Predicting the size and morphology of nanoparticle clusters driven by biomolecular recognition

Nanoparticle aggregation is a driving principle of innovative materials and biosensing methodologies, improving transduction capabilities displayed by optical, electrical or magnetic measurements. This aggregation can be driven by the biomolecular recognition between target biomolecules (analytes) and receptors bound onto nanoparticle surface. Despite theoretical advances on modelling the entropic interaction in similar systems, predictions of the fractal morphologies of the nanoclusters of bioconjugated nanoparticles are lacking. The morphology of resulting nanoclusters is sensitive to the location, size, flexibility, average number of receptors per particle f, and the analyte-particle concentration ratio. Here we considered bioconjugated iron oxide nanoparticles (IONPs) where bonds are mediated by a divalent protein that binds two receptors attached onto different IONPs. We developed a protocol combining analytical expressions for receptors and linker distributions, and Brownian dynamics simulations for bond formation, and validated it against experiments. As more bonds become available (e.g., by adding analytes), the aggregation deviates from the ideal Bethe's lattice scenario due to multivalence, loop formation, and steric hindrance. Generalizing Bethe's lattice theory with a (not-integer) effective functionality f(eff) leads to analytical expressions for the cluster size distributions in excellent agreement with simulations. At high analyte concentration steric impediment imposes an accessible limit value f(acc) to f(eff), which is bounded by f(acc) < f(eff) < f. A transition to gel phase, is correctly captured by the derived theory. Our findings offer new insights into quantifying analyte amounts by assessing nanocluster size, and predicting nanoassembly morphologies accurately is a first step towards understanding variations of physical properties in clusters formed after biomolecular recognition.