Measuring binding of protein to gel-bound ligands using magnetic levitation

Article abstract of DOI:10.1021/ja211788e

This paper describes the use of magnetic levitation (MagLev) to measure the association of proteins and ligands. The method starts with diamagnetic gel beads that are functionalized covalently with small molecules (putative ligands). Binding of protein to

Full text of DOI:10.1021/ja211788e

Article
pubs.acs.org/JACS
Measuring Binding of Protein to Gel-Bound Ligands Using Magnetic
Levitation
Nathan D. Shapiro,† Katherine A. Mirica,† Siowling Soh,† Scott T. Phillips,† Olga Taran,†
Charles R. Mace,† Sergey S. Shevkoplyas,§ and George M. Whitesides*,†,‡
‡
†Department of Chemistry & Chemical Biology and Wyss Institute for Biologically Inspired Engineering, Harvard University,
Cambridge, Massachusetts 02138, United States
§Department of Biomedical Engineering, Tulane University, New Orleans, Louisiana 70118, United States
S
* Supporting Information
ABSTRACT: This paper describes the use of magnetic levitation (MagLev) to
measure the association of proteins and ligands. The method starts with
diamagnetic gel beads that are functionalized covalently with small molecules
(putative ligands). Binding of protein to the ligands within the bead causes a
change in the density of the bead. When these beads are suspended in a
paramagnetic aqueous buffer and placed between the poles of two NbFeB
magnets with like poles facing, the changes in the density of the bead on
binding of protein result in changes in the levitation height of the bead that can
be used to quantify the amount of protein bound. This paper uses a reaction−
diffusion model to examine the physical principles that determine the values of
rate and equilibrium constants measured by this system, using the well-defined model system of carbonic anhydrase and aryl
sulfonamides. By tuning the experimental protocol, the method is capable of quantifying either the concentration of protein in a
solution, or the binding affinities of a protein to several resin-bound small molecules simultaneously. Since this method requires
no electricity and only a single piece of inexpensive equipment, it may find use in situations where portability and low cost are
important, such as in bioanalysis in resource-limited settings, point-of-care diagnosis, veterinary medicine, and plant pathology. It
still has several practical disadvantages. Most notably, the method requires relatively long assay times and cannot be applied to
large proteins (>70 kDa), including antibodies. The design and synthesis of beads with improved characteristics (e.g., larger pore
size) has the potential to resolve these problems.
INTRODUCTION
■
Bioassays that involve the binding of proteins to resin-bound
small molecules are often used to screen for inhibitors of
proteins, and to identify cellular targets of bioactive small
molecules.1 On-bead binding assays are also used to determine
the concentrations of specific proteins in solutions.2 Current
methods for on-bead binding assays often use fluorescent or
radioactive labels to quantify the binding of a receptor to its
ligand.3 The installation and measurement of these labels
requires access to relatively expensive equipment and materials.
While these methods are very broadly useful, we believe that a
Figure 1. Schematic representation of the device and method based on
low-cost, label-free alternative would be valuable for specific
applications (for example, in point-of-care diagnosis, especially
in resource-limited environments).4
MagLev for detecting proteins binding to small molecules immobilized
on a diamagnetic bead. The device consists of two 0.4 T NdFeB
magnets oriented with like poles facing each other. A diamagnetic bead
suspended in a paramagnetic solution levitates in the presence of the
magnetic field when the gravitational force (Fg) acting on the bead is
balanced by the magnetic force (Fm). Binding of protein to the bead
alters its density, and thus its vertical position within the device.
This article describes a method for measuring the association
of proteins and ligands that uses magnetic levitation
(MagLev).5 The method employs porous diamagnetic beads
that are functionalized with covalently bound small molecules
(putative ligands). We suspend these diamagnetic beads in a
paramagnetic aqueous solution, which is placed in a cuvette
between two permanent NdFeB magnets oriented with like
poles facing each other (Figure 1). The balance of gravitational
and magnetic forces acting on the diamagnetic bead causes
beads within a range of densities to levitate; the density of the
bead determines its equilibrium position in the magnetic field.6
With an appropriate choice of bead, binding of protein to
Received: December 18, 2011
Published: February 24, 2012
© 2012 American Chemical Society
5637
dx.doi.org/10.1021/ja211788e | J. Am. Chem. Soc. 2012, 134, 5637−5646

Journal of the American Chemical Society
Article
ligands within the bead causes a change in the overall density of
the bead, and results in a change in the position at which it
levitates.6a
in the average density of the bead. (iv) Mass transport (i.e.,
diffusion) of protein through the gel-based bead is rate-limiting;
measurement of protein−ligand on- and off-rates is, therefore,
not possible. (v) The effective pore size of the gel must be
sufficiently large to allow protein in solution to partition into
the bead to a concentration that produces a perceptible change
in density.
This analytical method has the potential to be simple
operationally. The underlying physical chemistry is, however,
more complicated: it requires partitioning of protein from
solution into the bead, diffusion of protein within the bead, and
binding of the protein to the immobilized ligands.7 To examine
the fundamental principles that determine rates and equilibrium
constants as measured by this system, we have developed a
model that enables us to explore all of these characteristics.
This model generates data in the form of density of the bead
as a function of time. We use this model to define the range of
physical parameters (e.g., concentration of protein, and dis-
sociation constant of the protein−ligand complex) over which
we expect the assay to work. Detailed experimental work using
a model system supports the validity of this analysis and leads
to predictions about how the system may be improved.
The objective of this paper is to use physical−organic
strategies to characterize a MagLev-based analytical tool for
detecting protein and analyzing protein−ligand interactions,
rather than to prove the generality and limits of this method in
practical analysis. This study is thus aimed at describing the
fundamental processes by which the system operates, and
building an analytical model for it, with the goal of constructing
the physical−chemical foundation for future use in bioanalysis.
Our model system consists of poly[acryloylated O,O′-bis(2-
aminopropyl) polyethylene glycol] (PEGA) beads that are
covalently labeled with known inhibitors of bovine carbonic
anhydrase (BCA; EC 4.2.1.1). We levitate these beads in
solutions of BCA and monitor the change in levitation height
and hence the change in density of the beadsover time, as
protein binds to the beads. We explain the observed kinetics
using a reaction−diffusion model, and validate this model by
using it to explain the effects of varying several experimental
parameters (the concentration of protein, the concentration of
immobilized ligand, the protein−ligand binding constant, and
the size of the beads) on the rate of protein binding to the
beads and the total amount of protein that binds to the beads.
This Maglev-based technique has six attributes that make it
an attractive approach for detecting protein−ligand binding
events. (i) It is inexpensive: it requires only a capillary tube or a
cuvette filled with a paramagnetic solution, and two NdFeB
magnets that cost ∼$5−20 each. (ii) It is easy to use: the results
can be visualized with the unaided eye. (iii) It is sensitive:
association or dissociation of pmoles of protein to or from an
appropriate bead results in an easily measurable change in its
levitation height. (iv) It is quantitative: with the correct
orientation and separation of magnets, the amount of protein
bound per bead correlates linearly with the levitation height of
the bead. (v) It can be multiplexed, and offers a method for
comparing binding constants of different ligands. (vi) It enables
monitoring of association and dissociation of proteins to and
from beads in real time.
Other techniques may also be used to detect protein binding
to solid supports directly (e.g., quartz microbalances,9 canti-
levers,10 force transduction,11 conductance modification,12
surface plasmon resonance,13 and other optical methods).
These techniques, however, certainly require electricity, and
also often require sophisticated laboratory equipment. We
believe that using MagLev to monitor protein−ligand binding
may, after further development, find use in several situations
requiring biochemical analysis: (i) in the developing world,
where access to electricity is not guaranteed, (ii) in point-
of-care settings, where a small and simple solution is desirable,
and (iii) in applications for other in-the-field settings where
simplicity may be important (e.g., veterinary or plant pathology,
forensics, food quality, and other types of chemical analysis).
MagLev-based binding assays may also find use in protein−
ligand binding assays in drug development and biochemistry,
where resin-bound small molecules are often used to identify
inhibitors of proteins, or as a research tool to aid in identifying
the cellular targets of small molecules.
EXPERIMENTAL DESIGN
■
Design of the Device. We used a device we described previously;
it consists of two commercial NdFeB magnets (50 × 50 × 25 mm)
positioned with like poles facing toward each other, 45 mm apart.6 In
this configuration of magnets, eq 1 describes the vertical position of
the levitating bead (h), and indicates that the position correlates
linearly with the density of the bead (ρbead).
2
(ρ
− ρ )gμ d
d
2
bead
(χ
m
0
h =
+
2
− χ )4B
(1)
0
bead
m
In this equation, ρbead and ρm, (both kg·m−3) and χbead and χm (both
unitless) are the densities and the magnetic susceptibilities of the bead
and the paramagnetic medium, respectively; g is the acceleration
due to gravity (m·s−2), μ0 is the magnetic permeability of free space
(N·A−2), d is the distance between the magnets (m), and B0 is the
magnitude of the magnetic field at the surface of the magnets (T).
Choice of the Paramagnetic Fluid. We chose to use buffered
aqueous solutions of disodium gadolinium(III) diethylenetriamine-
pentaacetic acid (2Na+·Gd(DTPA)2−) as the medium for levitation.
Gd(DTPA) is a relatively low-cost ($3/g), commercially available,
water-soluble MRI contrast agent with high magnetic susceptibility.
The complex is non-denaturing to many proteins, and has a stability
constant of 1017.7 M−1 in aqueous solutions at pH 7.4.14,15 Adjusting
the concentration of the paramagnetic ion tunes the dynamic range
and sensitivity of the assay. Higher concentrations of the paramagnetic
ion increase the dynamic range of the assay; lower concentrations
increase the sensitivity.6c The absolute range can also be adjusted by
addition of a diamagnetic material with higher or lower density than
the solution (e.g., sucrose or ethanol, respectively).6c
The experiments described in this paper can be conveniently
performed in 300 mM solutions of Gd(DTPA) in phosphate-buffered
saline (1100 mOsm·kg−1). We quantified the magnetic susceptibility
(|χbead − χm| ≅ χm = 8.400 × 10−5) and density (ρm = 1.099 g·mL−1) of
this levitation buffer using density standard beads (see Supporting
Information).6c We used two magnets separated by 45 mm in an anti-
Helmholtz configuration. In this configuration the magnetic field
strength was 0.38 T at the surface of the magnets; this value provided a
dynamic range in density of 1.056−1.143 g·mL−1.
The technique, however, has at least five characteristics that
either are of uncertain value, or are limitations. (i) The detec-
tion is carried out in non-physiological medium containing a
non-natural ion at moderate ionic strength (e.g., 300 mM
chelated gadolinium, 6 mM phosphate, pH 7.4).8 (ii) The assay
requires at least one ligand (with Kd < 1 mM) that can be
attached covalently to the diamagnetic bead. (iii) The bead
must be different in density from the protein, so that the
association of protein and ligand in the bead results in a change
5638
dx.doi.org/10.1021/ja211788e | J. Am. Chem. Soc. 2012, 134, 5637−5646

Journal of the American Chemical Society
Article
We used a ruler with a millimeter scale to measure the distance from
the bottom magnet to a levitating bead (i.e., the levitation height of the
bead). Using a digital camera outfitted with a macro lens, we could
measure this distance with an uncertainty of 0.1 mm; measuring
the levitation height with the unaided eye increased this uncertainty
to 0.3 mm. In this study, the greatest source of uncertainty in
calculating the density of a bead from the levitation height of that bead
is the measurement of its levitation height. Using a camera, we could,
therefore, measure the change in density of a bead with an uncertainty
of 0.0002 g cm−3; without the camera the uncertainty increased
to 0.0006 g cm−3.
Choice of Model Protein−Ligand System. We defined the basic
biophysical chemistry of protein binding using BCA as a model
system16 for the following reasons: (i) BCA is inexpensive and
commercially available. (ii) Numerous inhibitors of BCA are known;
many are commercially available, and have well-characterized binding
constants. Many inhibitors of CA contain aryl sulfonamides, which
bind to the active site Zn(II) ion as anionic ligands, and several of the
reported inhibitors can be covalently attached to the polymeric
support using standard coupling chemistry. (iii) BCA is a small protein
(∼30 kDa) and will diffuse in and out of the PEGA beads (vide supra)
used in this study. (iv) BCA has an exceptionally stable tertiary
structure,16 and is not adversely affected by the levitation media. (v)
There is extensive background on the use of carbonic anhydrase in
physical organic studies of protein binding.16 In particular values of Kd,
kon, and koff are known for a number of ligands.
The change in density, ρbead,p − ρbead, is proportional to the difference
in the amount of protein present in the bead, after displacing an
equivalent volume of the buffer solution out of the bead (eq 3). Here,
[P] is the concentration of protein within the bead (M), MWprotein
(g·mol−1) and Vprotein (m3) are the molecular weight and volume
of a protein molecule, NA (mol−1) is the Avogadro constant, and ρsol
(kg·m−3) is the density of the solution. Using this relationship, Δh can
be expressed linearly in terms of [P] (eq 4).
ρ
− ρ
= [P](MW
− V
N ρ )
sol
protein
protein A
bead,p
bead
(3)
2
(MW
− V
N ρ )gμ d
sol 0
protein
protein A
Δh = [P]
2
(χ
− χ )4B
(4)
0
bead
m
BCA has a molecular weight of 29.1 kg·mol−1 and a volume of 3 ×
10−26 m3 (the protein is assumed to be a sphere with radius ∼20 Å).27
Equation 4, therefore, predicts that, under our standard levitation
conditions, a 1-mM increase in the concentration of protein within a
bead will result in a 5-mm decrease in levitation height. Exper-
imentally, we obtained a similar value (Δh/[P] = −8.6 mm/mM, see
Supporting Information); the difference between these experimental
and theoretical values is likely due to a discrepancy between the
assumed and actual volume of the protein, Vprotein, and/or to
inaccuracies in measurements of the volume of the beads.
Model for Kinetic Analysis of Binding. MagLev enables the
detection of a change in density that occurs when a soluble protein
associates with or dissociates from a ligand that is covalently
immobilized on a gel or solid support (provided that there is a
difference in density between the protein and the gel/solid support).
We model the binding of protein to ligands immobilized in a gel
matrix by a three-step process (Figure 2A): (i) partitioning of the
protein from solution to the gel (thereby displacing an equivalent
volume of buffer solution from the bead into the bulk solution), (ii)
diffusion of protein within the gel, and (iii) binding and unbinding of
protein to the ligands immobilized in the gel.
Before each experiment, the gel beads are first equilibrated with a
buffered solution of Gd(DTPA). Using a magnetic susceptibility
balance, we found that the magnetic susceptibility of these equilibrated
beads is similar to the magnetic susceptibility of the buffer; this
observation indicates that the concentration of Gd(DTPA) in solution
is approximately the same both inside and outside the bead (see
Supporting Information). At the beginning of each experiment (t = 0),
the beads are transferred to a solution of protein dissolved in the same
Gd(DTPA) buffer. The process that follows, involving protein
diffusing into the beads and binding to the ligands immobilized
there, can be described mathematically as follows.
Choice of Solid Support (Resin). We used commercially available
poly[acryloylated O,O′-bis(2-aminopropyl) polyethylene glycol]
(PEGA) beads for this study (300−500 μm diameter in water).17
This resin is synthesized from 1900 MW PEG. These beads present
amine functionality (0.2 mmol·g−1); this functional group makes
chemical modification straightforward. In addition, previous studies
have demonstrated that PEGA beads resist non-specific adsorption of
proteins.18−21 This combination of properties has resulted in their
widespread use for applications, including the identification of target
proteins of resin-bound small molecules,18 the screening of libraries
of inhibitors,19 the synthesis of peptides,20 and the covalent immo-
bilization of proteins.21
The density of PEGA beads (ρPEGA ≈ 1.07 g·cm−3) is significantly
different from the density of the protein (ρprotein ≈ 1.3−1.5 g·cm−3).22
This difference in density is required if binding of protein to the bead
is to cause a usefully quantifiable change in the overall density of the
bead.23
The main disadvantage of these commercial PEGA beads is that
their small pores (as a cross-linked acrylamide gel) slow the mass
transport of proteins into and through the interior of the bead, and
excludes proteins with molecular weight greater than ∼40−70 kDa.24
We used fluorescein-labeled BCA (FITC-BCA) to estimate both the
diffusion coefficient of BCA in PEGA beads (Dbead ≈ 5 × 10−13 m2·s−1)
and the partition coefficient of BCA between the beads and solution
(Kbead/sol ≈ 0.4, see the Supporting Information). This value for the
diffusion coefficient of BCA within the bead agrees well with data from
the literature,25 and is approximately 2 orders of magnitude slower
than the diffusion coefficient in water (∼9 × 10−11 m2·s−1).26
Unmodified PEGA beads are also difficult to visualize during
levitation because their refractive index is close to that of the solution.
To improve the visibility of these beads, we functionalized a small
portion of the amines on them with dyes (e.g., by reaction with the
isothiocyanates of rhodamine, malachite green, and 7-dimethylamino-
4-methylcoumarin). These modifications make the beads easily visible
under ambient or UV light.
Sulfonamide 1, when bound to resin, is expected to bind tightly to
BCA (the Kd of an analogous ligand in solution is 0.7 μM, see
Supporting Information). Sulfonamide 2 should not associate
measurably with BCA;16 this functionalized bead serves as a control.
The PEGA beads we used have a density of amine groups of 0.2 mmol g−1
(when dry); this value gives a final concentration of ligand within the bead
of 1−10 mM (when swollen in water).
The partitioning of the protein between the bead and the solution is
ext
bead
described by the partition coefficient, Kbead/sol (eq 5), where [P]
denotes the concentration of proteins at the external boundary of the
bead and [P]sol denotes the concentration of protein in the bulk
solution. Once inside the bead, the protein, Pbead, diffuses toward the
center of the bead, reacting with the immobilized ligands, *L, to form
protein−ligand complexes, *PL, according to eq 6. (Throughout this
text, * is used to indicate a species immobilized on the gel.)
ext
Model for Quantifying the Amount of Protein Bound Per
Bead with MagLev. Using eq 1, we derived eq 2 to correlate changes
in the amount of protein bound to the beads and changes in the
levitation height of the bead (Δh, m).
K
= [P]
/[P]
sol
bead/sol
(5)
bead
k
on
P
+ *L ⎯⎯⎯⇀ *PL
↽⎯⎯⎯
bead
k
(6)
off
2
(ρ
− ρ
)gμ d
Together, the dynamics of all these three steps can be expressed
mathematically in terms of a system of reaction−diffusion equations
(eqs 7 and 8).28 In these equations, r is the radial coordinate of the
bead,p
bead
0
Δh =
2
(χ
− χ )4B
(2)
0
bead
m
5639
dx.doi.org/10.1021/ja211788e | J. Am. Chem. Soc. 2012, 134, 5637−5646

Journal of the American Chemical Society
Article
surface area of the bead, r is the radial coordinate, Vsol is the volume of
solution, and NB is the number of beads used.
∂[P]
bead
∂[P]
∂t
V
N
sol sol
−D
A
=
bead
∂r
B
(10)
r=R
To correspond with our experiments, we used the following
parameters for our calculations: (i) The radius of each bead, R, is
170 μm. (ii) There are 15 beads in each experiment (NB). (iii) The
volume of the solution, Vsol, is 0.6 mL. (iv) The initial concentration of
ligand within the bead, [*L]0, is 3.2 mM. (v) The partition coefficient,
Kbead/sol, is 0.4. (vi) The diffusion coefficient, Dbead, is ∼10−12 m2·s−1, as
observed in a previous study and confirmed experimentally by us (see
Supporting Information).25 Solving this system of equations using a
finite-difference method30 in spherical coordinates (implemented in
Matlab), gives the concentration profiles of protein, ligand, and bound
protein−ligand complex with respect to both space and time.
Integrating the concentration profile of bound protein−ligand
throughout the bead gives the total amount of protein−ligand com-
plex in the bead, nPL (eq 11).31
R
2
n
= 4π
[*PL]r dr
∫
PL
(11)
0
Experimentally, we determined that the change in levitation height,
Δh (mm), is proportional to nPL (mmol) and inversely proportional
to the volume of the bead, Vbead (L) according to the relationship
Δh = −8.6nPL/Vbead (see Supporting Information; eq 4 provides a
theoretical approximation of this relationship).
Characteristic Time, τ, of the Reaction−Diffusion Process.
We describe here our derivation of a characteristic time parameter, τ,
which describes the time required for the reaction−diffusion process
to reach equilibrium; we begin by proving that this process is diffusion-
limited. Equation 12 describes the characteristic time for the binding of
protein to ligands within a bead, τrxn. In this expression, kon (M−1·s−1)
is the reaction rate constant and [P]bead is a characteristic concentra-
tion of protein in the bead; this concentration can be represented by
the product of the partition coefficient, Kbead/sol, and the initial con-
centration of protein in the solution, [P]0,sol. Based on the known
values of kon (∼105 M−1·s−1),16 Kbead/sol (0.4), and [P]0,sol (∼100 μM), the
characteristic time (τrxn) for the forward reaction is, therefore, ∼0.25 s.
Equation 13 describes the characteristic time for diffusion of the protein
within the bead (τdiff).
Figure 2. Reaction−diffusion model describing the binding of protein
from solution to ligands immobilized in a gel bead. (A) The model
consists of three distinct steps: (i) partitioning of the protein into the
bead, (ii) diffusion within the bead, and (iii) binding of protein to the
ligand immobilized on the bead. (B) In a diffusion-limited process
(fast/instantaneous reaction), reaction only occurs at the propagating
front, lF, when the flux of protein (before the front) encounters the
unconsumed ligands at the front. This approximation of the diffusion-
limited process allows us to derive a simplified characteristic time, τ,
for the reaction−diffusion process.
1
1
τ
∼
∼
rxn
k
[P]
k
K
[P]
on bead
on bead/sol 0,sol
(12)
(13)
bead, t is time, and Dbead is the diffusion coefficient of the protein in
the bead.
2
τ
∼ R /D
diff
bead
∂[P]
(r, t)
bead
∂t
2
= D
∇ [P]
(r, t) − k [P]
(r, t)[*L]
bead
bead on bead
Given the diffusion coefficient of the protein in the bead, Dbead
≈
10−12 m2·s−1, and a bead of radius R (∼170 μm), we estimate τdiff to be
on the order of 8 h. Since τdiff ≫ τrxn (8 h ≫ 0.25 s), the reaction−
diffusion process is diffusion-limited. We, therefore, make the
following two assumptions in order to derive a simple, analytical
expression for the characteristic time of the reaction−diffusion
process: (i) the reaction to form the protein−ligand complex is
instantaneous in comparison to the rate of diffusion, and (ii) once
formed, the protein−ligand complex, *PL, does not dissociate (the
rate of dissociation is typically much slower than the rate of
association). Given these assumptions, there exists a propagation
front of the protein (Figure 2B), that is a boundary where the
concentration of diffusive protein penetrating into the bead is zero.
At the propagation front, the incoming flux of protein is immediately
consumed to form the protein−ligand complex (eq 6) according to
eq 14.
× (r, t) + k [*PL](r, t)
off
(7)
∂[*L](r, t)
∂t
= −k [P]
on bead
(r, t)[*L](r, t) + k [*PL](r, t)
off
(8)
The initial parameters (at t = 0) are defined as follows: (i) The
concentration of ligand within the bead, [*L], is defined as [*L]0. (ii)
The concentration of protein in solution ([P]sol) is equal to [P]0,sol
.
(iii) There is no protein within the bead ([P]bead = 0). (iv) At the
external boundary of the bead, the concentration of protein is
described by the partition coefficient and the concentration of protein
in solution (eq 9).
ext
[P]
= K
[P]
bead/sol 0,sol
(9)
bead
The volume of the bead is assumed to be constant; therefore, [*PL]
= [*L]0 − [*L].29 Equation 10 describes the process of penetration of
protein into the bead at its external boundary. In this equation, A is the
∂[P]
bead
D
A
dt = [*L] A dl
0 F F
bead F
∂r
l
(14a)
F
5640
dx.doi.org/10.1021/ja211788e | J. Am. Chem. Soc. 2012, 134, 5637−5646

Journal of the American Chemical Society
dl
∂[P]
Article
to pH 7.4 using sodium hydroxide (referred to throughout this
text as the “standard levitation buffer”). This composition provided
a buffer with an approximate match in density to that of the PEGA
beads. The chosen concentration of gadolinium(III) provided a
useful compromise between sensitivity and dynamic range of
detection by MagLev. Addition of the non-denaturing surfactant,
polysorbate 20, reduced non-specific binding of proteins to the
PEGA beads, and prevented the beads from adhering to the
cuvette.
D
F
bead
[*L]
bead
∂r
=
dt
0
l
(14b)
F
In this equation, r is the radial coordinate, AF is the cross-sectional
area of the front, lF is the radial position of the front, and dlF/dt is the
velocity of the propagating front. We derive an estimate of the term
∂[P]bead/∂r by considering the region before the propagating front,
where the incoming protein is subject only to diffusion. In this region,
we can apply a pseudo-steady approximation to the concentration
profile of diffusing protein (eq 15).
MagLev Provides a Spectroscopy-Free Method of Mea-
suring the Binding of Protein to Ligand-Functionalized
PEGA Beads. Initially, we verified that protein would adsorb to
PEGA beads only when these beads were functionalized with a
small-molecule ligand that bound specifically to that protein.
We reasoned that the binding of most proteins (average density ≈
1.3−1.5 g·cm−3) to PEGA beads (density ≈ 1.07 g·cm−3)
should increase the density of the beads, and result in quan-
tifiable changes in levitation height between bound and
unbound states.
⎛
⎞
∂[P]
bead
1 ∂
r
2
r
= 0
⎜
⎝
⎟
⎠
2
∂r
∂r
(15)
This approximation assumes that the concentration profile of
diffusing protein is established much more rapidly than the
propagating front moves (this approximation is reasonable when
[P]0,solKbead/sol/[*L]0 ≪ 1, as is the case in our system).32 We derive
the average value ⟨1/∂[P]bead/∂r|l ⟩r across the bead by solving eq 15
using the following boundary conditions: at r = R, [P]bead
[P]0,solKbead/sol, and at r = lF, [P]bead = 0 (eq 16).
F
=
Throughout these studies, we used a well-characterized
system of proteins and ligands: BCA and derivatives of
benzenesulfonamide.16 We immobilized 4-carboxybenzene-
sulfonamides 1 and 2 on Rhodamine-dyed PEGA beads using
standard coupling chemistry (eq 20, EDC = N-(3-dimethyl-
−1
⎛
⎜
⎞
⎟
∂[P]
bead
R
=
⎜
⎝
⎟
⎠
∂r
6[P]
K
0,sol bead/sol
l
F
(16)
r
For the system we describe here, the characteristic time τ of the
reaction−diffusion process is proportional to the radius of the bead R
over the average velocity of the propagating front, dlF/dt (eq 17).32
Finally, combining eqs 14, 16, and 17 yields an expression that
describes the characteristic time τ as a function of a number of
experimental variables (eq 18).
τ ∼ R/⟨dl /dt⟩
(17)
F
r
−1
⎛
⎜
⎞
R[*L]
∂[P]
bead
0
⎟
τ ∼
⎜
⎝
⎟
D
∂r
bead
l
⎠
F
aminopropyl)-N′-ethylcarbodiimide, NHS = N-hydroxysuccin-
imide, see Supporting Information for more information).
At least 1 h before each experiment, the PEGA beads were
placed in a solution of the standard levitation buffer in order to
ensure that they equilibrated completely with this buffer. We
then transferred 7−10 beads functionalized with either
sulfonamide 1 or 2 into a microcuvette containing 0.6 mL of
a solution of BCA in the standard levitation buffer. We observed
only a very small decrease (<0.1 mm) in the levitation height of
beads functionalized with 4-dimethylsulfamoylbenzoic acid 2
after incubation with 0.33 mM BCA for 7 days. In contrast, we
observed a time- and concentration-dependent change in the
levitation height of beads functionalized with sulfonamide 1.
We plotted the change in levitation height of beads
functionalized with sulfonamide 1 (Δh, in millimeters) versus
time (t, in hours) for each concentration of BCA and fit these
data to our model of the reaction−diffusion process (eqs 7 and 8).
The comparison demonstrates good agreement (Figure 3A).33
We estimate the dissociation constant from the model to be Kd ≈
1.5 μM. We note that since the process of protein binding to
ligands within the beads is diffusion-limited (see the section on
characteristic time for further discussion), we can only determine
Kd, and not the on and off rates (koff and kon).
r
2
R [*L]
0
=
6D
[P]
K
bead 0,sol bead/sol
(18)
This expression indicates that the time required for the system to
reach steady-state is proportional to the square of the radius of the
beads, R2, the initial concentration of the ligands in the bead, [*L]0,
and is inversely proportional to the diffusion coefficient, Dbead, the
initial concentration of protein in solution, [P]0,sol, and the partition
coefficient, Kbead/sol. These mathematical relationships agree well
with experiment (vide supra). In practice, the characteristic time τ
can be derived from a plot of levitation height (h) versus time (t)
by fitting the data to a first-order exponential equation (eq 19),
where hf and h0 are the final and initial levitation heights, res-
pectively.
−t/τ
h = (h − h ) e
+ h
f
(19)
0
f
RESULTS AND DISCUSSION
■
This section outlines a detailed physical−organic study of a
MagLev-based analytical tool that can be used for (i)
quantifying the amount of protein bound to beads, and (ii)
monitoring the kinetics and thermodynamics of association of
proteins with resin-bound small molecules. We use this
physical−organic study to identify the parameters that
ultimately influence the function and practicality of this tool.
Unless specified otherwise, all MagLev measurements were
performed in a solution of 300 mM Gd(DTPA), and 0.05%
polysorbate 20, dissolved in 6 mM phosphate buffer and adjusted
Equation 21 presents an alternative method of calculating the
dissociation constant using the equilibrium conditions of the
5641
dx.doi.org/10.1021/ja211788e | J. Am. Chem. Soc. 2012, 134, 5637−5646

Journal of the American Chemical Society
Article
characteristic time, τ, we inferred that both increasing the
concentration of protein in solution, and decreasing the con-
centration of ligand within the bead, should increase the rate at
which the bead would reach an equilibrium concentration of
protein and protein−ligand complex (τ ∼ [L]0/[P]0,sol, eq 18).
In addition to decreasing the assay time, experimenting with
these parameters would also allow us to test the validity of our
model. To vary the concentration of ligand within the beads, we
combined benzene sulfonamides 1 and 2 in molar ratios of 1:0,
1:2, 1:8, 1:26, and 1:80. We used these mixtures to synthesize
batches of PEGA beads containing different concentrations
(3.2−0.040 mM) of benzene sulfonamide (eq 22).
Figure 3. Monitoring the association of bovine carbonic anhydrase
(BCA) with 4-carboxybenzenesulfonamide (1) immobilized on PEGA
beads. We levitated functionalized PEGA beads in cuvettes in the
standard levitation buffer. (A) Adding BCA to the levitation media
resulted in a change in levitation height (h) that depended on time,
and on the concentration of protein. The figure shows the fit of the
experimental plots to the estimates from the reaction−diffusion model.
The reaction−diffusion model predicts that the time to reach
equilibrium should be proportional to the protein concentration
(equilibration is predicted to be faster with higher protein
concentrations). (B) We illustrate the effect of the ligand
concentration within the bead on the rate of change in levitation
height. The data confirm that the time to reach equilibrium is inversely
proportional to the ligand concentration, as predicted by the reaction−
diffusion model.
We placed 7−10 beads from each batch in a microcuvette
containing a solution of 100 μM BCA dissolved in the standard
levitation buffer, and plotted the change in levitation height
(Δh, in millimeters) versus time (t, in hours) for each
concentration of ligand (Figure 3B). Fitting these data to our
reaction−diffusion numerical integration model (eqs 3 and 10)
revealed the expected correlations: lower concentrations of
ligand within the bead resulted in smaller changes in levitation
height (Δh = h0 − hf); the equilibration time was, however,
inversely proportional to the concentration of ligand in the
bead.
reaction summarized in eq 6, and assuming that protein is in
excess.
In order to verify these results further, we repeated the same
experiment with several different concentrations of BCA. Each
plot was fit to a first-order exponential curve (eq 19) from
which we derived the calculated characteristic times τ. Figure 4
illustrates the expected mathematical relationships. In Figure 4A,
we plot characteristic time against the concentration of
ligand 1 within the bead (τ versus [*1]bead); the data
demonstrate the expected linear relationship, with the
exception of the datum at 100% concentration of sulfonamide
1 and 10 μM protein.35 Similarly, Figure 4B reveals the linear
relationship between the characteristic time and the inverse of
the concentration of protein in solution, (1/[BCA]0,sol; again
with exclusion of the datum at 100% concentration of 1 and
10 μM protein). Thus, equilibration is much faster with lower
concentrations of ligand within the bead ([*L]0), and with
higher concentrations of protein in solution ([P]0,sol), as
predicted by both the reaction−diffusion model and our
derivation of the characteristic time τ (eqs 10 and 18).
The Rate of Equilibration Is Faster for Smaller Beads.
PEGA beads, as supplied commercially, span a range of sizes.
For our studies, beads purchased from Polymer Laboratories
were reported to range in diameter from 300 to 500 μm (when
swollen in water). To quantify the effect of bead size on the rate
of binding of protein to ligands within the bead, we isolated the
[*L] − [*PL]
0
eq
K = K
[P]
bead/sol 0,sol
d
[*PL]
eq
(21)
Experimentally we found that with [P]0,sol = 100 μM, [*L]0 =
3.2 mM and Kbead/sol = 0.4, the final change in height of the
beads is 26.5 mm; this value indicates that the [*PL]eq is
3.08 mM (eq 4). Substituting these values into eq 21 gives a
dissociation constant, Kd, of 1.5 μM.
These results demonstrate that this MagLev-based method
provides reasonable estimates of binding constants for BCA
with benzenesulfonamides, without the need for spectroscopy.
The small difference between the measurements using MagLev
and more conventional spectroscopic methods may be due to an
increase in the protein−ligand dissociation constant as a result of
immobilization of the ligand. We previously found that the
observed dissociation constants of BCA with ligands in solution
are ∼10 times lower than the dissociation constants of the
corresponding ligands presented on the surface of a monolayer.34
The System Reaches a State of Equilibrium More
Rapidly When Higher Concentrations of Protein in
Solution and/or Lower Concentrations of Ligand within
the Beads Are Used. Based on our derivation of the
5642
dx.doi.org/10.1021/ja211788e | J. Am. Chem. Soc. 2012, 134, 5637−5646

Journal of the American Chemical Society
Article
the relationship between the radius of the bead (R) and τ (τ ∼
R2, eq 18).
MagLev Enables Multiple Binding Interactions To Be
Monitored Simultaneously. MagLev provides the basis for
an on-bead assay that can measure the affinity of multiple
different resin-bound small molecules for the same protein. To
make it possible to differentiate resin-bound inhibitors visually,
we functionalized a small portion of the available amines on
PEGA beads with one of five different dyes (isothiocyanates of
rhodamine, fluorescein, malachite green, eosin, and 7-
dimethylamino-4-methylcoumarin). Using standard coupling
chemistry, we attached five different ligands (4-carboxybenzene
sulfonamide, 4-(isothiocyanatomethyl) benzenesulfonamide 3-
carboxybenzene sulfonamide, 3-carboxy-4-methoxybenzene
sulfonamide, and 4-dimethylsulfamoylbenzoic acid) of carbonic
anhydrase to the differently colored beads.
We then suspended these five color-coded beads, each
functionalized with a different inhibitor of BCA (∼15 beads per
inhibitor) in a microcuvette containing a solution of 100 μM
BCA dissolved in the standard levitation buffer. Initially, the
beads all levitate at nearly the same height (Figure 6).36 In the
Figure 4. Effect of the concentration of protein in solution, and the
ligand concentration within the beads, on rates of equilibration. We
calculated each characteristic time, τ, by fitting a plot of levitation
height versus time to eq 18. The combined data substantiate our
derivation of the characteristic time (eq 17) by illustrating the
predicted linear relationships between (A) the characteristic time τ and
the concentration of ligand within the bead (expressed as the
percentage of the bead functionalized with sulfonamide 1), and (B)
the characteristic time τ and the reciprocal of the concentration of
protein in solution (1/[BCA]0,sol).
largest and smallest beads by filtering through several sizes of
mesh (see Supporting Information).
We levitated eight large beads (average radius of 166
5 μm) and eight small beads (average radius of 136 7 μm) in
a solution of 130 μM BCA dissolved in the standard levitation
buffer. Figure 5 shows the comparison of the change in
Figure 6. Using MagLev to measure the binding of BCA to several
immobilized ligands. This figure presents a series of photographs
showing changes in levitation height over time that result from
incubating PEGA beads functionalized with five different inhibitors of
BCA in the presence of 100 μM BCA dissolved in the standard
levitation buffer. We used eq 21 to calculate the dissociation constants
of the immobilized ligands from BCA; also shown, in parentheses, are
the dissociation constants of analogous ligands in solution from BCA
(see Supporting Information).
Figure 5. Effect of the radius of the bead on the rate of binding of
BCA to ligand-functionalized beads. We levitated functionalized PEGA
beads in cuvettes in the presence of 130 μM BCA dissolved in the
standard levitation buffer. We plot the average levitation height for
eight large beads (⟨R⟩ = 166 5 μm), and eight small beads (⟨R⟩ =
136 7 μm) versus time, and show the predictions of the reaction
diffusion model (the dotted and dashed lines).
presence of BCA, the beads begin to sink, and begin to
segregate based on binding affinities. The relative levitation
height of the beads represents the relative differences in binding
affinities of the ligands attached to the beads; the bead
containing the ligand with the lowest dissociation constant for
BCA levitates at the lowest value of h because it has more
protein bound to it than the other two beads. Using eq 21, we
calculated the dissociation constants of the immobilized ligands
from BCA. We also measured the dissociation constants of
analogous ligands in solution using fluorescence (see
Supporting Information). A comparison of the values measured
using both methods demonstrates good agreement (Figure 6).
levitation height (Δh, in millimeters) versus time (t, in hours)
for each batch of beads. When these data were fit to first-order
exponential curves (eq 19), the calculated characteristic times,
τ, were 14.6 2.7 h for the small beads, and 26.9 2.1 h for
the large beads. This ratio is in accord with our prediction of
5643
dx.doi.org/10.1021/ja211788e | J. Am. Chem. Soc. 2012, 134, 5637−5646

Journal of the American Chemical Society
Article
At the beginning of the experiment, the beads form relatively
tight clusters because they have equal densities. As the beads
approach 50% equilibration, however, they become increasingly
disperse. We hypothesize that this dispersion results from
differences in the percentage of ligands that are bound to
protein as a result of differences in the size of the beads or the
size of the pores in the beads.6b As the beads approach their
final levitation height, their dispersion in levitation heights
decreases because each bead contains the same concentration
of ligand, and the final equilibrium levitation height ultimately
depends only on the density of the bead, not on its radius.
MagLev Is a Useful Tool for Quantifying the
Concentration of a Specific Protein. Methods for the
detection of small amounts (nmol to fmol) of protein have
revolutionized biotechnology, and comprise some of the most
heavily used methods for the diagnosis of disease.37 In order to
adapt the MagLev-based methods described in this paper to the
detection of small amounts of protein, we utilize a semi-kinetic
approach. We begin by incubating a single bead in a solution of
a target protein. To provide optimal detection of small amounts
of protein, we fully functionalize this bead with a ligand that
binds tightly to the target protein. Specifically, we use PEGA
beads functionalized with sulfonamide 1 to detect BCA.
With the goal of detecting low concentrations of protein, it is
beneficial to maximize the sensitivity of the system to changes
in the density of the bead by performing measurements of
levitation height using the lowest practical concentration of
paramagnetic salt. For these measurements, we, therefore,
utilize a lower concentration of Gd(DTPA) than what is
present in the standard levitation buffer: 150 mM Gd(DTPA)
provides a practical compromise between sensitivity and
equilibration time. With this concentration of Gd(DTPA),
the beads reach their equilibrium levitation height in ∼30 min,
and we are able to differentiate between differences in density
of 0.0004 g·cm−3. With lower concentrations of Gd(DTPA),
sensitivity is increased, but the beads take significantly longer to
reach their equilibrium levitation height.6c Future studies will
focus on increasing the rate of adsorption of protein by using
smaller beads, lower concentrations of ligand within the beads,
or beads with larger pore volumes.
Reaching an equilibrium state at low concentrations of
protein requires an impractically long time (for example, a bead
functionalized with sulfonamide 1 requires more than one
thousand hours to equilibrate fully with a 10 μM solution of
BCA). A calibration curve, however, can easily be generated to
relate the change in levitation height after a given period of
time to the concentration of protein in the sample. Figure 7
demonstrates this relationship.38
To generate the data in Figure 7A, we incubated individual
beads, functionalized with sulfonamide 1, in solutions (20 μL)
of BCA (40 nM−40 μM) dissolved in 10 mM PBS at room
temperature (20 °C), for either 3 or 24 h. We then transferred
these beads into a microcuvette containing a solution of
150 mM Gd(DTPA) and 200 mM sucrose dissolved in 6 mM
phosphate buffer and adjusted to pH 7.4 with NaOH (referred
to hereafter as the “high sensitivity levitation buffer”), and
measured their levitation height (in comparison to the
levitation height of a bead that had been incubated in a
solution free of BCA). After 3 h, beads that have been
incubated in a 600 nM solution of BCA can be distinguished
from beads that have been incubated in a solution free of BCA;
after 24 h the detection limit is lowered to 300 nM. Notably,
Figure 7. Detecting BCA using MagLev. For these experiments, beads
were levitated in the high sensitivity levitation buffer. (A) We
incubated individual beads, functionalized with sulfonamide 1, in
solutions (20 μL) of BCA (40 nM−40 μM) dissolved in 1 x PBS at
room temperature (20 °C), for either 3 or 24 h. After incubation, we
transferred the beads into microcuvettes containing the high-sensitivity
levitation buffer, and measured their levitation heights (in comparison
to a bead that had been incubated in a solution free of BCA). We then
repeated this experiment, changing the incubation media to whole
blood (the beads were filtered and washed before levitation). The
error bars show one standard deviation (n = 7). (B) We examined the
temperature dependence of the protein detection process. Over a 24-h
period, beads that were incubated at 5 °C absorbed slightly less protein
than beads that were incubated at 40 °C.
this method requires only 20 μL of sample (the volume of
blood in a typical finger prick).
The initial rate of protein absorption correlates linearly with
the concentration of protein in solution (τ ∼ 1/[P]0,sol, eq 18);
as the ligands become saturated with protein, however, the rate
of net protein diffusion into the beads decreases. The result is
that at short incubation times, there is an approximately linear
relationship between the concentration of protein in the
incubation solution and the amount of protein adsorbed on the
bead, while at longer incubation times this simple correlation
no longer holds true (at very long incubation times the system
approaches equilibrium, where binding is described by eq 21).
MagLev Can Be Used To Detect BCA in Blood. This
short study was intended to determine if MagLev could operate
successfully starting with samples as complex as blood and
serum. We incubated individual beads, functionalized with
sulfonamide 1, in 20 μL aliquots of whole blood containing 2-
fold dilutions of BCA (40 nM−40 μM). After 3 h we separated
these beads from the blood by filtration through a fine mesh
and rinsed them with levitation buffer. We then transferred the
beads into a microcuvette containing the high sensitivity
levitation buffer (described above), and measured their
levitation heights (in comparison to the levitation height of a
bead that had been incubated in whole blood containing no
added BCA; Figure 7A). These results indicate that this method
is capable of detecting a specific protein in a complex biological
5644
dx.doi.org/10.1021/ja211788e | J. Am. Chem. Soc. 2012, 134, 5637−5646

Journal of the American Chemical Society
Article
medium such as blood without the need for initial separation or
purification steps.
point-of-care diagnosis, especially in resource-limited, military,
and home environments, or in veterinary medicine, plant
pathology, and food safety. (ii) It is easy to use; results can be
visualized with the naked eye. (iii) It has the capability to
monitor binding accurately in real time. This attribute provides
a quantitative means of determining the concentration of a
specific protein in solution. (iv) It can qualitatively distinguish
the binding affinities of a protein to several resin-bound small
molecules simultaneously. Using analogous procedures,
MagLev should also be capable of measuring the binding of
multiple proteins simultaneously to an array of resin-bound
small molecules. This property should allow for the ready
design of multiplexed binding assays. (v) Protein−ligand
binding directly results in a change in levitation height. This
method, therefore, does not require intermediate reagents, such
as enzyme-linked secondary antibodies.
In its present form, this method also has several
disadvantages; we summarize them briefly, but note that
there are clear development paths to reduce or eliminate them.
(i) The kinetics of protein−ligand binding are relatively slow
(on the order of several days). This problem may potentially be
resolved through the design and synthesis of beads with
improved characteristics (e.g., larger pore size). (ii) This
method is only applicable to ligands that are amenable to
chemical immobilization on a gel support; this limitation,
however, is inherent to most detection methods that occur on
solid support. (iii) This method is currently not applicable to
large proteins, most notably antibodies, due to the restricted
pore size of the PEGA beads we used. (iv) For detection of
proteins in blood or other biological samples, the gel beads
must be separated from this sample (e.g., by filtration) before
analysis using Maglev; this process adds time and complexity to
the method.
The Temperature of Incubation Has Only a Small
Influence on the Reaction−Diffusion Process. We also
examined the temperature dependence of this method of
detecting protein (Figure 7B). We incubated PEGA beads,
functionalized with sulfonamide 1, in solutions of BCA
(40 nM−40 μM) at two different temperatures (5 and 40 °C)
for 24 h. Only slightly more protein was absorbed into the beads
that were incubated at the warmer temperature. The difference
between the levitation heights of the beads that were incubated at
these two temperatures is predicted by the inverse relationship
between the characteristic time, τ, of the reaction−diffusion
process and the diffusion coefficient of the protein within the bead
(τ ∼ 1/Dbead, eq 18). The dependence of the diffusion coefficient,
D, on temperature, T, can be approximated by the Stokes−
Einstein equation (eq 23),
k T
6πηR
B
D =
(23)
where kB is Boltzmann’s constant, η is the dynamic viscosity of the
levitation media inside the bead, and R is the hydrodynamic radius
of the protein inside the bead. We assume that the levitation media
has a dynamic viscosity similar to that of water (η5°C = 1.519,
η40°C = 0.653), and that R is independent of temperature; the
ratio of Dbead,40°C and Dbead,5°C is, therefore, ∼2.1. This value
agrees qualitatively with the increased rate of the reaction−
diffusion process at higher temperatures.
CONCLUSION
■
MagLev provides a new way to detect and measure specific
protein−ligand interactions. Its simplicity and independence of
electricity and infrastructure suggest that, with development, it
has the potential to be useful in resource-limited environments.
In this method, the binding of protein to ligands immobilized
within a gel bead results in a change in the density of the bead.
MagLev allows the density of the bead to be monitored in real
time with high accuracy, and, therefore, provides a direct readout
of the amount of protein bound to the bead.
ASSOCIATED CONTENT
* Supporting Information
■
S
General methods and additional experimental information. This
material is available free of charge via the Internet at http://
pubs.acs.org.
AUTHOR INFORMATION
Corresponding Author
gwhitesides@gmwgroup.harvard.edu
We have developed a mathematical model of the reaction−
diffusion processes that result in the binding of protein to
ligands immobilized within the bead. This model provides good
quantitative agreement between theory and experiment. The
magnitude of the change in levitation height as a function of
time depends on a number of controllable parameters including
(i) the concentration of protein in solution, (ii) the structure,
concentration, and binding constant of the ligand immobilized
in the bead, and (iii) the size of the bead. The rate of change in
levitation height also depends on a number of factors that are
more difficult to manipulate, such as (i) the partition coefficient
of the protein between the bead and the bulk solution, and (ii)
the diffusion coefficient of protein within the bead. We
developed eq 17, which describes the dependence of the
characteristic time, τ, for protein binding to ligands
immobilized within gel beads, on all of the reaction parameters.
This equation, therefore, allows the performance of the system
to be predicted, under a variety of conditions.
■
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
This work was partially supported by the Bill & Melinda Gates
Foundation (no. 51308), the Wyss Institute of Biologically
Inspired Engineering, the U.S. Department of Energy (no. DE-
FG02-00ER45852, funding used for the development of the
multiplexed assays), and postdoctoral fellowships from the
Damon Runyon Cancer Research Foundation (S.T.P.) and
NIH (S.T.P. and N.D.S.).
REFERENCES
■
(1) (a) Cuatrecasas, P. J. Biol. Chem. 1970, 245, 3059. (b) Lam, K. S.;
Lebl, M.; Krchn
̌
ak
́
, V. Chem. Rev. 1997, 97, 411. (c) Rademann, J.;
Overall, the MagLev-based method for detecting protein−
ligand binding has a number of significant advantages. (i) This
method requires no electricity, and only a single piece of
equipment. It may, therefore, find use in situations where
portability and low cost are a high priority; for example, in
Jung, G. Science 2000, 287, 1947. (d) Salisbury, C. M.; Maly, D. J.;
Ellman, J. A. J. Am. Chem. Soc. 2002, 124, 14868. (e) Vegas, A.; Fuller,
J.; Koehler, A. N. Chem. Soc. Rev. 2008, 37, 1385. (f) Gault, V. A.;
McClenaghan, N. H. Understanding Bioanalytical Chemistry: Principles
and Applications; John Wiley & Sons, Ltd.: West Sussex, UK, 2009.
5645
dx.doi.org/10.1021/ja211788e | J. Am. Chem. Soc. 2012, 134, 5637−5646

Journal of the American Chemical Society
Article
(2) (a) Venn, R. F. Principles and Practice of Bioanalysis; Taylor &
Francis: London, UK, 2000. (b) Walker, J. M.; Rapley, R., Eds.
Molecular Biomethods Handbook; Humana Press: Totowa, NJ, 2008.
(3) Stockwell, B. R. Nature 2004, 432, 846.
(17) (a) Auzanneau, F.-I.; Meldal, M.; Bock, K. J. Pept. Sci. 1995, 1,
31. (b) Renil, M.; Ferreras, M.; Delaisse, J. M.; Foged, N. T.; Meldal,
M. J. Pept. Sci. 1998, 4, 195.
(18) Kuramochi, K.; Miyano, Y.; Enomoto, Y.; Takeuchi, R.; Ishi, K.;
Takakusagi, Y.; Saitoh, T.; Fukudome, K.; Manita, D.; Takeda, Y.;
Kobayashi, S.; Sakaguchi, K.; Sugawara, F. Bioconjugate Chem. 2008,
19, 2417.
(19) (a) Meldal, M.; Svendsen, I.; Breddam, K.; Auzanneau, F. I. Proc.
Natl. Acad. Sci. U.S.A. 1994, 91, 3314. (b) Meldal, M.; Svendsen, I. J.
Chem. Soc., Perkin Trans. 1 1995, 1591.
(20) (a) Meldal, M.; Auzanneau, F. I.; Hindsgaul, O.; Palcic, M. M.
J. Chem. Soc., Chem. Commun. 1994, 1849. (b) Renil, M.; Meldal, M.
Tetrahedron Lett. 1995, 36, 4647. (c) Haddoub, R.; Dauner, M.;
Stefanowicz, F. A.; Barattini, V.; Laurent, N.; Flitsch, S. L. Org. Biomol.
Chem. 2009, 7, 665.
(4) (a) Ahn, C. H.; Choi, J. W.; Beaucage, G.; Nevin, J. H.; Lee, J. B.;
Puntambek, A.; Lee, J. Y. Proc. IEEE 2004, 92, 154. (b) Whitesides, G.
M. Nature 2006, 442, 368. (c) Yager, P.; Edwards, T.; Fu, E.; Helton,
K.; Nelson, K.; Tam, M. R.; Weigl, B. H. Nature 2006, 442, 412.
(d) Chin, C. D.; Linder, V.; Sia, S. K. Lab Chip 2007, 7, 41. (e) Yager,
P.; Domingo, G.; Gerdes, J. Annu. Rev. Biomed. Eng. 2008, 10, 107.
(f) Konry, T.; Walt, D. R. J. Am. Chem. Soc. 2009, 131, 13232.
(5) (a) Beaugnon, E.; Tournier, R. Nature 1991, 349, 470.
(b) Catherall, A. T.; Eaves, L.; King, P. J.; Booth, S. R. Nature
2003, 422, 579. (c) Ikezoe, Y.; Hirota, N.; Nakagawa, J.; Kitazawa, K.
Nature 1998, 393, 749. (d) Kimura, T.; Mamada, S.; Yamato, M.
Chem. Lett. 2000, 1294.
(21) Wong, L. S.; Thirlway, J.; Micklefield, J. J. Am. Chem. Soc. 2008,
130, 12456.
(6) (a) Winkleman, A.; Perez-Castillejos, R.; Gudiksen, K. L.;
Phillips, S. T.; Prentiss, M.; Whitesides, G. M. Anal. Chem. 2007, 79,
6542. (b) Mirica, K. A.; Phillips, S. T.; Shevkoplyas, S. S.; Whitesides,
G. M. J. Am. Chem. Soc. 2008, 130, 17678. (c) Mirica, K. A.;
Shevkoplyas, S. S.; Phillips, S. T.; Gupta, M.; Whitesides, G. M. J. Am.
Chem. Soc. 2009, 131, 10049. (d) Mirica, K. A.; Phillips, S. T.; Mace,
C. R.; Whitesides, G. M. J. Agric. Food Chem. 2010, 58, 6565.
(e) Mirica, K. A.; Ilievski, F.; Ellerbee, A. K.; Shevkoplyas, S. S.;
Whitesides, G. M. Adv. Mater. 2011, 23, 4134.
(7) (a) Halling, P. J.; Ulijn, R. V.; Flitsch, S. L. Curr. Opin. Biotechnol.
2005, 16, 385. (b) Laurent, N.; Haddoub, R.; Flitsch, S. L. Trends
Biotechnol. 2008, 26, 328. (c) Schuck, P.; Zhao, H. Methods Mol. Biol.
2010, 627, 15.
(8) Mammalian cells typically have intracellular ionic strengths on the
order of 200−300 mM, and contain ∼200 mg/mL protein, see: Storey,
K. B. Functional Metabolism: Regulation and Adaptation; John Wiley &
Sons: Hoboken, NJ, 2004; p403.
(9) (a) Ebersole, R. C.; Ward, M. D. J. Am. Chem. Soc. 1988, 110,
8623. (b) Rickert, J.; Brecht, A.; Gopel, W. Biosens. Bioelectron. 1997,
12, 567. (c) Nishino, H.; Murakawa, A.; Mori, T.; Okahata, Y. J. Am.
Chem. Soc. 2004, 126, 2264. (d) Su, X.; Zhang, J. Sens. Actuators B
2004, 100, 309. (e) Muratsugu, M.; Ohta, F.; Miya, Y.; Hosokawa, T.;
Kurosawa, S.; Kamo, N.; Ikeda, H. Anal. Chem. 1993, 65, 2933.
(10) (a) Fritz, J.; Baller, M. K.; Lang, H. P.; Rothuizen, H.; Vettiger,
(22) (a) Chick, H.; Martin, C. J. Biochem. J. 1913, 7, 92. (b) Quillin,
M. L.; Matthews, B. W. Acta Crystallogr. 2000, 56, 791. (c) Fischer, H.;
Polikarpov, I.; Craievich, A. F. Protein Sci. 2004, 13, 2825.
(23) It would also be possible to use beads with density greater than
the density of protein. This experimental design, however, would
require that the levitation media contain a diamagnetic cosolute of
high density in order to match the density of the levitation media (ρm)
with the density of the bead.
(24) (a) Kress, J.; Zanaletti, R.; Amour, A.; Ladlow, M.; Frey, J. G.;
Bradley, M. Chem.Eur. J. 2002, 8, 3769. (b) Auzanneau, F.-I.;
Meldal, M.; Bock, K. J. Pept. Sci. 1995, 1, 31.
(25) (a) Thornton, P. D.; McConnell, G.; Ulijn, R. V. Chem.
Commun. 2005, 5913. (b) Bosma, A. Y.; Ulijn, R. V.; McConnell, G.;
Girkin, J.; Halling, P. J.; Flitsch, S. L. Chem. Commun. 2003, 2790.
(26) Tyn, M. T.; Gusek, T. W. Biotechnol. Bioeng. 1990, 35, 327.
(27) Gao., J.; Whitesides, G. M. Anal. Chem. 1997, 69, 575.
(28) Wei, Y.; Wesson, P. J.; Kourkine, I.; Grzybowski, B. A. Anal.
Chem. 2010, 82, 8780.
(29) Previous studies have demonstrated that protein binding to
PEGA beads does not significantly change the volume of the beads;
see ref 25.
(30) Morton, K. W.; Mayers, D. F. Numerical Solution of Partial
Differential Equations: An Introduction; Cambridge University Press,
Cambridge, UK, 2005.
(31) Although both bound and unbound protein increase the density
of the bead, the influence of the unbound protein is negligible because
its concentration is significantly lower than the concentration of the
bound protein.
(32) Deen, W. M. Analysis of Transport Phenomena; Oxford
University Press: New York, 1998.
P.; Meyer, E.; Guntherodt, H.-J.; Gerber, Ch.; Gimzewski, J. K. Science
̈
2000, 288, 316. (b) Savran, C. A.; Knudsen, S. M.; Ellington, A. D.;
Manalis, S. R. Anal. Chem. 2004, 76, 3194. (c) Burg, T. P.; Godin, M.;
Knudsen, S. M.; Shen, W.; Carlson, G.; Foster, J. S.; Babcock, K.;
Manalis, S. R. Nature 2007, 446, 1066. (d) Goeders, K. M.; Colton, J. S.;
Bottomley, L. A. Chem. Rev. 2008, 108, 522. (e) Datar, R.; Kim, S.;
Jeon, S.; Hesketh, P.; Manalis, S.; Boisen, A.; Thundat, T. MRS Bull.
2009, 34, 449.
(33) The plots shown in Figure 3 are also presented in the
Supporting Information with error bars.
(34) Mrksich, M.; Grunwell, J. R.; Whitesides, G. M. J. Am. Chem.
Soc. 1995, 117, 12009.
(11) Ndieyira, J. W.; Watari, M.; Barrera, A. D.; Zhou, D.; Vogtli, M.;
Batchelor, M.; Cooper, M. A.; Strunz, T.; Horton, M. A.; Abell, C.;
Rayment, T.; Aeppli, G.; Mckendry, R. A. Nat. Nanotechnol. 2008, 3,
691.
(12) Chua, J. H.; Chee, R. E.; Agarwal, A.; Wong, S. M.; Zhang, G. J.
Anal. Chem. 2009, 81, 6266.
(13) (a) Schasfoort, R. B., Tudos, A. J., Eds. Handbook of Surface
Plasmon Resonance; Royal Society of Chemistry: Cambridge, UK,
2008. (b) Homola, J. Chem. Rev. 2008, 108, 462. (c) Stewart, M. E.;
Anderton, C. R.; Thompson, L. B.; Maria, J.; Gray, S. K.; Rogers, J. A.;
Nuzzo, R. G. Chem. Rev. 2008, 108, 494. (d) Mayer, K. M.; Hafner, J.
H. Chem. Rev. 2011, 111, 3828.
(35) We monitored the levitation height of beads functionalized with
100% sulfonamide 1 in the presence of 10 μM BCA for more than 500 h
(3 weeks). Even after this extended period of time, protein−ligand
binding had not yet reached its equilibrium state. This fact hindered our
ability to calculate accurately the characteristic time for this system; as a
result, we have excluded this datum point from further analysis.
(36) The small variations in the initial levitation heights of the color-
coded beads are likely due to differences in the densities of the beads
resulting from differences in the densities of the covalently
immobilized ligands, see ref 6b.
(37) (a) Wild, D., Ed. The Immunoassay Handbook; Macmillan Press:
Basingstoke, UK, 1994. (b) Lost, G. J. Principles & Practice of Point-
of-Care Testing; Lippincott Williams & Wilkins: Philadelphia, PA, 2002.
(38) The plot shown in Figure 7A is also presented in the Supporting
Information with a logarithmic concentration axis.
(14) Weinmann, H.-J.; Brasch, R. C.; Press, W.-R.; Wesbey, G. E. Am.
J. Roentgenol. 1984, 142, 619.
(15) Caravan, P.; Ellison, J. J.; McMurry, T. J.; Lauffer, R. B. Chem.
Rev. 1999, 99, 2293.
(16) Krishnamurthy, V. M.; Kaufman, G. K.; Urbach, A. R.; Gitlin, I.;
Gudiksen, K. L.; Weibel, D. B.; Whitesides, G. M. Chem. Rev. 2008,
108, 946.
5646
dx.doi.org/10.1021/ja211788e | J. Am. Chem. Soc. 2012, 134, 5637−5646