Cryo-EM is a vital technique for determining 3D structure of biological
molecules such as proteins and viruses. The cryo-EM reconstruction problem is
challenging due to the high noise levels, the missing poses of particles, and
the computational demands of processing large datasets. A promising solution to
these challenges lies in the use of amortized inference methods, which have
shown particular efficacy in pose estimation for large datasets. However, these
methods also encounter convergence issues, often necessitating sophisticated
initialization strategies or engineered solutions for effective convergence.
Building upon the existing cryoAI pipeline, which employs a symmetric loss
function to address convergence problems, this work explores the emergence and
persistence of these issues within the pipeline. Additionally, we explore the
impact of equivariant amortized inference on enhancing convergence. Our
investigations reveal that, when applied to simulated data, a pipeline
incorporating an equivariant encoder not only converges faster and more
frequently than the standard approach but also demonstrates superior
performance in terms of pose estimation accuracy and the resolution of the
reconstructed volume. Notably, $D_4$-equivariant encoders make the symmetric
loss superfluous and, therefore, allow for a more efficient reconstruction
pipeline.

冷冻电子显微术是一种确定蛋白质和病毒等生物分子三维结构的重要技术。本文探索了 cryoAI 管道中收敛问题的出现和持久性以及等变的摊解推理对增强收敛的影响，研究发现在模拟数据上，集成了等变编码器的管道不仅收敛更快、更频繁，而且在姿态估计准确度和重建体积的分辨率方面表现出优越性。值得注意的是，$D_4$- 等变编码器使对称损失变得多余，从而允许更高效的重建管道。

Cryo-EM 图像中姿态的等变化摊销推理

Equivariant amortized inference of poses for cryo-EM

Designing novel proteins with desired functions is crucial in biology and
chemistry. However, most existing work focus on protein sequence design,
leaving protein sequence and structure co-design underexplored. In this paper,
we propose GeoPro, a method to design protein backbone structure and sequence
jointly. Our motivation is that protein sequence and its backbone structure
constrain each other, and thus joint design of both can not only avoid
nonfolding and misfolding but also produce more diverse candidates with desired
functions. To this end, GeoPro is powered by an equivariant encoder for
three-dimensional (3D) backbone structure and a protein sequence decoder guided
by 3D geometry. Experimental results on two biologically significant
metalloprotein datasets, including $\beta$-lactamases and myoglobins, show that
our proposed GeoPro outperforms several strong baselines on most metrics.
Remarkably, our method discovers novel $\beta$-lactamases and myoglobins which
are not present in protein data bank (PDB) and UniProt. These proteins exhibit
stable folding and active site environments reminiscent of those of natural
proteins, demonstrating their excellent potential to be biologically
functional.

本研究论文提出了一种名为 GeoPro 的方法，用于联合设计蛋白质骨架结构和序列。该方法基于三维骨架结构的等变编码器和由三维几何图形指导的蛋白质序列解码器。实验证明，在两个重要的生物金属蛋白数据集上，GeoPro 在大多数度量标准上优于其他基准方法，能够发现在蛋白质数据库和 UniProt 中不存在的新型 $eta$- 内酰胺酶和肌红蛋白，表现出与天然蛋白类似的稳定折叠和活性位点环境，展示了其在生物功能方面的巨大潜力。