Moment-based metrics for molecules computable from cryogenic electron microscopy images.

Single-particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution three-dimensional (3D) structure of biological macromolecules from many noisy and randomly oriented projection images. One notable approach to 3D reconstruction, known as Kam's method, relies on the moments of the two-dimensional (2D) images. Inspired by Kam's method, we introduce a rotationally invariant metric between two molecular structures, which does not require 3D alignment.

Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms.

The number of noisy images required for molecular reconstruction in single-particle cryoelectron microscopy (cryo-EM) is governed by the autocorrelations of the observed, randomly oriented, noisy projection images. In this work, we consider the effect of imposing sparsity priors on the molecule. We use techniques from signal processing, optimization, and applied algebraic geometry to obtain theoretical and computational contributions for this challenging nonlinear inverse problem with sparsity constraints.

EARTHMOVER-BASED MANIFOLD LEARNING FOR ANALYZING MOLECULAR CONFORMATION SPACES.

In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction. We demonstrate the potential benefits of this approach for learning shape spaces of proteins and other flexible macromolecules using a simulated dataset of 3-D density maps that mimic the non-uniform rotary motion of ATP synthase. Our results show that EMD-based diffusion maps require far fewer samples to recover the intrinsic geometry than the standard diffusion maps algorithm that is based on the Euclidean distance.