X-ray Crystallography of Biomolecules

How the diffraction of X-rays by a crystal of a biomolecule is turned into an electron-density map and, from it, an atomic model.

Definition

X-ray crystallography of biomolecules is the determination of atomic structure by measuring the diffraction of X-rays from a crystal and reconstructing the electron density of the repeating unit.

Scope

This topic covers the workflow and physics of macromolecular X-ray crystallography: crystallisation, the diffraction experiment, the central phase problem and how it is solved, and the construction and refinement of an atomic model. It treats the method in depth as the historically dominant route to atomic structures, complementing the broader structure-determination topic and the cryo-EM topic.

Core questions

• Why must the molecule be crystallised, and what does the crystal provide?
• How does a diffraction pattern encode the structure?
• What is the phase problem, and how is it solved?
• How is an atomic model built into and refined against the data?

Key theories

Diffraction as a Fourier transform

The diffraction pattern of a crystal is the Fourier transform of its electron density, so measuring the reflections and recovering their phases lets the density—and hence the structure—be computed by inverse transform.

Solving the phase problem

Because experiments record intensities but not phases, the phases must be obtained separately—through heavy-atom methods, anomalous scattering, or a related known structure—before an interpretable electron-density map can be produced.

Mechanisms

A purified macromolecule is coaxed into an ordered crystal, which amplifies the weak scattering of single molecules into measurable diffraction. X-rays scatter from the crystal's electrons, and the recorded reflection intensities give the amplitudes of the structure's Fourier components but lose their phases. The phases are recovered by introducing heavy atoms, exploiting anomalous scattering, or using a homologous model, after which an electron-density map is computed, a model of the atoms is built into the density, and the model is refined to optimise agreement with the data and stereochemistry.

Clinical relevance

Crystallography supplies the structures used in structure-based drug design and in interpreting disease mutations, providing educational and methodological grounding rather than clinical guidance.

History

Building on the Braggs' founding of crystallography and Hodgkin's structures of small biomolecules, Kendrew and Perutz solved the first protein structures in the late 1950s, establishing macromolecular crystallography as the principal source of atomic-resolution biology for decades.

Key figures

• Max Perutz
• John Kendrew
• Dorothy Hodgkin
• William Lawrence Bragg

Seminal works

• kendrew1958
• rhodes2006

Frequently asked questions

Why do you need a crystal?

A single molecule scatters X-rays far too weakly to measure; a crystal contains many identical molecules in a regular array that reinforce the scattering into a measurable diffraction pattern.

What does the resolution of a crystal structure mean?

It reflects how far out in the diffraction pattern usable data extend, and thus how finely the electron density—and the atomic positions—can be resolved; higher resolution means more detail.