Single Molecule Optics

Report
Single Molecule Optics
Michel Orrit
Molecular Nano-Optics and Spins
Leiden University
Winterschool:
Spectroscopy and Theory
15-18 December 2008, Han-sur-Lesse, Belgium
1. Introduction
• Optical detection of single molecules by
fluorescence
• High signal/background ratio thanks to
resonance
• Made possible by advances in sources,
detectors, optics
Molecular Photophysics
• Electronic levels are
split in a series of
harmonic oscillator
levels
• Transitions between
levels are related to
overlaps between
oscillator wavefunctions
Mirror Image
Absorption and
fluorescence
spectra are related
by a mirror
symmetry around
the 0-0 transition
Absorption & Emission of Cy3
wavenumber (cm-1)
30000
25000
x 10
S1S0
3
S1S0
120
-O S
3
SO3-
100
N
80
N
vibronic
O
vibronic
NH2
60
40
20
S2S0
0
300
400
500
600
wavelength (nm)
700
fluorescence
molar extinction (1/cm M)
140
15000
20000
Transition dipole moment


12  1  er 2
12
1

12
2
2
characterizes the strength of the optical transition
Kasha’s Rule
• Radiative and non-radiative relaxation between
electronic levels
• Fluorescence can only arise from the lowest
excited singlet state S1;
• higher excited states relax to S1 faster than they
can emit;
• triplet states emit weak phosphorescence.
Fluorescence quantum yield
1
 fluo
kr knr
S1
kr
S0
knr
kr
 fluo
1
kr knr
Jablonski diagram: relaxation between
electronic states
Typical fluorophores
O
O
N
O
O
N
O
N
N
tryptophane
l = 280 nm
eGFP
l = 490 nm
TDI
+
HN
N
H2N C
-O
N
NH
DAPI
l = 355 nm
l = 630 nm
N
O
3S
SO3-
N
O
C NH2
N
+
O
HN
S
TMR
l = 514 nm
O
NH2
Cy5
l = 630 nm
green-fluorescent protein (GFP)
K. Brejc et.al., PNAS 94 (1997) 2306
1 nm
2. Optical Microscopy
object
intermediate
image
R
R
objective
lens
eye-piece
Working principle of an optical microscope
d min  1.22 
l
2 NA
NA  n  sin 
Diffraction-limited resolution
Both Collection Efficiency and Point Spread
Function depend on the Numerical Aperture
NA
Immersion favors collection efficiency
Aberrations must be corrected
Spherical aberration, coma, pincushion/barrel deformation
Polarization structure in focal plane
Confocal Scanning Microscope
sample scanning
beam scanning
Total Internal Reflection
Other focusing and collecting elements used
in single-molecule experiments
Near-Field Optics
3. Excitation and Detection of
Fluorescence
• Sources: Lasers cw (ion), pulsed (Nd-YAG,
Ti-sapphire, diodes)
• Photon Detectors: PhotoMultiplier Tube,
Avalanche PhotoDiode, Charge Coupling
Device
• Spectral Filters: colored glass, notch
holographic, multidielectric
Photon Counting Analyses
• Field and Intensity Correlation Functions
Field
g (1) ( ) 
E (t   ) E* (t )
2
E (t )
Intensity
g
( 2)
( ) 
I (t   ) I (t )
I (t )
2
Thermal or Chaotic Light (Lamp)
Coherent Light (cw Laser)
m
n
n
p(m) 
e
m!
Poisson statistics:
- independent photons,
- correspondence with
classical light wave
for large numbers
n2  n2  n
2
 n
Correlation function versus Start-Stop
The two functions are
identical for short times,
but differ for long times
Time-Correlated Single Photon Counting
• Histogram of delays between fluorescence
photon and laser pulse
• Full time information: macroscopic arrival
time of photon, and delay with respect to
laser pulse
4. Single Molecules in Fluid
Solutions
Molecules diffuse, bursts of fluorescence,
photon-by-photon studies
.
• Burst analysis (intensity)
• Multiparameter analysis, statistical
correlations
• Fluorescence Correlation Spectroscopy
Translational Diffusion
1  4D 
(2)
g ( )  1 
1 2
N  t 
1
 4D 
1 

  2
a 

1/ 2
D diffusion coefficient, t and a transverse and axial beam waists
N average number of molecules in the excitation volume.
Rotational Diffusion
For isotropic diffusion on a sphere, the correlation function
decays exponentially, on some nanoseconds for small
fluorophores in water, more slowly for bigger molecules
or more viscous fluids.
Blinking due to a Dark State
(Triplet)
g
( 2)
k2 k1  k2 
( )  1  e
k1
Single-exponential decay of the correlation function with the sum
of the two rates.
5. Immobilized Molecules
Signal/Background ratio must be large enough
S  3 B/t
or
2
t  10 B / S
Sample preparation
Spin-coating
Langmuir-Blodgett films
Microscopy images
• Counting, stoichiometry, colocalization
• Orientation
Comparison of polarization modulation for epi-illumination
and total internal reflection.
Photophysics, Blinking
I
I
flickering
t
Triplet state
 Electron transfer
 Other photochemical reactions
 Bleaching

blinking
t
6. Fluorescence Resonance
Energy Transfer (FRET)
Dipole-dipole interaction
(near-field)




ˆ
ˆ
VAD 
 1  3RR D
3 A
40 R
1
Donor
Acceptor
Förster transfer rate
k DA 
2
2
WDA  FD ( E ) AA ( E ) dE

-6
• Decreases as (distance)
• Spectral Overlap between Donor Fluorescence and
Acceptor Absorption
• Angular dependence 2
  2 cos D cos A  sin D sin A cos
isotropic:
<2> = 2/3
Transfer Efficiency
• Fraction of excitations transferred to
acceptor
E
k DA

k DA  k fD
1
 R 
1   
 R0 
6
• R0 Förster radius, maximum 10 nm for large
overlap
FRET Histograms and Dynamics

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