Fig 1.
The flow of data is shown with black arrows, and losses are shown in blue. First, Ramachandran angles and distance matrices are computed from the full-atom backbone coordinates of a training example. The distance matrix is passed to the encoder network (E), which generates a latent embedding that is passed to the decoder network (D). The decoder directly generates coordinates in 3D space, from which the reconstructed Ramachandran angles and distance matrix are computed. Errors from both the angles and distance matrix are back-propagated through the 3D coordinate representation to the encoder and decoder. Note that both the torsion and distance matrix losses are rotationally and translationally invariant, and that the coordinates of the training example are never seen by the model. The shown data are real inputs and outputs of the VAE for the immunoglobulin chain in PDB:4YXH(L).
Fig 2.
Analysis of Full-Atom Reconstructions.
Reconstruction data for 500 randomly chosen, non-redundant structures in the training set. (A) Overlays of the pairwise distance and Ramachandran distributions of the real and reconstructed data. (B) A table of the reconstruction errors in pairwise distance and Ramachandran angle before and after refinement. The distance errors are reported as per-pairwise-distance error averaged over all structures in the dataset, and analogously for the angle errors. (C) Overlays of the real (blue), reconstructed (pink) and refined (green) structures. (D) Overlays of the bond length and bond angle distributions of the real, reconstructed and refined data. Overall, structures are accurately reconstructed, and errors in atom placement are small enough that they can be corrected with minimal changes to the model outputs.
Fig 3.
Analysis of Generative Sampling.
Data for 500 of randomly selected non-redundant training samples and generated structures. (A) Overlays of the pairwise distance and Ramachandran distributions of the real and generated data. (B) A comparison of the real and generated structural ensembles. (C) Overlays of the bond length and bond angle distributions of the real, generated and refined data. (D) The left panel shows a plot of the post-refinement per-residue centroid energy against normalized nearest neighbor distance for the generated structures. The nearest neighbor distance is computed as the minimum Frobenius distance between the generated distance matrix and all distance matrices in the training set. Each point is colored based on whether the nearest neighbor is a heavy or light chain Ig. The center panel shows an overlay of the generated structures (pink) and their nearest neighbors (blue) in the training set. These six structures were selected using a combination of centroid energy, nearest neighbor distance, heavy/light classification, and manual inspection. The right panel shows sequence design results for structures III and VI. The energies in the left panel are centroid energies, while the energies in the right panel are full-atom Rosetta energies using the ref2015 score function.
Fig 4.
Latent Space Analysis and Interpolation.
(A) Linear interpolation between two randomly selected embeddings. The starting and ending structures are 1TQB(H) and 5JW4(H) respectively. The backbones are unaltered, full-atom model outputs. Structures are colored by residue index in reverse rainbow order. (B) Centroid energy profiles of the structures from panel A after constrained refinement. (C) Higher frequency overlays of 80 sequential structures in the unrefined interpolation trajectory. The roman numerals correspond to the blue labels in panel A. A lighter shade of blue indicates an earlier structure while the darker shade indicates a later structure. Structure transitions are smooth and follow a near-continuous trajectory. (D) The top panel shows a tSNE dimensionality reduction of the embedding means of the 4154 non-redundant structures in the training set. Colorings correspond to k-means clusters (k = 40) of the post-tSNE data, and ten structures from three clusters are visualized to the right. The bottom panel depicts a principal components reduction of the latent space, showing five sampled data points per non-redundant structure.
Fig 5.
Towards Epitope-Specific Generative Design.
(A) Design of two generated immunoglobulin (Ig) structures, I and II, targeting the ACE2 epitope of the SARS-CoV2 receptor binding domain (RBD). The left-most column shows an alignment of the unrefined generated structures (pink) to their respective nearest neighbors (blue) in the training set. The second column depicts the designed interfaces with the full-sequence Ig’s shown in green. The SARS-Cov2-RBD is rendered as a white surface, with the ACE2 epitope shown in yellow. The ddG’s and Rosetta energies (ref2015) of the Ig’s are shown below each complex. The third column depicts the lowest energy structures from a RosettaDock global-docking trajectory. The recovered Ig structures are shown in orange. The right-most column shows the full docking trajectory (100,000 decoys), with the lowest energy structures shown as red dots. (B) Ig-backbone design by constrained latent vector optimization. The loop constraints are taken from PDB:5X2O(L, 32–44) with the target shape shown by orange spheres. The constrained regions of the optimization trajectory are shown in blue. In the post-optimization ensemble the full 5X2O(L) backbone is shown in orange. The ensemble depicts the outputs of 62 optimization trajectories (out of 100 initialized) that successfully recovered the target loop shape.