Macromolecular X-ray Crystallography and Structural Biology

Comprehensive practice flashcards covering protein crystallization, X-ray generation, wave diffraction, Bragg's Law, data collection and processing, phase determination (MIR, MAD, MR), Patterson functions, and crystallographic model refinement.

Structural Biology

A branch of molecular biology, biochemistry, and biophysics concerned with the 3D molecular structure of biological macromolecules (especially proteins and nucleic acids), how those structures are acquired, how they define function, and how alterations in structure affect function.

Protein Crystal

A regular 3D array of identical protein molecules or molecular complexes arranged in the same orientation relative to each other so that a repeating unit cell extends throughout the lattice, averaging approximately $50\%$ solvent content.

Nucleation

The phenomenon whereby a nucleus—such as a dust particle, a tiny seed crystal, or a small protein aggregate—initiates the crystallization process in a supersaturated solution.

Metastable Zone

The region on a crystallization phase diagram where the protein solution is supersaturated enough to sustain the growth of existing crystal nuclei, but the concentration is insufficient for spontaneous nucleation to occur.

Mother Liquor

The solution in which a crystal exists and remains bathed after vapor diffusion, equilibration through dialysis, or evaporation has reached equilibrium.

Deamidation

A chemical reaction causing protein heterogeneity wherein an amide functional group in the side chain of asparagine (Asn) or glutamine (Gln) is removed or converted to an acid form (Asp or Glu).

Hanging Drop Vapor Diffusion

A crystallization technique in which a drop containing equal volumes of protein solution and reservoir precipitant (giving half the reservoir precipitant concentration) is inverted over a greased well to slowly equilibrate via vapor diffusion.

Sitting Drop Vapor Diffusion

A vapor diffusion crystallization method where the sample drop rests on a raised pedestal or bridge within a sealed well, allowing for larger drop volumes ($20\text{--}40\,\mu\text{L}$) than the hanging drop geometry.

Microbatch under Oil

A crystallization technique where drops are placed under an oil layer; pure paraffin oil allows almost no diffusion (true batch), whereas a $1:1$ mixture of paraffin and silicon oil (Al's Oil) allows slow evaporation.

Microdialysis (Salting-In)

A crystallization technique using dialysis buttons ($5\text{--}350\,\mu\text{L}$) where a protein initially at high ionic strength equilibrates across a semipermeable membrane against lower salt concentrations, exploiting the minimum solubility of proteins at low ionic strength.

Vitrification

The rapid flash-freezing of aqueous solutions within and around a protein crystal into an amorphous, glass-like state using liquid nitrogen and cryoprotectants (such as glycerol or PEG) to eliminate crystalline ice formation and reduce radiation damage.

Synchrotron Radiation

Intense, highly polarized, tangential electromagnetic radiation emitted when ultra-high-energy charged particles (electrons or positrons) traveling at relativistic speeds are accelerated or redirected by magnetic fields in a storage ring.

Insertion Device

A specialized periodic magnetic array (such as a wiggler or undulator) inserted into the straight sections of a synchrotron to force the beam into undulating paths, shifting the emitted spectrum to shorter wavelengths and higher intensities.

Bragg's Law

The fundamental relationship predicting constructive interference of diffracted X-rays from crystal lattice planes spaced $d$ apart at an incident angle $\theta$, expressed as $n\lambda = 2d\sin(\theta)$.

Fourier Transform (FT)

A reversible mathematical operation that converts a signal or function between real space and reciprocal (frequency) space without loss of data, decomposing a repeating continuous spatial pattern into its individual constituent wave cycles.

Unit Cell

The smallest repeating parallelepiped volume of a crystal lattice defined by edge lengths $a, b, c$ and interaxial angles $\alpha, \beta, \gamma$ that contains the full symmetry of the crystal structure.

Miller Indices

A set of three integers $(h, k, l)$ that denote a specific family of parallel lattice planes in a crystal, inversely proportional to the fractional intercepts of the planes along the unit cell edges $a, b, c$.

Indexing

The crystallographic step of identifying the crystal lattice dimensions, unit cell geometry, and space group symmetry by assigning unique Miller indices $(h, k, l)$ to each diffraction spot based on its geometric position.

Integration

The process of extracting the raw intensity $I(hkl)$ and its associated experimental error $\sigma_I(hkl)$ for every indexed reflection spot while subtracting local background noise and correcting for saturated or obstructed pixels.

Structure Factor ($F_{hkl}$)

A complex quantity representing the resultant scattered wave from all atoms in a unit cell for reflection $(h, k, l)$, having an amplitude $|F(hkl)| = \sqrt{I(hkl)}$ and a phase angle $\alpha(hkl)$.

Phase Problem

The fundamental dilemma in X-ray crystallography that detectors can only measure wave intensities ($I \propto |F|^2$), entirely losing the phase angles ($\alpha$), which contain the majority of the information required to calculate the electron density map.

Patterson Function

A Fourier synthesis computed directly from squared structure factor amplitudes ($|F(hkl)|^2$) with all phase angles set to zero ($P(u, v, w) = \mathcal{F}\{|F(hkl)|^2\}$), producing a 3D map of all interatomic distance vectors in the unit cell.

Molecular Replacement (MR)

A computational phasing technique formulated by Michael G. Rossmann where the known atomic coordinates of a homologous structure are positioned and oriented within the target unit cell to provide initial calculated phases ($\alpha_{\text{calc}}$).

Rotation Function

A Patterson search calculation in molecular replacement that determines the three angular orientations ($\omega, \phi, \kappa$) of a search model by maximizing the overlap of its intramolecular (self-Patterson) vectors with those of the unknown crystal.

Translation Function

The second search step in molecular replacement that shifts the correctly oriented search model across the asymmetric unit to locate its exact Cartesian position relative to the crystallographic origin by matching intermolecular (cross-Patterson) vectors.

Multiple Isomorphous Replacement (MIR)

An experimental phasing method pioneered by Max Perutz requiring diffraction data from a native crystal and at least two distinct heavy-atom soaked derivative crystals that maintain identical unit cell dimensions and crystal packing.

Difference Patterson Map

A Patterson synthesis using coefficients $H = (|F_{\text{PH}}| - |F_{\text{P}}|)^2$ to subtract the native protein contribution, yielding a map that displays exclusively the interatomic vectors between heavy-atom sites.

Back-Soaking

A technique in heavy-atom derivatization where crystals are washed in native mother liquor after soaking to remove non-specifically bound heavy atoms while retaining covalently bound ones, improving isomorphism and specificity.

Multiwavelength Anomalous Diffraction (MAD)

An experimental phasing method where anomalous dispersion effects near the absorption edge of an incorporated heavy element (typically selenium in selenomethionine) break Friedel's law, allowing phases to be calculated from a single crystal measured at multiple X-ray wavelengths.

Model Bias

The artifactual phenomenon wherein calculated electron density maps regenerate erroneous features of the search model because the phases used in the Fourier synthesis were derived from that model rather than the true structure.

Composite Omit Map

A map constructed by systematically omitting small portions of the structural model (typically $5\text{--}10\%$ at a time), recalculating phases, and assembling the unbiased regions to eliminate model bias.

Solvent Flattening

A density modification technique that improves initial electron density phases by defining a molecular envelope mask, multiplying non-protein bulk solvent regions by zero (or setting them to a uniform average density), and retaining protein features.

Non-Crystallographic Symmetry (NCS) Averaging

A density modification and refinement technique applied when multiple identical molecules or subunits are present within the same asymmetric unit, averaging their electron densities according to local symmetry operators to improve signal-to-noise.

B-factor (Temperature Factor)

An isotropic or anisotropic parameter in an atomic model (ranging typically from $\sim 10\,\text{Å}^2$ to $\sim 100\,\text{Å}^2$) that quantifies thermal vibrations and static disorder, exponentially dampening the scattering factor via $\exp\left(-B\left[\frac{\sin(\theta)}{\lambda}\right]^2\right)$.

Rigid Body Refinement

An early refinement stage that groups domains, subunits, or the whole protein into inflexible blocks, adjusting only their six external degrees of freedom (three rotational, three translational) to optimize the parameter-to-observation ratio.

Torsion Angle Refinement

A refinement protocol that keeps bond lengths and bond angles fixed to ideal stereochemical values, restricting atomic movement strictly to rotations about allowable rotatable dihedral bonds.

Simulated Annealing

A global optimization method using molecular dynamics that computationally "heats" the atomic model (e.g., to $2500\,\text{K}$) and slowly cools it in small decrements to cross energetic barriers and escape local minima.