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Description
Pareto trade-offs in nanobody binding affinity and its correlation with the geometry of nanobody–antigen structural space
Nanobodies (Nb), truncated versions of heavy-chain–only antibodies from camelids, are the smallest known antigen (Ag)-binding protein fragments and therefore represent a more traceable system for understanding the principles that determine antibody binding affinity. We assembled a database of approximately 80 crystal structures of Nb–Ag complexes and the associated thermodynamic binding parameters measured by isothermal titration calorimetry (ITC). We then formulated the generation of Nb–Ag affinity as a multitask Pareto optimality problem: in order to achieve low Gibbs free energy (high binding affinity), Nb–Ag complexes face a trade-off between optimizing enthalpy or entropy of binding. In the thermodynamic space, the solutions of this trade-off are observed to fall on a line connecting enthalpy-driven and entropy-driven complexes. To understand how this trade-off is resolved at the structural level, we analyzed the geometry of Nb–Ag structural space. We demonstrate that in the space of structural features, Nb–Ag complexes fall within a triangle whose vertices represent structural phenotypes specialized in optimizing (i) enthalpy, (ii) hydrophobic (desolvation) entropy, or (iii) conformational entropy. The triangle thus represents the Pareto front in structural space, and a given Nb–Ag complex is a structural compromise in optimizing these three thermodynamic tasks that are required to achieve high-affinity Nb–Ag binding. These results have important implications for the prediction and optimization of Nb–Ag affinity and for understanding the structure–affinity relationship in protein interactions.
