Dynamic Light scattering

How is a size distribution for a protein sample derived?

(QELS), uses the scattered light to measure the rate of diffusion of the protein particles. This motion data is conventionally processed to derive a size distribution for the sample, where the size is given by the "Stokes radius" or "hydrodynamic radius" of the protein particle. This hydrodynamic size depends on both mass and shape (conformation).

Beam of a 5mW green laser pointer...

...is visible at night due to Rayleigh scattering and airborne dust.

How does dynamic light scattering work?

1. Beam of laser light focussed in sample 2. Particles in scattering volume scatter light in all directions - the scattered photons are measured by a photomultiplier tube 3. The intensity appears to fluctuate randomly 4. A digital correlator is used to compute the autocorrelation function

Principles behind dynamic light scattering

1. PArticles, emulsions and molecules in suspension undergo Brownian motion - This is motion induced by bombardment by solvent molecules that themselves are moving due to ther thermal energy 2. Brownian motion causes fluctuations of local concentration of the particles, resulting in local in-homogeneities of the refractive index. 3. This in turn results in fluctuations of intensity of the scattered light 4. The diffusion coefficient of the particles is inversely proportional to the decay time of light scattering fluctuations. The decay time is obtained from the time-dependent correlation function of the scattered light.

What are the requirements of DLS?

1. The particles being measured are spherical 2. The suspension is dilute, such at the scattered light is measured before it is rescattered by other particles 3. Optical properties of the particles and the medium surrounding them is known 4. Particles are homogenous

Brownian motion

Chaotic movement of colloidal particles

What does DLS actually measure?

Hydronamic radius The translational diffusion coefficient will depend not only on the size of the particle "core", but also on any surface structure

What is observed if the light source is a laser?

If the light source is a laser, and thus is monochromatic and coherent, then one observes a time-dependent fluctuation in the scattering intensity. These fluctuations are due to the fact that the small molecules in solutions are undergoing Brownian motion and so the distance between the scatterers in the solution is constantly changing with time.

If the particles or molecules are illuminated with a laser, what does the fluctuation of the rate of intensity of scattered light depend on?

If the particles or molecules are illuminated with a laser, the intensity of the scattered light fluctuates at a rate that is dependent upon the size of the particles.

CLouds at sunset

In contrast, the water droplets which make up clouds are of a comparable size to the wavelengths in visible light, and the scattering is described by Mie's model rather than that of Rayleigh. Here, all wavelengths of visible light are scattered approximately identically and the clouds therefore appear to be white or grey.

What is Rayleigh scattering inversely proportional to?

It is inversely proportional to the fourth power of the wavelength of light, which means that the shorter wavelength in visible white light (violet and blue) are scattered stronger than the longer wavelengths toward the red end of the visible spectrum.

What is this exponential decay related to?

Motion of the particles specifically to the diffusion coeffiecient.

Small particles...

Move faster

Large particles...

Move slower

Applications of DLS

Protein Crystallography Small angle X-ray diffraction Nanotechnology

What is Rayleigh scattering proportional to?

Rayleigh scattering intensity has a very strong dependence on the size of the particles (it is proportional to the sixth power of their diameter).

Crepuscular rays

Rays of sunlight that appear to radiate from a single point in the sky. These are columns of sunlit air separated by darker cloud-shadowed regions.

Rayleigh scattering

Scattering of light caused by atmospheric particles smaller than the wavelength being scattered When light hits small particles the light scatters in all directions (Rayleigh scattering) so long as the particles are small compared to the wavelength (below 250nm)

Mie Scattering

Scattering of light or other electromagnetic radiation by particles with similar size or larger than the wavelength of the light Causes the white glare around the sun

What is DLS useful for comparing?

Stability of different formulations including real time monitoring of changes at elevated temperatures

Why is the sky blue?

The air molecules scatter blue light better than red light, so more blue light reaches our eyes.

What happens as the time delays get longer?

The correlation decays exponentially meaning that after a long time period has elapsed, there is no correlation between the scattered intensity of the initial and final states.

Why is the correlation high at short time delays?

The particles do not have a chance to move to a great extent from the initial state. The two signals are thus essentially unchanged when compared after only a very short time interval.

Autocorrelation function

The second order autocorrelation curve is generated from the intensity trace as follows: where g2(q;τ) is the autocorrelation function at a particular wave vector, q, and delay time, τ, and I is the intensity.

WHat does the scattered light then undergo?

This scattered light then undergoes either constructive or destructive interference by the surrounding particles and within this intensity fluctuation, information is contained about the time scale of movement of the scatterers.

What is used to fit the decay (the autocorrelation function)?

To fit the decay (i.e., the autocorrelation function), numerical methods are used, based on calculations of assumed distributions. If the sample is monodisperse then the decay is simply a single exponential.

Light scattering

the process by which light bounces off particles in its path - deflection of a ray from a straight path

Back scattering

the scattering of incident radiation back in the direction of the energy source due to too many particles

Classical/ Static Light Scattering

• Scattering is constant (static) • At various angles • Direct measure of MM • Determine oligomeric state of protein • Determine that mass of aggregates • Can also be used for measuring the stoichiometry of complexes between different proteins (e.g. receptor ligand complexes or antibody-antigen complexes e.g. crepuscular rays

Dynamic light scattering ((a.k.a. photon correlation spectroscopy quasi electric light scattering)

• The scattering is observed to be changing over time (dynamic) • At one angle • Measure rate of diffusion of protein particles • Determine the 'Stoke radius' or hydrodynamic radius • Senses very small amounts of aggregated protein (,0.015) e.g. dust