{ "cells": [ { "cell_type": "markdown", "id": "41b4d6ab", "metadata": {}, "source": [ "(ch:single-particle-analysis)=\n", "# Single-Particle Analysis\n", "\n", "(sec:spa-introduction)=\n", "## Introduction\n", "\n", "Single-particle analysis (SPA) is a cryo-EM method that determines the three-dimensional structure of a macromolecule by computationally combining images of thousands to millions of individual copies of the molecule, each captured in a different, unknown orientation. The fundamental physical insight driving SPA is that a three-dimensional object can be reconstructed from a sufficient number of its two-dimensional projections — a relationship known as the **projection theorem** (see also {numref}`ch:tomography`). In SPA, the challenge is that the orientations of individual particles are not known in advance and must be inferred from the images themselves.\n", "\n", "```{figure} images/Images11/beta-gal.png\n", ":name: fig:beta-gal\n", ":width: 70%\n", "A cryo-EM micrograph of beta-galactosidase particles in vitrified ice. Individual particles (bright and dark blobs) are visible, but a single micrograph contains too little SNR to resolve molecular detail. Combining images of many such particles through SPA reveals the protein structure at near-atomic resolution.\n", "```\n", "\n", "In the below video, we explain how a three-dimensional structure is recovered from many noisy projection images: back projection in real space, the equivalent route in Fourier space via the projection theorem, and the iterative single-particle workflow that leads from micrographs to a final Coulomb potential map.\n", "\n", "---\n", "\n", "