A Multivalent entity, which could represent a protein, nanoparticle, polymer, virus or a lipid bilayer, has the ability to form multiple bonds to a substrate. Hence, a multivalent interaction can be strong, even if the individual bonds are weak. However, much more interestingly, multivalency enables the design of highly specific interactions using non-specific individual bonds. We attempt to rationalise multivalent effects using simple physical models complemented with numerical simulations. Based on physiochemical characteristics of multivalent binders, we aim to predict the overall strength of interaction and its sensitivity to variation in parameters.

We start with a simple model of homo-multivalency, where all bonds are equivalent. Such systems can exhibit a super-selective response, which denotes the high sensitivity of the strength of multivalent binding to the number of accessible binding sites on the target surface. We present a theoretical analysis of systems of multivalent particles and show that a certain degree of disorder is necessary for super-selective behaviour. Moreover, we formulate a set of simple design rules for multivalent interactions that yield optimal selectivity.

In the second stage, we expand the model to hetero-multivalency, accounting for multiple distinct types of binding partners. We consider targeting of cells based on a density profile of different membrane receptors types and demonstrate, that speci city towards a desired receptor density profile can be obtained. Hence, cells can be reliably targeted in the absence of specific markers. Crucially, we show that for optimal selectivity, individual bonds must be weak.

Finally, we add information about specific geometry and positions of binding sites on the multivalent entity. We focus on molecular imprinting; the process whereby a polymer matrix is cross-linked in the presence of template molecules. The cross-linking process endows the polymer matrix with a chemical ‘memory’, such that the target molecules can subsequently be recognised by the matrix. We show how the binding multivalency and the polymer material properties affect the efficiency and selectivity of molecular imprinting.