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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