Evaluation of ligand-selector interaction from effective diffusion coefficient

Article abstract of DOI:10.1021/ac1008207

We present an analytical technique for determination of ligand-selector equilibrium binding constants. The method is based on the measurements of effective molecular diffusion coefficient of the ligand during Poiseuille flow through a long (approximately 25 m), thin (0.254 mm ± 0.05 mm ID) capillary with and without the selector. The data are analyzed using the Taylor dispersion theory. Bovine Serum Albumin (BSA) and cyclodextrin (CD) were taken as model selectors. We have tested our method on the following selector-ligand complexes: BSA with warfarin, propranolol, noscapine, salicylic acid, and riboflavin, and cyclodextrin with 4-nitrophenol. The results are in good agreement with data from the literature and with our own results obtained within classical chromatography. This method works equally well for uncharged and charged compounds.

Full text of DOI:10.1021/ac1008207

Anal. Chem. 2010, 82, 5463–5469
Evaluation of Ligand-Selector Interaction from
Effective Diffusion Coefficient
Anna Bielejewska,*,† Andrzej Bylina,† Kazimiera Duszczyk,† Marcin Fiałkowski,† and
Robert Hołyst*,†,‡
Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland, and
WMP-College of Science, UKSW, Dewajtis 5, Warsaw, Poland
We present an analytical technique for determination of
ligand-selector equilibrium binding constants. The method
is based on the measurements of effective molecular
diffusion coefficient of the ligand during Poiseuille flow
through a long (approximately 25 m), thin (0.254 mm (
0.05 mm ID) capillary with and without the selector. The
data are analyzed using the Taylor dispersion theory.
Bovine Serum Albumin (BSA) and cyclodextrin (CD) were
taken as model selectors. We have tested our method on
the following selector-ligand complexes: BSA with war-
farin, propranolol, noscapine, salicylic acid, and ribofla-
vin, and cyclodextrin with 4-nitrophenol. The results are
in good agreement with data from the literature and with
our own results obtained within classical chromatography.
This method works equally well for uncharged and charged
compounds.
in the protein due to immobilization may cause of erroneous
results when using SPR or affinity chromatography. Capillary
electrophoresis suffers from protein adsorption to the capillary
and at least one of the reagents in electrophoresis must carry a
charge. Each technique has its own limitations and only a judicious
choice of various technique can lead to reliable results. We present
a new technique for determination of ligand-selector binding
constants and additionally use the classical chromatography to
test the method.
The Poiseulle flow, characterized by a parabolic velocity profile
across the capillary, leads to the flow-induced widening of the
initially narrow injection zone of the analyte. The shape of the
zone is mapped on the concentration distribution of the analyte
by the UV adsorption intensity of the analyte. The distribution, at
the capillary end, is predicted by the Taylor theory to be
Gaussian.17,18 According to the Taylor theory the width of the
concentration distribution is proportional to the square of the
velocity and inversely proportional to the effective diffusion
coefficient of the studied ligand (in a capillary filled with a
selector). The ligand-selector binding constant influence the
effective diffusion coefficient of the ligand and change the width
of the concentration distribution. Therefore the latter quantity can
The formation of a macromolecule-ligand complex in a solution
is an important process in chemistry, pharmacy, and molecular
biology.1,2 Drugs-protein binding properties1-14 have been exam-
ined using equilibrium dialysis, ultracentrifugation and ultrafil-
tration. These traditional methods involve the physical separation
of the free and bound analyte (drug, ligand), followed by an
analysis step. Equilibrium dialysis is often considered as a
reference method in drug-protein binding studies.3 Ultrafiltration
has been used as a routine method in clinical laboratories due to
its simplicity.2 Spectroscopic methods such as circular dichroism,5
fluorescence,6-8 UV/vis absorption6 and also NMR9,10 have been
added to the list of applied techniques. NMR studies and one color
FCS (fluorescence correlation spectroscopy) are suitable for
studies of drug complexes characterized by weak interactions and
fast exchange between free and complexed drug. Other recent
techniques developed for characterization of ligand-receptor
(protein) binding are based on chromatographic and electro-
phoretic methods.11-15 Surface plasmon resonance (SPR) biosen-
sor technology, such as BIACORE16 can give high sensitivity and
high throughput information. However conformational changes
(3) Lindup, W. E. In Progressin Drug Metabolism, Chapter 4; Bridges, J. W.;
Chesseud, L. F.; Gibson, G. G., Eds.; Taylor and Francies: New York, 1987;
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Vaccher, C. J. Chromatogr., A 2008, 1215, 185–193
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* Address correspondence to either author. E-mail: annab@ichf.edu.pl (A. B.);
holyst@ptys.ichf.edu.pl (R. H.).
.
† Polish Academy of Sciences.
‡ WMP-College of Science.
.
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10.1021/ac1008207  2010 American Chemical Society
Published on Web 06/10/2010
Analytical Chemistry, Vol. 82, No. 13, July 1, 2010 5463

be used for the determination of the constant. For the rest of this
paper we will denote the method TDA (Taylor Dispersion
Analysis).
introduced into the eluent. The distance along the tube from the
injection point to the detection point is L. At the detection point
we measure the shape of the concentration distribution of the
compound, for example, by absorbance as a function of time t.
The normalized distribution inside a capillary near its end is given
by the Gaussian distribution according to the Taylor theory:17,29
TDA was used to obtain distribution of organic substrates
between aqueous and micelle phases.19,20 Based on Taylor
dispersion monitored by electrospray mass spectrometry Clark
et al.21,22 identified monocovalent complexes of macromolecules.
Capillary electrophoresis (CE) instrument combined with TDA
was used to obtain the diffusion coefficient of phenylalanine,
proteins and nanoparticles.23-25 In this approach the first step is
the separation of the studied mixture by capillary electrophoresis
and the second step is online measurement of diffusion coefficient
by TDA.25,26 Propranolol and proteins were the model systems
to demonstrate the first application of TDA-CE approach facilitat-
ing simultaneous measurement of protein size and quantification
of ligand protein affinity.27 Noncovalent interaction between
cyclodextrin and naphthol and naproxen were quantified by TDA
in Jensen and Ostergaard recent communication.28
In our method we use typical chromatographic equipment,
where the chromatographic column is replaced by a long (around
25 m) and thin (0.254 mm 0.05 mm ID) capillary filled with an
appropriate eluent (e.g., Tris buffer, water-ethanol mixture etc.)
or an eluent with a selector of interest. This eluent flows in the
capillary with a typical flow rate of 0.1-0.05 mL/min. A narrow
injection of the sample (eluent-ligand or eluent-selector) is applied
to the system and the diffusion coefficients of the free ligand and
the free selector is determined by TDA. Next we fill the capillary
with the eluent with the selector of known concentration and inject
ligand-selector sample. The concentration of ligand is the same
as in the experiment without selector. The concentration of the
selector is the same as in the eluent. The effective diffusion
coefficient of the ligand during the flow in the presence of the
selector depends on the diffusion coefficient of free and complexed
ligand and on also stability constant of the ligand-selector complex.
This diffusion coefficient is also determined by TDA.
1
(L - ut)2
4σt
P(t) )
exp -
(1)
[
]
√
2 πσt
The width of P(t) is determined by the dispersion coefficient:
u2R2
48Deff
σ )
(2)
The dispersion coefficient, σ, is proportional to the square of the
velocity and inversely proportional to the effective molecular
diffusion coefficient Deff. The former dependence is due to the
shape of the velocity profile (parabolic) across the capillary.
The latter dependence is due to the compound diffusion during
the flow with or without complexing agent. The compound may
diffuse freely without any binding or it may diffuse as a complex
with the selector, added to the eluent. If there is no selector in
the eluent and we monitor only one compound, say ligand, Deff
) DL, where DL is the molecular diffusion coefficient of the
ligand. If the ligand injected into the capillary forms L:S
complex with the selector present in the eluent, Deff will depend
on K the equilibrium constant of the reaction
L + S S L:S
The dependence of Deff on K can be determined on the basis of
the following assumptions. The time of the flow of the ligand
between the injection point and the detector is long and given
by tF (we use a very long capillary and a small flow rate). The
reaction mixture of L and S is assumed to come to the
equilibrium in a much shorter time than tF.
During the flow the L compound is in a complex with S on
average during the time tLS and in the free state during the time
tL and consequently tF = tL + tLS and
The properties of the measuring system were checked by
injection of a solution of KNO3 as the inert substance. Albumin-
warfarin, propranolol, noscapine, salicylic acid, and riboflavin
experiments were used to demonstrate the usefulness of the
method for studying biologically important interactions. In
order to compare the new method with the classical chromato-
graphic method, experiments with 4-nitrophenol and cyclodex-
trin were performed using both methods.
DLtL + DLStLS
Deff
)
(3)
tL + tLS
THEORY
We consider an eluent moving at the average velocity u along
a tube of radius R. At an injection point a compound of interest is
The time spent in the free state, tL, and in the bound state, tLS,
determine the ratio of the molar concentration of free, cL and
bound ligands, cLS. From this simple observation we calculate
the equilibrium constant K multiplied by the molar concentra-
tion of the selector, cS, in the eluent as
(19) Burkey, T. J.; Griller, D.; Lindsay, D. A.; Scaiano, J. J. Am. Chem. Soc. 1984,
196, 1983–1985
(20) Yang, X.; Matthews, M. A. J. Colloid Interface Sci. 2000, 229, 53–61
(21) Clark, S. M.; Leaist, D. G.; Konermann, L. Rapid Commun. Mass Spectrom.
2002, 16, 1454–1562
(22) Clark, S. M.; Konermann, L. J. Am. Soc. Mass Spectrom. 2003, 14, 430–
441
(23) Bello, M. S.; Rezzonico, R.; Righetti, P. G. Science 1994, 266, 773–776
(24) Sharma, U.; Gleason, N. J.; Carbeck, J. D. Anal. Chem. 2005, 77, 806–
813
(25) d’Orlye´, F.; Varenne, A.; Gareil, P. J. Chromatogr., A 2008, 1204, 226–
232
(26) Le Saux, T.; Cottet, H. Anal. Chem. 2008, 80, 1829–1832
(27) L´stergaard, J.; Jensen, H. Anal. Chem. 2009, 81, 8644–8648
.
.
.
cLS
cL
tLS
tL
Kcs )
)
(4)
.
.
.
Under the experimental condition the selector is in large
excess over the ligand and can therefore be approximated by total
selector concentration in the mobile phase (amount of selector,
.
.
.
(28) Jensen, H.; L´stergaard, J. J. Am. Chem. Soc. 2010, 132, 4070–4071
.
(29) Lewicz, B. G. Fiz-Khim. Gidrodin., G.I.F-M. 1959, 123–127, Moskwa.
5464 Analytical Chemistry, Vol. 82, No. 13, July 1, 2010

which fills the whole capillary (1.4 mililiters), is much higher than
ligand injected in a small volume of 10 µL). Finally we find from
eqs 3 and 4 that
thermostat. The binding constants obtained as a result of these
-32
experiments were calculated as presented earlier.30
Materials and Solutions. Bovine serum albumin (BSA) was
purchased from Across Organics (NJ). Warfarin, propranolol,
(S,R)-noscapine base, (-) riboflavin, 4-nitrophenol, ortho-phos-
phoric acid (H3PO4), and alpha, alpha, alpha-tris-(hydroxy-
methyl)-methylamine (Tris) were purchased from Sigma-
Aldrich Chemie (Steinheim, Germany). ꢀ-Cyclodextrin (ꢀ-CD)
came from Chinoin (Budapest, Hungary). Salicylic acid and
potassium nitrate (KNO3) were from POCH (Gliwice, Poland).
Experiments. Precision Procedure. The PEEK capillary length
was measured on a tube with known diameter. The dry PEEK
capillary was connected to the end of the stainless steel capillary
of the sampling device. Next the capillary was filled with a mobile
phase. The PEEK capillary volume was measured by the time of
the capillary filling. The pump mass outflow and mobile phase
density were also measured. The dimensions of the stainless steel
capillaries connected to the sampling device and the detector were
taken from their specification and added to the capillary length
and the volume of the PEEK capillary. The obtained total volume
value was verified by experimental determination of the time of
filling the capillary with the KNO3 solution. The total capillary
length was 2749.8 cm and the total capillary volume was 1.3775
cm3, as obtained from both the calculation and the calibration
experiments. These values were used in all further experiments
and calculations.
DL + DLSKcS
1 + KcS
Deff
)
(5)
The molecular diffusion of ligand L, is much larger than the
diffusion coefficient of S (DL . DS) if the selector S is a
macromolecule much larger than the ligand L. Therefore the
diffusion coefficient of the L:S complex can be approximated
by the diffusion coefficient of the selector S, DLS ) DS. In our
experiment with albumin DL and DS are first determined in
two separate experiments, where a single substance is used
such as L or S separately. In this case Deff = DL or DS.
Summarizing the theoretical consideration: from the experi-
ment we determine P(t). Using eq 1 we obtain the dispersion
coefficient σ from P(t). In the framework of the Taylor theory we
get the effective diffusion Deff from σ according to eq 2. Deff
depends on the equilibrium constant as given in eq 5. Thus
our method allows to determine the appropriate equilibrium
constants from the dependence of Deff on the molar concentration
cS. The Taylor condition for the applicability of our technique
can be written as follows:
The mobile phase was prepared using an 18 mM Tris solution
adjusted to pH 7.4 with H3PO4. The stock solution of KNO3 was
prepared by dissolving 10 mg of salt in a 10 mL volumetric
flask with the mobile phase. For measurements the stock
solution was diluted 10 times by the mobile phase. The sample
of KNO3 (0.1 mg/mL, 1 mM) was injected into the capillary.
The injected volume was 5, 10, and 20 µL and all experiments
were repeated three times. The UV absorbance was measured
at 220 nm wavelength.
LDeff
> >1
(6)
R2u
In all cases studied here the range of LDeff/R2u values is between
9.5 (for albumin) and 147 (for KNO3). Therefore the condition
is satisfied in our experiments.
EXPERIMENTAL SECTION
Apparatus. Our experiments were performed using a Waters
(Vienna, Austria) HPLC pump model 515 and autosampler model
717 plus. The PEEK (polyether ether ketone) capillary was
Experiments with BSA and Ligands. Three different pH were
chosen: pH 7.4, 4.8, and 3.0. The buffer solution was prepared
using 18 mM Tris solution adjusted to the appropriate pH with
thermostatted at 25
0.2 °C by a WO Industrial Electronics
H
3PO4. The albumin, propranolol and riboflavin samples were
(Langenzersdorf, Austria) Jetstream 2 thermostat. The absorbance
was measured by Waters UV VIS detector model 2487 and
recorded by PC computer using Empower Pro build number 1154
software (Empower Software Waters Corporation).
For almost all experiments the flow rate was 0.05 mL/min and
the injection volume was 10 µL. For experiments of the precision
procedure the flow was 0.1 mL/min and the injection volume was
5, 10, and 20 µL.
We applied standard chromatography to the system of 4-ni-
trophenol with cyclodextrin and compared the obtained equilib-
rium constants to the ones obtained in our method based on the
effective diffusion coefficient. We used the Waters (Vienna,
Austria) model 590 pump, a Rheodyne type injector with 5 µL
loop and a Waters UV VIS detector model 490 (detection: 254
nm). The mobile phases were water ethanol mixture (90:10 v/v)
with the appropriate concentration of CDs (concentration range
5 × 10-5-1.5 × 10-2 M). We used the column Luna 5 µ C18(2)
100A 150 × 1 mm, Phenomenexs (Aschaffenburg, Germany).
studied in all three pH. The salicylic acid and warfarin samples
were studied only at pH 7.4 and noscapine only at pH 3.0. The
samples were dissolved in the appropriate Tris solution and
injected (three times each) into the capillary with the same
Tris solution as the mobile phase. The sample concentrations
were albumin, 2.3 × 10-5 M; propranolol, 9.6 × 10-5 M;
riboflavin, 3.3 × 10-5 M; salicylic acid, 9.9 × 10-5 M; warfarin,
9.7 × 10-5 M; noscapine, 6.1 × 10-5 M. The chemical formulas
for the model compounds are presented in Table 1. For the
albumin solution the absorbance was measured at 275 nm and
for the rest of the compounds at 308 nm.
To determine the BSA-ligand equilibrium binding constants,
a new mobile phase was prepared by dissolving BSA in the
appropriate Tris solution. For albumin warfarin complex we
prepared six solution of albumin in the concentration range 0-4.5
(30) Dodziuk, H.; Demchuk, C. M.; Bielejewska, A.; Kozminski, W.; Dolgonos,
G. Supramol. Chem. 2004, 16, 287–292
(31) Fujimura, K.; Ueda, T.; Kitagawa, M.; Takayanagi, H.; Ando, T. Anal. Chem.
1986, 58, 2668
(32) Terabe, S. J. Chromatogr., A 1994, 666, 295–319
.
The column was thermostatted at 25
Industrial Electronics (Langenzersdorf, Austria) Jetstream 2
0.2 °C by a WO
.
.
Analytical Chemistry, Vol. 82, No. 13, July 1, 2010 5465

Table 1. Diffusion Coefficients and Stability Constants for Studied Compounds and BSA Complexes SD Standard
Deviation, RSD Relative Standard Deviation (*, data taken from ref 16)a
a SD standard deviation, RSD relative standard deviation (*- data taken from ref 16). Experimental conditions: for the free compoundssmobile
phase was 18 mM Tris at pH as in table, for complex studysmobile phase was 9.0 × 10-5 M or 4.5 × 10-5 M BSA (see Experimental Section) in
18 mM Tris at pH as shown in the table. Detection was 275 nm for albumin and 308 for the rest studied systems. Flow 0.05 mL/min. Temperature
25 0.2 °C.
× 10-5 M. For the rest of compounds single concentration
experiment was done (concentration of BSA 9.0 × 10-5 M for
pH 7.4 and 4.8 and 4.5 × 10-5 M for pH 3.0). The absorbance
was measured at 308 nm.
the column for the comparative chromatographic experiment)
with the appropriate mobile phase. The absorbance was
measured at 254 nm.
Calculations Applied to the Experiment. The concentration
distribution of ligand is given by eq 1. After correcting eq 1 for
the finite injected volume of the sample33 we get
We also injected warfarin into serum of blood and observed a
clear peak from warfarin. Serum was 20 times dissolved by Tris
solution pH 7.4 and used as the mobile phase for warfarin sample.
Experiment with 4-Nitrophenol and Cyclodextrin. The mobile
phases in these experiments were a water-ethanol mixture (90:
10 v/v) with concentrations of CDs in the range 0-2 × 10-2 M.
We prepared eleven such solutions Additionally only for TDA
analysis seven solution of CD in phosphate buffer pH 7.3 were
prepared in concentration range 0-1.6 × 10-2 M. The samples
of 4-nitrophenol were prepared by dissolving 2.8 mg in 25 mL
of each mobile phase and injected into the capillary (or into
(L - u · t + m1)2
2(2σ · t + m2)
1
Ah
P(t)c )
exp -
(7)
[
]
√
2π 2σ · t + m
√
2
where the injection length in the capillary is h ) (νinj/νcap)L, where
Vinj is the injection volume, Vcap is the volume of the capillary,
L is its length and (m1), (m2) are corrections for the rectangular
injection. These corrections are related to h and given by the
5466 Analytical Chemistry, Vol. 82, No. 13, July 1, 2010

formulas m1 ) h/2 and m2 ) h2/12. Finally we rewrite eq 6
with these formulas included:
6(L - u · t + h/2)2
(24σt + h2)
√
2π
2 3
√
Ah
P(t)c )
exp -
[
]
2
√
24σt + h
(8)
where h is calculated from the injection volume and the only fitting
parameters are: the amplitude A, the velocity u and the dispersion
coefficient σ given by eq 2.
The data were collected at times ti from ti = 1 s up 40 min
with∆t ) 1 s time step. The absorbance was measured in the
10 µL absorbance cell for which the filling time is 12 s with
0.05 mL/min flow. The detector integrates the signal given by
eq 8 over 12 consecutive seconds and therefore the measured
absorbance is given by:
i
AU(ti) ) ∑ P(ti)
(9)
i-12
where the times ti - ti-1 ) 1 s. Additionally the absorbance
signal is recorded after a 1 s RC filter. The fit was performed
only for AU larger than 0.5 AUmax. The absorbance was
recorded at constant wavelength. Zero drift of the detector
signal was corrected before fitting. The number of points used
for fitting depended on the width of the peak and changed in
our experiments from 68 to 253. Least square fitting was
performed. The fitting procedure was done using the Microsoft
Excel Office 2007 solver.
Figure 1. The peaks obtained for warfarin in Tris solution, albumin
in Tris solution and warfarin in Tris solution with albumin (each
measurements were repeated three times) The peaks of warfarin
obtained in Tris solution and in 20× diluted serum. Experimental
conditions: (A) for peaks 1 and 2-mobile phase was 18 mM Tris pH
7.3, for 3-mobile phase was 9.0 × 10-5 M BSA in 18 mM Tris pH
7.3, B) for 1-mobile phase was 18 mM Tris pH 7.3, for 2-mobile phase
was serum 20× diluted with 18 mM tris pH 7.3. Detection was 275
nm for albumin and 308 nm for the rest studied systems. Flow 0.05
mL/min. Temperature 25 ( 0.2 °C.
RESULTS AND DISCUSSION
Precision of Molecular Diffusion Coefficient Measure-
ments. The objective of the procedure was to assess the precision
with which we measured the diffusion coefficients. The molecular
diffusion coefficient of KNO3 was determined for three different
injection volumes of 5, 10, and 20 µL, each measured three
times. The determined mean σ was 2.32 cm2s-1 with the
standard deviation (SD) 0.08 cm2s-1 and relative standard
deviation (RSD) 3.4%. The molecular diffusion coefficient for
KNO3 was 1.60 × 10-5 cm2s-1 with (SD) equal to 5.0 × 10-7
cm2s-1. Thus the relative standard deviation (RSD, %) was 3.4%.
From literature data the diffusion coefficient of KNO3-H2O
solution at 25 °C measured on the volume fixed frame of
reference over the concentration range 0.025-2.61 M de-
creased from 1.928 × 10-5 to 1.166 × 10-5 cm2 ·s-1 as the
concentration increased.34 Our value of 1.6 × 10-5 cm2 ·s-1
measured in a Tris buffer was well inside the range of the
literature values.
Albumin and Drugs. The interaction between albumin and
small drug molecule was determined in three experiments. From
the first two experiments we obtained the molecular diffusion
coefficient of the drug DL and the albumin DS. In the last
experiment we determined the effective diffusion coefficient
Deff of the drug (eq 5) with the albumin present in the mobile
phase.
The experimental peaks obtained for albumin, warfarin and
warfarin with albumin are presented in Figure 1A. In Figure 1B
the peak of warfarin obtained in 20 times diluted serum is
presented. The experiment showed a possibility to use the method
in medical analysis of blood samples; for example to predict
concentration of the free drug in the serum. Additionally typical
fits and errors are presented in Figure 2.
For all the studied compounds the stability constant was
determined from eq 5, assuming that DLS=DS which is reasonable
providing that the ligand L is much smaller than the selector
S (albumin). The results, for warfarin, obtained for a single
concentration (K ) 1.35 × 105 M-1) are in good agreement
with a measurement for various concentration of albumin
(K ) 1.40 × 105 M-1). This comparison proves that for the
single concentration experiment good concentration range was
chosen. However we suggest to use caution when calculating
Study of Molecular Interaction. Two types of selectors were
chosen: albumin and cyclodextrin. Serum albumin is an abundant
plasma protein that plays an important role in transporting
compounds in blood plasma.1 The most characteristic property
of cyclodextrin is its remarkable ability to form inclusion com-
plexes with various organic and inorganic compounds.35
(33) Alizadeh, A.; Nieto de Castro, C. A.; Wakeham, W. A. Int. J. Thermophys.
1980, 1, 243
.
(35) Dodziuk, H. Cyclodextrin and Their Complexes; Chemistry, Analytical methods,
Application; John Wiley & Sons: Weinheim, 2006.
(34) Daniel, V.; Albright, J. G. J. Solution Chem. 1991, 20, 633–642
.
Analytical Chemistry, Vol. 82, No. 13, July 1, 2010 5467

Figure 3. Deff as a function of selector concentration, experimental
points and fitted plots for eq 5 (A) for warfarin-BSA complex (B) for
4-nitrophenol-CD complex. Experimental conditions: flow 0.05 mL/
min, temperature 25 ( 0.2 °C (A) mobile phase 18 mM Tris with
appropriate concentration of BSA (B) mobile phase 90:10 v/v water:
ethanol mixture with appropriate concentration of CD.
Figure 2. (A) The absorbance measured at the end of 25 m capillary
by UV detector 308 nm for the warfarin-BSA complex together with
theoretical fit. (B) The difference between measured and fitted
absorbance Experimental conditions: mobile phase was 9.0 × 10-5
M BSA in 18 mM Tris pH 7.3. Flow 0.05 mL/min Temperature 25 (
0.2 °C.
Cyclodextrin with 4-Nitrophenol. The cyclodextrin complex
with 4-nitrophenol was studied first by the standard chromato-
graphic method. The data were analyzed by the model described
earlier.39-41 The stability constant K was fitted by the nonlinear
least-squares procedure according to the following equation:
binding constants using data generated at a single concentra-
tion of substrate and ligand. In our case it did not appear to
introduce significant error. However it can introduce significant
error if the location of the data point on the binding isotherm
is not known. You need to understand your system before you
can assume that the single point is appropriate.36 The experi-
mental points and fitted curve are presented in Figure 3A. All
results are presented in Table 1. Results obtained from the
literature are also presented.16
K1[CD]
K1K2[CD]2
K1K2K3[CD]3
1
1
k0
)
+
+
+
+
k1
k0
k0
k0
(10)
We used three different pH, below, above and at the isoelectric
point of BSA. The diffusion coefficient of BSA depends slightly
on pH. Such dependence may be caused by the changes of
conformation of albumin induced by the pH shift.37 The value of
the molecular diffusion coefficient found from our data ranged
from 7.3 to 9.7 × 10-7 cm2s-1 depending on pH. In the literature
this diffusion coefficient depends on pH, ionic strength and
concentration of albumin and varies38 between 4.9 × 10-7
where k0 is the retention factor without cyclodextrin (CD) and
k1 is the retention with CD. The function of 1/k1 versus CD
concentrations provides information on the stoichiometry and
stability constants of the complex. For the 4-nitrophenol
complex in 10% etanol-aquous solution in the studied range of
cyclodextrin concentration, 1:1 stoichiometry was found. The
stability constants K1 ) 108 11 M-1 were found from the
fitting procedure.
For our method, changes of the effective diffusion coefficient
Deff with growing concentration of CD was followed. The results
are shown in Figure 3B. The stability constant was fitted using
eq 5. The obtained diffusion coefficient for 4-nitrophenol and 1:1
complex with CD (in ethanol-water mixture 10:90 v/v) were 5.87
× 10-6 cm2 ·s-1 and 1.78 × 10-6 cm2 ·s-1 respectively (from
literature we found the diffusion coefficient for 4-nitrophenol
in aqueous equal to 6.92 × 10-6 cm2 ·s-1).42 The obtained
cm2s-1 and 9.5 × 10-7 cm2s-1
.
For propranolol, salicylic acid and riboflavin, the stability
constants for BSA complexes are 2 orders of magnitude lower
than the BSA-warfarin complex. Near the isoelectric point of BSA
the propranolol complex with BSA was not detected and for
riboflavin it was weaker than for pH 3.0 and 7.4. The complex of
noscapine and BSA was not detected at all. The results for warfarin
and salicylic acid are in good agreement with the literature data
at pH 7.4.
(39) Armstrong, D. W.; Nome, F. Anal. Chem. 1981, 53, 1662–1666
(40) Armstrong, D. W.; Gail, T. S. J. Am. Chem. Soc. 1983, 105, 2962–2964
(41) Armstrong, D. W.; Nome, F.; Spino, L. A.; Golden, T. D. J. Am. Chem. Soc.
1986, 108, 14
(42) Armstrong, D. W.; Ward, T. J. Anal. Chem. 1988, 58, 579–582
.
(36) Bowser, M. T.; Chen, D. D. J. Phys. Chem. 1998, 102, 8063–8071
(37) Peters, T., Jr. All about Albumin: Biochemistry, Genetics and Medical
.
.
Applications; San Diego, CA: Academic Press, 1996.
.
(38) Raj, T.; Flygare, W. H. Biochemistry 1974, 13, 3336–3340
.
.
5468 Analytical Chemistry, Vol. 82, No. 13, July 1, 2010

stability constant K1 ) 98 12 M-1 were in good agreement
ACKNOWLEDGMENT
This work was supported by the Foundation for Polish Science
“Team Programme” cofinanced by the EU European Regional
Development Fund TEAM/2008-2/2. R.H. acknowledges support
from the Foundation for Polish Science under the MISTRZ grant.
We also the financial support of the Polish Ministry of Science
and Higher Education (Grant No. N204 04432/1046).
with the results from the chromatographic method. However,
the literature values obtained from calorimetric study for 1:1
43
complex in aqueous solution were 350
50 M-1
)
which
seemed to disagree with our results. We found that the
difference between literature and our results was due to the
composition of the mobile phase which in our case contained
10% of ethanol and most probably the ethanol made also
complexes with cyclodextrin.44 Therefore we repeated our
experiment without ethanol in the phosphorus buffer pH 7.3.
For this buffer the diffusion coefficients for 4-nitrophenol and
1:1 complex with CD were 7.58 × 10-6 cm2 ·s-1 and 2.38 × 10-6
cm2 ·s-1, respectively, and the stability constant was 276 40
GLOSSARY
u
R
L
average velocity
radius of the capillary
distance along the tube from the injection point to the
detection point
M
-1, well within the error bar of the literature data.
t
tL
time
CONCLUSION
time of flowing as a free L
Our method allows to study ligand-selector interaction in a
solution. Various solvents with various selectors can be used.
There is no need to use derivatives of the reagents. Compounds
can be neutral or charged. The range of stability constants
measured using the method was between 102 and 105 M-1. For
fast search of ligand-protein interaction even one point analysis
(single concentration) gives sufficient information about various
ligands affinity to the protein. However we suggest to use
caution when calculating binding constants using data gener-
ated at a single concentration of substrate and ligand. In our
case it does not appear to introduce significant error. However
it can introduce significant error if the location of the data point
on the binding isotherm is not known. Additionally the study
of Deff as a function of selector concentration gives the
possibility to measure even low stability constants with reason-
able small errors as we show in the manuscript (for 4-nitro-
phenol cyclodextrin in ethanol-water mixture 10:90 v/v K )
98 12 M-1). Our additional experiments with human serum
and warfarin demonstrate that technically the method can be
used in medical analysis of blood samples.
tLS
tF
P(t)
σ
Deff
time of flowing as a complex L:S
tL + tLS
the concentration distribution
dispersion coefficient
effective diffusion coefficient obtained from the experi-
ment according to eq 2
molecular diffusion coefficient of ligand
molecular diffusion coefficient of selector
molecular diffusion coefficient of complex
equilibrium constant
DL
DS
DLS
K
xL, xLS
cS
molar fraction of free, and bound ligands
molar concentration
the injection length in the capillary h ) (νinj/νcap)L
injection volume
h
Vinj
Vcap
m1,m2
volume of the capillary
corrections for the rectangular injection, are given by
the formulas m1 ) h/2 and m2 ) h2/12
Received for review December 2, 2009. Accepted May 30,
2010.
(43) Bertrand, G. L.; Faulkner, J. R., Jr; Han, S. M.; Armstrong, D. W. J. Phys.
Chem. 1989, 93, 6863–6867
(44) Matsui, Y.; Mochida, K. Bull. Chem. Soc. Jpn. 1979, 52, 2808–2811
.
.
AC1008207
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