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<!DOCTYPE html>
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<title>ADP-3D</title>
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<h1 class="title is-1 publication-title">Solving Inverse Problems in Protein Space Using
Diffusion-Based Priors</h1>
<div class="is-size-5 publication-authors">
<span class="author-block">
<a href="https://axlevy.com/" target="_blank">Axel Levy</a><sup>1</sup>,</span>
<span class="author-block">
<a href="https://ericryanchan.github.io/" target="_blank">Eric R. Chan</a><sup>1</sup>,</span>
<span class="author-block">
<a href="https://sarafridov.github.io/" target="_blank">Sara Fridovich-Keil</a><sup>1</sup>,</span>
<span class="author-block">
<a href="https://scholar.google.fr/citations?user=qz6POUsAAAAJ&hl=en" target="_blank">Frédéric Poitevin</a><sup>2</sup>,</span>
<span class="author-block">
<a href="https://ezlab.princeton.edu/" target="_blank">Ellen D. Zhong</a><sup>3</sup>,</span>
<span class="author-block">
<a href="https://www.computationalimaging.org/" target="_blank">Gordon Wetzstein</a><sup>1</sup></span>
</div>
<div class="is-size-5 publication-authors">
<span class="author-block">1: Stanford University - 2: SLAC National Laboratory - 3: Princeton University</span>
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<span>arXiv</span>
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<h2 class="title is-3">Abstract</h2>
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<p>
The interaction of a protein with its environment can be understood and controlled via its 3D structure.
Experimental methods for protein structure determination, such as X-ray crystallography or cryogenic electron microscopy, shed light on biological processes but introduce challenging inverse problems.
Learning-based approaches have emerged as accurate and efficient methods to solve these inverse problems for 3D structure determination, but are specialized for a predefined type of measurement.
Here, we introduce a versatile framework to turn raw biophysical measurements of varying types into 3D atomic models.
Our method combines a physics-based forward model of the measurement process with a pretrained generative model providing a task-agnostic, data-driven prior.
Our method outperforms posterior sampling baselines on both linear and non-linear inverse problems.
In particular, it is the first diffusion-based method for refining atomic models from cryo-EM density maps.
</p>
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</section>
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<h2 class="title is-3">Methods</h2>
<img src="static/images/method_white.png" alt="teaser" class="center">
<div class="content has-text-justified">
<br>
<b>Overview of ADP-3D.</b> Our method turns partial and noisy measurements (the ''conditioning information'') into a
3D structure by leveraging a pretrained diffusion model (here, Chroma [1]) and physics-based models
of the measurement processes.
Starting from a random structure, our method iterates between a denoising step and a data-matching step.
The denoiser comes from the pretrained diffusion model.
The data-matching step aims at maximizing the likelihood of the measurements.
</div>
<div class="content has-text-justified is-small">
[1] Ingraham, John B., et al. "Illuminating protein space with a programmable generative model." Nature 623.7989 (2023): 1070-1078.
</div>
<br>
<br>
<img src="static/images/algo_adp-3d_white.png" alt="teaser" class="center">
<div class="content has-text-justified">
<br>
<b>ADP-3D in pseudo-code.</b> Our method performs MAP estimation by taking inspiration from the plug-n-play framework [2, 3].
It relies on an iterative process, alternating between a data-matching step and a diffusion-based regularization step.
</div>
<div class="content has-text-justified is-small">
[2] Venkatakrishnan, Singanallur V., Charles A. Bouman, and Brendt Wohlberg. "Plug-and-play priors for model based reconstruction." 2013 IEEE global conference on signal and information processing. IEEE, 2013.
<br>
[3] Zhu, Yuanzhi, et al. "Denoising diffusion models for plug-and-play image restoration." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023.
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</section>
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<h2 class="title is-3">Results</h2>
<h3 class="title is-4 has-text-justified">Atomic Model Refinement</h3>
<div class="content has-text-justified">
ADP-3D can refine incomplete atomic models obtained with the model building algorithm ModelAngelo [4] on synthetic cryo-EM density maps.
</div>
<img src="static/images/model_building_white.png" alt="results" class="center">
<div class="content has-text-justified">
<br>
<b>Left.</b> Qualitative results on the TecA bacterial toxin (<a href="https://www.rcsb.org/structure/7PZT" target="_blank">PDB:7pzt</a>, 160 residues). We show, from left to right, the input density map at 2.0 Å resolution, the incomplete
model given by ModelAngelo and our refined models (1 sample and 5 samples), overlaid on the target structure in transparency.<br><br>
<b>Right.</b> RMSD of alpha carbons vs. completeness (number of predicted residues / total number of residues)
with ModelAngelo (MA) and our method. We run 5 experiments and report the mean of the lowest RMSD on
α-carbons over 8 replicas (±1 std). The experimental (deposited) resolution is indicated with a dashed line.
</div>
<br>
<img src="static/images/ablation_white.png" alt="results" class="center">
<div class="content has-text-justified">
<br>
We analyze the importance of the different input measurements (incomplete model, density map, amino-acid sequence) and that of the generative prior.
Removing the partial atomic model leads to the largest drop in accuracy. The cryo-EM density map is
the second most important measurement, followed by the generative prior and the sequence.
</div>
<div class="content has-text-justified is-small">
[4] Jamali, Kiarash, et al. "Automated model building and protein identification in cryo-EM maps." Nature (2024): 1-2.
</div>
<br>
<h3 class="title is-4 has-text-justified">Structure Completion</h3>
<div class="content has-text-justified">
Given a fixed number of diffusion steps, ADP-3D outperforms posterior sampling baselines on a linear inverse problem (structure completion).
</div>
<img src="static/images/structure_completion_white.png" alt="results" class="center">
<div class="content has-text-justified">
<br>
<b>Left.</b> Qualitative results on the ATAD2 protein (<a href="https://www.rcsb.org/structure/7QUM" target="_blank">PDB:7qum</a>, 130 residues). The input structure is a subsampled version of the target structure (subsampling factor in the top row).
In the input row, we show the target structure (unknown) in transparency and the locations of the known α-carbons in colors.
We report the lowest RMSD over 8 runs.<br><br>
<b>Right.</b> RMSD vs. subsampling factor. Our method is compared to a posterior sampling baseline (Chroma conditioned with the SubstructureConditioner).
The importance of the diffusion-based prior is shown. We report the mean RMSD (±1 std) over 8 runs.
The experimental (deposited) resolution is indicated with a dashed line.
</div>
<br>
<h3 class="title is-4 has-text-justified">Distances to Structure</h3>
<div class="content has-text-justified">
ADP-3D efficiently solves non-convex inverse problems, like estimating a 3D structure from sparse pairwise distances between atoms.
</div>
<img src="static/images/distance_to_structure_white.png" alt="results" class="center">
<div class="content has-text-justified">
<br>
<b>Left.</b> Qualitative results on BRD4 (<a href="https://www.rcsb.org/structure/7R5B" target="_blank">PDB:7r5b</a>, 127 residues).
The reconstructed structures are shown in colors, depending on the number of known pairwise distances.
We report the lowest RMSD over 8 runs. The target structure is shown in transparency along with its pairwise distance matrix.<br><br>
<b>Right.</b> RMSD vs. number of known pairwise distances. Each experiment is ran 10 times with randomly sampled distances.
We report the mean of the lowest RMSD obtained over 8 replicas (±1 std).
The plot demonstrates the importance of the diffusion model.
The experimental (deposited) resolution is indicated with a dashed line.
</div>
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</div>
</div>
</section>
<section class="section hero is-white" id="BibTeX">
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<h2 class="title">Citing this work</h2>
<pre><code>@article{adp3d,
title={Solving Inverse Problems in Protein Space Using Diffusion-Based Priors},
author={Levy, Axel and Chan, Eric R and Fridovich-Keil, Sara and Poitevin, Fr{\'e}d{\'e}ric and Zhong, Ellen D and Wetzstein, Gordon},
journal={arXiv preprint arXiv:2406.04239},
year={2024}
}</code></pre>
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