Fluctuation, correlation and perturbation-response behavior of nature-made and artificial nanobodies

Nanobodies, like other antibodies bind their targets through complementarity determining regions (CDRs). Improving nanobody-antigen binding affinities by introducing mutations in these CDRs is critical for biotechnological applications. However, any mutation is expected to introduce changes in the behavior of the protein, such as fluctuations of residues, correlation of fluctuations of residue pairs, response of a residue to perturbation of another. Most importantly, the nanoscale dynamics of the protein may change. In these respects, the problem is similar to the general problem of dynamic allostery, a perturbation at one site affecting the response at another site. Using the Gaussian Network Model of proteins, we show that CDR mutations indeed modify the fluctuation profile and dynamics of the nanobody. Effects are not confined to CDR regions but extend throughout the full structure. We introduce a computational scheme where fluctuations of a residue are perturbed by a force and response amplitude and response time of the remaining residues are determined. Response to a perturbation of a residue shows a synchronous and an asynchronous component. The model is used to quantify the effects of mutation on protein dynamics: highly perturbable residues and highly responsive residues of the nanobody are determined. Residues whose perturbation has no effect on protein behavior may also be determined with the present model. Three known nanobodies produced by nature are used as an illustrative example and their various modifications which we generated by CDR residue mutations are analyzed.