Multivalent systems have recently drawn increasing interest due to their unique capability of reacting ultrasensitively to small changes in the applied conditions. This property has been validated as a tool for a wide range of applications, spacing from diagnostics to nanomedicine: exploiting the multivalent supereselectivity, it is possible to improve accuracy in diagnostic methods or enhance the targeting of diseased cells in nanomedicine.

This thesis extends the theoretical and computational framework of multivalent system, focusing on the case of multivalent colloids. Our modelling introduces novel details of multivalent colloids, allowing for the evaluation of their effect on supereselectivity. With this model, we implement MC simulations to predict the behaviour of multivalent systems in function of the parameters of interest. Specifically, we consider the effect of: reduced mobility of ligands and receptors; a realistic model of repulsion interactions; colloidal anisotropy; localization of ligands into patches.

Using our model we also implemented simulations to predict the phase diagram of multivalent colloids, looking at the specific case of DNA Coated Colloids (DNACC). We implemented MC to compute the phase diagram of DNACC when in solution with linker molecules capable of forming bridges between colloidal pairs. This models the application of multivalent colloids as diagnostic tools, in which a phase transition of the colloids signals a specific biomarker in the analyte. We also modelled sample contamination
introducing a distribution of interaction energies between colloids and linkers.

Finally we adapted the theoretical framework for multivalency to model an experimental data produced by collaborators. We show that applying pure theory, one can predict experimental results with remarkable accuracy. Moreover, we derived a kinetic model for the absorption of multivalent colloids to a receptor decorated surface, validating it against experimental data. Our model captures experimental trends accurately providing new insights on the kinetics of multivalency.