
the literature, employing various methods of determination, are
also quoted.
The dissociation half-life is determined by the kinetic dissocia-
tion rate constant and represents the half-life of dissociation for
the bound drug when placed in an infinite sink, i.e., where all
unbound drug is effectively removed.
stock solution of L-tryptophan or 1 mM DMSO in mobile phase
were made. For chromatographic profiling and frontal analysis,
the diode array detector response at 220 nm was employed.
The 5-cm column used contains silica with a median pore
diameter of 300 Å and has a pore volume of 0.7 cm3 g-1 and
surface area of 90 m2 g-1 (data supplied by the manufacturer; for
reference). The mobile-phase volume of the column was deter-
mined to be 0.66 mL from measurements made for unretained
compounds across a range of flow rates.
td1/ 2 ) ln(2)/ kd
(9)
For the frontal analysis experiments, used to determine the
concentration of binding sites, L-tryptophan solutions from 20 to
This may be considered to crudely simulate the case where
partitioning or transport into other body compartments (tissues,
etc.) rapidly occurs. As such, it provides an approximate measure
of how quickly drug dissociation can occur, for comparison with,
say, the few seconds blood resides in a capillary.
The in vivo percentage bound is the percentage of drug that
would be bound to HSA under in vivo circumstances, ignoring
other sources of binding. It is calculated from the equilibrium
constant, taking the in vivo concentration of HSA in plasma as
[ivHSA] ) 6.75 × 10-4M (assuming this is in great excess over
the drug):
200 µM were run. This procedure is relatively time-consuming
but provides results that are then found to remain constant over
the lifetime of the column. The accessible receptor concentration
(as used in eqs 6 and 8) at a flow rate of 3.5 mL min-1 was thereby
determined as 1.81 10-4 M.
The HPLC instrumentation was configured to minimize extra-
column time and effects. Furthermore, as the algorithm (i.e., eqs
6-8) refers to “on-column” times, all retention times were
corrected for extracolumn periods by subtracting the time taken
from injection to detection when the column was replaced by a
zero-volume connector.
Although the chromatographic peak position and variance
could be directly determined from the raw data, it was found
convenient for analysis to fit a curve to the data. The data were
exported into the software program PeakFit (Jandel Scientific
Software, AISN Software Inc.), an EMG + GMG (exponentially
modified Gaussian + half-Gaussian modified Gaussian) function
fitted from which the mean and variance were calculated. This
concentration of bound drug
total concentration of drug
% bound )
× 100%
[ivHSA]Ka
)
× 100%
(10)
[ivHSA]Ka + 1
The results determined by the chromatographic profiling method
Analytical Chemistry, Vol. 74, No. 2, January 15, 2002 449

reported here compare well with those from previous literature
determined by equilibrium dialysis18,19 and by chromatography,12,20
as shown in Table 1. Furthermore, the results reported here were
determined in a completely aqueous pH 7.4 environment at 37
°C and thus are directly comparable to in vivo conditions.
The results are, as shown in Table 1, in broad agreement with
those found in the literature. Where differences exist, these can
be explained by differences in the pH or in the temperature used
broadening, it is necessary for the t0 unretained reference
compound (DMSO here) to have a diffusion coefficient similar to
that of the retained compound under study (L-tryptophan). This
is true for small compounds such as these, such that the lack of
equivalence is unlikely to lead to errors, especially at higher flow
rates where binding kinetics dominate. However, the diffusion
coefficient of large protein molecules is significantly smaller.
Therefore, if traditional affinity chromatography is used, in which
the protein is passed through a column of immobilized ligand
rather than vice versa, the mass-transfer term is far more likely
to dominate, even at higher flow rates.
A variety of compounds purportedly thought not to bind to
HSA were explored as possible unretained references, including
DMSO, sodium citrate, uridine, sodium nitrate, and carbohydrate
derivatives. However, all but DMSO and sodium citrate had
distinct retention, albeit small, on the HSA columns used. For
convenience, DMSO was chosen as the unretained reference
compound.
for the study. L-Tryptophan is known to bind more strongly to
HSA at lower temperatures18 and at higher pHs.11 The discrepancy
with the results of Yang and Hage12 may be due to the fact that
they appear to have used results obtained using two different
columns to derive their data, yet we have observed that the
concentration of binding sites may vary very significantly between
nominally identical columns. In support of this, the kd is ap-
proximately the same, but ka and Ka differsand these are the
parameters with a dependence on the protein concentration.
HSA has a variety of potential binding modes. The molecule
consists of three structurally homologous domains denoted I, II,
and III, with each domain composed of two smaller subdomains,
A and B, giving a “heart-shaped” structure.21,22 Two principal
binding sites for drug binding have been identified from binding
studies.23,24 These are located in subdomains IIA and IIIA and are
referred to as site I and site II, respectively. Site II binds a broader
variety of drug molecules, including diazepam and ibuprofen, and
the amino acid tryptophan. Site I is the primary binding site of
warfarin and phenylbutazone.
For the kinetics to be apparent in the chromatogram, it is
necessary to employ flow rates sufficiently rapid that equilibrium
cannot be established before the compound is eluted. This can
be quantified by the “critical ratio”, deduced from the denominator
of eqs 6 and 7:
σR/ E[tR]
critical ratio ) η )
(11)
σ0/ E[t0]
It is assumed in the Denizot-Delaage formalism that there is
a single type of receptor and mode of binding for each compound.
While this is true for tryptophan interactions with HSA, it is not
universal. In the case of multiple sites, the Denizot-Delaage
method represents each interaction as with an equivalent single
“pseudosite”. Consequently, care has to be taken in interpreting
results if binding is occurring at more than one site or with more
than one mode (orientation, etc.). However, the kinetic and
equilibrium constants for individual sites can be determined, if
required, by introducing inhibitors or blockers of the unwanted
sites into the mobile phase. Nonetheless, the primary use of these
measurements is foreseen to be in quantitative structure-property
relationship (QSPR)-based rational drug discovery and optimiza-
tion or for the rationalization of pharmacokinetics. In this context,
the kinetic and equilibrium constants for a pseudo single receptor
are appropriate parameters to describe the overall interactions to
sufficient approximation.
For the kinetics to be measurable, this ratio must be greater than
1. A value of 1 indicates that the compound has eluted under
equilibrium conditions and therefore no kinetic information is
available from the chromatogram, although the equilibrium
constant can still be determined from the retention times via eq
8. Values greater than 1 indicate a degree of kinetic broadening
in the peak shape.
η ) 1
w equilibrium chromatography
w kinetic broadening
(12)
(13)
η > 1
By considering the effect of flow rate on eqs 6 and 7, it can be
established that the kinetics are well determined when the “kinetic
factor”, κ, defined as
2
κ ) (η2 - 1)σR u/ η2
(14)
A typical chromatogram of L-tryptophan is presented in Figure
1. The Denizot-Delaage formalism, through the incorporation of
the parameters for an unretained compound, accounts for the
various sources of band broadening beyond that due to binding
kinetics. In particular, it encompasses the broadening due to
diffusion within the mobile phase. However, for the Denizot-
Delaage equations to fully compensate for these forms of band
is constant with increasing linear flow rate u.
dκ/ du f 0
w kinetics well determined
(15)
Comparison with the van Deemter equation for plate height25
shows condition 15 as equivalent to requiring the van Deemter
equation to be dominated by the “C term”, the term containing
kinetic dispersion, as might be expected.
At very low flow rates, the chromatography approaches
equilibrium control. The kinetics are not well determined unless
(18) McMenamy, R. H.; Seder, R. H. J. Biol. Chem. 1 9 6 3 , 238, 3241-3248.
(19) McMenamy, R. H.; Oncley, J. L. J. Biol. Chem. 1 9 5 8 , 233, 1436-1447.
(20) Lagercrantz, C.; Larsson, T.; Denfors, I. Comp. Biochem. Physiol. C:
Pharmacol. Toxicol. Endocrinol. 1 9 8 1 , 69 (2), 375-378.
(21) Peters, T. Adv. Protein Chem. 1 9 8 5 , 37, 161-245.
(22) Carter, D. C.; He, J. X. Adv. Protein Chem. 1 9 9 4 , 45, 153-203.
(23) Curry, S.; Mandelkow, H.; Brick, P.; Franks, N. Nat. Struct. Biol. 1 9 9 8 , 5,
827-835.
(25) van Deemter, J. J.; Zuiderweg, F. J.; Klinkenberg, A. Chem. Eng. Sci. 1 9 5 6 ,
5, 271-289.
(24) Olson, R. E.; Christ, D. D. Annu. Rep. Med. Chem. 1 9 9 6 , 31, 327-336.
450 Analytical Chemistry, Vol. 74, No. 2, January 15, 2002

the flow rate is greater than 3.0 mL min-1, under the conditions
reported here, whereupon the kinetic factor, η, tends to a constant
value. For intermediate flow rates, kinetics make a detectable
contribution to the band broadening. However, in these circum-
stances, they are less well determined and poorly distinguishable
from other mechanisms of band broadening or artifacts not
accounted for within the Denizot-Delaage formalism, such as
differential diffusion due to nonequivalent diffusion coefficients
mentioned above.
Altering the conditions used, such as flow rate or length of
column, increases the range of compounds for which rate
constants are measurable. However, at high flow rates, one may
encounter problems with HPLC pumping efficiency and increased
errors due to the shortness of retention time. Therefore, there
has to be a compromise between the desire to have very high
flow rates in order to enhance the contribution of kinetics to the
chromatogram and the ability of current instrumentation to
perform at these levels. In practice, a flow rate of 3.5 mL min-1
another. This is more likely to be achieved if it is the protein rather
than the ligand that is bound as the protein is a much larger
molecule and the binding site may poorly accessible within the
protein. An immobilized small ligand may find it difficult to access
the binding site simply because it is tethered to the stationary
phase. Furthermore, the linkage tethering an immobilized small
ligand will, at best, impinge on the entrance to the binding site,
so altering the binding characteristics from that of a free ligand
or, at worst, change or eliminate the mode of binding. In contrast,
with care, a protein can be tethered through positions remote from
the binding site, so allowing full, unmodified, access to a ligand.
A previously reported example of the use of the Denizot-
Delaage method in traditional affinity chromatography is in a study
of the binding of pancreatic ribonuclease to uridine-5′-(Sepharose-
4-aminophenyl phosphate)-2′(3′)-phosphate beads.29 Chaiken found
that the rate constants obtained were too small by several orders
of magnitude relative to those measured in free solution. The
reference relates to unpublished results of R. H. Long and I. M.
Chaiken. Chaiken concluded that for valid rate data the use of
ligands immobilized onto low-porosity supports would be required.
However, the issue of porosity is only one of a number of factors
that could have led to the results they obtained. In addition to
the comments made above, Sepharose-bound ligand was used.
Sepharose has a relatively large particle diameter, and mass
transfer in the mobile phase is proportional to the square of the
particle size.
From the study reported here, we have established that
porosity is not an issue if the accessible receptor concentration is
determined at the flow rates employed for the Denizot-Delaage
analysis. Although the total protein loading may be much greater,
a significant proportion, deep within porous stationary supports,
will be inaccessible at higher flow rates during the time scale of
the chromatographic elution. In effect, the continuous flow
provides no opportunity for the molecules to diffuse deep into
the porous support before being carried onward by the flow. By
performing frontal analysis at a range of flow rates, it is possible
to quantitate this effect. At high flow rates, where the eluted
compound has little opportunity to access the inner regions of
the stationary phase, the accessible concentration drops to 1 ×
10-4 M for the column used for this study. At lower flow rates,
the accessible concentration increases, although never to the
nominal concentration calculated from the protein loading of the
column. For instance, at a flow rate of 0.4 mL min-1, the
concentration of binding sites, as measured by frontal analysis, is
some 41% greater for this study.
was found optimal for L-tryptophan, ensuring the compound was
retained for a sufficient period to be distinct from an unretained
compound.
Key to the success of the method is the ability to establish
effective mass transfer of the solute through diffusion from the
bulk mobile phase to within the solvation shell of the stationary
phase at a rate faster than the kinetics of association. The
chromatographic process then becomes controlled by the rates
of association and dissociation to/ from the immobilized protein.
This is easily achieved by small druglike molecules in solution,
with their fast diffusion rates.
The application of the Denizot-Delaage model to obtain rate
data in affinity chromatography has been criticized26,27 on the basis
that it is only valid when the effect of mass-transfer kinetics (i.e.,
diffusion) on the mean and variance of the profile is negligible.
In traditional affinity chromatography, the small molecule is
immobilized and the protein added to the mobile phase. Under
such circumstances, the diffusion rate of the large macromolecule
in the mobile phase is sufficiently slow that it causes the
chromatographic process to become diffusion controlled and the
kinetics of association and dissociation become obscured. Typical
drug-sized molecules have diffusion coefficients of the order of
10-9 m2 s-1 compared to some 10-10-10-11 m2 s-1 for proteins
the size of HSA (the diffusion coefficient of HSA itself is 6.1 ×
10-12 m2 s-1 28). Thus, by immobilizing the protein and placing
the small ligand in the mobile phase, we have overcome this
diffusion limitation. Hethcote and DeLisi have described the use
of immobilized protein versus the immobilized ligand as reversed-
role affinity chromatography.27
Previous reports17,30 of the apparent reduction in active recep-
tors when proteins are immobilized, determined by frontal
analysis, have invoked the argument that the protein is partially
denatured on immobilization. However, the results reported here
indicate that flow rate is a significant factor. This phenomenon
will be explored further in a future publication. On initial reflection,
it may appear that the existence of inaccessible sites is contrary
to the discussion above regarding the need for effective diffusion
from the bulk mobile phase. However, they are actually fully
consistent: the stationary phase may be imagined as divided into
two zones, a core that is inaccessible and an accessible surface
Further benefits of using immobilized protein rather than
immobilized ligand are that the smaller size of the free species
leads to greater accessibility to sites within the pores of the
support and the interactions are more representative of those in
free solution. In order for binding to take place, the protein and
ligand need to be in the correct orientation with respect to one
(26) Hethcote, H. W.; DeLisi, C. J. Chromatogr. 1 9 8 2 , 248, 183-202.
(27) Hethcote, H. W.; DeLisi, C. In Affinity Chromatography and Biological
Recognition; Chaiken, I., Wilchek, M., Parikh, I., Eds.; Academic Press,
Inc.: New York, 1983; pp 119-134.
(28) Oncley, J. L.; Scatchard, G.; Brown, A. J. Phys. Colloid Chem. 1 9 4 7 , 51,
(29) Chaiken, I. M. Anal. Biochem. 1 9 7 9 , 97, 1-10.
184-198.
(30) Yang, J.; Hage, D. S. J. Chromatogr. 1 9 9 3 , 645, 241-250.
Analytical Chemistry, Vol. 74, No. 2, January 15, 2002 451

where diffusion from the mobile phase is efficient within the time
scale of the experiment. The requirement of efficient diffusion
thus defines the extent of the accessible receptors. All the
inaccessible receptors have no influence in the chromatography
and may be considered as absent.
discernible. However, care should be taken to ensure that the
components of a mixture are not interacting either with each other
or allosterically with the receptor. Although inferior to separate
injections, it holds the possibility of determining the individual
binding characteristics of both enantiomers of a chiral molecule
from the racemic mixture without the need for prior resolution
of each stereoisomer. As a corollary, by incorporation of additives
into the mobile phase, it is possible to investigate their role and
effects, including the modulation of allosteric changes in receptors
and action of binding inhibitors. Moreover, by the use of
immobilized serum albumin from different species (e.g., rat), it
is possible to identify potential species differences in animal
studies and validate animal models for biometabolism and phar-
macokinetic investigations. We are testing this method with a wide
variety of compounds with different binding strengths. The results
will be presented in forthcoming publications.
CONCLUSIONS
The chromatographic profiling method described here has
potential as a medium-throughput screen for determining the
binding characteristics of drugs under aqueous conditions simu-
lating the in vivo environment. Having first established the
accessible receptor concentration of a column by frontal analysis,
it is possible to subsequently determine the kinetic and equilib-
rium binding parameters of a wide range of compounds by simple
chromatographic analysis. Typical retention times are in the 0.1-
20-min range, depending on the strength of binding. To minimize
potential interference, the tryptophan and DMSO were run as
separate injections for this study. However, to maximize through-
put, they may be co-injected or a single DMSO t0 reference run
for multiple samples.
ACKNOWLEDGMENT
The authors thank the BBSRC and Glaxo Smith Kline for
funding A.M.T.
Furthermore, by the use of multiple peak fitting to determine
the mean and variance of each component chromatographic peak,
it is also possible to study multiple compounds simultaneously
co-injected, providing they have sufficiently different retention
times such that their individual chromatographic peaks are
Received for review June 8, 2001. Accepted September
18, 2001.
AC010643C
452 Analytical Chemistry, Vol. 74, No. 2, January 15, 2002