1. 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 light We’ll remove some of these restrictions later

2. Classical Wave description The incident electric field is E = E o cos(2  x/ – 2  t/T) Interaction with molecules drives their electrons at the same f to induce an oscillating dipole p induced =  E o cos(2  x/ – 2  t/T) This dipole will radiate producing a scattered E field from the single molecule  r Obs. Pt. dipole

3. Rayleigh scattering 1.E ~ 1/r so I ~ 1/r 2 - necessary since I ~energy/time/area and A ~ r 2 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  related to n, but how?

4. 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 n solv, we have n 2 – n 2 solv = 4  N  so

5. Scattered Intensity Detect intensity, not E, where Substituting for a, we have

6. Scattered Intensity II If there are N scatterers/unit volume and all are independent with N = N A c/M, then We define the Rayleigh ratio R  :

7. Basic Measurement If the intensity ratio I  /I o, n solv, 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

8. 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!

9. 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(  )

10. Particle Scattering Factor Different shapes give different P(  )

11. Analysis of LS Data Measure I ( , c) and plot Kc/R  vs sin 2 (  /2) + (const)c –Extrapolations: c 0  0

12. Final result Slope~R G Slope~B Problems: Dust, Standard to measure I o, low angle measurement flare

13. Dynamic Light Scattering - Basic ideas – what is it? - The experiment – how do you do it? - Some examples systems – why do it?

14. Double Slit Experiment screen Coherent beam Extra path length ++ = =

15. Light Scattering Experiment Laser at f o Scattered light Scatterers in solution (Brownian motion) f fofo Narrow line incident laser Doppler broadened scattered light ff 0 is way off scale  f ~ 1 part in 10 10 - 10 15

16. More Detailed Picture detector  Inter-particle interference time Detected intensity I average How can we analyze the fluctuations in intensity? Data = g(  ) = t = intensity autocorrelation function

17. Intensity autocorrelation g(  ) = t For small   For larger   g(  )  cc

18. What determines correlation time? Scatterers are diffusing – undergoing Brownian motion – with a mean square displacement given by = 6D  c (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 of  c can range from 0.1  s (small proteins) to days (glasses, gels)

19. 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 

20. 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

21. Antibody molecules Technique to make 2-dimensional crystals of proteins on an EM grid (with E. Uzgiris at GE R&D) Change pH 60 o 120 o Conformational change with pH results in a 5% change in D – seen by LLS and modeled as a swinging hinge

22. Aggregating/Gelling Systems Studied 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?

23. 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?

24. Current Projects  -amyloid – small peptide that aggregates in the brain – believed to cause Alzheimer’s disease-

25. Current Projects Add silver ions – causes DNA to increase pitch – finding virus straightens and lengthens 2.Structure of bacterial virus -

26. 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”

27. Energy Levels

29. 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 Q fluorescence : –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

30. Instrumentation 1.90 o measurement to avoid scattering or direct transmitted beam 2.Very low concentration can be used to keep I fluor 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 & 90 o emission – better machines use gratings and scan to get a spectrum

32. Spectra 7.Record uncorrected spectra directly – 3 types of corrections needed: a.Output I o 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

33. Fluors Intrinsic: “chromophore” = e.g. Try, Tyr, Phe – best is Try; I fluor 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

35. Two Application Examples 1.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

36. FRAP High power bleach pulse Low power probe Look at 2-D diffusion = 4Dt ~ size 2 beam focus

37. TIR-FRAP Rhodamine labeled actin/phalloidin