ELSEVIER
JOURNALOF
IMMUNOLOGICAL
METHODS
Journal of Immunological Methods 168 (1994) 227-234
Effect of antibody density on the displacement kinetics
of a flow immunoassay
S i n a Y. R a b b a n y a, A n n e W . K u s t e r b e c k b, R e i n h a r d B r e d e h o r s t c,
F r a n c e s S. L i g l e r .,b
a Bioengineering Program, Department of Engineering, Hofstra University, Hempstead, NY 11550, USA, b Centerfor Bio ~Molecular
Science and Engineering, Code 6900, Naval Research Laboratory, Washington, DC 20375-5320, USA, c Department of Biochemistry
and Molecular Biology, University of Hamburg, Hamburg, Germany
(Received 19 July 1993, revised received 4 October 1993, accepted 4 October 1993)
Abstract
This study investigates the effect of antibody density on the kinetics of a solid-phase displacement immunoassay.
Conducted in flow under nonequilibrium conditions, the assay utilizes a monoclonal antibody to the cocaine
metabolite benzoylecgonine, which has been immobilized onto Sepharose beads and saturated with fluorophorelabeled antigen. Displacement of antibody-bound labeled antigen by non-labeled antigen occurs when sample is
introduced in the buffer flow. Comparison of matrices coated with two different antibody densities revealed that the
displacement efficiency is a function of the density of antibody-bound labeled antigen. A higher density of antibody
provides a higher amount of displaced labeled antigen, but the displacement efficiency of the assay is decreased. The
effect of antibody density on the immunoassay kinetics was analyzed using a mathematical formulation developed to
characterize antibody-antigen interactions at solid-liquid interfaces. Higher antibody density proved to be associated
with a lower apparent dissociation rate constant. The implications of these results on the design of immunoassays in
flow are discussed.
Key words: Biosensor; Displacement immunoassay; Antibody kinetics; Solid-phase immunoassay
1. Introduction
Recently, we introduced a flow immunoassay
which detects picomole quantities of low molecular weight antigens within seconds of sample injection (Kusterbeck et al., 1990). The specificity
* Corresponding author. Tel.: (202) 767-1681; Fax: (202) 7671295.
of the assay for the detection of cocaine and its
major metabolite benzoylecgonine was demonstrated (Ogert et al., 1992). In this assay, immobilized antibody is saturated with fluorophorelabeled antigen and placed in a buffer flow. When
unlabeled antigen is introduced, a proportional
amount of fluorophore-labeled antigen is displaced from the binding sites of immobilized antibodies and subsequently detected downstream.
Concentrations of cocaine as low as 5 ppb (5
ng/ml) could be detected in less than 1 min.
0022-1759/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved
SSDI 0022-1759(93)E0260-0
228
S.Y. Rabbany et al. /Journal of Immunological Methods 168 (1994) 227-234
The kinetics of antigen binding in the flow
immunoassay differ fundamentally from those described for fluid phase systems and solid-phase
ELISA-type assays. Therefore, we developed a
theoretical framework describing antibody-antigen interactions at solid-liquid interfaces under
non-equilibrium conditions of the flow immunoassay to evaluate the importance of individual
assay parameters (Rabbany et al., 1992; Wemhoff
et al., 1992).
In this study, we investigate the effect of antibody density on the nonequilibrium kinetics of
the flow immunoassay in order to develop a theoretical basis for an optimal assay design. By increasing the density of immobilized antibodies
and, concomitantly, the concentration of antibody-bound labeled antigen, we alter the probability of unlabeled antigen displacing the labeled
antigen. Using two matrices coated with different
antibody densities, we analyzed the displacement
efficiency and the apparent dissociation constant
at different flow rates.
2. Materials and methods
2.1. Preparation of immunoassay columns
Antibody immobilization. A monoclonal antibody
specific for both cocaine and its major metabolite, benzoylecgonine, was obtained as ascites from
Biodesign (Kennebunkport, ME). A 10 mg membrane affinity separation system (MASS) cartridge (Nygene, Yonkers, NY) was used to isolate
the IgG fraction from the ascites, as described
previously (Wemhoff et al., 1992). Different densities of the IgG anti-benzoylecgonine antibody
were immobilized on tresyl chloride-activated
Sepharose 4B (Pharmacia, Piscataway, N J) using
the following protocol. Tresyl chloride-activated
Sepharose 4B gel was suspended in 1 mM HC1
and washed with approximately 200 ml of 1 mM
HCI/g dry powder. Two concentrations of antibody, 1.0 mg of antibody/g dry Sepharose gel
and 0.5 mg of antibody/g dry Sepharose gel,
were prepared separately in 5 ml of coupling
buffer (0.1 M NaHCO 3 with 0.5 M NaC1).
Aliquots of freshly washed, activated Sepharose
were added to the antibody solutions and incubated overnight with rocking in a stoppered vessel at 4°C. Uncoupled antibody was removed with
coupling buffer and any remaining reactive groups
were blocked by incubating with excess 0.1 M
Tris-HCl, pH 8.0, for 4 h at 4°C (Bredehorst et
al., 1991). The gel was washed with three cycles
of alternating buffers consisting of: (i) 0.1 M
acetate buffer, pH 4.0 containing 0.5 M NaC1,
and (ii) 0.1 M Tris buffer, pH 8.0 containing 0.5
M NaCI. The amount of antibody coupled to the
Sepharose 4B was measured with a dye-binding
assay for immobilized proteins (Ahmad and
Saleemuddin, 1985). The high and low antibody
density Sepharose had 3.9-4.9 pmol and 0.8-1.0
pmol antibody immobilized on 1.0 mg of gel (approximately 4 ml of hydrated gel), respectively.
Fluorophore-labeled antigen preparation. The fluorophore-labeled antigen was synthesized as described previously (Wemhoff et al., 1992). The
starting materials, benzoylecgonine hydrate and
fluorescein cadaverine, were obtained from Sigma
Chemical Co. (St. Louis, MO) and Molecular
Probes (Eugene, OR), respectively. The concentration of fluorophore-labeled benzoylecgonine
was calculated by comparison to a standard curve
depicting the absorbance at 490 nm of a known
concentration of fluorescein cadaverine.
Flow immunoassay. Antibody-coated Sepharose
and a 100-fold molar excess of fluorophorelabeled antigen to immobilized antibody were
incubated at 4°C. For each experiment, a 50 mg
aliquot of the Sepharose matrix was dispensed
into a small, disposable column (Isolab, Akron,
OH) and phosphate buffer solution (PBS) was
pumped through to remove unbound fluorophore-labeled antigen. The column eluent was
monitored at an excitation of 490 nm and emission of 520 nm using a Jasco 821-FP fluorimeter
(Easton, MD) equipped with an 8 /xl flow cell.
When background fluorescence was less than 0.04
arbitrary fluorescence units, 200 jzl samples of
cocaine diluted in PBS to various concentrations
were introduced to the buffer flow. The samples
were in the midrange of the concentrations which
are measurable using these columns. Approxi-
S.Y. Rabbany et al. /Journal of Immunological Methods 168 (1994) 227-234
229
mately 1 ml of buffer was used to wash the
columns between samples. Ecgonine at a concentration of 1 /zg/ml was also injected as a negative control. A Hewlett Packard integrator (Palo
Alto, CA) was used to record all data and quantify peaks.
where the [loaded Ag] was constant during the
repetitive displacement experiments (Wemhoff et
al., 1992). The effect of antibody density at different flow rates on the apparent dissociation constant (k d) was analyzed by the following equation:
Repetitive displacement experiments. For analysis
kd
of the kinetics of the displacement reaction,
columns containing Sepharose 4B-immobilized
antibody specific for both cocaine and its major
metabolite, benzoylecgonine were prepared. After saturation of the antigen-binding sites with
fluorophore-labeled benzoylecgonine, the total
amount of labeled Ag* bound to the immobilized
antibody ([bound Ag*]t= 0) was determined by
repeated injections of large amounts of cocaine
samples (100-fold molar excess of cocaine to immobilized antibody). Identical amounts of cocaine
were injected repeatedly into the buffer flow and
the fluorescence of the displaced labeled antigen
was measured until the column was depleted of
labeled antigen.
For each density of immobilized antibody, the
density of active antibody was determined by
measuring the amount of displaceable labeled
antigen. All calculations are relative to this value
which is independent of any denatured or inactive antibody.
3. Mathematical analysis
The undissociated fraction of labeled antigen
was calculated from the difference between total
bound labeled antigen and the amount displaced
after each addition of unlabeled antigen using the
following relation:
[bound Ag*] - [displaced Ag*]
0=
[bound Ag* ]t=0
(1)
where Ag* represents the amount of displaceable labeled antigen and the denominator represents the concentration of Ag* initially bound to
the column. The displacement efficiency (D e) is
described by the relationship:
[displaced Ag* ] 1
De =
[loaded Ag]
"O
(2)
In 0
t
(3)
where the time period available for displacement
(t) was determined by dividing the volume of the
column containing the immobilized antibody by
the flow rate. The term "apparent" dissociation
reflects the fact that the constant is calculated
from the amount of labeled antigen released from
the column. This constant is a function not only
of the actual k d of the antibody but also of other
factors such as nonspecific binding and accessibility of the antigen-binding sites.
4. Results
4.1. Determination o f undissociated fraction
Fig. 1 depicts the labeled antigen released
from the matrices coated with different densities
of antibody. The upper panel illustrates the actual fluorescence signal released upon repeated
addition of antigen, whereas the lower panel depicts the calculated values for the undissociated
fraction (0) plotted as a function of the number
of injections for the first ten injections at equimolar antigen-antibody concentrations. Neither column was depleted of more than 60% of the
labeled antigen after ten injections. Using the
1 : 1 molar ratio of loaded unlabeled antigen per
immobilized antibody, different slopes were observed for the two matrices. The exponential decrease of the undissociated fraction occurred
faster on the low density matrix, suggesting an
inverse relationship of antibody density and the
rate of labeled antigen depletion.
When the amount of displaced labeled antigen
was normalized against the amount of loaded
unlabeled antigen, a more complex relationship
between antibody density and assay kinetics
emerged. Using the low density matrix, the
S.Y. Rabbany et aL /Journal of Immunological Methods 168 (1994) 227-234
230
8"
•
O
E
~o
High Density
6"
~
3
4-
0.02
0.01
2~5
0
¢-
.g
0.9"
1
2
3
4
"~
"0
e-
0,5"
0.4"
0.3
0
7
8
9
10
Fig. 2. Comparison of assay response with different antibody
density. Shown is the repetitive displacement of labeled antigen from a high and a low antibody density matrix. The
experimental calculations are identical to those described in
Fig. 1. The assay response is expressed as a ratio of displaced
labeled antigen to loaded unlabeled antigen. The data represent the mean of two experiments.
LL
"0 0.7"
0.6"
6
Injection Number
0.8"
~
5
.
,
2
•
,
4
-
,
6
,
8
•
,
10
12
Injection Number
Fig. 1. Effect of antibody density on the displacement of
labeled antigen (upper panel) and undissociated fraction, 0
(lower panel). Samples of cocaine were injected repeatedly at
a flow rate of 0.75 m l / m i n into 200/zl columns containing 50
pmol or 245 pmol of immobilized anti-cocaine antibody. The
concentration of cocaine in the samples was equivalent to the
concentration of immobilized antibody. The data represent
the m e a n + SE of two experiments.
amount of labeled antigen displaced upon the
first injection of unlabeled antigen was two-fold
higher than that from the high density matrix
(Fig. 2). Upon the second injection of unlabeled
antigen, however, the amounts of displaced labeled antigen were almost identical for both matrices. Subsequent injections displaced larger
amounts of labeled antigen from the high density
matrix.
4.2. Effect of density on displacement efficiency
Using the high density matrix, the relatively
low displacement efficiency of the first injection
increased by a factor of two upon the second
injection step (Fig. 3). For subsequent injection
steps, a slight decrease of the displacement efficiency was observed, most likely due to a gradual
depletion of antibody-bound labeled antigen. For
the low density matrix, the calculated displacement efficiency of the first injection was two to
three-fold higher than that of high density matrix.
0.04
0.75 ml/min
O
C
--0
::1=
W
0.03
"~
0.02
E
0
~t~.
o.o~
~ L o w
Density
a
0.00
2
'~
"
6
"
~
'10"12
Injection Number
Fig. 3. Effect of antibody density on displacement efficiency.
Samples of cocaine were injected repeatedly at a flow rate of
0.75 m l / m i n into a column containing matrix with a low or
h i g h density of immobilized antibody. For experimental details see Fig. 1. The displacement efficiency was calculated
using Eq. 2. T h e data represent the m e a n of two experiments.
S.Y. Rabbany et aL /Journal of Immunological Methods 168 (1994) 227-234
Beginning with the third injection step, however,
the displacement efficiency decreased sharply as
a result of rapid depletion of antibody-bound
labeled antigen.
4.3. Effect of flow rate
0.5 ml/mln
0.03
0.02
t""
o.o~
0.4
i
0.2
i
0.0
0
2'0
40
60
80
100
Time (sec)
Fig. 5. A p p a r e n t dissociation constant ( k d) as a f u n c t i o n o f
a n t i b o d y density. T h e undissociated f r a c t i o n ( 8 ) calculated in
Fig. 1 for the low and high antibody density matrices is
plotted as - I n 0 versus time.
~o
4.4. Calculation of apparent dissociation constant
0.00
1.0 ml/min
0
~_
•
XD.,x_
Low Density
LU
EID
0.6
displacement efficiencies at the lower flow rate
and, accordingly, decreased displacement efficiencies at the higher flow rate. The depletion of
labeled antigen apparently alters the response of
the low density columns after the first four injections. At the higher flow rate, the displacement
efficiency for the low antibody density assay is
decreased due to reduction in the time period
available for displacement.
0.04
i-~
0.8-
~)
=
To evaluate the effect of different flow rates
on the displacement efficiency for low and high
density matrices, the same experiment, originally
performed at a flow rate of 0.75 ml/min, was
repeated at lower and higher flow rates (Fig. 4).
An increase of the flow rate to 1.0 ml/min, and a
decrease to 0.5 m l / m i n , caused significant
changes in the rate of labeled antigen release.
The high density column and the first four injections of the low density column show increased
231
0.03-
a
0.02 "
0.01
0.00
2
4
"
6
8
1(3
12
Injection Number
Fig. 4. Relationship of antibody density, flow rate, and displacement efficiency. Samples of cocaine were injected repeatedly at flow rates of 0.5 m l / m i n (upper level), and 1.0
m l / m i n (lower panel) into the high and the low antibody
density column as described in Fig. 1.
Taking the analysis further, we investigated
the effect of antibody density at different flow
rates on the apparent k d. Fig. 5 depicts - I n 0 as
a function of time, for both antibody densities, at
a flow rate of 0.75 ml/min. A linear relation was
observed for the first five consecutive injections.
Table 1 summarizes the values calculated from
the slope of - l n 0 versus time for these points at
three different flow rates. The data demonstrate
a reciprocal relationship between these two parameters and the density of immobilized antibody. An approximately five-fold increase in antibody density is associated with a two-fold decrease of the apparent dissociation constant. The
apparent k d values are dependent on both antibody density and flow rate. For the high antibody
density matrix, the apparent k d values are ap-
232
S.Y. Rabbany et al. /Journal of Immunological Methods 168 (1994) 227-234
Table 1
Relationship between antibodydensity, flow rate and apparent dissociation constant
Antibodydensity
Flow rate Apparentkd x 10 - 3
(ml/min)
(I/s)
Low density
0.5
4.5
0.75
8.0
1.0
10.0
High density
0.5
0.75
1.0
3.0
4.0
5.0
proximately two-fold lower than those obtained
for the low antibody density matrix. Furthermore,
an increase of the flow rate from 0.5 to 1.0
m l / m i n is associated with a two-fold increase of
the apparent k d values, independent of the density of immobilized antibodies.
5. Discussion
Immunological assays performed at solid-liquid
interfaces have increased in popularity in recent
years, since they provide a simple means of separating bound and free reactants. The density of
immobilized antibodies has been shown to play
an important role for antibody-antigen reactions
in ELISAs, performed under static conditions.
Coated microwells routinely used in ELISAs, with
high densities of immobilized antibody or antigen, favor rapid reassociation instead of diffusion
and transport away from the surface following
dissociation. One study demonstrated that even
in the presence of a large excess of free antigen
the dissociation of antibodies from surface immobilized antigen was negligible over a period of
approximately 3 days, although the affinity in
solution was in the range of 10 -8 M (Nygren et
al., 1985). These investigators observed that antibody binding can be so stable that the antibodyantigen reactions have been considered virtually
irreversible. This functionally irreversible nature
of antibody binding has been attributed primarily
to mass transport limitations (Stenberg and Nygren, 1988). In contrast to the very slow dissocia-
tion in ELISAs, the antibody-bound labeled antigen in the flow immunoassay is rapidly displaced
from the binding sites upon the introduction of
free antigen.
Several mechanisms may account for the discrepancy between antibody-antigen interactions
at solid-liquid interfaces in ELISA-type systems
versus the continuous flow system. The low surface density of the immobilized antibodies appears to be one mechanism contributing to the
discrepancy between antibody-antigen interactions in these systems. Assuming the smallest
possible surface area of the solid support in the
flow immunoassay columns, that of a perfectly
smooth sphere of approximately 100/xm wet diameter (i.e., with no available internal surface
area), the surface density of antibody immobilized onto the Sepharose beads in a high density
column would be 3 x 10-14mol/cm z. This density is still 2-3 orders of magnitude lower than
that of approximately 10-12mol/cm 2 typically
found on ELISA microtiter plates (Stenberg and
Nygren, 1988). Assuming an average diameter of
10 n m / I g G molecule, the surface of microtiter
wells is completely covered with antibodies at a
density of 1 pmol I g G / c m 2 (Nygren et al., 1987).
Whereas maximally 1% of the external surface of
spherical Sepharose beads would be covered with
IgG molecules at a density of 30 f m o l / c m 2. If the
internal surface area of the Sepharose beads is
also considered for the calculations, the density
of immobilized antibodies in the flow immunoassay is several orders of magnitude lower than
those in ELISA type assays. As a result, the
probability of reassociation events is significantly
reduced in the flow immunoassay.
Under flow conditions, however, reassociation
of displaced antigen is not the only event that is
affected by the density of immobilized antibody.
A percentage of antibody-bound labeled antigen
is slowly washed off the column by the flow,
leaving some of the antibody-binding sites unoccupied. These unoccupied binding sites appear to
be capable of binding unlabeled antigen, thereby
reducing the available amount of unlabeled antigen for the displacement of labeled antigen as
the first sample is added to the column. Furthermore, they may also rebind displaced labeled
S.Y. Rabbany et al. /Journal of lmmunological Methods 168 (1994) 227-234
antigen, resulting in a reduced fluorescent signal.
Our data suggests that the low and high antibody
density matrices are affected to a different extent
by the unoccupied binding sites. Using the high
antibody density matrix, the displacement efficiency upon the first injection of unlabeled antigen was two to three-fold lower than that of the
low antibody density matrix. Four injection steps
were required to obtain displacement efficiencies
that are comparable to that of low density matrix.
One explanation for the different effect of unoccupied binding sites on the performance of low
and high antibody density matrices may be that
the binding efficiency of unlabeled antigen by
unoccupied antibody binding sites is more a function of the density than of the absolute number of
unoccupied binding sites. Furthermore, the local
antibody densities of the two matrices used in this
study could differ by a factor far beyond five.
Studies from other laboratories provide support
for the formation of antibody clusters (patches)
upon immobilization onto solid supports (Werthern and Nygren, 1988; Schramm and Paek,
1992). Accordingly, local densities of antibody
binding sites on the two antibody matrices could
be very different.
To allow for an improved design of the flow
immunoassay, understanding of the dynamics of
the relationship between antibody density and
flow rate is critical. Both matrices exhibited an
inverse relationship between displacement efficiency and flow rate. For the first four injections,
the low antibody density matrix appears to be
more affected by an increased flow rate than the
higher antibody density matrix. Therefore, to optimize assay performance, parameters such as
antibody density and flow rate must be carefully
chosen. Furthermore, calculation of the apparent
dissociation constant will enable development of
an assay such that the sensitivity falls within the
selected detection threshold. For example, low
antibody density matrices are preferable if a high
detection sensitivity is the most critical factor and
columns are used for only a few analyses. If a
flow immunoassay column is used to analyze many
samples containing antigen, high antibody density
matrices are preferable due to the slow depletion
of labeled antigen.
233
In summary, this study reveals a complex relationship between antibody density, flow rate and
apparent dissociation constant. Additional factors
known to influence the performance of the flow
immunoassays including antibody affinity, antibody immobilization procedures, and effects of
the solid phase, such as nonspecific adsorption of
displaced labeled antigen, remain to be analyzed.
A detailed analysis of all these factors is necessary to allow for the development of a unified
mathematical framework capable of considering
the individual characteristics of the assay in question and predicting the response to a given sample.
6. Acknowledgements
The authors wish to thank Dr. Greg Wemhoff
and Mr. Bob Ogert for their assistance in the
data collection. Dr. Sina Y. Rabbany is the recipient of the American Society for Engineering
Education Summer Faculty Research Award at
the Center for Bio/Molecular Science and Engineering, Naval Research Laboratory. This work
was supported by the Office of Naval Research
through the Naval Research Laboratory. The
views expressed here are those of the authors and
do not represent those of the US Navy or the
Department of Defense.
7. References
Ahmad, H. and Saleemuddin, M. (1985) A Coomassie Bluebinding assay for the microquantitation of immobilized
proteins. Anal. Biochem. 148, 533-541.
Bredehorst, R., Wemhoff, G.A., Kusterbeck, A.W., Charles,
P.T., Thompson, R.B., Ligler, F.S. and Vogel, C.-W. (1991)
Novel trifunctional carrier molecule for the fluorescent
labeling of haptens. Anal. Biochem. 193, 272-279.
Kusterbeck, A.W., Wemhoff, G.A., Charles, P., Bredehorst,
R. and Ligler, F.S. (1990) A continuous flow immunoassay
for rapid, sensitive detection of small molecules. J. Immunol. Methods 135, 191-197.
Nygren, H., Czerkinsky, C. and Stenberg, M. (1985) Dissociation of antibodies bound to surface-immobilized antigen.
J. Immunol. Methods 85, 87-95.
Nygren, H., Werthen, M. and Stenberg, M. (1987) Kinetics of
antibody binding to solid-phase-immobilised antigen. J.
Immunol. Methods 101, 63-71.
234
S.Y. Rabbany et al. /Journal of lmmunological Methods 168 (1994) 227-234
Ogert, R.A., Kusterbeck, A.W., Wemhoff, G.A., Burke, R.
and Ligler, F.S. (1992) Detection of cocaine with a flow
immunosensor. Anal. Lett. 25, 1999-2019.
Rabbany, S.Y., Wemhoff, G., Kusterbeck, A.W., Bredehorst,
R. and Ligler, F.S. (1992) Kinetics of antibody binding in a
flow immunosensor. FASEB J. 5, 6242.
Schramm, W. and Paek, S.-H. (1992) Antibody-antigen complex formation with immobilized immunoglobulins. Anal.
Biochem. 205, 47-56.
Stenberg, M. and Nygren, H. (1988) Kinetics of antigen-anti-
body reactions at solid-liquid interfaces. J. Immunol Methods 113, 3-315.
Wemhoff, G.A., Rabbany, S.Y., Kusterbeck, A.W., Ogert,
R.A., Bredehorst, R. and Ligler, F.S. (1992) Kinetics of
antibody binding at solid-liquid interfaces in flow. J. Immunol. Methods 156, 223-230.
Werthen, M. and Nygren, H. (1988) Effect of antibody affinity
on the isotherm of antibody binding to surface-immobilized antigen. J. Immunol. Methods 115, 71-78.