Backbone flexibility of CDR3 and immune recognition of antigens

Conformational entropy is an important component of protein-protein interactions; however, there is no reliable method for computing this parameter. We have developed a statistical measure of residual backbone entropy in folded proteins by using the ϕ-ψ distributions of the 20 amino acids in common secondary structures. The backbone entropy patterns of amino acids within helix, sheet or coil form clusters that recapitulate the branching and hydrogen bonding properties of the side chains in the secondary structure type. The same types of residues in coil and sheet have identical backbone entropies, while helix residues have much smaller conformational entropies. We estimated the backbone entropy change for immunoglobulin complementarity-determining regions (CDRs) from the crystal structures of 34 low-affinity T-cell receptors and 40 high-affinity Fabs as a result of the formation of protein complexes. Surprisingly, we discovered that the computed backbone entropy loss of only the CDR3, but not all CDRs, correlated significantly with the kinetic and affinity constants of the 74 selected complexes. Consequently, we propose a simple algorithm to introduce proline mutations that restrict the conformational flexibility of CDRs and enhance the kinetics and affinity of immunoglobulin interactions. Combining the proline mutations with rationally designed mutants from a previous study led to 2400-fold increase in the affinity of the A6 T-cell receptor for Tax-HLAA2. However, this mutational scheme failed to induce significant binding changes in the already-high-affinity C225-Fab/huEGFR interface. Our results will serve as a roadmap to formulate more effective target functions to design immune complexes with improved biological functions.