CryoFormer: Continuous Reconstruction of 3D Structures from Cryo-EM Data using Transformer-based Neural Representations

High-resolution heterogeneous reconstruction of 3D structures of proteins and other biomolecules using cryo-electron microscopy (cryo-EM) is essential for understanding fundamental processes of life. However, it is still challenging to reconstruct the continuous motions of 3D structures from hundreds of thousands of noisy and randomly oriented 2D cryo-EM images. Existing methods based on coordinate-based neural networks show compelling results to model continuous conformations of 3D structures in the Fourier domain, but they suffer from a limited ability to model local flexible regions and lack interpretability. We propose a novel approach, cryoFormer, that utilizes a transformer-based network architecture for continuous heterogeneous cryo-EM reconstruction. We for the first time directly reconstruct continuous conformations of 3D structures using an implicit feature volume in the 3D spatial domain. A novel deformation transformer decoder further improves reconstruction quality and, more importantly, locates and robustly tackles flexible 3D regions caused by conformations. In experiments, our method outperforms current approaches on three public datasets (1 synthetic and 2 experimental) and a new synthetic dataset of PEDV spike protein. The code and new synthetic dataset will be released for better reproducibility of our results. Project page: https://cryoformer.github.io

Oriented tensor reconstruction: tracing neural pathways from diffusion tensor MRI

In this paper we develop a new technique for tracing anatomical fibers from 3D tensor fields. The technique extracts salient tensor features using a local regularization technique that allows the algorithm to cross noisy regions and bridge gaps in the data. We applied the method to human brain DT-MRI data and recovered identifiable anatomical structures that correspond to the white matter brain-fiber pathways. The images in this paper are derived from a dataset having 121x88x60 resolution. We were able to recover fibers with less than the voxel size resolution by applying the regularization technique, i.e., using a priori assumptions about fiber smoothness. The regularization procedure is done through a moving least squares filter directly incorporated in the tracing algorithm

Proto-Plasm: parallel language for adaptive and scalable modelling of biosystems

This paper discusses the design goals and the first developments of Proto-Plasm, a novel computational environment to produce libraries of executable, combinable and customizable computer models of natural and synthetic biosystems, aiming to provide a supporting framework for predictive understanding of structure and behaviour through multiscale geometric modelling and multiphysics simulations. Admittedly, the Proto-Plasm platform is still in its infancy. Its computational framework—language, model library, integrated development environment and parallel engine—intends to provide patient-specific computational modelling and simulation of organs and biosystem, exploiting novel functionalities resulting from the symbolic combination of parametrized models of parts at various scales. Proto-Plasm may define the model equations, but it is currently focused on the symbolic description of model geometry and on the parallel support of simulations. Conversely, CellML and SBML could be viewed as defining the behavioural functions (the model equations) to be used within a Proto-Plasm program. Here we exemplify the basic functionalities of Proto-Plasm, by constructing a schematic heart model. We also discuss multiscale issues with reference to the geometric and physical modelling of neuromuscular junctions

A Multiscale Model for Virus Capsid Dynamics

Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows

ePlant and the 3D Data Display Initiative: Integrative Systems Biology on the World Wide Web

Visualization tools for biological data are often limited in their ability to interactively integrate data at multiple scales. These computational tools are also typically limited by two-dimensional displays and programmatic implementations that require separate configurations for each of the user's computing devices and recompilation for functional expansion. Towards overcoming these limitations we have developed “ePlant” (http://bar.utoronto.ca/eplant) – a suite of open-source world wide web-based tools for the visualization of large-scale data sets from the model organism Arabidopsis thaliana. These tools display data spanning multiple biological scales on interactive three-dimensional models. Currently, ePlant consists of the following modules: a sequence conservation explorer that includes homology relationships and single nucleotide polymorphism data, a protein structure model explorer, a molecular interaction network explorer, a gene product subcellular localization explorer, and a gene expression pattern explorer. The ePlant's protein structure explorer module represents experimentally determined and theoretical structures covering >70% of the Arabidopsis proteome. The ePlant framework is accessed entirely through a web browser, and is therefore platform-independent. It can be applied to any model organism. To facilitate the development of three-dimensional displays of biological data on the world wide web we have established the “3D Data Display Initiative” (http://3ddi.org)

3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques