Protein Crystallography

X-rays are waves of

sinusoidally varying electrical and magnetic fields

At any particular in time can plot

the height of the wave as a function of distance

All electromagnetic waves propagate at

the speed of light

Can describe waves using 3 terms:

Wavelength, amplitude and phase

Phase is a parameter that describes

how out of register two waves are with each other

Electromagnetic waves have an

alternating electric field component

Electrons that interact with an X-ray

oscillate

Oscillating charges act as

new sources

X-rays are scattered in all directions from

the electrons they encounter

Scattering is

elastic

Incident X-ray photon and emitted X-ray photon have the same energy therefore

Same wavelength

Different atoms scatter by different amounts proportional

to how many electrons they have

Scattering is very

inefficient

Scattered waves from each atom add up

in all different directions of scattering

Incident X-rays

same amplitude, same phase

Scattered X-rays

different amplitudes, different phases

X-rays scatter when

they encounter electrons in atoms

Scattered waves from electrons in different atoms

interact

The phase of scattered waves is related to

Atom position in the scattering object

The electron density in the scattering object is related to

the scattering pattern by a Fourier transform

In any given direction electron density through three atoms can be thought of as

an electron density curve with three peaks

An electron density curve can be described as

The sum of sine and cosine functions

What is a crystal?

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

Unit cell =

Unit lattice + Motif

Unit cell is defined by

Three vectors a, b and c and three angles alpha, beta and gamma

For scattered signal to be measurable

we need scattering from a large number of molecules

A crystal amplifies weak X-ray scattering from

Individual molecules

X-rays are very

damaging - a single molecule would be rapidly destroyed

A crystal minimises

radiation damage per molecule

Radiation damage is

Spread across all molecules in the crystal

Primary radiation damage

An X-ray interacts directly with atoms in a protein molecule - dose dependent only

Secondary radiation damage

Radiolysis of H2O generates mobile OH- ions or OH radicals that diffuse and chemically damage the protein - Dose, time and temp dependent

Scattering arises from

Individual objects

Diffraction arises from

Planes within an ordered lattice

Diffraction pattern is

A convolution of the object and the lattice

Braggs Law

nλ = 2d sinθ

Each spot in a diffraction pattern arises from a

Reflection from one set of Bragg planes

The position of the discrete spot depends on

The geometry of the crystal lattice

The intensity of the discrete spot is related to the

amplitude of the scattering vector from each plane depending on how many electrons there are between planes

The resolution limit of the diffraction pattern is the smallest

inter plane distance for which reflections are still measurable

The resolution limit of the diffraction determines the

level of detail in the electron density

Resolution limit is related to how

well the unit cells pack together

Spacing of diffraction spots tell us about

the dimensions of the unit cell

Very small unit cell

Spots are far apart, none at low resolution

Large unit cell

Spots close together, many at low resolution

Crystals of small or inorganic molecules are

often very highly tightly packed with few gaps

To have a regular arrangement

there must be gaps

How is a regular arrangement achieved

Through symmetry

Symmetry means the unit cell

contains more than one molecule

Proteins are

homochiral polymers of L-amino acids

Centers of inversion and mirror planes require molecules in the crystal to have

opposite hardness - mirror symmetry is therefore impossible in protein crystals

Two fold axis between the molecules allows

For a 180 degree rotation to create a motif identical to the starting motif

A four-fold axis between the molecules allows for

a 90 degree rotation to create a motif identical to the starting motif

A three-fold axis between the molecules allows for a

120 degree rotation to create a motif identical to the starting motif

Existence of a three-fold axis imposes

Constraints on the shape of the unit cell

Unit cell

Smallest volume from which the entire crystal can be constructed by translation only

Asymmetric Unit

The smallest volume from which the unit cell can be constructed by application of the crystallographic symmetry

Six fold axis

60 degree rotation to create a motif identical to the starting motif

Point group

collection of symmetry operators that all pass through the same point.

What must a point group be?

Closed, have an identity element and every element must have an inverse

Cubic point groups

Defined in terms of three fold symmetry

Solvent channels

the gaps created by symmetry

As volume decreases

Salt concentration increases

What happens when the salt approaches the solubility limit

The solution becomes metastable and supersaturated → crystal nucleation occurs

Protein crystals are formed by a

sparse network of weak intermolecular interactions

Why can’t we just grow protein crystals by evaporating water?

They are fragile, difficult to form, sensitive to mechanical stress and also highly hydrated structures

How do we grow protein crystals?

Mix purified proteins with a chemical cocktail designed to induce crystallisation by altering protein solubility

All proteins contain

Charged amino acids that are surface-exposed

Small amounts of salt increase

protein solubility

For every protein a pH value exists (isoelectric point) in solution at which

there is no net change per molecule

pH above isoelectric point

proteins have net negative charge (acidic)

pH at isoelectric point

no net charge

pH below isoelectric point

proteins have net positive charge

Organic precipitants are very soluble molecules that

compete with protein for space in solution

Organic precipitants are often

long polymers with a high molecular weight

Classic crystallisation method

hanging drop vapour diffusion

High-throughput robotics help to

screen hundreds of crystallisation buffers in parallel with very small volumes of protein

In a diffraction experiment

the position of the incident beam is constant

Based on distances between diffraction spots

can determine the unit cell constants → tells us what type of lattice we are dealing with and its dimensions

Some types of symmetry are only possible with

a certain type of lattice

Summation process

Adds up all the pixel counts corresponding to each spot

Integration accurately measures

The intensity of each reflection

Intensities also allow us to determine

symmetry and the likely space group

Diffraction pattern has the same point group symmetry as the crystal this means

reflections from symmetry-related planes have an equal intensity

Averaging the intensities from symmetry related reflections

Improves the signal to noise ratio

The electron density is the

average of all the unit cells

To produce strong electron density

Atoms must be in exactly the same position in all unit cells

Local rigidity is imposed by

Secondary structure

Crystal contacts can create

Artefactual order

Peptidoglycan

Major carbohydrate component of bacterial cell walls

Lowest energy conformation for any carbohydrate ring

Chair

GALC is located in

Lysosomes

What is GALC

Acidic organelles for degradation of macromolecules

GALC crystals grew at

pH 6.8 in a buffer where the rate of reaction is 50 times lower

The GALC active sites are exposed to solvent channels due to

crystal symmetry

GALC protein is catalytically active in

crystallo

Active site cavity

is shallow

In galactose the -OH group at the C4 position is

Stabilished by a hydrogen bond with Thr93

Amount of thermal stabilisation correlates

perfectly with the delta G of binding

Basic amine nitrogen should be at the

C1 position → it can make electrostatic interactions with the negatively charged nucleophile