Fluorescence Spectroscopy

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1 Fluorescence Spectroscopy Thomas Schmidt Department of Biophysics Leiden University, The Netherlands Biophysical Structural Biology Course (November 2002)

2 references P. Atkins Physical Chemistry Addison Wesley J.R. Lakowicz Principles of Fluorescence Spectroscopy Kluwer Academic W. Demtröder Laser Spectroscopy Springer Series in Chemical Physics 5 2

3 typical fluorophores O O N O N N tryptophane λ = 280 nm egfp λ = 488 nm O N O HN N O N + TDI λ = 630 nm N H 2 C N - O 3 S SO 3 - DAPI NH C NH 2 O O N N λ = 355 nm S HN TMR λ = 514 nm O NH 2 Cy5 λ = 630 nm 3

4 green-fluorescent protein (GFP) K. Brejc et.al., PNAS 94 (1997) nm 4

structure and photophysics of eyfp N-terminal C-terminal 238 amino acid residues Ala 72 Leu 68 Tyr 203 Fluorophore Gly65,Tyr66, Gly67 λ abs,max = 514

5 structure and photophysics of eyfp N-terminal C-terminal 238 amino acid residues Ala 72 Leu 68 Tyr 203 Fluorophore Gly65,Tyr66, Gly67 λ abs,max = 514 nm λ em,max = 527 nm ε = 84,000 M -1 cm -1 Φ F = 0.63 τ F = 3.7 ns τ T = 1 µs k ISC = s strand β sheet in β-barrel; central α-helix 4 nm 5

6 spectra of autofluorescent proteins extinction (cm -1 M -1 ) egfp 8 ecfp egfp eyfp 6 DsRed flavin x fluorescence x QE ecfp egfp eyfp DsRed flavin wavelength (nm) wavelength (nm) 6

7 absorption spectra extinction (cm -1 M -1 ) 8 ecfp egfp eyfp 6 DsRed flavin x Clontech GFP FAD wavelength (nm) 7

8 emission spectra fluorescence x QE ecfp egfp eyfp DsRed flavin wavelength (nm) 8

9 fluorescence microscopy 9

10 absorption & emission of Cy3 140 x O 3 S SO 3 - molar extinction (1/cm M) O N NH 2 N fluorescence wavelength (nm) 10

11 energy scales engery E [E] = J frequency E = hν [ν] = Hz wavelength E = hc/λ wavenumber E = hc ν ~ ν ~ [λ] = nm [ ] = 1/cm 11

12 absorption & emission of Cy3 molar extinction (1/cm M) 140 x O 3 S O wavenumber (cm -1 ) N N NH 2 SO wavelength (nm) fluorescence 12

13 Jablonski-scheme electronic transitions ν ~ ~ 10 4 cm -1 τ s ~ 10 ns τ T ~ 1 µs 1 ms vibrational transitions ~ ν ~ cm -1 τ ~ 1 ps rotational transitions ~ ν ~ 1-10 cm -1 τ ~ 100 ps 13

14 Kasha s rule fluorescence signal S 2 n 2 n S 1 1 k ic k fl k fl F i ~n i k fl occupation n n 2 α 0 ( ic fl ) 1 = = N = k n ic 0 I n n 2 + n k 1 + n mainly fluorescence fl k n k n 2 from S 1 S 0 F k k ~ F fl fl 2 << ~ k fl + kic k fl 1 14

15 absorption & emission of Cy3 molar extinction (1/cm M) 140 x S 2 S 0 wavenumber (cm -1 ) S 1 S 0 S 1 S 0 vibronic vibronic wavelength (nm) fluorescence 15

16 Einstein coefficients 2> n 2 ρ(ν) B 12 A 21 ρ(ν) B 21 rate equations n 1 n 2 = B = + B ρ( ν ) n 1 ρ( ν ) n 1 + ( A21 + B21ρ( ν )) n2 ( A 21 + B 21 ρ( ν )) n 2 1> n 1 A 21 spontaneous emission B 12, B 21 stimulated absorption cq emission detailled balance n n hν = exp kbt steady-state ρ( ν ) = 2 1 B 12 B 21 A21 B21 hν exp kbt 1 16

17 Einstein coefficients & Planck Einstein coefficients radiation ρ( ν ) = B 12 B 21 A21 B21 hν exp kbt Planck radiation 8π hν ρ( ν ) dν = 3 c 3 exp 1 1 ( hν k T ) B 1 dν comparison yields B A = = B 21 8π hν c 3 3 B 21 17

18 Einstein coefficients & Planck Einstein coefficients radiation ρ( ν ) = B 12 B 21 A21 B21 hν exp kbt Planck radiation 8π hν ρ( ν ) dν = 3 c 3 exp 1 1 ( hν k T ) B 1 dν comparison yields B A = = B 21 8π hν c 3 3 B 21 17

19 absorption & emission of Cy x 10 3 extinction (1/cm M) fluorescence wavenumber (cm -1 ) 18

20 binding potentials Lennard-Jones potential V(R) ~ (b/r) 12 (b/r) 6 energy Morse potential V(R) ~ [1 exp (-ß(R-R 0 ))] 2 configuration coordinate for small R-R 0 : harmonic potential V ~ (R-R 0 ) 2 19

21 Born-Oppenheimer approximation adiabatic approximation the state of a molecule is characterized by its electronic state, S, its vibrational state, n, and its rotational state, L: S,n,L > cq Ψ (r,r) because of the large mass difference between electrons and nuclei (m p /m e = 1860) the electrons will immediately follow any rearrangement of the nuclei. The total state can be written as S,n,L > = S nl > n,l > cq Ψ (r,r) = ψ R (r) Φ (R) 20

22 harmonic oscillator Solve Schrödinger equation for H = 1 2m P 2 m 2 + ω Q

23 anharmonic oscillator energy configuration coordinate 22

24 configurationcoordinate diagram each electronic state is split into its vibrational levels the (vibrational) wavefunctions are described by the harmonic oscillator 23

25 absorption & emission of Cy x 10 3 (0 n) (n 0) 120 extinction (1/cm M) (0 n+1) (n+1 0) fluorescence wavenumber (cm -1 ) 24

26 Fermi s golden rule probabilitity for a transition from an initial state i > to a final state f > π 2 ( ( )) E E E p = f V i δ + if 2 f i 2 V specifically interaction of a dipole with an electromagnetic field π 2 2 p = µ E with µ = if 2 if 0 if 2 f er transition dipole-moment i 25

27 Franck-Condon factors transition from 0,n,L> to 1,n,L > transition dipolemoment µ if = <1,n,L er 0,n,L> adiabatic approximation µ if = <1 er 0> <n,l n,l> Franck-Condon factors S n,n = <n,l n,l> calculate the overlap integral between the two vibronic wavefunctions for harmonic oszillator S p n p = e n! mω = ( R 2 2 0, n p 0 R ' 0 ) 2 Stokes losses 26

28 Franck-Condon factors adiabatic approximation the electrons are instantaneously in the final state transitions vertical the highest intensity is where the vertical line crosses the potential of the final state R 0 R 0 27

29 Franck-Condon factor Franck-Condon factor S 2 0, n n p = n! e p Stokes losses m p = ω ( R 2 ' 2 0 R0 ) 28

30 absorption & emission of Cy x extinction (1/cm M) Stokes shift 410 cm -1 fluorescence wavenumber (cm -1 ) 29

31 mirror-image 30

32 absorption & emission of Cy3 molar extinction (1/cm M) 140 x S 2 S 0 wavenumber (cm -1 ) S 1 S 0 S 1 S 0 vibronic vibronic wavelength (nm) fluorescence 31

33 epi-fluorescence microscopy 32

34 multicolor 2P-microscopy 33

35 specific labeling with various colors 34

36 the fluorescence signal 1> 0> σi n 1 n 0 k fl rate equations for 1 molecule n n 1 0 = σi + n 1 n 0 = 1 k fl n 1 steady state & fluorescence F = n 1 k fl k fl F = ; I S = I 1+ S I σ typical numbers (incl triplett F = 1000 photons/s I S = 10 kw/cm 2 k fl 35

37 fluorescence microscopy is extremely sensitive: single molecule imaging 36

38 5 µm 37

39 4-Level System S 1 T 1 S 0 I s photoproduct N hc 1/ τ + k = ln( 10) λε 1+ k τ A S ISC ISC T I S = 11 kw/cm 2 τ S = 2.1 ns; τ T = 2 µs; k ISC = 10-3 s -1 38

40 300 tetramethylrhodamine (a) t ill = 5 ms saturation TS, G.J.Schütz, W.Baumgartner H.J.Gruber & H.Schindler J.Phys.Chem. 99 (1995) F sm (cnts) I s = 7.6 kw/cm I L (kw/cm 2 ) 39

41 fluorescence loss at high concentration concentration quenching Förster, Ann Physik 6 (1948) 55 40

42 41 weak dipole-dipole coupling dipole-dipole interaction probability for the transition weak coupling D *,A> = D * > A> D,A * > = D> A * > D onor A cceptor R ( )( ) R r R r r r R R V A D A D D A ˆ ˆ ˆ ˆ 3 ˆ ˆ 4 ) ( 3 = = κ µ µ πε κ 2 * *, ) (, 2 A D R V A D p ET π = 2 * 2 * A A D D R n p A D ET µ µ π κ =

43 Förster energy transfer identification of the matrix-elements p ET R 0 = = <D µ D D * > : donor emission <A * µ A A> : acceptor absorption 1 τ D ln π R 0 R 6 2 κ N c n A 4 ~ ε dν energy transfer efficiency A k fl ( ~ ν ) fˆ ~ ν D 4 D E ( ~ ν ) = 1+ k ET k fl 1 A ( R R )

44 Förster overlap integral Förster, Ann Physik 6 (1948) 55 43

45 molecular ruler Stryer & Haugland, PNAS 58 (1967) 719 FRET efficiency E = 1+ 1 ( R R ) FRET efficiency R 0 donor-acceptor distance 44

46 fluorescence loss at high concentration concentration quenching Förster, Ann Physik 6 (1948) 55 45

47 Colocalization figure from: S Weiss, Science 283 (1999)

48 single-molecule DNA assay W Trabesinger, GJ Schütz, HJ Gruber, H Schindler & TS, Anal.Chem. 71 (1998)

49 single-oligonucleotide pairing W Trabesinger, GJ Schütz, HJ Gruber, H Schindler & TS, Anal.Chem. 71 (1998)

50 FRET for dynamical studies figure from: S Weiss, Science 283 (1999)

51 S4-movement of the K + -channel (1) Cha A, et al. Nature 402 (1999)

52 S4-movement of the K + -channel (2) Cha A, et al. Nature 402 (1999)

53 single-molecule microscopy to study protein dynamics [ figure from: S. Weiss, Science 283 (1999) 1676] 52

single-molecule fluorescence resonance energy transfer

single-molecule fluorescence resonance energy transfer (2) determing the Förster radius: quantum yield, donor lifetime, spectral overlap, anisotropy michael börsch 26/05/2004 1 fluorescence (1) absorbance