Quantifying Intramolecular Binding in Multivalent Interactions: A Structure-Based Synergistic Study on Grb2-Sos1 Complex

Numerous signaling proteins use multivalent binding to increase the specificity and affinity of their interactions within the cell. Enhancement arises because the effective binding constant for multivalent binding is larger than the binding constants for each individual interaction. We seek to gain both qualitative and quantitative understanding of the multivalent interactions of an adaptor protein, growth factor receptor bound protein-2 (Grb2), containing two SH3 domains interacting with the nucleotide exchange factor son-of-sevenless 1 (Sos1) containing multiple polyproline motifs separated by flexible unstructured regions. Grb2 mediates the recruitment of Sos1 from the cytosol to the plasma membrane where it activates Ras by inducing the exchange of GDP for GTP. First, using a combination of evolutionary information and binding energy calculations, we predict an additional polyproline motif in Sos1 that binds to the SH3 domains of Grb2. This gives rise to a total of five polyproline motifs in Sos1 that are capable of binding to the two SH3 domains of Grb2. Then, using a hybrid method combining molecular dynamics simulations and polymer models, we estimate the enhancement in local concentration of a polyproline motif on Sos1 near an unbound SH3 domain of Grb2 when its other SH3 domain is bound to a different polyproline motif on Sos1. We show that the local concentration of the Sos1 motifs that a Grb2 SH3 domain experiences is approximately 1000 times greater than the cellular concentration of Sos1. Finally, we calculate the intramolecular equilibrium constants for the crosslinking of Grb2 on Sos1 and use thermodynamic modeling to calculate the stoichiometry. With these equilibrium constants, we are able to predict the distribution of complexes that form at physiological concentrations. We believe this is the first systematic analysis that combines sequence, structure, and thermodynamic analyses to determine the stoichiometry of the complexes that are dominant in the cellular environment. Author Summary: Many biochemical interactions are mediated by multivalent binding where signaling proteins use relatively weak promiscuous interactions to increase the strength and specificity of complex formation. For a bivalent adaptor protein binding to a multivalent ligand, the tethering of one of the adaptors binding sites to a motif on a multivalent ligand constrains the adaptors second binding site to a region with a high local concentration of ligand binding motifs. Intramolecular equilibrium constants associated with multivalency are difficult to measure. Typically, polymer models are utilized to estimate the enhancement in local concentration and, when the biomolecular equilibrium constants for the individual sites are known, to obtain intramolecular equilibrium constants. However, flexibility of structured regions in proteins that contain the binding motifs restricts the application of simple polymer models for many systems. Here, we develop a hybrid method combining molecular dynamics simulations and polymer models to estimate the intramolecular equilibrium constants. We apply this method to study the multivalent interactions between the widely expressed adaptor protein growth factor receptor bound protein-2 (Grb2) and the nucleotide exchange factor son of sevenless 1 (Sos1).