How antibody surface coverage on nanoparticles determines the. activity and kinetics of antigen capturing for biosensing

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1 How antibody surface coverage on nanoparticles determines the activity and kinetics of antigen capturing for biosensing Bedabrata Saha, Toon H. Evers, and Menno W. J. Prins Philips Research, High Tech Campus, 5656 AE Eindhoven, The Netherlands Supporting Information

2 Quantification of number of antibodies per nanoparticle: The amount of immobilized antibody was quantified by a supernatant assay using a commercial Easy Titer Antibody Assay Kit (Thermo Scientific, Pdt. No ), as mentioned in the main text. Briefly, the antibody assay kit is based on agglutination of anti IgG antibody functionalized micrometer-sized polystyrene particles. Upon incubation with antibody sample, the polystyrene particles aggregate which leads to an increased transmittance of light. A standard curve was generated where the increased transmittance is proportional to the increased antibody concentration. Unknown concentrations could be accurately determined by interpolating between points on the standard curve, over a dynamic range of ng ml -1 with a precision of about 5%. Optomagnetic biosensor technology: determining supernatant ctni concentration for quantification of active antibodies For active antibody quantification, the antibody immobilized magnetic nanoparticles were incubated with increasing concentration of ctni, and the supernatant concentration of the remaining ctni was measured using optomagnetic biosensor platform as developed by Philips. In this optomagnetic biosensor technology, superparamagnetic nanoparticles are used as a detection label. Briefly, the sample with ctni molecules is injected into a microchamber inside a disposable cartridge, where the ctni is captured by antibody functionalized magnetic nanoparticles. The disposable cartridges were printed and assembled as described by Dittmer et al. 16 After ctni capturing, the nanoparticles are attracted by magnetic fields for fast and specific binding with the sensor surface, which is functionalized with a secondary antibody (MAb2) for a sandwich assay. After binding on the sensor surface, unbound and weakly, non-specifically bound nanoparticles are removed by a magnetic force directed away from the sensor surface (see Figure S1). Thereafter nanoparticles bound at the sensor surface are detected by scattering and absorption of an evanescent optical field, by so-called frustrated total internal reflection (f-tir). The f-tir detection technology was found to be a fast and sensitive way to measure low amounts of target molecules 3 and has been used to detect the supernatant ctni concentration in our experiments. The optical signals of the calibration curve and of the supernatant ctni solution were plotted in one graph, and the concentration of captured ctni was calculated from the distance between the calibration curve and supernatant ctni points (see Figure S2). To optimally map the samples into the dynamic range of the f-tir assay, 3 samples having higher ctni concentration were diluted known times (1x, 10x or 20x) before analysis. Thereafter, the distance of the diluted sample points from the dilution-shifted calibration curve was measured (see Figure S2).

Figure S1: Nanoparticle-based opto-magnetic biosensor platform which we have used to detect ctni in our experiments. The figure is adopted from a previous report.

3 Figure S1: Nanoparticle-based opto-magnetic biosensor platform which we have used to detect ctni in our experiments. The figure is adopted from a previous report. 3 The target detection process consists of three steps as described above. Briefly: (1) capturing of target molecule by antibody functionalized magnetic nanoparticles inside the micro-chamber in a disposable cartridge, (2) Magnetic attraction of target captured nanoparticles towards lower sensor surface, which is functionalized with a secondary antibody (MAb2) for a sandwich assay. (3) Magnetic wash by a top magnet to remove unbound and weakly non-specifically bound nanoparticles from sensor surface, and (4) optical detection of surface-bound nanoparticles by scattering and absorption of an evanescent optical field (frustrated total internal reflection).

4 Figure S2: Analysis method for the quantification of the number of ctni molecules captured onto antibody (MAb1) functionalized magnetic nanoparticles, using a supernatant ctni assay. The supernatant ctni samples were analyzed in the opto-magnetic biosensor platform (described in Figure S1), yielding optical signals which were plotted together with the calibration curve measured using the same ctni concentration. The captured ctni amount in pm was determined from the distance between the measured samples and the calibration curve in each case (panel a). With higher ctni concentration, the samples were diluted. For analyzing the samples accurately, the calibration curve was also shifted by the same factor as used for the dilution of the samples (panels b and c). The bound ctni amount was calculated from the distance between diluted sample points and the shifted calibration curve (panels b and c). From this distance, the amount of ctni per nanoparticle was calculated by dividing the captured ctni (in pm, determined from graph) by the known nanoparticle concentration (MAb1 functionalized) in solution. All measurements were done in triplicate; error bars represent the standard deviations. The panels show supernatant ctni samples at increasing concentration, measured by diluting a factor 1, 10 and 20. The calibration curves (red lines) were shifted by the same factor (1, 10 and 20); and the distance between the calibration curve and the measured points was used to calculate the captured ctni concentration.

5 Figure S3: Saturation plot of ctni capture by bare nanoparticles (panel a) and by antibody functionalized nanoparticles (panels b to g) at different antibody coverages. From the saturation plot the number of active antibodies was derived. The antibody functionalized nanoparticles were saturated with ctni using increasing ctni concentrations and the supernatant ctni was measured in the optomagnetic biosensor platform (as in Figure S1). In each case the number of captured ctni molecules per nanoparticle was calculated as described in Figure S2, and plotted separately. The numbers of active antibodies at different surface coverages were then calculated from the average of the saturation points in each plot (indicated by the dashed line). The same data is fitted to the Langmuir isotherm model in Figure S6.

6 Figure S4: (a) Hydrodynamic diameter (nm) and (b) surface potential (mv) of bare carboxylic superparamagnetic nanoparticles with increasing anti-troponin antibody (MAb1) surface coverage.

7 Analysis of ctni capturing kinetics The kinetic data of ctni capturing was analyzed with the Langmuir kinetic model where the fractional 29, 30 coverage of immobilized antibodies by ctni, θ(t) at time t, is expressed as: (S1) Here C T (t) is the ctni concentration in solution at time t, and k on (M -1 sec -1 ) and k off (sec -1 ) are the kinetic parameters. Now, the concentration of ctni captured antibodies, C A-T (t) at time t, can be derived from the fractional coverage of the antibodies: (S2) where C A (0) is the volume concentration of active antibodies, which can be calculated from the number of active antibodies per nanoparticle multiplied by the nanoparticle concentration in the solution. The active antibody concentration at different antibody coverages was obtained from the ctni saturation experiments described in Figure S3. As ctni is captured by the antibodies, gradually the concentration of free ctni molecules in solution is lowered. Assuming that the depletion is global, the time-dependent target concentration, C T (t), can be expressed as: (S3) Now, putting the values of Eq. S2 and Eq. S3 into Eq. S1, and rearranging, we get: { } { ( ) } (2) The kinetic data with different ctni concentrations and with different antibody concentrations was fitted with Eq. 2 (also represented in main manuscript) using MATLAB software, in order to extract the kinetic parameters. The active antibody concentration, C A (0), and the initial ctni concentration, C T (0), have been used as input parameters for the respective curve fitting.

8 Figure S5. Kinetic analysis of solution-based ctni capture in buffer (PBS buffer, ph 7.4). (a) ctni capture by antibody-coated nanoparticles with MAb1/MNP, recorded as a function of incubation time. Kinetic data was measured at different ctni concentrations 150 pm, 500 pm and 1000 pm (corresponding to 30, 100 and 200 ctni molecules available per antibody functionalized nanoparticle respectively). The kinetic model expressed in Eq. 2 has been fitted to the data; fits are represented by the solid lines. (b) Association rate constant k on of ctni capture by anti-ctni antibody functionalized magnetic nanoparticles, at 150, 500 and 1000 pm of initial ctni solution (corresponding to 30, 100, and 200 ctni per nanoparticle) derived from the fits in panel a. (c) Dissociation rate constant k off derived from the fits. (d) Equilibrium dissociation constants K d derived from the fits. Error bars represent the standard deviation calculated from triplicate experiments which includes the experimental error.

9 Figure S6: Fits of the Langmuir isotherm model [Eq. (3)] to the data of Figure S3.

10 Figure S7: Fitted dissociation constant values (K d ) for ctni capture as a function of antibody surface coverage. The K d values were derived from the kinetic fits in Figure 3 and the equilibrium fits in Figure S6. Heterogeneity of immobilized antibodies: From the equilibrium ctni capture data we know that the target binding affinity of immobilized antibodies is heterogeneous, because the amount of ctni that can be captured is much lower than the amount of antibodies immobilized on the particle surface. Therefore, we can assume that the immobilized antibodies consist of a heterogeneous population with different binding affinities for the target molecules in solution. For calculational simplicity, we assume a two-fraction model. K d1 indicates the lower dissociation constant (antibodies with highest binding affinity) of a fraction of antibodies (C A1 ) for ctni capture (C T ), and K d2 indicates the higher dissociation constant (weak binding affinity) of the remaining immobilized antibodies (C A2 ): [ ] [ ] [ ] (Eq. S4) [ ] [ ] [ ] (Eq. S5) where, C A1-T and C A2-T are the concentration of ctni captured antibodies. Now the Langmuir isotherm model can be expressed as (Eq. 3):

11 By rearranging: (Eq. S6) Substituting the fractions from Eq. S4 and Eq. S5 in the Langmuir isotherm equation (Eq. S6) ( ) [ ] [ ] (Eq. S7) The above equation (Eq. S7) represents the linearized form of the Langmuir isotherm with two fractions of immobilized antibodies having different dissociation constant values for ctni molecules. The term C A1- T(max) and C A2-T (max) are the maximum possible ctni that can be captured by high affinity and weak affinity immobilized antibodies respectively. If the dissociation constant values of the large fraction of the immobilized antibodies (having weaker binding affinity) is significant to influence this system, we would have seen two different slopes in the plots. However, experimental data does not show multiple slopes in the fitted Langmuir plot for all antibody surface coverage (Figure S6). This implies from Eq. S7: (Eq. S8) (Eq. S9) We have experimentally obtained a molar ratio C A1-T (max)/c A2-T (max) of 0.04 or lower (see Figure 2), and a dissociation constant value for strong affinity binding (K d1 ) is in the range of M (see Figure 3 and Figure S7). Substituting in Eq. S9, we find that K d2 >> M. This gives an estimation of the dissociation constant range for the majority (96% or more) of antibodies on the nanoparticles.

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