Transcript Fluorescence lifetime - UFCH JH

Fluorescence Lifetimes
Martin Hof, Radek Macháň
The Jablonski Diagram
The life history of an excited state electron in a luminescent probe
Internal conversion
ki ~ 1012 s-1
S2
Radiationless decay
knd > 1010 s-1
ki ~ 106 1012 s-1
Inter-system crossing
kx ~ 104 – 1012 s-1
S1
kx ~ 10-1 – 105 s-1
Absorption
Fluorescence
kf ~ 107 – 109 s-1
T1
Phosphorescence
kph < 106 s-1
S0
•
Fluorescence is observed if kf ~> ki + kx
•
The time a molecule spends in the excited state is determined by the sum of
the kinetic constants of all deexcitation processes
What is meant by the “lifetime” of a fluorophore???
Absorption and emission processes are almost always studied on
populations of molecules and the properties of the supposed typical
members of the population are deduced from the macroscopic properties
of the process.
In general, the behavior of an excited population of
fluorophores is described by a familiar rate equation:
d n* (t )
*
= - k n (t )  f (t )
dt
where n* is the number of excited elements at time t, k is the rate
constant of all deexcitation processes and f(t) is an arbitrary function of
the time, describing the time course of the excitation. The dimensions of k
are s-1 (transitions per molecule per unit time).
If excitation is switched off at t = 0, the last equation, takes the form:
d n* (t )
= - n* (t ) k
dt
and describes the decrease in excited molecules at all further
times. Integration gives:
*
(
t
)
=
n
n (0) exp (- kk t )
*
The lifetime

is equal to k
-1
If a population of fluorophores are excited, the lifetime is the time
it takes for the number of excited molecules to decay to 1/e or
36.8% of the original population according to:
n*(t )
t / 

e
n*(0)
The deexcitation rate k is the sum of the rates of all possible
deexcitation pathways:
k = kf + ki + kx + kET + …= kf + knr
kf is the rate of fluorescence, ki the rate of internal conversion and vibrational
relaxation, kx the rate of intersystem crossing, kET the rate of inter-molecular
energy transfer and knr is the sum of rates of radiationless deexcitation pathways.
non-radiative processes:
• isolated molecules in “gas-phase” only internal conversion and
intersystem crossing
•
in condensed phase additional pathways due to interaction with
molecular environment: excited state reactions, energy transfer,…
non-radiative processes:
• isolated molecules in “gas-phase” only internal conversion and
intersystem crossing
•
in condensed phase additional pathways due to interaction with
molecular environment: excited state reactions, energy transfer,…
ANS in water is ~100
picoseconds but can
be 8 – 10 ns bound
to proteins
Ethidium bromide is 1.8 ns
in water, 22 ns bound to
DNA and 27ns bound to
tRNA
The lifetime of
tryptophan in
proteins ranges from
~0.1 ns up to ~8 ns
Note: fluorescence lifetime tends to be shorter in more polar environment, because
larger dipole moments of surrounding molecules can increase the efficiency of
energy transfer
The radiation lifetime r = kf-1 is practically a constant for a given molecule
The fluorescence lifetime  = k-1 = (kf + knr)-1 depends on the
environment of the molecule through knr.
Fluorescence quantum yield:
QY 
kf
k

 f 

kf  knr
k
r
is proportional to fluorescence lifetime.
Addition of another radiationless pathway increases knr and, thus,
decreases  and QY.
However, the measurement of fluorescence lifetime is more robust than
measurement of fluorescence intensity (from which the QY is
determined), because it depends on the intensity of excitation nor on
the concentration of the fluorophores.
The fluorescence intensity I (t) = kf n*(t) is proportional to n*(t) and
vice versa
How to measure fluorescence lifetime ???
Time (or pulsed) domain
Frequency (or harmonic) domain
f
intensity
a
b
A
B
t
Molecules are excited by a very
short pulse (close to a d-pulse)
at t = 0 and the decay of
florescence intensity is
measured. Usually by Time
Correlated Single Photon
Counting (TCSPC)
I (t) = I (0) exp (- t /  )
time
Excitation light is harmonically
modulated with circular
frequency w and so is the
emission. Fluorescence lifetime
can be deduced from the phase
shift f and modulation m.
1
 f = tan f
w
1 1
m =
1
2
w m
Time (or pulsed) domain
Ideal single-exponential decay of fluorescence intensity (excited by a d-pulse at t = 0)
I(t )  I(0) exp(t /  )
The real fluorescence decay is a convolution with the profile of the excitation pulse
IR(t )  I(t )  P(t )
The measured fluorescence decay is a convolution of the real decay with the response
of the detection
IM (t )  IR(t )  R(t )
IM (t )  I(t)  P(t)  R(t)  I(t )  iREF (t )
The instrument response function iREF is typically measured as a response of the
instrument to scattered excitation pulse.
The parameters of I(t) (the lifetime ) are usually obtained by nonlinear fitting
combined with a deconvolution procedure.
The deconvolution is not necessary when the excitation pulse is very short
compared to the lifetime (fs-lasers) and/or high precision of lifetime
determination is not required. A part of the measured decay closest to the
excitation pulse is then excluded from the analysis (“tail fitting”).
Time (or pulsed) domain
single-exponential decay
multi-exponential decay (at least two
distinct lifetimes)
I t   I 0   i e
I(t )  I(0) exp(t /  )
t
i
i
An analogous analysis is performed in the case of multi-exponential decay to extract
lifetimes i and fractions i. An increase in the number of fitted parameters
represents increases the risk of artefacts (more than 3 lifetimes not recommended)
Alternatively maximum entropy method can be used – allows analysis of continuous

distributions of lifetimes.
2
Mean lifetime – an average time a
molecule spends in the excited state
m 
 t I(t ) dt
0

 I(t )dt
0

 
 
i
i
i
i
i
i
Time correlated single photon counting (TCSPC)
monochromator /
filter
pulsed
laser
sample
trigger pulse from a reference
detector and discriminator or
from the pulse generator which
drives the laser pulses
START
TAC
monochromator /
filter
detector
STOP
discriminator
multichannel analyzer
generates an array of numbers of detected photons within short time
intervals – photon arrival histogram
detector: multichannel plate photomultiplier tube (MCP PMT), avalanche
photo diode (APD)
Discriminator
eliminates noise (dark counts of the photodetector) and generates pulses which are
independent of the actual shape and amplitude of the detector pulse (which is
generated when a photon hits the detector)
Leading edge discriminator
voltage
•
the pulse timing depends on its
amplitude  increases time jitter
threshold
Dt
time
Constant fraction discriminator
(1-f) I(t-d)
•
•
- f I(t)
the signal is divided to two branches,
the signal in one branch is inverted and
in the other delayed and then they are
added together
the zero point used for timing
independent of amplitude
10 V
Time to Amplitude Converter (TAC)
• TAC generates a linear voltage
ramp by charging a capacitor
voltage
• TAC is the limiting step in TCSPC
START
• the charging is started by a trigger
pulse (synchronized with the excitation
pulse)
time
STOP
50 ps
• the charging is stopped by a pulse from the detector (photon arrival) and
the reached voltage is stored by the multichannel analyzer.
• if no photon is detected TAC is reset when reaching the maximum voltage
• TACs are usually operated in reverse mode:
 the charging is triggered by photon arrival and stopped by the excitation
pulse
 the capacitor is charged in those excitation cycles when a photon is detected
Time correlated single photon counting (TCSPC)
monochromator /
filter
sample
monochromator /
filter
voltage
reference pulse
pulsed
laser
STOP
detector
TAC
time to
amplitude
convertor
START
discriminator
value of voltage
reached
multichannel analyzer
generates an array of numbers of detected photons within short time intervals –
photon arrival histogram
TCSPC - Artefacts
If more photons arrive within a single time interval (ti + Dt) after excitation, only a
single count is registered – the discriminator does not take into account the size of
the pulse from the detector once it is larger than the discrimination level
The average number of photons wi reaching the detector with each interval (ti + Dt)
should be less then one
Dt
TAC however detects only one photon in each excitation cycle
The average number of photons reaching the detector in each excitation cycle should
be less then one
TCSPC - Theory
Consider that within one excitation cycle in the time interval (ti + Dt) after excitation
(which corresponds to the i-th channel of the multichannel analyzer) on average wi
photons reach the detector.
The probability of z photons reaching the detector in that interval is given by Poisson
z
distribution:
w
pi (z ) 
Specifically:
i
z!
exp(wi )
pi (1)  wi exp(wi )
pi (0)  exp(wi )
pi (z  1)  1  pi (0)  pi (1)  1  (1  wi ) exp(wi )
After many (NE) excitation cycles, Ni counts will be detected in the i-th interval
Ni  NE pi (1)  pi (z  1)
Low intensities are used in TCSPC, therefore wi << 1 and:
pi (1)  wi

2

pi (z  1)  wi
2
Ni  NE wi  wi  NE wi  wi
The number of counts in the i-th interval is indeed proportional to the intensity in the
interval (ti + Dt).
TCSPC - Theory
TAC however detects only one photon in each excitation cycle
The actual number of counts NSi stored in the i-th channel of the multichannel
analyzer is lower than Ni.
NSi

1
 Ni 1 
NE


N j 

j 1

i 1
That is called the pile-up effect
To prevent the need for corrections of the measured decays for pile-up effect very low
intensities are used to make the effect negligible. The intensities are usually adjusted
to ensure that Ni is approximately 1% of NE, that means that a photon is detected
only in 1% of excitation cycles.
High repetition rates of excitation pulses are used to decrease the time necessary for
measurement. However, the fluorescence intensity has to decay completely between
the pulses – repetition rates usually ≈ 1 – 10 MHz.
Note: an advantage of TCSPC is the known statistical distribution of noise
(Poisson distribution) and it can be included in the data analysis.
Here are pulse decay data on anthracene in cyclohexane taken on an IBH 5000U
Time-correlated single photon counting instrument equipped with a LED short
pulse diode excitation source.
 = 4.1ns
c2 = 1.023
56ps/ch
Time domain – An alternative detection method
The decay of fluorescence can be also recorded with high temporal resolution using a
streak camera (analogous to an oscilloscope)
voltage sweep
phosphor
screen
photon
photoelectron
photocathode
Modern streak cameras have time resolution superior to photomulpliers. Parallel
detection in all channels – intensity is not limited by pile-up effect.
Frequency (harmonic) domain
bB
m=
aA
f
a
intensity
1
tan f
w
1 1
m =
1
2
w m
f =
b
A
B
time
The frequency domain measurement does not provide a direct information on the
shape of the fluorescence decay
The equality of f and m indicates single-exponential decay. If they are not equal,
more general expressions have to be used.
High excitation intensity can be applied to shorten the measurement time
Frequency (harmonic) domain - derivation
derivation of equations for a single-exponential decay:
d n* (t )
= - k n* (t )  f (t )
dt
considering the harmonic excitation:
f (t ) = A  a sin(wt)
we assume a solution in the form: n * (t ) = B  b sin(wt  f)
bw cos(wt  f ) =  1 B  b sin(wt  f )  A  a sin(wt )
to ensure that the equation is solved for all values of t, we search for such values
of phase shift f and modulation m that satisfy the equality of terms containing t,
terms containing cos(wt) and terms containing sin(wt) on both sides of the
equation.
sinf
= tanf  w
cos f
bB
= m
a A
1
1  w 2 2
Frequency (harmonic) domain – general expressions
An integral transform of the fluorescence decay I(t) gives:

Gw 
 I(t ) cos(wt ) dt
0

 I(t ) dt

 i i
 mw cos fw

2 2
  i i i 1  w  i
1
i
0

Sw 
 I(t ) sin(wt ) dt
0

 I(t ) dt
2
 iw i

 mw sinfw

2 2
  i i i 1  w  i
1
i
0
The excitation intensity is harmonically modulated by a Pockels cell or a
harmonically modulated LED or laser diode is used. The frequency is typically in the
range of ~10 – 100 MHz
An example of the use of lifetime data is given by a study of a rhodamine
labeled peptide which can be cleaved by a protease (from Blackman et al.
(2002) Biochemistry 41:12244)
N
D
A
D
N
I
S
D
V
I
C
Rho
C
Weak fluorescence
E1
A
I
D
S
V
I
C
C
Rho
Rho
Strong fluorescence
In the intact peptide the rhodamine
molecules form a ground-state dimer
with a low quantum yield (green curve).
Upon cleavage of the peptide the
rhodamine dimer breaks apart and the
fluorescence is greatly enhanced (blue
curve).
Lifetime data allow us to better
understand the photophysics of this
system
Lifetime data for two rhodamine isomers (5’ and 6’) linked to the peptide
N
D
A
D
N
I
S
D
V
I
C
Rho
C
Weak fluorescence
A
I
D
S
V
I
C
C
Rho
Rho
Strong fluorescence
E1
As the lifetime data
indicate, before protease
treatment the rhodamine
lifetime was biexponential
with 95% of the intensity
due to a long component
and 5% due to a short
component. Hence one
can argue that the intact
peptide exists in an
equilibrium between open
(unquenched) and closed
(quenched) forms.
E2
Hydrophobicity – sensing with lifetime sensitive dyes
exc = 467 nm
100×, 1.3 N.A. oil immersion
300 × 300 pixels
fluorescence lifetime image of a part of a membrane of
a living hepatocyte cell stained with the dye NBD (7nitrobenz-2-oxa-1,3-diazole) → lifetime is depending
on the hydrophobicity of the environment
Fluorescence lifetime
Lifetime distribution
5x104
Frequency [cps]
Fluorescence intensity
acquisition time: 2 ms/pixel
4x104
3x104
4
2x10
4
1x10
0
0
2
4
6
8
10
Lifetime [ns]
12
14
Acknowledgement
The course was inspired by courses of:
Prof. David M. Jameson, Ph.D.
Prof. RNDr. Jaromír Plášek, Csc.
Prof. William Reusch
Financial support from the grant:
FRVŠ 33/119970