Antibodies have become the Swiss Army tool for molecular biology and nanotechnology. Their outstanding ability to specifically recognise molecular antigens allows their use in many different applications from medicine to the industry. Moreover, the improvement of conventional structural biology techniques (e.g., X-ray, NMR) as well as the emergence of new ones (e.g., Cryo-EM), have permitted in the last years a notable increase of resolved antibody-antigen structures. This offers a unique opportunity to perform an exhaustive structural analysis of antibody-antigen interfaces by employing the large amount of data available nowadays. To leverage this factor, different geometric as well as chemical descriptors were evaluated to perform a comprehensive characterization.

This work explores the impact of knots, knot depth and motif of the threading terminus in protein folding properties (kinetics, thermodynamics and mechanism) via extensive Monte Carlo simulations of lattice models. A knotted backbone has no effect on protein thermodynamic stability but it may affect key aspects of folding kinetics. In this regard, we found clear evidence for a functional advantage of knots: knots enhance kinetic stability because a knotted protein unfolds at a distinctively slower rate than its unknotted counterpart. However, an increase in knot deepness does not necessarily lead to more effective changes in folding properties. In this regard, a terminus with a non-trivial conformation (e.g. hairpin) can have a more dramatic effect in enhancing kinetic stability than knot depth. Nevertheless, our results suggest that the probability of the denatured ensemble to keep knotted is higher for proteins with deeper knots, indicating that knot depth plays a role in determining the topology of the denatured state. Refolding simulations starting from denatured knotted conformations show that not every knot is able to nucleate folding and further indicate that the formation of the knotting loop is a key event in the folding of knotted trefoils. They also show that there are specific native contacts within the knotted core that are crucial to keep a native knotting loop in denatured conformations which otherwise have no detectable structure. The study of the knotting mechanism reveals that the threading of the knotting loop generally occurs towards late folding in conformations that exhibit a significant degree of structural consolidation.

The folding properties of a protein whose native structure contains a 52 knot are investigated by means of extensive Monte Carlo simulations of a simple lattice model and compared with those of a 31 knot. A 52 knot embedded in the native structure enhances the kinetic stability of the carrier lattice protein in a way that is clearly more pronounced than in the case of the 31 knot. However, this happens at the expense of a severe loss in folding efficiency, an observation that is consistent with the relative abundance of 31 and 52 knots in the Protein Data Bank. The folding mechanism of the 52 knot shares with that of the 31 knot the occurrence of a threading movement of the chain terminus that lays closer to the knotted core. However, co-concomitant knotting and folding in the 52 knot occurs with negligible probability, in sharp contrast to what is observed for the 31 knot. The study of several single point mutations highlights the importance in the folding of knotted proteins of the so-called structural mutations (i.e., energetic perturbations of native interactions between residues that are critical for knotting but not for folding). On the other hand, the present study predicts that mutations that perturb the folding transition state may significantly enhance the kinetic stability of knotted proteins provided they involve residues located within the knotted core.

Nanobodies offer a viable alternative to antibodies for engineering high affinity binders. Their small size has an additional advantage: it allows exploiting computational protocols for optimizing their biophysical features, such as the binding affinity. The efficient prediction of this quantity is still considered a daunting task especially for modelled complexes. We show how molecular dynamics can successfully assist in the binding affinity prediction of modelled nanobody–protein complexes. The approximate initial configurations obtained by in silico design must undergo large rearrangements before achieving a stable conformation, in which the binding affinity can be meaningfully estimated. The scoring functions developed for the affinity evaluation of crystal structures will provide accurate estimates for modelled binding complexes if the scores are averaged over long finite temperature molecular dynamics simulations.