Volume 25, Issue 11, Pages 1771-1780.e3 (November 2017) Rotamer Libraries for the High-Resolution Design of β-Amino Acid Foldamers  Andrew M. Watkins, Timothy W. Craven, P. Douglas Renfrew, Paramjit S. Arora, Richard Bonneau  Structure  Volume 25, Issue 11, Pages 1771-1780.e3 (November 2017) DOI: 10.1016/j.str.2017.09.005 Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 1 Schemes of Chemical Species Referred to in the Text (A) The α- and β-amino acids are marked with two main-chain torsions that were considered equivalent in prior representations of β-amino acids in Rosetta. While this work only considers rotamer libraries for β3-amino acids, the expansions to the Rosetta code enables representation of any β-amino acid or, indeed, any polyamide, using the same framework. (B) The 20 β3-amino acid side chains, 18 of which are described with rotamer libraries developed in this study. β3-Glycine and β3-alanine do not possess side-chain degrees of freedom. (C) The g+, g−, and a conformations described here, for χ1: N-Cβ-Cγ-X dihedrals of 60°, −60°, and 180°. Structure 2017 25, 1771-1780.e3DOI: (10.1016/j.str.2017.09.005) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 2 Rotamer Steric Compatibility Depends Not Just on the Local Backbone Dihedrals but on the Entire Polymer Context The (a, g+) rotamer imposed on every fourth residue (a leucine) in the 314 helix (A) and the α3β helix (B). Molprobity clash analysis reveals that the 314 helix is free of clashes (C), while the α3β helix (D) has a clash score of 114, far worse, in 12 residues, than low-quality electron microscopy structures of hundreds of residues. The distinct clash, shown in red dots, is with the i + 3 alanine methyl group. Structure 2017 25, 1771-1780.e3DOI: (10.1016/j.str.2017.09.005) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 3 The Process by Which Rotamer Libraries Are Constructed To construct rotamer libraries for β-amino acids, we create parameters for the residue by geometry optimization and charge fitting by quantum mechanics, as described previously. We seed backbone conformations and, for each one, we create hundreds or thousands of χ-combination seed conformations (omitting the final non-rotameric χ for semi rotameric amino acids). We minimize each χ combination (and, for semirotameric residues, obtain a probability distribution for the terminal χ). Finally, we cluster, obtain an SD in each dimension for each resulting rotamer well, and convert the minimized energies to probabilities via the Boltzmann distribution. Structure 2017 25, 1771-1780.e3DOI: (10.1016/j.str.2017.09.005) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 4 Side-Chain Probability Distributions as Computed by Quantum Mechanics and Molecular Mechanics Two dimensional probability distributions for three residues (β3I, β3L, and β3W; columns) were determined by quantum mechanics (B3LYP optimization followed by Hartree-Fock energy; first and third row) and molecular mechanics (the energy function employed in the rotamer library protocol; second and fourth row). These distributions were generated for two distinct backbone conformations: one for a conformation common to the 314 and α3β helix (first and second rows) and one for an extended conformation (third and fourth rows). QM, quantum mechanical; MM, molecular mechanics. Structure 2017 25, 1771-1780.e3DOI: (10.1016/j.str.2017.09.005) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 5 Rotamer Libraries Accurately Capture Experimentally Determined Rotamers root-mean-square error in degrees for the nearest rotamer across all resolved β3-amino acid samples in the PDB. The number of examples of that β-amino acid are above each bar. No data exist on β3-homocysteine or β3-homohistidine, and rotamer libraries do not apply to β3-homoalanine or β3-homoglycine. Errors are comparable with those found in prior work on fitting peptoid and non-canonical amino acid rotamer libraries (Renfrew et al., 2012, 2014) and to the effective uncertainty of Dunbrack rotamer libraries (see the STAR Methods). Structure 2017 25, 1771-1780.e3DOI: (10.1016/j.str.2017.09.005) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 6 Many Crystal Structures Possess Poorly Resolved Density for β-Amino Acid Residues Many native side chains “missed” by these rotamer libraries are in very unlikely conformations in the crystal structure. Due to the challenges of fitting atomic coordinates to electron density, and due to the additional challenge of phasing diffraction data for novel heteropolymers, structural data might be particularly uninformative for these molecules. Indeed, maps frequently provided minimal density near β-amino acid residues, as in the four examples above (PDB: 3G7A and 4BPI). Structure 2017 25, 1771-1780.e3DOI: (10.1016/j.str.2017.09.005) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 7 The Fully Backbone-Dependent Rotamer Libraries Perform Considerably Better than the Old Model in Real Applications We compared experimental ΔΔG values (kcal/mol) for mutations in a series of 314 helical p53 mimetics, which were assayed against the proteins mdm2 and mdm4, to computational predictions. The original predictions made by Schepartz (A) provided a standard of comparison; our Rosetta protocol performed poorly with the old (B) rotamer libraries but quite well using the rotamer libraries developed in this work (C). Structure 2017 25, 1771-1780.e3DOI: (10.1016/j.str.2017.09.005) Copyright © 2017 Elsevier Ltd Terms and Conditions