**3. Discussion**

Nb23 was raised against ∆N6β2m to inhibit its amyloid formation, and could potentially be used for inhibiting fibril formation of other amyloidogenic β2m-variants. By using typical TROSY 3D experiments for backbone and aliphatic sidechain assignments, and 2D aromatic sidechain experiments for aromatic assignments, the chemical shifts of Nb23 were assigned. These chemical shift assignments were used for chemical shift-based homology modeling with CS-Rosetta giving a representative protein model as output. The model was in turn used together with the chemical shifts for NOE-restrained structure calculation supported by prior-knowledge of the structure. Relying on the experimental character of this prior knowledge, the choice was deliberately made to include only the unambiguously assigned NOEs to determine the solution structure of Nb23. Despite using what is considered a low number of NOE constraints (619) for structure determination—usually one would need ten NOEs per residue and Nb23 has ~130 residues—the resulting structures showed the general features of a single variable immunoglobulin domain and the general features of a nanobody. This minimalist approach was employed because of extensive signal overlap (especially for sidechains) making the unambiguous assignment not possible. Unfortunately, the issue of ambiguity could not be addressed because the necessary improvements of signal-to-noise and resolution conflicted with (i) the solubility and stability limits of Nb23 samples, which form precipitate in a matter of hours after dissolving the protein, and (ii) the current difficulties of accessing higher magnetic field facilities. Strictly speaking, the adopted minimalist approach is more rigorous than assigning NOEs, even when they are ambiguous, and then minimizing the constraints violations by progressive refinement with repeated trial-and-error calculations. When the spectral quality is not sufficient to remove assignment incompleteness or/and ambiguity, managing to reach the minimal restraint violation level with arbitrary release or retain of the internuclear distance attribution may only improve the precision of the determination, but definitely not its accuracy, as recently pointed out [29]. Thus, instead of relying on the number of NOE constraints as a quality determinant, the structures restrained with only unambiguous NOEs were evaluated on their similarities to the CS-Rosetta modelled ensemble, that was anyway based on the experimental chemical shifts (CS-Rosetta modelling included more than 700 chemical shift values constraining more than 350 dihedral angles).

The structures resulting from this protocol were subjected to energy minimization to adjust energetically unfavored sidechain conformations and to reduce the number of too-close contacts between adjacent atoms. A cluster of ten similar structures, deemed as representative of the structure of nanobody Nb23, was deposited in the PDB. The overall quality of this deposited ensemble was ranked to be far above average by the PDB validation server with respect to the deposited NMR structures (see Supplementary Materials).

The clustered structures were subjected to MD simulations to assess the conformational space available to the CDR3. The CDR3 showed particularly high values in RMSF, conforming that this functionally crucial region indeed could possibly have a range of conformations.

The deposited Nb23 structures (PDB ID 7EH3) have the main structural features observed in nanobodies: a β-core structure, and an extended CDR3, both for shielding solvent exposed hydrophobic sidechains (in particular Phe37, Phe47, Ile51, and Trp119)

and for binding cryptic epitopes [1]. A comparative superposition of the solution structure of free Nb23 and the Nb24 structure to explain their activity differences can be misleading at the present stage. For Nb24, in fact, no structure of the free protein in solution is available as of now, whereas the crystal structures of the complexes with β2m variants were reported [11,12] to exhibit peculiar aspects that may be related to the crystalline state [11] or to the specifically selected β2m variant [12].

Structural characterization is fundamental to uncover subtle conformational differences that lead to changes in thermodynamic and kinetic parameters for the complexation of different nanobodies such as Nb23 and Nb24 with the β2m-mutants. In this respect, the lack of some fragments of secondary structure elements in the β-core of Nb23 is not of concern, because the departure from the canonical geometry amounts to small deviations that are consistent with loose arrangements and absence of inter-strand NOEs, especially at strand edges. This contributes to decreasing the number of employed NOE contacts, barely half of the required minimum threshold of ten contacts per residue. It was reasoned that the β-core of those immunoglobulin domains, so well represented in the PDB and in literature, would be well evidenced by the convergence of the CS-Rosetta models that guided the NOE search and could therefore determine a satisfactory result.

The impact of the 'lacking' β-strand content on the function of the nanobody should not be of great relevance, considering that the paratope of the nanobodies and immunoglobulin domains in general lies in the CDRs. Moreover, some loosening of the β-scaffold in the solution structure of isolated immunoglobulin domains is not surprising [8,10]. Of much more importance is instead the definition of the interactions that shape the CDR3 conformation, partially uncovered in this study. The structure and orientation of the CDR3 in Nb23 was found to both satisfy one of its principal tasks, i.e., shielding of conserved hydrophobic residues in the isolated protein, and be similar to that of the best CS-Rosetta model. In particular, Nb23 shows an interesting series of contacts between the sidechains of Arg50 and Tyr104 which could reflect the occurrence of a cation–π electrostatic interaction between the guanidinium and the phenolic ring. This interaction may vicariate for the disulfide bridge of Cys33 and Cys104 that occurs in camel-derived nanobodies such as Nb24. Besides the canonical disulfide linking the two β-sheets of immunoglobulins, camelderived VHH domains exhibit in fact an additional cystine in the CDR3 region, that of course affects the local conformational options. Llama-derived VHH domains such as Nb23 do not possess this additional covalent constraint, but the occurrence of an energetically non-labile interaction such as a cation–π electrostatic one could help to modulate more precisely the available conformational repertoire. Importantly, the non-trivial character of this interaction should not conflict with the mobility in other regions of the CDR3, as suggested by the pattern of <sup>15</sup>N{1H} NOE histogram (Figure 2) and the hypothesized conformational exchange that prevents the observation of the Ser105 NH signal.

In conclusion, Nb23′ s structure determination is a first characterization step that will enable a more holistic assessment of its performance in inhibiting amyloidogenic β2m variants, once the solution structure of the isolated Nb24 and those of the complexes of both nanobodies with their antigens are also available. One possible outcome for this type of comparison could be the rational design of new hybrid nanobodies that perform better in fibril inhibition than the already existing ones.
