Structure-informed theoretical modeling defines principles governing avidity in bivalent protein interactions.

In signaling cascades, where domain-motif interactions tend to interact with relatively low affinity (allowing for reversibility), signaling proteins often encode multiple domains or motifs, which present the possibility of avidity - drastically increasing the interaction strength and duration as a result of multivalent binding. However, given the large combinatorial space, predicting and validating multivalent interactions that interact with avidity is a challenge. Here, we integrate mechanistic modeling, structure-based analysis, and experimental approaches as a framework for defining the conditions under which avidity plays a role. We explore the tandem SH2 domain family of interactions with bisphosphorylated partners as a multivalent archetype, which encompasses key secondary messengers in tyrosine kinase signaling networks. While certain multivalent interactions have been shown to be necessary in immune receptor recruitment of partners, bivalent recruitment of tandem SH2 domains more broadly is poorly understood. Theoretical modeling suggests that maximum avidity occurs with closely spaced or flexibly linked phosphotyrosine sites, combined with moderate monovalent affinities - exactly around the innate range of SH2 domain affinity. Surprisingly, despite sequence diversity, structure-based analysis showed remarkably conserved three-dimensional spacing between SH2 domains across all tandem SH2 families, which we corroborate experimentally, suggesting evolutionary optimization for avidity interactions. The combination of structure-based analysis of domain spacing with available monovalent experimental data appears to be sufficiently accurate to predict and rank order high affinity interactions of tandem SH2 domain recruitment to the EGFR C-terminal tail. These approaches lay the groundwork for larger utility in multivalent prediction and testing to help better understand protein interactions that drive cell signaling.