Light scattering, X-ray crystallography

Mitesh Shrestha

Light scattering

• Form of scattering in which light in the form of propagating energy is scattered.

• Deflection of a ray from a straight path, for example by irregularities in the propagation medium, particles, or in the interface between two media.

• The interaction of light with matter can reveal important information about the structure and dynamics of the material being examined.

Light scattering

• If the scattering centers are in motion, then the scattered radiation is Doppler shifted.

• An analysis of the spectrum of scattered light can thus yield information regarding the motion of the scattering center.

• Periodicity or structural repetition in the scattering medium will cause interference in the spectrum of scattered light.

• Thus, a study of the scattered light intensity as a function of scattering angle gives information about the structure, spatial configuration, or morphology of the scattering medium.

Light scattering

• With regard to light scattering in liquids and solids, primary material considerations include:

– Crystalline structure: How close-packed its atoms or molecules are, and whether or not the atoms or molecules exhibit the long-range order evidenced in crystalline solids.

– Glassy structure: Scattering centers include fluctuations in density and/or composition.

– Microstructure: Scattering centers include internal surfaces in liquids due largely to density fluctuations, and microstructural defects in solids such as grains, grain boundaries, and microscopic pores

Methods to measure particle size Light scattering

• Measures - Area diameter or volume diameter, polymers Radius of gyration or molecular mass

• Principal of operation

– Interaction with laser light the light are scattered and the intensity of the scattered light are measured

– Two principals • Static light scattering

• Dynamic light scattering

– Size range- 0.0001-1000 m

• Benefits

– Well established

– instruments are easy to

operate

– yield highly reproducible

data Drawbacks

• Diluted samples-changes

in properties

• Tendency to

– Oversize the large particles

– Over estimates the number

of small particles

Static light scattering

• Particle size information is obtained from intensity of the scattering pattern at various angles.

• Intensity is dependent on

– wavelength of the light

– Scattering angle

– particle size

– relative index of refraction n of the particle and the medium.

Micromeritics Technical Workshop Series (Fall 2000)

Light scattering Small and large particles

• Small particles one scattering center < 10 nm

• Scatter intensity independent of scattering angle (Rayleigh scattering)

• Large particles multiple scattering centres

• Scattering depend on angle and gives diffraction pattern

Q u i c k T i m e ™ a n d a d e c o m p r e s s o ra r e n e e d e d to s e e th i s p i c tu r e .

Light scattering Mie theory

• The complete solution to Maxwells equation for homogeneous sphere – Incident light of only a single wavelength is

– considered.

– No dynamic scattering effects are considered.

– The scattering particle is isotropic.

– There is no multiple scattering.

– All particles are spheres.

– All particles have the same optical properties.

– Light energy may be lost to absorption by the particles.

• Applicable for all sizes

• Needs to know the refractive index to calculate the size

Light scattering Fraunhofer theory

• Treats that the particle as completely adsorbing disc

• does not account for light transmitted or refracted by the particle.

• Only applicable to particles much larger than the wavelength of the light

• Do not need to know the refractive index

• Much simpler math

Light scattering Dynamic light scattering

• Particle size is determined by correlating variations in light intensity to the Brownian movement of the particles

• Related to diffusion of the particle

X-ray crystallography

• A technique used for determining the atomic and molecular structure of a crystal, in which the crystalline atoms cause a beam of incident X-rays to diffract into many specific directions.

• By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal.

• From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their disorder and various other information.

X-ray crystallography

• Most favoured technique for structure determination of proteins and biological macromolecules.

• Obtain a three dimensional molecular structure from a crystal.

Braggs law

http://www.eserc.stonybrook.edu/ProjectJava/Bragg/

Scattered beams in phase, they add up

Scattered beams not in phase, they cancel each other

nl = 2d sinq

Methods to determine protein structure

• X-Ray and NMR methods allow to determine the structure of proteins and protein complexes

• These methods are expensive and difficult

– Could take several work months to process one proteins

• A centralized database (PDB) contains all solved protein structures

– XYZ coordinate of atoms within specified precision

– ~19,000 solved structures

Overview of steps

Growing a Crystal

Collecting X-ray diffraction pattern

Solving of Phase Problem

Calculate Electron Density Map

Constructing a Structural Model

Refining the Structural Model

Growth of Crystals - Background Why? Diffraction pattern of single molecule too weak for detection => sum of several diffraction patterns of identically oriented molecules with identical conformation

Supersaturated Solution: Concentration higher than intrinsic solubility S0

Porcine Elastase

Growth of Crystals - Approaches

Empirical Approach: Test hundreds of conditions Parameters: • pH • salt type & concentration • precipitant (ammonium sulfate, polyethylene glycol, 2-methyl-2,4-dimethyl-pentane diol (MPD), propanol) • temperature (2 – 30°C) • protein concentration (1 – 100 mg/ml) • additional substances (substrates, inhibitors, cofactors etc.)

Hanging Drop Method:

Alternative: Sitting Drop Microdialysis

X-ray crystallography and NMR are the two major techniques for determining protein structures

Protein isolation

Protein Purification

Protein Crystallisation

X-ray crystallography:

Crystal

X-ray

Phases of diffracted rays

Electron density

Protein model

Liquid nitrogen is used to freeze the crystal which allows for increased

reliability of information gathered from testing. The area detector, which

collects the diffracted x-rays once they pass through the crystal, is the

black plate located behind the nitrogen stream, (right) sample x-ray

diffraction pattern.

X-ray crystallography

The phase problem:

Isomorphous Replacement: combination of diffraction data from the native crystal with data from other crystals containing the same protein packed in the same way but adding a heavy atom

Molecular Replacement: placement of a known relative structure in different positions and orientations, providing approximate phases

Multiwavelength Anomalous Dispersion: Measurements of the variation of the intensity distribution in the diffraction pattern over a range of wavelengths

Direct Methods: Knowledge of electron density distributions in crystals permits calculation of phases directly from experimental data

Molecular Replacement

1. Method to obtain Phase information

• Only possible if structure of a very similar molecule is

known (native vs. Mutant, close homolog), at least 25%

sequence identity

• Calculate structure factors Fcalc for known molecule

• Compare with data set to estimate phase for known

structure (acalc)

• Use this Phase information together with observed

structure factors (Fobs) to calculate first electron density

map

• Refine Structure (see below)

Multiple Isomorphous Replacement

2. Method to obtain Phase information

• Use crystals containing heavy atoms at specific positions

(isomorphous crystals) as well as crystal of native protein

• Heavy atoms strongly diffract

• Difference data set of heavy atom derivative and native crystals

gives structure factors of heavy atoms only = limited data set

• Can be used to determine position and phase of heavy atoms (as for small molecule crystals, Patterson function)

• Needs to be done for at least 2 heavy atom derivatives to

obtain enough information to estimate phase of native data set

and to solve the structure

Multiple Anomalous Dispersion

3. Method to obtain Phase information

• Use one crystal containing heavy atoms at specific

positions as well as crystal of native protein

• Heavy atoms not only diffract X-rays, but also absorbs X-rays of

certain wavelength

• Using synchroton X-ray source, diffraction data are generated

at different wavelenghts of the heavy-atom crystal

• Different data sets can be used to obtain phase information

similar to multiple isomorphous replacement

Limitations

• An extremely pure protein sample is needed.

• The protein sample must form crystals that are relatively large without flaws. Generally the biggest problem.

• Many proteins aren’t amenable to crystallization at all (i.e., proteins that do their work inside of a cell membrane).

X-ray crystallography