Lifetime Measurements

1
Lifetime Measurements

• Chapter 4

2
Time Domain and Frequency Domain Measurements

• Sample excited with pulse of light. Width shorter
  than the decay time of the sample
• Measured through a polarizer oriented at 54.7
  degrees (magic angle). Avoids effects of
  rotational diffusion and anisotropy

3
Frequency Domain Measurements

• Sample excited with intensity modulated light
• Intensity of light is varied at high frequency (?
  2p times frequency in hertz)
• Emission delayed relative to the excitation
  measured in phase shift (?)
• Polarizers at magic angle are also used

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Meaning of Lifetime Decay

• dn(t) / dt -(? knr) n(t) , where n(t) is the
  number of excited molecules
• n(t) n0exp(-t/?)
• Experimentally observe intensity, I(t) , which
  is proportional n(t)
• I(t) I0 exp (-t/?)
• Time at which intensity reaches 1/e
• Plot log I(t) versus t
• Average period of time fluorophore in excited
  state complicated with multiexponential decay

5
Phase Modulation Lifetimes

• Modulation of emission is measured relative to
  modulation of the excitation m (B/A)/(b/a)
• Phase angle (?) measured from the zero-crossing
  times of the modulated components
• ?? ?-1tan ? ?m ?-11/m2-11/2

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Frequency Domain
Time Domain
7
Multiexponential Decays
Protein containing to tryptophan probes two
lifetimes equal to 5 ns Addition of a collisional
quencher reduces the lifetime of exposed
tryptophan altering the decay to contain to
components I(t) a1e-t/5 a2e-t/1 Preexponential
factors fractional amount of each flourophore
in each environment
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• Anisotropy decays also use exponential decay laws
  and are on the nanosecond time scale
• Anisotropy decays are subject to more factors -
  rotation of the fluorophore and the protein
  (shape of the protein or protein complex)

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Fitting Time Multiexponential Decays

• Difficult to distinguish between a change in
  amplitude or lifetime
• Because they are correlated parameters

10
Time Correlated Single Photon Counting

• Start signal triggers voltage ramp of the time
  amplitude converter (TAC)
• Voltage ramp stopped when first photon emitted
• Produces an output signal that is proportional to
  the time between start and stop signals
• Multi-channel analyzer (MCA) converts this
  voltage into a time channel using a analog to
  digital converter
• Histogram generated of counts vs. time channels
• No more than one photon per 100 laser pulses

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• Counted Photons are collected in discrete
  channels with known time and width
• Instrument response function (IRF) shortest
  time profile that can be measured by the
  instrument
• The fitted decay curve takes into account the
  IRF

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Removing IRF from the Data
Measured decay is the sum of the exponential
decays due to the IRF and the sample
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Picosecond Dye Lasers
Mode Locking prevents continuous output.
Changes to an 80 MHz pulse train by a
mode-locking crystal within the laser
cavity. Cavity Dumping acousto-optic device. A
burst of radio frequency signal is put on the AO
crystal. Laser beam deflected 1-3 degrees,
deflects the beam out of the laser cavity.
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Wavelength Tunable to be monochromatic
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Femtosecond Dye Lasers
TitaniumSapphire - Capable of pulse widths of
100 fs
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Flashlamps

• Larger pulse width (2 ns)
• Lower intensity
• Gas used determines wavelength
• Time-profile of lamp can change during acquisition

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Assumptions of Non-linear Least Squares Analysis

• All experimental variability is in the dependent
  variable
• Uncertainties in the dep. Variable are
  distributed in a Guassian
• There are no systematic errors in the dep. or
  indep. Value
• The assumed fitting function is the correct
  mathematic description of the system
• The data points are all independent observations
• There is a sufficient number of data points so
  that the parameters are over determined

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Least Squares Analysis

• ?2 ?(1/?2k)N(tk) NC(tk)2
• ?2 ?N(tk) NC(tk)2 / N(tk)
• Standard deviation is known to be the square root
  of the number of photons
• Relative uncertainty decreases as the number of
  photons increases
• ?2 is expected to be equal to the number of data
  points (channels)
• Values of ? and ? are varied until ?2 is
  minimized

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Reduced ?2

• ?2R ?2 / n-p ?2 /?
• ? (degrees of freedom) n-p, number of data
  points number of floating parameters
• Value close to 1 is expected for good fit
• Number of data points is much larger than
  parameters
• Start with least complex model if data does not
  fit significantly better with more complex model
  then do not use

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Goodness of fit

• ?2R can be related to the probability that the
  values obtained are a result of randomness in
  data
• P 0.05 is a good cut-off - Systematic errors
  can contribute up to 10-20 elevation of ?2R
• Small deviations in ?2R may not be significant
  2-fold decrease is significant
• Autocorrelation Function deviations randomly
  distributed about zero. Correlation between the
  deviations in all the channels

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Two Widely Spaced Lifetimes

• Mixture of p-T in Ethanol
• Data does not fit well to single exponential
  decay
• Log plot shows two phases
• Residuals should be randomly distributed about
  zero
• F-statistic ratio of ?2R values, probability of
  random error contributing to differences between
  fits

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Two Closely Spaced Lifetimes

• Mixture of anthranilic acid (AA) and
  2-aminopurine (2-AP)
• Data does not fit well to single exponential
  decay
• Amplitudes of each component not well determined
• As lifetimes become closer together parameter
  values become more closely correlated

24
Three Closely Spaced Lifetimes

• Indole, AA, and 2-AP
• Indole at long times plot becomes non-linear,
  long tail
• Due to impulse response function continued
  excitation (must be removed from fit)
• Improvement in ?2R value with single to triple
  exp.
• F-statistic 90-95 probability that two decay
  time not adequate description of data

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Intensity Decay Laws

• Pre-exponential factors
• Single fluorophore same radiative decay rate in
  each environment fraction of molecules in each
  environment at t0
• Mixture of fluorophores quantum yield,
  intensity, observation wavelength, concentrations

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Single Tryptophan Protein

• R6G dye with frequency doubled to 295
• Emission monochrometer set at 360 nm
• What fit would you accept?

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Microsecond Decays

• Direct digitation of time dependent intensity
• Wide IRF 14 ns
• Deconvolution not necessary

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Picosecond Decays

• Need femtosecond laser
• Fast detector