Quantification of Protein–Ligand Dissociation Kinetics in

Article pubs.acs.org/ac

Quantification of Protein−Ligand Dissociation Kinetics in Heterogeneous Affinity Assays Asha Jacob,† Leo J. van IJzendoorn,† Arthur M. de Jong,† and Menno W.J. Prins*,†,‡ †

Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands Philips Research, Eindhoven, The Netherlands

‡

S Supporting Information *

ABSTRACT: Biochemical affinity assays inherently involve interactions of heterogeneous nature. We report a methodology to discriminate between and accurately characterize specific and nonspecific interactions in force-induced dissociation assays. Ligand-coupled superparamagnetic particles are incubated on surfaces coated with a mixture of specific receptors and nonspecifically interacting proteins. Consequently, a mixed population of surface bound particles is formed with different binding natures. Magnetic field gradients are used to apply translational forces on the bound particles. Using a multicomponent dissociation analysis, we are able to make a distinction between weak nonspecific interactions, strong nonspecific interactions, and specific interactions. We validate the model by comprehensive experiments in which the biochemical components and applied forces are varied. The low-force data yield reliable values for the spontaneous dissociation rates of single-molecule specific bonds, and at high forces, the bond barriers are modified by the applied force. The results generate a new perspective for applications of magnetic force affinity assays in studies of heterogeneous molecular biorecognition.

P

surfaces in order to unravel the characteristics of different bond types. We will propose a model to describe the parallel dissociation processes and demonstrate the ability to accurately characterize the dissociation properties of specific protein bonds in the midst of nonspecific bonds. The results will shed new light on interpretations reported in literature and will give new perspectives for force-induced dissociation studies.

rotein affinity assays exploit the specificity and strength of protein interactions for the sensitive detection of biomarkers in samples of complex biochemical composition. The specificity in the assays is generated by the use of affinity molecules such as antibodies, which are often coupled to a structural polymer material in the shape of a particle or a planar surface.1−4 Inherently, affinity assays involve specific as well as nonspecific interactions. Specific binding is generated by dedicated functional regions on the affinity molecules, namely, the paratopes on an antibody. Nonspecific binding of biomarkers can for example originate from the nonparatope regions of antibodies and from the substrate materials used in the assay. It is a scientific challenge to develop methodologies to classify, to discriminate between, and to accurately quantify specific and nonspecific interactions, with the longer term goal to understand the origins of the specific and nonspecific interactions and to optimize these for the highest possible sensitivity and specificity in novel assay technologies. For a few years now, superparamagnetic particles are being used in affinity biosensing technologies5−7 and in fundamental biophysical investigations.8−12 A key advantage of using magnetic particles is that forces13−16 and torques17−19 can be accurately applied to the particles and to the attached biological molecules. In this paper, we study the dissociation properties of heterogeneous bonds by the application of magnetic forces. Ligand-coupled superparamagnetic particles are incubated on polymer surfaces coated with a mixture of specific receptors and nonspecific proteins. We systematically vary the properties of the © 2012 American Chemical Society

■

MATERIALS AND METHODS Figure 1 sketches the magnetic force immunoassay experiment. A fluid cell with particles bound to the top polystyrene surface is placed on an electromagnet. The magnet consists of a coil around a soft iron core with a tapered end. The radius of the tip is 1 mm. The distance of the binding surface to the tip is 300 μm. The magnetic field is controlled by the current through the coil. The electromagnet is water-cooled to prevent excessive heating. In the experiments, the maximum current and field were 1 A and 300 mT, respectively. Superparamagnetic particles with a diameter of 2.8 μm (Dynabeads M270 carboxylic acid) were used in the experiments. We have calibrated the applied forces by magnetophoresis experiments in the setup, in which the velocity of the particles reveals the forces via the Stokes drag.21−24 The magnetic field profile has also been simulated in Comsol Multiphysics. The magnetic force applied to particles is highly Received: July 22, 2012 Accepted: September 20, 2012 Published: September 20, 2012 9287

dx.doi.org/10.1021/ac301894k | Anal. Chem. 2012, 84, 9287−9294

Analytical Chemistry

Article

Figure 1. Schematic diagram of a magnetic force immunoassay. (a) The instrumental setup with a microscope and an electromagnet. The fluid cell is placed on top of a magnet pole with a 1 mm tip radius. (b) Image of particles bound on the surface as recorded by the camera. (c) Image analysis software counts the number of particles bound as a function of time, to give the force-induced dissociation curve. (d) Sketch of different bond types via which the particles can be bound to the polystyrene surface. The particles exert a magnetic pulling force (F) on the bond. (e) Sketch of the potential energy of a biomolecular bond, with and without an applied force, in the limit of low forces.20

■

uniform across the binding surface due to the large tip radius (1 mm). Above the center of the magnet, the variation of the force was calculated to be less than 2% over a disk with a diameter of 300 μm. Another source of force variability is the presence of neighboring particles. Calculations show that the disturbance of magnetic force is negligible when particles are more than 10 μm apart. Particles with smaller interparticle distances were excluded from the data analysis. The particles on the surface are imaged with a Leica DM6000 microscope at a magnification of 630× (Figure 1b), and images are recorded at 10 Hz with a Redlake MotionPro HS-3 high speed camera. The camera is triggered by the electromagnetic system via a function generator (Agilent, 33250A). The number of bound particles in every movie frame is quantified by a Matlab program. The first frame at t = 0 captures the total number of particles bound on the surface before the application of force, which we denote as Ntot(t = 0). The magnetic field of the electromagnet is driven by running a current through the windings. To reduce the rise time, we have developed a push−pull current controller that temporarily applies a higher voltage up to a maximum of 25 V. With the push−pull circuit, the rise time of the current until 95% is reduced to 4 ms. In our movies, with 10 Hz frame rate, the detachment of magnetic particles is observed starting from the second movie frame. The controller also allows the application of time-dependent currents for demagnetization of the core. The magnet core was demagnetized after every force application. In the Supporting Information, the (bio)chemical procedures are described that we used to functionalize the superparamagnetic particles and the polystyrene surfaces, and to incubate the functionalized superparamagnetic particles on the treated polystyrene surfaces. Details are also given of the surface plasmon resonance (SPR) reference experiment that we conducted.

RESULTS AND DISCUSSION

Model Description for Multicomponent Force-Induced Dissociation. We assume that an ensemble of surface-bound particles can be viewed as a sum of particles that are bound by bonds of different nature i. At time t during a dissociation experiment, the total number of bound particles is given by Ntot(t)=∑Ni(t) and can be expressed as a ratio n(t) calculated with respect to the number of bound particles at t = 0: n(t ) =

∑i Ni(t ) Ntot(t ) = Ntot(t = 0) Ntot(t = 0) with

i

Ni(t ) = Ni(0)e−koff (F )·t

(1)

where Ni(t) describes the time-dependent dissociation of particles of class i. The exponential dependence results from dissociation processes with first-order reaction rate constants kioff(F). The dissociation rate of a bound particle depends on the force because the applied force alters the shape of the energetic dissociation pathway (cf. Figure 1e). The force dependence of dissociation has been extensively worked out in literature for the case of single molecular bonds.20,26 An energy diagram is sketched in Figure 1e. According to the model of Bell and Evans,20 the dissociation rate constant ksoff(0) of a single molecular bond at zero force depends on the height of the energy barrier Eb(0) and the attempt frequency ν as follows: s koff (0) = ν·e[−E b(0)/ kBT ]

(2)

The application of a translational pulling force (F) to the particle tilts the energy landscape of the bond and lowers the height of the energy barrier by −Fxβ, which is the work (force times distance) performed along the reaction path xβ (the distance between the energy minimum and the maximum of the barrier). In the limit of small forces,27 the dissociation rate of a single molecular bond can be expressed as follows:20,26 9288

dx.doi.org/10.1021/ac301894k | Anal. Chem. 2012, 84, 9287−9294

Analytical Chemistry

Article

Figure 2. Force-induced dissociation curves showing multiple components. (a) Biotin-coupled particles on a control surface blocked with nonspecific proteins (curve fit: Ntot = Nnsw + Nnss). (b) Biotin-coupled particles on a surface coated with 5 × 10−12 M solution concentration of antibiotin and blocked with nonspecific proteins (curve fit: Ntot = Nnsw + Ns + Nnss+m). A mid fraction of specific bonds (depicted by s) is revealed. The closed lines represent curve fits. The dotted lines indicate the contributions of the different components. Data were recorded at an applied force of 50 pN. s koff (F ) = ν · e

−[

E b(0) − F ·xβ ] kBT

s = koff (0) ·e[F·xβ / kBT ]

The nsw fraction in Figure 2b shows complete dissociation within the first 0.6 ± 0.1 s after force application. Therefore, the fitting procedure can be simplified by separately regarding two time regimes. At time t = 0, all fractions are bound to the surface, so Ntot(0) = Nnsw(0) + Ns(0) + Nnss+m(0). At times t > 1 s, the nonspecific weak fraction has completely dissociated, so Ntot(t) = Ns(t) + Nnss+m(t). These equations yield the following fitting formula with four independent fitting parameters, for the regime t > 1 s:

(3)

The logarithm of ksoff (F) increases linearly with an increase of the force applied, and an extrapolation to zero force gives an estimate of the spontaneous dissociation rate constant ksoff(F = 0).13 In practice, particles can also bind in other ways than by single molecular bonds, for example, by nonspecific bonds or by multiple bonds, in which case a multicomponent dissociation pattern is expected (cf. eq 1). In the following sections, we will describe experiments in which the different binding classes are differentiated and systematically varied. In regimes where a significant number of particles are bound by single molecular bonds, we will apply eq 3 to characterize the protein−ligand bond. Experimental Deduction of a Tricomponent Model to Analyze Dissociation Data. In this section, we show the general character of the dissociation data and propose the equations for data analysis. Figure 2a shows a typical rupture curve of biotin-coupled particles from a polystyrene surface that has been blocked and does not contain any specific antibodies; Figure 2b shows data for an experiment in which specific antibodies have been included on the surface. The data on the blocked surface shows two clearly distinguishable fractions, namely, a fraction that ruptures within the first second and a smaller fraction that is strongly coupled to the surface. We have observed such dissociation curves with two distinct components in several nonspecific materials systems (see the Supporting Information, Figure S2). When specific antibodies are present on the surface (Figure 2b), a third fraction appears with an intermediate rupture rate. This leads us to hypothesize that the population of bound particles can be viewed as consisting of three fractions, which we denote as the following: a weakly bound fraction with fast dissociation, originating from nonspecific weak binding (nsw); a fraction with intermediate dissociation rate, originating from single molecular specific interactions (s); and a strongly bound fraction with very slow dissociation, originating from nonspecific strong binding (nss) and/or multiple specific bonds (m).

n=

Ns(0) −koffs ·t ⎡ N (0) N (0) ⎤ −koffnss+m·t e + ⎢1 − nsw − s ⎥e Ntot(0) Ntot(0) Ntot(0) ⎦ ⎣ (4)

The curve fits are performed in Origin, and we check that they give good R2 values. In the following sections, we will present and evaluate the fit parameters for dissociation data as a function of the biochemical composition of the polystyrene surface and as a function of the applied force. Dissociation Curves as a Function of the Biochemical Surface Composition. We have recorded dissociation curves for surfaces coated with different solution concentrations of antibiotin, and the curves have been fitted with eq 4. For very high antibiotin concentrations, the rupture curves are flat or nearly flat as the particles hardly dissociate from the surface (see Supporting Information, Figure S3, antibiotin concentration above 10−9 M). This is the regime where a high density of antibodies are present on the surface and multiple bonds occur between the biotin-coated particles and the surface. For low antibiotin concentrations (< 4 × 10−10 M in the Supporting Information, Figure S3), the curves bunch into a single curve with a double-exponent character. We attribute the fact that the curves collapse into a single curve to the presence of dominantly single specific bonds. From the rupture curves, the binding fractions and the corresponding dissociation constants can be extracted using eq 4. Figure 3a shows the fit parameters for the biotin/antibiotin curves. For antibiotin coating solution concentrations above 10−9 M, the particles are strongly bound with dissociation rate constants below 0.01 s−1, which we attribute to the binding by multiple bonds. In the antibiotin 9289

dx.doi.org/10.1021/ac301894k | Anal. Chem. 2012, 84, 9287−9294

Analytical Chemistry

Article

Figure 3. Fractional occupancy of the three bond type populations and the deduced dissociation rates of single specific and multiple bonds. The magnetic assays were performed at 50 pN force. Panels (a) and (b) represent direct assays on surfaces coated with antibiotin and streptavidin, respectively. Panel (c) represents an inhibition assay. Panel (d) represents an assay with mixed specific binders. The error bars are calculated from three replicas. Dashed and straight lines are guides to the eye.

concentration range between 10−12 and 4 × 10−10 M, the fits converge with values for the fraction of single specific bonds in the range between 30% and 50%. The fits in this concentration range give consistent dissociation rate values of about 0.14 ± 0.02 s−1, which we attribute to the dissociation of single specific bonds. Below 10−12 M, a very low number of particles are bound to the surface (cf. Supporting Information, Figure S1), and the

dissociation characteristics of single specific bonds could not be resolved. The data for biotin streptavidin (Figure 3b) also show three concentration regimes and a concentration window (10−11 to 10−9 M) wherein a consistent dissocation rate of 0.07 ± 0.01 s−1 for single bonds is recorded. To demonstrate that the observed koff (F) was specific to the force-induced dissociation of the protein−ligand bonds, an inhibition assay was used (Figure 9290

dx.doi.org/10.1021/ac301894k | Anal. Chem. 2012, 84, 9287−9294

Analytical Chemistry

Article

continuously increasing. Interestingly, above 35 pN, the dissociation rate slows to increase with force. For clarity, the dissociation curves at higher forces are shown in separate panels, in Figure S4 in the Supporting Information. Above 35 pN, the dissociation curves still show distinct changes with force, but the differences are smaller. The extracted dissociation rates of the single specific bonds are plotted as a function of force on lin−log scales in Figure 5a. Between 15 and 35 pN, a clear linear force dependence is observed, in agreement with the Bell−Evans model as expressed in eq 3. The axis intercept at F = 0 of the linear fit reveals the thermal dissociation rate (koff(F = 0)) and the slope of the curve reveals the energy barrier distance (xβ); the deduced parameters are given in Table 1. At forces between 35 and 70 pN, the dissociation rate does not increase linearly with the force and has an undulating character. We attribute these observations to deformations of the molecules at high force, which causes inner energy barriers to become dominant and change the dissociation rate.20 The high force data hold interesting information on the structure and energy landscape of the molecules, but there is no straightforward translation to a thermal dissociation rate. It is important to check whether the observed dissociation is caused by the dissociation of the antibiotin/biotin complex or by the desorption of antibiotin or biotin from the surface. We have recorded force-dependent biotin/antibiotin data for two very different substrate attachment chemistries (see Figure 5a, b). Interestingly, the extracted values for koff and xβ are very similar (Table 1). This proves that the proteins physisorb onto the polystyrene surface through strong interactions, stronger than the protein−ligand bond.28 The weakest link in the polystyrene− protein−ligand−polystyrene complex is the intermolecular bond between the protein and its ligand, allowing a characterization of the dissociation of the protein−ligand bond by the magnetic force assay. To demonstrate the generalizability of the methodology, we have also conducted force-dependent dissociation experiments on the streptavidin/biotin (Figure 5c) and protein G/IgG complexes (Figure 5d), where the IgG is the antibiotin goat IgG that was also used in the earlier experiments. Streptavidin/biotin is the system with highest known biological affinity, having an equilibrium constant KD of about 10−14 M.29 The extrapolated thermal dissociation rate constant at zero force is lower for the streptavidin/biotin bond than for the antibiotin/biotin bond, while the xβ is larger (Table 1). This is in agreement with the fact that the streptavidin−biotin bond is much stronger than the antibiotin−biotin bond. The linear low-force regime terminates at about 45 pN, and at higher forces, a reduction is observed of the dissocation rate. The protein G/IgG bond dissociates the fastest and has the smallest xβ; the linear regime extends up to the maximum applied force. These data show that our method resolves clear distinctions between the different protein−ligand pairs and that reproducible values for the dissociation parameters can be extracted. To further validate our technique, we compare the deduced dissociation rate constants to the rate constants determined by SPR, see Table 1. The extrapolated zero-force dissociation constants are in good agreement with the values obtained by SPR; overall, the values from the magnetic force assay tend to be somewhat higher than the values from SPR. The obtained xβ for biotin−streptavidin is in good relation to values determined by other force techniques such as laminar flow32 (1.2 nm), bio membrane force probe33 (1.2 nm), and molecular dynamics34 (1.2 nm).

3c). Here, streptavidin-coupled particles in an assay buffer containing varying concentrations of free biotin were bound on surfaces coated densely with biotinylated BSA (10−7 M BSA− biotin). High concentrations of free biotin (>10−7 M) resulted in only nonspecific binding, showing that free biotin competitively inhibits specific bonds to form on the surface by the particles. In the free biotin solution concentration window between 10−8 and 10−7 M, single streptavidin−biotin bonds were identified, while at lower concentrations (