KD measurement: methods and materials

Understand K_D measurement methods and materials: microarray printing, binding curve measurement and langmuir binding model analysis.

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OI-RD Scanner

Real-time binding curve measurements for kinetic analysis were made with a label-free optical scanner for microarray detection based on polarization-modulated oblique-incidence reflectivity difference (OI-RD) [1-7]. The method measures changes in magnitude and phase of a laser beam when it reflects off a biomolecule covered solid surface, particularly in response to complex formation on the surface.  

During incubation of a microarray in a probe solution, these “optical” changes are proportional to the surface mass density change when probe molecules are captured from solution and “added” to the printed target layer. The method does not need specially structured substrates such as gold films or dielectric waveguide layers for detection. 

It is thus compatible with microarrays printed on comparatively inexpensive chemically functionalized glass slides. When the thickness of the biomolecule layer is much less than the light wavelength and all of the materials are optically transparent, then the dominant response is in the phase change, given by:

Here,  is the surface mass density of bound probe molecules,  is a function of the light angle of incidence and wavelength, and are the refractive indices of the probe layer, glass microarray substrate, and flowing probe solution buffer, respectively.  In the present measurements, a layer of protein with  = 1 ng / mm² gives 

Figure 1. OI-RD scanner in combination with a fluidic system for real-time microarray detection, illustrated for parallel measurement of antibody binding affinities against immobilized peptide antigen fragments. The scanner measures the extra phase Δδ and extra magnitude Δr due to surface-bound targets (peptides) and subsequently captured probes (antibodies) on a chemically-functionalized glass slide. The focused laser beam is rapidly swept across the microarray to track the surface mass density of bound probe against time for all target spots in the microarray. 

Peptide microarrays were printed on epoxy-functionalized glass slides (ArrayIt, Sunnyvale, CA) using an OmniGrid 100 contact-printing robot (Digilab, Holliston, MA) and 100 µm diameter stainless steel pins (Majer Precision Engineering, Tempe, AZ). The 108 peptide targets were 15 residues long (average molecular weight ~2 kDa) and included a cysteine residue at either the N or C terminus. 

Lyophilized peptide was dissolved in DMSO and diluted with 1× PBS to a final printing concentration of 0.25 mg/mL peptide (~125 µM) with 5% (v/v) residual DMSO. After printing, nucleophillic residues in the peptides, including the terminal cysteines, react covalently with the epoxides on the glass surface, immobilizing the peptides in random orientations on the surface.

Figure 2. OI-RD image of a 15-mer peptide microarray in one of the 8 chambers after the microarray is washed with 1×PBS + 2 mg/mL BSA and before incubation with antibody probes. The variation in spot size from peptide to peptide reflects variation in wetting behavior of the peptide solutions (125 µM printing concentration). peptide to peptide reflects variation in wetting behavior of the peptide solutions (125 µM printing concentration).

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Binding Curve Measurement

For real-time binding curve measurement, we select one pixel from each target spot and two pixels from the neighboring unprinted regions above and below each spot as references. We repeatedly scan and record the signals from this subset of pixels. 

The average signal from the two neighboring reference pixels is subtracted from the corresponding spot pixel, reducing background from instrumental drift, ambient refractive index changes, and flow-induced signal transients.  The background-corrected spot signal during a probe binding reaction constitutes a “binding curve”.

After washing and blocking the microarray with a 2 mg/mL solution of BSA in 1× PBS for 30 minutes, we acquire an image before probe reaction, then flow probe solution to react the microarray (while recording all of the binding curves), and finally acquire an image after the reactions are complete. In these measurements, the microarrays were reacted at ambient temperature (25 °C) with mixtures of 100 rabbit monoclonal antibodies, with each antibody type at equal concentrations of ~99 nM, 33 nM, 11 nM, or 3.7 nM in 1´ PBS. 

Subarrays in separate flow chambers of the optical scanner were used to perform reactions at the four concentrations. For each reaction, we first acquire a baseline for 30 min (1´ PBS flowing at 0.01 mL/min), quickly replace the buffer with probe solution and monitor the association reaction for 15 min (probe solution flowing at 0.01 mL/min), and lastly quickly replace the probe solution with buffer and monitor the dissociation reaction for 120 min (1´ PBS flowing at 0.01 mL/min).

Langmuir Binding Model Analysis

The simple 1-to-1, or Langmuir, reaction model was used to analyze the measured sets of binding curves through global nonlinear curve fitting.  In this model, solution-phase probes bind to surface-immobilized targets at a rate , with C being the probe concentration.  The captured probes dissociate from probe-target complexes at a rate , independent of C.  When the probe solution is introduced to the microarray at  and is replaced with buffer again later at , the surface mass density of probe on the surface is:

For .  is the maximum probe surface mass density, which depends on factors such as the target density, probe molecular shapes, and probe molecular orientations on the surface.  The rate constants  and  are extracted from binding curves by nonlinear fitting to Eq. (2a) and (2b) simultaneously.  To further constrain the nonlinear curve fit, we measure a set of binding curves by varying the probe concentration C over roughly one order of magnitude and fit all of the curves in the set (including microarray spot replicates) simultaneously.  Generally,  varies from spot to spot in a microarray and from microarray to microarray.  Because each binding curve is measured with a different microarray spot, we treat  as a fitting parameter that may vary from curve to curve within a set while treating  and  as common (global) parameters to all the curves.  The equilibrium dissociation constant for the reaction is obtained from the relation .

References

1. Landry, J. P., Fei, Y. & Zhu, X. Simultaneous Measurement of 10,000 Protein-Ligand Affinity Constants Using Microarray-Based Kinetic Constant Assays. Assay Drug Dev. Tech. 10, 250-259 (2012). PubMed PMID: PMC3374384.

2. Landry, J. P., Fei, Y. Y. & Zhu, X. D. High Throughput, Label-free Screening Small Molecule Compound Libraries for Protein-Ligands using Combination of Small Molecule Microarrays and a Special Ellipsometry-based Optical Scanner. International Drug Discovery 6, 8-13 (2012). PubMed PMID: PMC3271728.

3. Fei, Y., Sun, Y.-S., Li, Y., Lau, K., Yu, H., Chokhawala, H. A., Huang, S., Landry, J. P., Chen, X. & Zhu, X. Fluorescent labeling agents change binding profiles of glycan-binding proteins. Mol. BioSyst. 7, 3343-3352 (2011). PubMed PMID: 22009201.

4. Sun, Y. S., Landry, J. P., Fei, Y. Y., Zhu, X. D., Luo, J. T., Wang, X. B. & Lam, K. S. Effect of Fluorescently Labeling Protein Probes on Kinetics of Protein-Ligand Reactions. Langmuir 24, 13399-13405 (2008). PubMed PMID: 18991423.

5. Landry, J. P., Sun, Y. S., Guo, X. W. & Zhu, X. D. Protein reactions with surface-bound molecular targets detected by oblique-incidence reflectivity difference microscopes. Appl. Opt. 47, 3275-3288 (2008). PubMed PMID: PMC2739384.

6. Zhu, X. D., Landry, J. P., Sun, Y. S., Gregg, J. P., Lam, K. S. & Guo, X. W. Oblique-incidence reflectivity difference microscope for label-free high-throughput detection of biochemical reactions in a microarray format. Appl Opt 46, 1890-1895 (2007). PubMed PMID: 17356635.

7. Landry, J. P., Zhu, X. D. & Gregg, J. P. Label-free detection of microarrays of biomolecules by oblique-incidence reflectivity difference microscopy. Opt. Lett. 29, 581-583 (2004).