Light Scattering & Fluorescence• First quantitative experiments in 1869 by Tyndall

(scattering of small particles in the air – Tyndall effect)

• 1871 – Lord Rayleigh started a quantitative study and theory

• Basic idea: incident monochromatic linearly polarized light beam incident on a sample. Assume– No absorption– Randomly oriented and positioned scatterers– Isotropic scatterers– Independently scattering particles (dilute)– Particles small compared to wavelength of lightWe’ll remove some of these restrictions later

Classical Wave description• The incident electric field is

E = Eocos(2x/ – 2t/T)

• Interaction with molecules drives their electrons at the same f to induce an oscillating dipole pinduced = Eocos(2x/ – 2t/T)

• This dipole will radiate producing a scattered E field from the single molecule

2

2

4 sin( , ) cos 2 / 2 /o

scattered

EE r t x t T

r

r Obs. Pt.

dipole

Rayleigh scattering1. E ~ 1/r so I ~ 1/r2 - necessary since I

~energy/time/area and A ~ r2

2. E ~ 1/2 dependence so I ~ 1/4 – blue skies and red sunsets (rises)

3. Elastic scattering – same f

4. sin dependence – when = 0 or – at poles of dipole – no scattering – max in horizontal plane

5. related to n , but how?

Polarizability and index of refraction• Note that if n ~ 1

where c is the weight concentration• Then

where N = number concentration• So,

• For a particle in a solvent with nsolv, we have n2 – n2

solv = 4N so

1dn

n cdc

2 21 2 ... 1 2 4dn dn

n c so n c Ndc dc

2 2 A

dn dnc M

dc dcorN N

2( )( ) / 4 ~

4 2solv solv

solv solvA

n ndn c dnn n n n N M

dc N N dc

Scattered Intensity• Detect intensity, not E, where

• Substituting for a, we have

22

2 4 2 2

2 2 4

1

4 sin

16 sino

scatt

o oparticle

E

rI

I E r

22 2 2 2

2 4 2

1

4 sinsolvscatt

o Aparticle

dnM n

I dcI r N

Scattered Intensity II• If there are N scatterers/unit volume and

all are independent with N = NAc/M, then

• We define the Rayleigh ratio R:

22 2 2

2 4

1

4 sin solvscatt scatt

o o Aper unit volume particle

dnn Mc

I I dcN

I I N r

22 2

2,

2 4

4

sin

solvscatt

o A

dnn Mc

I r dcR KMc

I N

Basic Measurement• If the intensity ratio I/Io, nsolv, dn/dc, , c, ,

and r are all known, you can find M.• Usually write Kc/R = 1/M• Measurements are usually made as a

function of concentration c and scattering angle

• The concentration dependence is given by

Where B is called the thermodynamic virial

12

KcBc

R M

Polydispersity• If the solution is polydisperse – has a

mixture of different scatterers with different M’s - then we measure an average M – but which average?

• So the weight-averaged M is measured!

i iw

i

c MR K c KM c

c

Angle Dependence• If the scatterers are small (d < /20), they

are called Rayleigh scatterers and the above is correct – the scattering intensity is independent of scattering angle

• If not, then there is interference from the light scattered from different parts of the single scatterer

• Derivation of Particle Scattering Factor P()

Particle Scattering Factor• Different shapes give different P()

Analysis of LS Data• Measure I(, c) and plot

Kc/R vs sin2(/2) + (const)c

– Extrapolations: c 0

0

Final resultSlope~RG

Slope~B

Problems: Dust, Standard to measure Io, low angle measurement flare

Dynamic Light Scattering

- Basic ideas – what is it?

- The experiment – how do you do it?

- Some examples systems – why do it?

Double Slit Experiment

screen

Coherent beamExtra path length

+ +

= =

Light Scattering Experiment

Laser at fo

Scattered light

Scatterers in solution (Brownian motion)

ffo

Narrow line incident laserDoppler broadenedscattered light

f

0 is way off scale f ~ 1 part in 1010 - 1015

More Detailed Picturedetector

Inter-particle interference

time

Detected intensity

Iaverage

How can we analyze the fluctuations in intensity?

Data = g() = <I(t) I(t + )>t = intensity autocorrelation function

Intensity autocorrelation• g() = <I(t) I(t + )>t

For small

For larger

g()

c

What determines correlation time?• Scatterers are diffusing – undergoing Brownian

motion – with a mean square displacement given by <r2> = 6Dc (Einstein)

• The correlation time c is a measure of the time needed to diffuse a characteristic distance in solution – this distance is defined by the wavelength of light, the scattering angle and the optical properties of the solvent – ranges from 40 to 400 nm in typical systems

• Values ofc can range from 0.1 s (small proteins) to days (glasses, gels)

Diffusion• What can we learn from the correlation time?• Knowing the characteristic distance and

correlation time, we can find the diffusion coefficient D

• According to the Stokes-Einstein equation

where R is the radius of the equivalent sphere and is the viscosity of the solvent

• So, if is known we can find R (or if R is known we can find

6Bk T

DR

Why Laser Light Scattering?1. Probes all motion

2. Non-perturbing

3. Fast

4. Study complex systems

5. Little sample needed

Problems: Dust and

best with monodisperse samples

Antibody molecules

• Technique to make 2-dimensional crystals of proteins on an EM grid (with E. Uzgiris at GE R&D)

Change pH

60o120o

Conformational change with pH results in a 5% change in D – seen by LLS and modeled as a swinging hinge

Aggregating/Gelling SystemsStudied at Union College

• Proteins:– Actin – monomers to polymers and networks

Study monomer size/shape, polymerization kinetics, gel/network structures formed, interactions with other actin-binding proteins

Epithelial cell under fluorescent microscope

Actin = red, microtubules = green, nucleus = blue

Why?

Aggregating systems, con’t– BSA (bovine serum albumin)– beta-amyloid +/- chaperones

• Polysaccharides:– Agarose– Carageenan

Focus on the onset of gelation –

what are the mechanisms causing gelation? how can we control them? what leads to the irreversibility of gelation?

what factors cause or promote aggregation?

how can proteins be protected from aggregating?

Current Projects

1.-amyloid – small peptide that aggregates in the brain – believed to cause Alzheimer’s disease-

Current Projects

Add silver ions – causes DNA to increase pitch – finding virus straightens and lengthens

2. Structure of bacterial virus -

Fluorescence• Absorption of light occurs within ~10-15 seconds,

leaving a molecule in an excited state• What happens next?

– If no photon is re-emitted, the molecule probably loses the energy via a collision with solvent molecules

– If a photon is emitted then it can be of several types:• Scattered at the same frequency/energy• Fluorescent at a longer wavelength (takes ~ ns)• Phosphorescent – similar to fluorescence but transition is

from a triplet state (with electrons parallel ↑↑ ; fluorescence is from a singlet state with paired e-↑↓) (takes 10 – 100 nsec)

• Resonant energy transfer (FRET) – donor and acceptor groups have a common vibrational energy level: A + hf A*; A* + B A + B* ; B* B + hf ; A & B must lie close to one another – technique can be used as a “yardstick”

Energy Levels

Quantum Yield• All of these processes compete with one another • The quantum yield for fluorescence

Each other process has a Q and all must add up to 1:

Two types of factors affecting Qfluorescence:

– internal – with more vibrational levels closely spaced (more flexible bonds), fluorescence is more easily quenched, losing energy to heat best fluors are stiff ring structures: Tryp, Tyr

– environmental factors such as T, pH, neighboring chemical groups, concentration of fluors; generally more interesting

#

#fluorescence

fluorescent photonsQ

absorbed photons

1iQ

Instrumentation1. 90o measurement to avoid scattering or direct

transmitted beam2. Very low concentration can be used to keep

Ifluor linear in concentration

3. Sensitivity is very high since no bkgd signal – no difference measurement (blank) needed as in absorption

4. Measure either I vs emitted for a given inc = emission spectrum OR measure I vs exciting at fixed emitted = excitation spectrum

5. Simple fluorometer uses interference filters for incident & 90o emission – better machines use gratings and scan to get a spectrum

(1 ) ( )co oI I Q e for small c I Q c Kc

Spectra7. Record uncorrected spectra directly –

3 types of corrections needed:

a.Output Io of light source varies with inc

b. Variable losses in monochromators with inc or emitted

c. Variable response of PMT with emitted

Typically absolute measurements are not done and so no corrections are made – only comparisons

Fluors• Intrinsic: “chromophore” = e.g. Try, Tyr, Phe –

best is Try; Ifluor depends strongly on environment

• Extrinsic: attach fluor to molecule of interest; must:– Be tightly bound at unique location– Have fluorescence that is sensitive to local

environment– Not perturb molecules being studied

Examples: ANS & dansyl chloride fluoresce weakly in water, but strongly in non-polar solvents;

Acridine O used with DNA – green on d-s, red-orange on s-s

Two Application Examples1. Detect conformational changes in an

enzyme when a co-factor binds

2. Denaturation of a protein

A w/o added co-factor; B with added co-factor; C = free Tryptophan

Helix-coil transition of a protein; in 0.15 M NaCl the protein is more stable – higher T needed for transition

FRAP• High power

bleach pulse

• Low power probe

• Look at 2-D diffusion

<r2> = 4Dt ~ size2 beam focus

TIR-FRAP

Rhodamine labeled actin/phalloidin