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Title: Fully differentiable full-atom protein backbone generation

Paper content:
The fast generation and refinement of protein backbones would constitute a major advancement to current methodology for the design and development of de novo proteins.
In this study, we train Generative Adversarial Networks (GANs) to generate fixed-length full-atom protein backbones, with the goal of sampling from the distribution of realistic 3-D backbone fragments.
We represent protein structures by pairwise distances between all backbone atoms, and present a method for directly recovering and refining the corresponding backbone coordinates in a differentiable manner.
We show that interpolations in the latent space of the generator correspond to smooth deformations of the output backbones, and that test set structures not seen by the generator during training exist in its image.
Finally, we perform sequence design, relaxation, and ab initio folding of a subset of generated structures, and show that in some cases we can recover the generated folds after forward-folding.
Together, these results suggest a mechanism for fast protein structure refinement and folding using external energy functions.
Deep generative models, which harness the power of deep neural networks, have achieved remarkable results in realistic sample generation across many modalities including images (1; 2; 3; 4; 5), video (6; 7), audio BID7 , and symbolic expressions BID8 .
These methods have been further applied to problems in biology and chemistry, such as the generation of small molecules BID9 and more recently, protein backbones BID10 .
The ability to easily sample from the distribution of viable proteins would be useful for the development of new therapeutics, where often the goal is to determine the structure of a putative ligand for a known target receptor or to realistically modify an existing protein.
As a more general engineering problem, speeding up and improving the de novo protein design process would be extremely valuable in the modeling and development of new biosensors, enzymes, and therapeutics.Recently, Generative Adversarial Networks (GANs) were trained to generate matrices ("maps") representing pairwise distances between alpha-carbons on fixed-length protein backbones BID10 .
This representation of the backbone is rotationally and translationally invariant and captures long-range 3-D contacts; training on these maps allows for the stable generation of highly varied structures.
However, a drawback to the approach in BID10 is that the underlying 3-D coordinates of the backbone must be recovered and local errors in the backbone due to errors in the generated maps must be corrected.
The reported method for coordinate recovery in BID10 is not differentiable and requires iterative optimization.In this study, we extend the methods in BID10 by
(i) generating full-atom pairwise distance matrices for fixed-length fragments and
(ii) training deep neural networks to recover and refine the corresponding coordinates.
Importantly, we show that for a subset of structures, we can design sequences onto the generated backbones, and recover their structures by forward-folding using the Rosetta macromolecular design suite (12; 13).
Our results suggest that a subset of the generated fragments can host folding sequences and thus are viable starting scaffolds for de novo protein design.
Our goal is The generator G generates a pairwise distance matrix, for which the underlying coordinates are recovered by network V .
Further coordinate refinement is done with additive updates by network R.to eventually incorporate external heuristic energy functions into the learning algorithm, to further refine the generated backbones.
In this paper, we propose a pipeline for generating fixed-length full-atom protein backbones in a fully differentiable manner.
We train a model to generate pairwise distance matrices between atoms on the backbone, which eliminates the need to explicitly encode structure invariances to arbitrary rotations and translations, while also modeling long-range contacts.
We show that we can then train networks to learn to recover and refine the underlying coordinates.Finally, we take steps to show the capacity of our pipeline for de novo protein design.
Specifically we show that interpolations in the latent space of the generator correspond to smooth deformations of the recovered peptide backbone, that native unseen structures exist in the image of the generator, and that a subset of generated backbones can host foldable sequences.
Together, these results suggest a mechanism for fast protein structure refinement and folding using external energy functions.We plan next to learn to generate relaxed, low-energy structures by directly optimizing our generative pipeline using the Rosetta energy function BID22 , differentiating through the coordinate recovery and refinement modules.
We plan to further extend our work by generating longer or arbitrary length backbones, as well as by conditioning our generative model on secondary structure, so that we can specify backbone topologies for design.

assistant: text: A generative model for protein backbone which uses a GAN, autoencoder-like network, and refinement process, and a set of qualitative evaluations suggesting positive results.