Exploratory Studies Detecting Secondary Structures in Medium Resolution 3D Cryo-EM Images Using Deep Convolutional Neural Networks

Using Curriculum Learning in Pattern Recognition of 3-dimensional Cryo-electron Microscopy Density Maps

Although Cryo-electron microscopy (cryo-EM) has been successfully used to derive atomic structures for many proteins, it is still challenging to derive atomic structure when the resolution of cryo-EM density maps is in the medium range, e.g., 5-10 Å. Studies have attempted to utilize machine learning methods, especially deep neural networks to build predictive models for the detection of protein secondary structures from cryo-EM images, which ultimately helps to derive the atomic structure of proteins. However, the large variation in data quality makes it challenging to train a deep neural network with high prediction accuracy. Curriculum learning has been shown as an effective learning paradigm in machine learning. In this paper, we present a study using curriculum learning as a more effective way to utilize cryo-EM density maps with varying quality. We investigated three distinct training curricula that differ in whether/how images used for training in past are reused while the network was continually trained using new images. A total of 1,382 3-dimensional cryo-EM images were extracted from density maps of Electron Microscopy Data Bank in our study. Our results indicate learning with curriculum significantly improves the performance of the final trained network when the forgetting problem is properly addressed.

The de Rham-Hodge Analysis and Modeling of Biomolecules

Biological macromolecules have intricate structures that underpin their biological functions. Understanding their structure-function relationships remains a challenge due to their structural complexity and functional variability. Although de Rham-Hodge theory, a landmark of twentieth-century mathematics, has had a tremendous impact on mathematics and physics, it has not been devised for macromolecular modeling and analysis. In this work, we introduce de Rham-Hodge theory as a unified paradigm for analyzing the geometry, topology, flexibility, and Hodge mode analysis of biological macromolecules. Geometric characteristics and topological invariants are obtained either from the Helmholtz-Hodge decomposition of the scalar, vector, and/or tensor fields of a macromolecule or from the spectral analysis of various Laplace-de Rham operators defined on the molecular manifolds. We propose Laplace-de Rham spectral-based models for predicting macromolecular flexibility. We further construct a Laplace-de Rham-Helfrich operator for revealing cryo-EM natural frequencies. Extensive experiments are carried out to demonstrate that the proposed de Rham-Hodge paradigm is one of the most versatile tools for the multiscale modeling and analysis of biological macromolecules and subcellular organelles. Accurate, reliable, and topological structure-preserving algorithms for implementing discrete exterior calculus (DEC) have been developed to facilitate the aforementioned modeling and analysis of biological macromolecules. The proposed de Rham-Hodge paradigm has potential applications to subcellular organelles and the structure construction from medium- or low-resolution cryo-EM maps, and functional predictions from massive biomolecular datasets.