Energy Transfer at the Single Molecule Level

1
Energy Transfer at the Single Molecule Level

• Kate Wooley
• 8/1/2007
• PI Jennifer Ogilvie

Topograph of LH2. Ring Diameter 65 Å
Bacteriochlorophylls DB800 - aqua AB850 -
yellow
2
Technique Single Molecule (two color)
Pump-Probe (SMPP)

• Objectives
• Background
• My Work
• Future Work
• Conclusions

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Objectives

• To use SMPP to make the first ultra-fast
  single-molecule measurements of energy transfer
• To probe the role of disorder in energy transfer
  in simple donor-acceptor pairs and in natural
  light-harvesting complexes
• To examine the relationship between
• intramolecular energy redistribution and
  energy transfer within the different regimes of
  weak (Förster) to strong (exciton) donor-acceptor
  coupling

4
Fluorescence

• Fluorescence is a radiative transition between an
  excited and ground state of the same spin
  multiplicity (i.e. singlet)
• During Internal Conversion, energy is dissipated
  through vibrational motion.
• Multiple decay channels in molecules

Jablonski Diagram Absorption Transitions -
t10-15s Internal Conversion - t10-12s Fluorescen
ce - t10-8s
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Pump-Probe Experiment

• Processes occur faster than any detector can
  time- resolve
• Problem You have a Pinhole camera with a slow
  shutter (assume you dont need long exposure
  time). You want time-resolved images of a horse
  galloping
• Solution Pump-Probe Strobe Photography

• Upon the first flash of light, the horse bolts
  into a gallop
• After a known delay a flash in front of the
  camera briefly illuminates the galloping horse,
  exposing the film.
• Repeat with a longer time delay to get a flip
  book movie.

Eadweard J. Muybridge  1879
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Resonance Energy Transfer (RET)
Radiationless transfer of energy from an
absorbing donor to an acceptor molecule

• Förster (weak coupling) energy transfer
  mechanism describes RET via Coulomb dipole-dipole
  interactions.
• Rate of energy transfer is
• where is the decay time of the donor in
  absence of an acceptor, r is the donor acceptor
  distance, and is the distance at which RET
  is 50 efficient.
• depends on spectral overlap between donor
  emission and the acceptor absorption, quantum
  yield of the donor, and the relative orientation
  of donor and acceptor transition dipoles.

7
Simulation

• Given a saturating pump or probe pulse,
  stimulated absorption and emission of the D00-D11
  or A00-A11 transitions balance, so there is a 50
  chance of excitation.
• At t 0, if the probe did not excite A00-A11
  and the pump excites D00-D11, then energy
  transfer (ET) excites A00-A11. So, Fluorescence
  Probability FP 50 5050 75.

• For tDerstate and ET is unlikely. Stimulated emission
  from D10,further reduces ET, and the FP decreases
  towards the 50 probe contribution.
• For tETdonor is excited, 50. If not, the probe can
  excite the acceptor, thus FP 50 5050 75

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Experimental Setup

• The SMPP experiment
• PCF photonic crystal fiber for broadening the
  bandwidth
• Pulse picker reduces pulse repetition rate to
  1MHz
• F1, F2 filter to select appropriate pump and
  probe bandwidth, respectively
• DC dispersion compensation
• DBS dichroic beamsplitter to separate
  fluorescence from pump and probe
• APD avalanche photodiode.

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My Work
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Group Velocity Dispersion (GVD) Compensation
with a Prism Compressor

• GVD (or 2nd-order dispersion) is defined as
• The effect of GVD is to create a chirped pulse
  in which larger (smaller) frequencies lead
  smaller (larger), called positive (negative)
  chirp. If a pulse is chirped, its pulse duration
  is lengthened.
• The dispersion of our oil immersion objective is
  equivalent to 250m of air.

Rich Trebino, GIT Hecht, Optics, 2001
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2nd Order Interferometric Autocorrelation

• For delay times t of more than the total pulse
  length the two pulses are no longer overlapping
  and G2(t) gives a constant background signal. The
  wings are due to higher order dispersion terms.
• Need pulse length 100fs.

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LabView Timing Issues!

• Trigger Data Acquisition and the Piezo Stage
  positioning and feedback voltage
• Match the position of the stage to the PMT
  fluorescence data
• Determine accuracy and repeatability of
  positioning

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Next Steps

• Supercontinuum generation with photonic crystal
  fiber larger bandwidth for biological systems
  that absorb white light.
• Single Photon Counter to detect WEAK! signals
  from single molecules
• Use fluorescent tagged DNA with known lengths
  between base pair donor-acceptor pairs to test
  setup.
• Examine systems of interest such as LH2

http//www.lumerical.com/mode_solver_applications
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Conclusions
SMPP

• We have demonstrated a method for measuring
  single molecule energy transfer
• We were able to compensate 2nd order dispersion
  of the oil immersion objective
• We have the resolution and accuracy to repeatedly
  find a single molecule

15
Questions?
Thanks! Brandon Bachler, Liz Auto,
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Answers to Potential Questions

• Laser TiSaphire mode-locked 16nW, sub 20fs
  pulses
• We only get 1nW, dispersion broadens to 70fs,
  800nm50nm

    Mode-locking How short pulses are achieved.
The Fourier transform (spectrum) of a plane
wave is a delta function at the single frequency
at the wave. A Gaussian pulse is the opposite
extreme from a plane wave, and thus its Fourier
transform is made of many different frequencies.
Fig 1 Synthesis of a periodic pulse train by
superposition of sinusoidal oscillations,
corresponding to different axial resonator modes
in a mode-locked laser. There is a fixed phase
relationship between these modes.
                                         
            Fig2 Temporal evolution of the
intracavity field in a laser, once with a fixed
phase relationship between the modes
(mode-locked state), once with random phases.
http//www.rp-photonics.com/encyclopedia.html
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Group Velocity Dispersion (GVD) Compensation
with a Prism Compressor
       GVD (or 2nd-order dispersion) is defined
as         
The Group Delay Dispersion (GDD) is defined as
GVDLength of material.
R.L. Folk, O.E. Martinez, J.P. Gorden, Optics
Letters, Vol 9, No. 5 (1984)
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Dispersion Compensation

• The zero-order term describes a common phase
  shift.
• The first-order term contains the inverse group
  velocity and
• describes an overall time delay without an effect
  on the pulse shape.
•       
• The second-order term contains the second-order
  dispersion
• (or group delay dispersion per unit length)
           

• The Taylor coefficients, specifically the
  second-order dispersion is calculated using the
  Sellmeier Equation n2(?) where the Bi and Ci
  coefficients are experimentally known material
  constants.

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Interferometric Autocorrelation
A Michelson Interferometer splits the beam and
it travels a path length differing by d in the
two arms. Thus it outputs two beams separated by
t d/c. A two-photon dye is used such that the
dye fluoresces at the second harmonic
frequency??, and it will only fluoresce when two
photons are incident at the same time, i.e. about
t 0. A slow detector then records G2(t)
the second order interferometric correlation.
For delay times t of more than the total pulse
length the two pulses are no longer overlapping
and the SOIC shows a constant background signal.
The wings are due to higher order dispersion
terms.
For a delay increment of one-half light period,
the two light fields add with opposite phase
resulting in a near-zero signal, giving the
fringes which contain pulse shape and phase info.
http//nanooptics.uni-graz.at/ol/work/fs_measure/f
s-measure.html
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One Color SMPP

• Van Dijk, et. al. P.R.L. 94, (2005) measured
  ultrafast energy redistribution
• Rabi oscillations (stimulated emission by the
  pump pulse) in a realistic molecule with in
  homogeneously broadened line widths are
  super-damped due to dephasing between the
  molecule and a strong exciting field of duration
  longer than the dephasing time(20fs)
• Thus our pulses leave the molecule with an equal
  probability of being in the ground or excited
  state

• At t 0, the S0-S11 is saturated by the pulse,
  thus the probe has no effect.
• FP Pump Probe 50 0
• As t increases, the molecule relaxes (via IC) to
  the S10 state and reducing stimulated emission.
  If the molecule is not excited by the pump, 50,
  then there is a 50 chance the probe will excite
  it. Thus
• FP Pump Probe 50 5050 75

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Simulation
Traditionally, coupled differential rate
equations are used to describe the energy
transfer in an ensemble. Transition rates,
absorption cross sections, Populations -
deterministic. A Monte Carlo approach was used
to model a single molecule. An large array of
decay times following an exponential distribution
are specified. The experiment is performed
10,000 with randomly chosen decay times.
Stochastic.
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RET- Forster Theory

• Förster theory - weak coupling between donor and
  acceptor results in incoherent energy transfer
• Note Förster theory is for ensembles, other
  theories for strong coupling
• Fluorescent Resonance Energy Transfer (FRET)
• Same ET process.
• Use fluorescence lifetimes to determine if ET has
  occurred.
• Strong D-A distance dependence ruler

http//www.plantmethods.com/content/2/1/12/figure/
F1
http//micro.magnet.fsu.edu/primer/techniques/fluo
rescence/fret/fretintro.html