Rationalizing 5000-Fold Differences in Receptor-Binding Rate Constants of Four Cytokines

The four cytokines erythropoietin (EPO), interleukin-4 (IL4), human growth hormone (hGH), and prolactin (PRL) all form four-helix bundles and bind to type I cytokine receptors. However, their receptor-binding rate constants span a 5000-fold range. Here, we quantitatively rationalize these vast differences in rate constants by our transient-complex theory for protein-protein association. In the transient complex, the two proteins have near-native separation and relative orientation, but have yet to form the short-range specific interactions of the native complex. The theory predicts the association rate constant as ka=ka0exp(−ΔGel∗/kBT) where ka0 is the basal rate constant for reaching the transient complex by random diffusion, and the Boltzmann factor captures the rate enhancement due to electrostatic attraction. We found that the vast differences in receptor-binding rate constants of the four cytokines arise mostly from the differences in charge complementarity among the four cytokine-receptor complexes. The basal rate constants (ka0) of EPO, IL4, hGH, and PRL were similar (5.2 × 105 M−1s−1, 2.4 × 105 M−1s−1, 1.7 × 105 M−1s−1, and 1.7 × 105 M−1s−1, respectively). However, the average electrostatic free energies (ΔGe1∗) were very different (−4.2 kcal/mol, −2.4 kcal/mol, −0.1 kcal/mol, and −0.5 kcal/mol, respectively, at ionic strength = 160 mM). The receptor-binding rate constants predicted without adjusting any parameters, 6.2 × 108 M−1s−1, 1.3 × 107 M−1s−1, 2.0 × 105 M−1s−1, and 7.6 × 104 M−1s−1, respectively, for EPO, IL4, hGH, and PRL agree well with experimental results. We uncover that these diverse rate constants are anticorrelated with the circulation concentrations of the cytokines, with the resulting cytokine-receptor binding rates very close to the limits set by the half-lives of the receptors, suggesting that these binding rates are functionally relevant and perhaps evolutionarily tuned. Our calculations also reproduced well-observed effects of mutations and ionic strength on the rate constants and produced a set of mutations on the complex of hGH with its receptor that putatively enhances the rate constant by nearly 100-fold through increasing charge complementarity. To quantify charge complementarity, we propose a simple index based on the charge distribution within the binding interface, which shows good correlation with ΔGe1∗. Together these results suggest that protein charges can be manipulated to tune ka and control biological function.