Improving membrane proteins' 3D reconstructions with cryo-electron microscopy

虽然冷冻电子显微镜（cryo-EM）的发展已经证明通过对溶液中的生物分子进行成像来彻底改变结构生物学领域，但绝大多数蛋白质无法以令人满意的分辨率重建。其中，膜蛋白仍然是生物学家的成像挑战-尽管是制药市场上一半以上处方药的突出目标。这项工作开发了一种新的数学和统计方法，将提高cryo-EM的分辨率，目标是膜蛋白的3D成像和重建。 我们解决的主要挑战，以及这种方法的新奇，来自统计和微分几何。从统计学的角度来看，该提案重新审视了冷冻EM形状重建的范例，通过将传统的“期望最大化”学习过程替换为其更快和可扩展的对应物，称为“变分推理”。为了在这种情况下应用“变分推理”，我们的解决方案实现了微分几何的三维形状空间内最近流行的降维方法“变分自动编码器”。通过提高图像重建算法的效率，同时对其准确性进行基准测试，我们利用了cryoEM产生的大量原始数据。反过来，处理更多的数据提高了重建的生物分子形状的分辨率。该项目的创意是利用尚未渗透到机器学习和生物成像社区的统计和数学。我们的建议也广泛适用于冷冻EM和生物成像之外。重建生物分子形状是几种成像模式的重点，例如用于单粒子成像的相干衍射，其产生的图像的分析是我们团队成员正在进行的研究。该提案转化为这些技术的形状表示。

While the development of cryo-electron microscopy (cryo-EM) has already proven to revolutionize the field of structural biology by imaging biomolecules in solution, the vast majority of proteins cannot be reconstructed at a satisfying resolution. Among them, membrane proteins still remain an imaging challenge for biologists - despite being prominent targets for over half of prescription drugs on the pharmaceutical market. The proposed work develops a novel mathematical and statistical method that will enhance the resolution of cryo-EM, targeting the 3D imaging and reconstruction of membrane proteins. The main challenges that we solve, and the novelty of this approach, come from statistics and differential geometry. From a statistical perspective, the proposal revisits the paradigm of cryo-EM shape reconstruction, by replacing the traditional "expectation-maximization" learning procedure by its faster and scalable counterpart, called "variational inference". In order to apply "variational inference" in this context, our solution implements the differential geometry of 3D shape spaces within the recent and popular dimension reduction method of "variational autoencoders". By improving the efficiency of the image reconstruction algorithm, while benchmarking its accuracy, we leverage the extraordinary amount of raw data produced by cryoEM. In turn, processing more data improves the resolution of the reconstructed biomolecular shapes. The originality of the proposed project is to leverage statistics and mathematics that have not yet penetrated the communities of machine learning and biological imaging. Our proposal is also broadly applicable beyond cryo-EM and biological imaging. Reconstructing biomolecular shapes is the focus of several imaging modalities, such as coherent diffraction for single particle imaging, that produce images whose analysis is an on-going research of members of our team. The proposal translates to the representation of shapes for these technologies.