X-ray Crystallography and Structural Biology

This set covers the fundamental principles of X-ray crystallography, including physics, crystal growth, data processing, and applications in enzyme mechanism and drug design.

Resolution

The ability of an imaging system to distinguish between two closely-spaced points in a specimen, limited in practice by the wavelength of the radiation used.

X-ray Wavelength Scale

A region of the electromagnetic spectrum where waves have lengths of approximately $0.1\,nm$ ($1\,\text{Å}$, $10^{-10}\,m$), matching the length scales on which amino acids are connected.

Elastic Scattering

An interaction where an electron encounters an X-ray and acts as a new source, re-emitting a photon with the same energy as the incident photon.

Fourier Transform

A mathematical process that decomposes a periodic function of time or distance into a sum of simpler sine or cosine functions; the scattering pattern of a molecule is a Fourier transform of its electron density.

The Phase Problem

The inability to measure the phases of scattered waves (only their amplitudes) during an experiment, resulting in lost information about the relative positions of atoms.

Crystal

A finite, translationally periodic arrangement of identical repeating units in three dimensions.

Unit Cell

The basic repeating block of a crystal defined by vectors $a$, $b$, $c$ and angles $\alpha$, $\beta$, $\gamma$.

Primary Radiation Damage

A direct effect of X-rays on a protein, such as ionization or the breakage of bonds, which is dependent solely on the X-ray dose.

Secondary Radiation Damage

Chemical damage to a protein caused by reaction with mobile $OH^{-}$ ions or $OH^{\bullet}$ radicals generated by the radiolysis of water; it is dose, time, and temperature dependent.

Bragg’s Law

The condition for constructive interference expressed by the equation $n\lambda = 2d\sin\vartheta$, where $n$ is the order of reflection, $\lambda$ is wavelength, $d$ is the distance between planes, and $\vartheta$ is the Bragg angle.

Miller Indices

A set of integers $(h, k, l)$ that define sets of Bragg planes based on how many times they cross the unit cell axes ($a, b, c$).

Homochiral Polymers

The property of proteins where every amino acid is the L-enantiomer, which prevents the existence of mirror symmetry or centers of inversion in protein crystals.

Solvent Channels

Gaps between proteins in a crystal where symmetry axes are located; protein crystals are on average $\sim 50\,\%$ solvent by volume.

65 Chiral Space Groups

The total number of allowed 3D symmetry arrangements for protein molecules within a crystal lattice.

Isoelectric Point ($pI$)

The pH value at which a protein has no net positive or negative charge per molecule and its solubility is at its lowest.

Precipitant

Long, highly soluble polymers like polyethylene glycol (PEG) that compete with protein for space in solution, thereby decreasing protein solubility.

Metastable Zone

The region in a crystallization phase diagram where a solution is saturated enough to allow for spontaneous nucleation.

Cryoprotectant

A substance such as glycerol added to the protein drop to prevent ice formation during the cryo-cooling of crystals in liquid nitrogen.

Goniometer

An instrument used in the diffraction experiment to center and rotate the crystal within the X-ray beam.

Indexing

The computational process of identifying spots on diffraction images and assigning them to specific Bragg planes to determine unit cell dimensions.

Integration

The process of adding up the pixel counts in each diffraction spot to determine intensities, which are proportional to the amplitudes of the diffraction vectors.

Molecular Replacement

A technique used to solve the phase problem by calculating phases from a known homologous structure or an AlphaFold prediction.

Experimental Phasing

A method to recover phases by introducing heavy atoms into the unit cell to cause anomalous scattering events.

Structure Factors

Diffraction vectors characterized by both amplitudes and phases, which are required to perform the inverse Fourier transform to calculate electron density.

Diffusion Trapping

An experiment where substrate is soaked into a crystal and rapidly harvested and cryo-cooled to capture an enzyme-substrate complex structure.

Rational Design

A drug design approach that utilizes biochemical, biophysical, and structural information to target a specific functional site on a protein.

Fragment Screening

A drug design method that systematically tests thousands of diverse chemical fragments to identify entirely new binding sites on a target protein.