Extended Data Fig. 4: Quantification of the number of available binding sites per FND.

a, Initially, binding constants of the anti-DIG antibody binding to DIG were measured using interferometry. Full experimental details are shown in Supplementary Information section 1. Binding at different concentrations was measured and the resulting curves were fitted to exponentials. To find the equilibrium dissociation constant (K_D), equilibrium binding values, B, were plotted here against concentration, C. A Langmuir adsorption isotherm was fitted \(({B}^{{\rm{\infty }}}=\frac{a\times C}{{K}_{{\rm{D}}}+C})\) giving a K_D value of 5.1 × 10⁻¹⁰ M. b, In order to find the on- and off-rates, k_on and k_off, the observed reaction rates, k_obs, at each concentration were plotted and fitted to the linear relationship: k_obs = k_off + C × k_on. The resulting fitted values are k_on = 1.6 × 10⁵ M⁻¹ s⁻¹ and k_off = 9.1 × 10⁻⁵ s⁻¹. c, A schematic of the assay to quantify the number of available binding sites per FND. After functionalization of FNDs with anti-DIG antibodies, an approximately 50-fold excess of DIG-modified DNA was added and left to bind for 2 h. The negative DNA control used the same sequence, but with no DIG modification to compensate for non-specific binding and adequate washing. After multiple washes by centrifugation to remove the excess DNA, the remaining DNA (bound to FNDs) was quantified by qPCR. See Extended Data Fig. 8d for template, primer and probe sequences, and Methods for full experimental details. d, A kinetic binding simulation was performed to verify that all available sites would be occupied after 2 h with the above excess. The graph shows the fraction of sites on the FNDs which are occupied, with this approximately 50-fold excess, over a range of K_D, k_on and k_off values. The red cross in circle marks the location of the anti-DIG antibody used in this paper (using the values measured in a and b), indicating that more than 99.9% of available sites will be occupied after 2 h. This means that quantifying the DNA gives a true measure of available binding sites. e, Amplification plot showing the normalized fluorescence intensity against the number of cycles. A standard curve of each decade from 40 copies to 4 × 10⁸ copies is plotted, along with the sample and negative control FND samples described above. The negative diluent controls are also plotted along with the C_q threshold. The lines show means and shaded areas show the s.d. of repeats (n = 3 technical replicates for standard curve, and n = 6 for samples). f, The resulting C_q values are plotted against copy number per reaction. Dots show means and error bars show s.d. (n = 3 technical replicates for standard curve and n = 6 for samples). The standard curve was fitted to a logarithmic curve (C_q = −3.2log₁₀ copies + 39), enabling calculation of the number of copies in the DIG–DNA sample and negative DNA control. Dividing by the particle concentration (measured as shown in Extended Data Fig. 5c) and subtracting the negative DNA control value gives the number of available binding sites per particle as 4,300 sites. This is within what is geometrically plausible, giving an area per antibody of at least 200 nm² (assuming at least 1 paratope available of at least 75% of the bound antibodies). The corresponding calculated values for 120 and 200 nm particles are 172 and 477 available binding sites per FND respectively, assuming the same loading density.