1. Lecture 5 FCS, Autocorrelation, PCH, Cross-correlation Enrico Gratton Principles of Fluorescence Techniques Laboratory for Fluorescence Dynamics

2. Fluorescence Parameters & Methods 1. Excitation & Emission Spectra Local environment polarity, fluorophore concentration 2. Anisotropy & Polarization Rotational diffusion 3. Quenching Solvent accessibility Character of the local environment 4. Fluorescence Lifetime Dynamic processes (nanosecond timescale) 5. Resonance Energy Transfer Probe-to-probe distance measurements 6. Fluorescence microscopy localization 7. Fluorescence Correlation Spectroscopy Translational & rotational diffusion Concentration Dynamics

3. First Application of Correlation Spectroscopy (Svedberg & Inouye, 1911) Occupancy Fluctuation Collected data by counting (by visual inspection) the number of particles in the observation volume as a function of time using a “ultra microscope” 120002001324123102111131125111023313332211122422122612214 2345241141311423100100421123123201111000111_2110013200000 10011000100023221002110000201001_333122000231221024011102_ 1222112231000110331110210110010103011312121010121111211_10 003221012302012121321110110023312242110001203010100221734 410101002112211444421211440132123314313011222123310121111 222412231113322132110000410432012120011322231200_253212033 233111100210022013011321113120010131432211221122323442230 321421532200202142123232043112312003314223452134110412322 220221 Experimental data on colloidal gold particles:

4. *Histogram of particle counts *Poisson behavior *Autocorrelation not available in the original paper. It can be easily calculated today. Particle Correlation They estimated the particle size to be 6 nm. Comments to this paper conclude that scattering will not be suitable to observe single molecules, but fluorescence could

5. In FCS Fluctuations are in the Fluorescence Signal Diffusion Enzymatic Activity Phase Fluctuations Conformational Dynamics Rotational Motion Protein Folding Example of processes that could generate fluctuations

6. Generating Fluctuations By Motion Sample Space Observation Volume 1. The Rate of Motion 2. The Concentration of Particles 3. Changes in the Particle Fluorescence while under Observation, for example conformational transitions What is Observed?

7. Defining Our Observation Volume: One- & Two-Photon Excitation. 1 - Photon 2 - Photon Approximately 1 um 3 Defined by the wavelength and numerical aperture of the objective Defined by the pinhole size, wavelength, magnification and numerical aperture of the objective

8. Brad Amos MRC, Cambridge, UK 1-photon 2-photon Need a pinhole to define a small volume

9. Data Treatment & Analysis Time HistogramAutocorrelation Photon Counting Histogram (PCH) Autocorrelation Parameters: G(0) & k action PCH Parameters: & 

10. Autocorrelation Function  Q = quantum yield and detector sensitivity (how bright is our probe). This term could contain the fluctuation of the fluorescence intensity due to internal processes W(r) describes our observation volume C(r,t) is a function of the fluorophore concentration over time. This is the term that contains the “physics” of the diffusion processes Factors influencing the fluorescence signal:

11. t1t1 t2t2 t3t3 t4t4 t5t5 The Autocorrelation Function G(0)  1/N As time (tau) approaches 0 Diffusion

12. Calculating the Autocorrelation Function Photon Counts t  t +  time Average Fluorescence

13. The Effects of Particle Concentration on the Autocorrelation Curve = 4 = 2

14. Why Is G(0) Proportional to 1/Particle Number? A Poisson distribution describes the statistics of particle occupancy fluctuations. In a Poissonian system the variance is proportional to the average number of fluctuating species:

15. G(0), Particle Brightness and Poisson Statistics 1 0 0 0 0 0 0 0 0 2 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 Average = 0.275 Variance = 0.256 Variance = 4.09 4 0 0 0 0 0 0 0 0 8 0 4 4 4 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 4 0 0 0 4 0 0 4 0 0 Average = 1.1 0.296 Lets increase the particle brightness by 4x: Time

16. What about the excitation (or observation) volume shape?

17. Effect of Shape on the (Two-Photon) Autocorrelation Functions: For a 2-dimensional Gaussian excitation volume: For a 3-dimensional Gaussian excitation volume: 1-photon equation contains a 4, instead of 8

18. Additional Equations:... where N is the average particle number,  D is the diffusion time (related to D,  D =w 2 /8D, for two photon and  D =w 2 /4D for 1-photon excitation), and S is a shape parameter, equivalent to w/z in the previous equations. 3D Gaussian Confocor analysis: Triplet state term:..where T is the triplet state amplitude and  T is the triplet lifetime.

19. Orders of magnitude (for 1 μM solution, small molecule, water) VolumeDevice Size(μm) MoleculesTime millilitercuvette100006x10 14 10 4 microliterplate well 1000 6x 10 11 10 2 nanolitermicrofabrication 100 6x 10 8 1 picolitertypical cell 106x10 5 10 -2 femtoliterconfocal volume 1 6x 10 2 10 -4 attoliternanofabrication 0.1 6x 10 -1 10 -6

20. The Effects of Particle Size on the Autocorrelation Curve 300 um 2 /s 90 um 2 /s 71 um 2 /s Diffusion Constants Fast Diffusion Slow Diffusion Stokes-Einstein Equation: and Monomer --> Dimer Only a change in D by a factor of 2 1/3, or 1.26

21. Autocorrelation Adenylate Kinase -EGFP Chimeric Protein in HeLa Cells Qiao Qiao Ruan, Y. Chen, M. Glaser & W. Mantulin Dept. Biochem & Dept Physics- LFD Univ Il, USA Examples of different Hela cells transfected with AK1-EGFP Examples of different Hela cells transfected with AK1  -EGFP Fluorescence Intensity

22. Time (s) G(  ) EGFP solution EGFP cell EGFP-AK  in the cytosol EGFP-AK in the cytosol Normalized autocorrelation curve of EGFP in solution (), EGFP in the cell ( ), AK1-EGFP in the cell(), AK1  -EGFP in the cytoplasm of the cell(). Autocorrelation of EGFP & Adenylate Kinase -EGFP

23. Autocorrelation of Adenylate Kinase –EGFP on the Membrane A mixture of AK1b-EGFP in the cytoplasm and membrane of the cell. Clearly more than one diffusion time

24. Diffusion constants (um 2 /s) of AK EGFP-AK  in the cytosol -EGFP in the cell (HeLa). At the membrane, a dual diffusion rate is calculated from FCS data. Away from the plasma membrane, single diffusion constants are found. Plasma Membrane Cytosol Autocorrelation Adenylate Kinase  -EGFP D D

25. Multiple Species Case 1: Species vary by a difference in diffusion constant, D. Autocorrelation function can be used: (2D-Gaussian Shape) G(0) sample is no longer  /N ! !

26. Antibody - Hapten Interactions Mouse IgG: The two heavy chains are shown in yellow and light blue. The two light chains are shown in green and dark blue..J.Harris, S.B.Larson, K.W.Hasel, A.McPherson, "Refined structure of an intact IgG2a monoclonal antibody", Biochemistry 36: 1581, (1997). Digoxin: a cardiac glycoside used to treat congestive heart failure. Digoxin competes with potassium for a binding site on an enzyme, referred to as potassium-ATPase. Digoxin inhibits the Na-K ATPase pump in the myocardial cell membrane. Binding site carb 2

27. Digoxin-FlIgG (99% bound) Digoxin-Fl Digoxin-FlIgG (50% Bound) Autocorrelation curves: Anti-Digoxin Antibody (IgG) Binding to Digoxin-Fluorescein Binding titration from the autocorrelation analyses: triplet state Kd=12 nM S. Tetin, K. Swift, &, E, Matayoshi, 2003

28. Two Binding Site Model IgG + 2 Ligand-Fl IgGLigand-Fl + Ligand-Fl IgG2Ligand-Fl [Ligand]=1, G(0)=1/N, K d =1.0 IgG2Ligand IgGLigand No quenching 50% quenching KdKd

29. Digoxin-FL Binding to IgG: G(0) Profile Y. Chen, Ph.D. Dissertation; Chen et. al., Biophys. J (2000) 79: 1074

30. Case 2: Species vary by a difference in brightness The autocorrelation function is not suitable for analysis of this kind of data without additional information. We need a different type of analysis assuming that The quantity Go becomes the only parameter to distinguish species, but we know that:

31. Photon Counting Histogram (PCH) Aim: To resolve species from differences in their molecular brightness Single Species: Sources of Non-Poissonian Noise Detector Noise Diffusing Particles in an Inhomogeneous Excitation Beam* Particle Number Fluctuations* Multiple Species* Poisson Distribution: Where p(k) is the probability of observing k photon counts

32. Photon Counts frequency PCH Example: Differences in Brightness  n =1.0)  n =2.2)  n =3.7) Increasing Brightness

33. Single Species PCH: Concentration 5.5 nM Fluorescein Fit:  = 16,000 cpsm N = 0.3 550 nM Fluorescein Fit:  = 16,000 cpsm N = 33 As particle concentration increases the PCH approaches a Poisson distribution

34. Photon Counting Histogram: Multispecies Snapshots of the excitation volume Time Intensity Binary Mixture: Molecular Brightness Concentration

35. Photon Counting Histogram: Multispecies Sample 2: many but dim (23 nM fluorescein at pH 6.3) Sample 1: fewer but brighter fluors (10 nM Rhodamine ) Sample 3: The mixture The occupancy fluctuations for each specie in the mixture becomes a convolution of the individual specie histograms. The resulting histogram is then broader than expected for a single species.

36. Sanchez, S. A., Y. Chen, J. D. Mueller, E. Gratton, T. L. Hazlett. (2001) Biochemistry, 40, 6903-6911. Examination of a Protein Dimer with FCS: Secreted Phospholipase A 2

37. sPLA 2 Membrane Binding sPLA 2 Self-Association Interfacial sPLA 2 Self-Association membrane sPLA 2 Interfacial Binding

38. Dodecylphosphocholine (DPC) Micellar Lipid Analog ( CMC = 1.1 mM ) Choline Group 12 Carbon Tail Lipid Interfaces Multibilayers (MLVs) Vesicles (SUVs, LUVs & GUVs) Micelles

39. In Solution: a Tight Dimer Fluorescein-sPLA 2 [Fl-sPLA 2 ] Steady-State Anisotropy Fluorescence Correlation Spectroscopy Time-Resolved Anisotropy : Rotational correlation time 1 = 12.8 ns (0.43) Rotational correlation time 2 = 0.50 ns (0.57) measured predicted (by sedimentation) Why this large discrepancy?

40. sPLA 2 G(0)=0.021 D = 72 um 2 /s sPLA 2 + 3M Urea G(0)=0.009 D = 95 um 2 /s In Solution: Fluorescein-sPLA 2 +/- Urea sPLA 2  = 0.6 N = 3.29 sPLA 2 + 3M Urea  = 0.6 N = 8.48 Change in number of particles, little change in brightness! 1. Autocorrelation 2. PCH analysis Adjusted for viscosity differences Increasing Particles

41. The Critical Question: Is sPLA 2 a Dimer in the Presence of Interfacial Lipid? Monomer LipidMicellar Lipid C.atrox sPLA 2 (Poor Substrate) (Preferred Substrate) Observing Fluorescein-labeled sPLA 2 D dimer N particles What Could We Expect to Find in the FCS Data? Upon dissociation, the mass could increase due to lipid binding. Better count the number of particles!

42. sPLA 2 G 0 = 0.0137 D = 75 um 2 /s sPLA 2 + 20 mM DPC G 0 = 0.0069 D = 55 um 2 /s FCS on Fluorescein - sPLA 2 in Buffer (RED) and with DPC Micelles ( BLUE ) 1. Autocorrelation Analysis sPLA 2  = 0.41 N = 6.5 sPLA 2 + 20 mM DPC  = 0.45 N = 12.2 2. PCH Analysis +DPC = increase in particles

43. The PLA 2 dimer dissociates in the presence of micelles. Active enzyme form in a micellar system is monomeric. Fluorescein-sPLA 2 Interaction with DPC 0.01 0.1 1 10 [DPC] (mM) EDTA Ca 2+ 6 8 10 12 D = 73 um 2 /s D = 55-60 um 2 /s (D micelle =57 um 2 /s) (D dimer = 75 um 2 /s) N N

44. + + + + + + + + + + + + + Schematic of sPLA 2 - Dodecylphosphocholine Interactions + +++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Co-Micelle sPLA 2 -Micelle Monomer-Lipid Association sPLA 2 + + + + + + + + + + + + +

45. Two Channel Detection: Cross-correlation Each detector observes the same particles Sample Excitation Volume Detector 1 Detector 2 Beam Splitter 1.Increases signal to noise by isolating correlated signals. 2.Corrects for PMT noise

46. Removal of Detector Noise by Cross-correlation 11.5 nM Fluorescein Detector 1 Detector 2 Cross-correlation Detector after-pulsing

47. Detector 1: F i Detector 2: F j t  Calculating the Cross-correlation Function t +  time

48. Thus, for a 3-dimensional Gaussian excitation volume one uses: Cross-correlation Calculations One uses the same fitting functions you would use for the standard autocorrelation curves. G 12 is commonly used to denote the cross-correlation and G 1 and G 2 for the autocorrelation of the individual detectors. Sometimes you will see G x (0) or C(0) used for the cross-correlation.

49. Two-Color Cross-correlation Each detector observes particles with a particular color The cross-correlation ONLY if particles are observed in both channels The cross-correlation signal: Sample Red filter Green filter Only the green-red molecules are observed!!

50. Two-color Cross-correlation Equations are similar to those for the cross correlation using a simple beam splitter: Information Content Signal Correlated signal from particles having both colors. Autocorrelation from channel 1 on the green particles. Autocorrelation from channel 2 on the red particles.

51. Experimental Concerns: Excitation Focusing & Emission Collection Excitation side: (1) Laser alignment (2) Chromatic aberration (3) Spherical aberration Emission side: (1) Chromatic aberrations (2) Spherical aberrations (3) Improper alignment of detectors or pinhole (cropping of the beam and focal point position) We assume exact match of the observation volumes in our calculations which is difficult to obtain experimentally.

52. Uncorrelated Correlated Two-Color Fluctuation Correlation Spectroscopy Interconverting Ch.2Ch.1 For two uncorrelated species, the amplitude of the cross-correlation is proportional to:

53. Does SSTR1 exist as a monomer after ligand binding while SSTR5 exists as a dimer/oligomer? Somatostatin Fluorescein Isothiocyanate (FITC) Somatostatin Texas Red (TR) Cell Membrane R1 R5 R1 Three Different CHO-K1 cell lines: wt R1, HA-R5, and wt R1/HA-R5 Hypothesis: R1- monomer ; R5 - dimer/oligomer; R1R5 dimer/oligomer Collaboration with Ramesh Patel* † and Ujendra Kumar* *Fraser Laboratories, Departments of Medicine, Pharmacology, and Therapeutics and Neurology and Neurosurgery, McGill University, and Royal Victoria Hospital, Montreal, QC, Canada H3A 1A1; †Department of Chemistry and Physics, Clarkson University, Potsdam, NY 13699

54. Green Ch.Red Ch. SSTR1 CHO-K1 cells with SST-fitc + SST-tr Very little labeled SST inside cell nucleus Non-homogeneous distribution of SST Impossible to distinguish co-localization from molecular interaction

55. Minimum Monomer A Maximum Dimer B = 0.22 G 12 (0) G 1 (0) = 0.71 G 12 (0) G 1 (0)

56. Experimentally derived auto- and cross-correlation curves from live R1 and R5/R1 expressing CHO-K1 cells using dual-color two-photon FCS. The R5/R1 expressing cells have a greater cross-correlation relative to the simulated boundaries than the R1 expressing cells, indicating a higher level of dimer/oligomer formation. R1R1/R5 Patel, R.C., et al., Ligand binding to somatostatin receptors induces receptor- specific oligomer formation in live cells. PNAS, 2002. 99(5): p. 3294-3299

57. Molecular Dynamics What if the distance/orientation is not constant? Fluorescence fluctuation can result from FRET or Quenching FCS can determine the rate at which this occurs This will yield hard to get information (in the  s to ms range) on the internal motion of biomolecules

59. A) 10 -3 10 -2 10 10 0 1 0 40 80 120 160 200  (s) G(  ) B). A) Cameleon fusion protein consisting of ECFP, calmodulin, and EYFP. [Truong, 2001 #1293] Calmodulin undergoes a conformational change that allows the ECFP/EYFP FRET pair to get close enough for efficient energy transfer. Fluctuations between the folded and unfolded states will yield a measurable kinetic component for the cross-correlation. B) Simulation of how such a fluctuation would show up in the autocorrelation and cross-correlation. Red dashed line indicates pure diffusion.

60. Crystallization And Preliminary X-Ray Analysis Of Two New Crystal Forms Of Calmodulin, B.Rupp, D.Marshak and S.Parkin, Acta Crystallogr. D 52, 411 (1996) Ca 2+ Saturated Are the fast kinetics (~20  s) due to conformational changes or to fluorophore blinking? In vitro Cameleon Data

61. Diffusion constants (um 2 /s) of AK EGFP-AK  in the cytosol -EGFP in the cell (HeLa). At the membrane, a dual diffusion rate is calculated from FCS data. Away from the plasma membrane, single diffusion costants are found. Plasma Membrane Cytosol Autocorrelation Adenylate Kinase  -EGFP D D

62. FRET Efficiency FRET Efficiency Distribution in Low Mg ++ Low-FRET Conformation High-FRET Conformation

63. What is scanning FCS? How is it implemented? What kind of information scanning FCS provides that cannot be obtained with single-point FCS? Definition: “Simultaneous” FCS measurements at multiple sample positions “Simultaneous” = multiplexing Principle: Return to the same location before the particle leaves the volume of observation

64. Explore spatial-temporal correlation. Detection and characterization of membrane rafts. GUV made from integral membrane fragment Visible raft-like domains 300nm “Invisible” raft Scenarios for Scanning FCS application Macro scale Nano scale How to see the invisible rafts? Probe must be selective for rafts Probe concentration must be large to properly paint the rafts If the rafts are stationary, measurement at only one position will not provide the number of rafts in a pixel If we know the number, we can determine the average size

65. Method developed by Angelova et al Chamber Design

66. BBM LIPID EXTRACT GUVs BLM LIPID EXTRACT GUVs minmax INTENSITY 20  m BBM and BLM Lipid Extract GUVs exhibit formation of lipid domains. GUVs composed of BBM and BLM natural lipid extracts. Micron-sized non- fluorescent circular domains appear on the surface of the GUVs. Domain formation occurs at 43 °C for the BBM and at 38°C for the BLM. Lipid Extract GUV Morphology

67. Integral BBM and BLM GUVs exhibit domain formation. GUVs composed of integral membrane fragments. On the surface of the GUVs appear micron-sized non-fluorescent domains which are irregularly shaped. Domain formation occurs at 43 °C for the BBM and at 41.5°C for the BLM. minmax INTENSITY 20  m Integral BBM GUV Integral Membrane GUV Morphology Integral BLM GUV

68. Measure the molecular weight of DNA (Weissman, Proc. Natl. Acad, Sci, USA 73: 2776 (1976)) Measure the Diffusion of Fluorescent Beads and DNA (Koppel and others. Biophysical J. Vol 66: 502, 1994) Advantages: Improved signal to noise ratio

69. Data analysis Time Measure association/dissociation equilibrium in protein systems (Berland et al, Biophys. J. 1996)

70. Fitting Model for Scanning FCS Calculation of the Autocorrelation Function: Fitting Model: D=5  m 2 /s

71. Conventional FCS (vs) Scanning FCS in solution Autocorrelation curve of fluorescein labeled beads in suspension.

72. FCS of fluorescent antibody (labeled with Alexa 488) in solution 1E-51E-41E-30.01 0.1 0.00 0.01 0.02 0.03 0.04 G(  ) D=21.4  1.3  m 2 /sec Free fluorophore D=20.6  1.1  m 2 /sec Point FCS Scanning FCS

73. Scanning FCS on GUV Laurdan labeled GUV, surface POPC Scanning frequency is 1 ms per orbit We have a bandwidth sufficient to observe diffusion of a small molecule such as Laurdan or prodan in a fluid membrane (POPOC) FCS at one point Scanning FCS

74. Advantage of scanning FCS for membrane and cellular studies Less photo damage Easy to locate membrane border Multiple points simultaneously Distinguish moving from immobile fraction Spatial cross correlation… Velocity direction and gradients

75. Protein interactions on GUVs can not be detected by imaging background Addition of fluorescent antibody to GUV The GUVs were made from rat kidney brush-border membrane extract containing all the integral membrane proteins. The antibody against one specific membrane protein (NaPi II) was labeled with Alexa 488, no enhanced fluorescence was observed on the GUV membrane bilayers. Performing FCS measurements on the bilayers was difficult due to the lack of contrast.

76. Protein interactions on GUVs can be detected by Scanning FCS Hyperspace: Vertical axis is time, horizontal axis is location along the orbit Autocorrelation at different positions Time One line is 1 ms Autocorrelation time (log axis)

77. D=20  m 2 /sec D1=24  m 2 /sec D2=0.11  m 2 /sec Diffusion coefficient of the antibody obtained from scanning FCS In solution On GUVs Inside GUVs

78. Mid section of GUV FCS-hyperspace Autocorrelation curve Time Membrane Undulation Detected by Scanning FCS: Example of spatial correlation Membrane labeled with Laurdan

79. ac time b G(  ) time IntensityAutocorrelation Protein Interactions on GUVs Detected by Scanning FCS The GUV is made out of whole membrane extract from the basolateral membrane (BLM) of OKP cells. The antibody labeled with Alexa488 was against NaPi II cotransporter. This protein was suppose to be present in the BLM. This experiment proved that our GUV generation method also incorporated the membrane proteins. It is relatively close to the natural composition of the plasma membrane.

80. Conclusions Scanning FCS is feasible both in solution, in model membranes and in cells When the characteristic times for diffusion (or reactions) are about 1 ms or longer, it could be convenient to perform scanning FCS Scanning FCS provides autocorrelation functions at many positions in the sample in a multiplexing way Scanning FCS offers the possibility to distinguish processes such as true diffusion and flow from local movements Scanning FCS allows to clearly distinguish the location (and movements) of membranes proteins and membrane domain while performing FCS measurements Scanning FCS can be used to determine with nanometer precision the positions of particles (molecules) and membranes