Fluorescence Lifetimes

CZECH TECHNICAL UNIVERSITY IN PRAGUE

FACULTY OF BIOMEDICAL ENGINEERING

Martin Hof, Radek Macháň

•Fluorescence is observed if kf ~> ki + kx

The Jablonski DiagramThe life history of an excited state electron in a luminescent probe

S0

T1

S2

S1

• The time a molecule spends in the excited state is determined by the sum of the kinetic constants of all deexcitation processes

Absorption Fluorescencekf ~ 107 – 109 s-1

Phosphorescencekph < 106 s-1

Internal conversion ki ~ 1012 s-1

Radiationless decay knd > 1010 s-1

ki ~ 106 -1012 s-1

kx ~ 10-1 – 105 s-1

Inter-system crossing kx ~ 104 – 1012 s-1

What is meant by the “lifetime” of a fluorophore???

In general, the behavior of an excited population of fluorophores is described by a familiar rate equation:

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).

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.

)( )( - = d

)( d * tftnkt

tn*

k

If excitation is switched off at t = 0, the last equation, takes the form:

)( - = d

)( d ktn

ttn *

*

and describes the decrease in excited molecules at all further times. Integration gives:

) (- exp )0( = )( ** tkntn

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:

/*

*

e)0()( t

ntn

k

k

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:

is proportional to fluorescence lifetime.

r

f

nrf

f

kk

kkk

QY

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

Molecules are excited by a very short pulse (close to a -pulse) at t = 0 and the decay of florescence intensity is measured. Usually by Time Correlated Single Photon Counting (TCSPC)

)/ (- exp )0( = )( tItI

Excitation light is harmonically modulated with circular frequency and so is the emission. Fluorescence lifetime can be deduced from the phase shift and modulation m.

tan1

=

111

= 2 mm

t

B

b

a

Ainte

nsity

time

Time (or pulsed) domain

Ideal single-exponential decay of fluorescence intensity (excited by a -pulse at t = 0)

)/exp()0()( tItI The real fluorescence decay is a convolution with the profile of the excitation pulse

)()()( tPtItI R The measured fluorescence decay is a convolution of the real decay with the response of the detection

)()()( tRtItI RM

)()()()()()( titItRtPtItI REFM

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”).

i

t

iieItI 0

Time (or pulsed) domain

)/exp()0()( tItI

single-exponential decaymulti-exponential decay (at least two distinct lifetimes)

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.

Mean lifetime – an average time a molecule spends in the excited state

iii

iii

m

ttI

ttIt

2

0

0

)d(

d)(

Time correlated single photon counting (TCSPC)

pulsed laser

monochromator / filter sample

monochromator / filter

detector

discriminatorTAC

multichannel analyzer

STOPSTART

trigger pulse from a reference detector and discriminator or

from the pulse generator which drives the laser pulses

detector: multichannel plate photomultiplier tube (MCP PMT), avalanche photo diode (APD)

generates an array of numbers of detected photons within short time intervals – photon arrival histogram

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)

time

volt

age

threshold

t

Leading edge discriminator

• the pulse timing depends on its amplitude increases time jitter

Constant fraction discriminator

• 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

(1-f) I(t-)

- f I(t)

Time to Amplitude Converter (TAC)

time

volt

age

50 ps

10

V

START STOP

• TAC generates a linear voltage ramp by charging a capacitor

• TAC is the limiting step in TCSPC

• 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

• the charging is started by a trigger pulse (synchronized with the excitation pulse)

• 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

monochromator / filter

monochromator / filter

detector

TAC

time to amplitude convertor

multichannel analyzer

STARTSTOP

generates an array of numbers of detected photons within short time intervals – photon arrival histogram

sample

discriminator

volt

age

pulsed laser

value of voltage reached

refe

rence

puls

e

Time correlated single photon counting (TCSPC)

TCSPC - ArtefactsIf more photons arrive within a single time interval (ti + t) 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 + t) should be less then one

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

t

TCSPC - TheoryConsider that within one excitation cycle in the time interval (ti + t) 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 distribution:

)exp(!

)( i

zi

i wz

wzp

Specifically: )exp()0( ii wp )exp()1( iii wwp

)exp()1(1)1()0(1)1( iiiii wwppzp

After many (NE) excitation cycles, Ni counts will be detected in the i-th interval

)1()1( zppNN iiEi

Low intensities are used in TCSPC, therefore wi << 1 and:

ii wp )1(2)1( ii wzp

iiEiiEi wwNwwNN 2

The number of counts in the i-th interval is indeed proportional to the intensity in the interval (ti + t).

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.

1

1

11

i

jj

EiSi N

NNN

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.

Note: an advantage of TCSPC is the known statistical distribution of noise (Poisson distribution) and it can be included in the data analysis.

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.

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.

= 4.1ns2 = 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)

photon photoelectron

photocathode

voltage sweep

phosphor screen

Modern streak cameras have time resolution superior to photomulpliers. Parallel detection in all channels – intensity is not limited by pile-up effect.

The frequency domain measurement does not provide a direct information on the shape of the fluorescence decay

Frequency (harmonic) domain

tan1

=

111

= 2 mm

The equality of 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

B

b

a

Ainte

nsity

time

AaBb

m

=

Frequency (harmonic) domain - derivation

derivation of equations for a single-exponential decay:

)( )( - = d

)( d * tftnkt

tn*

)sin( = )( taAtf considering the harmonic excitation:

we assume a solution in the form: )sin( = )(* tbBtn

)sin()sin( = )cos( 1 taAtbBtb

to ensure that the equation is solved for all values of t, we search for such values of phase shift and modulation m that satisfy the equality of terms containing t, terms containing cos(t) and terms containing sin(t) on both sides of the equation.

tan = cossin

221

1 =

m

AaBb

Frequency (harmonic) domain – general expressions

An integral transform of the fluorescence decay I(t) gives:

cos

1

1

d)(

d)cos()(

22

0

0 m

ttI

tttI

Gi i

ii

iii

sin

1

1

d)(

d)sin()(

22

2

0

0 m

ttI

tttI

Si i

ii

iii

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)

C C

V

S

AD N

I

I

D

RhoRho Rho

C C

I

I

D

N

A

D

S

V

Weak fluorescenceStrong 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

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.

Lifetime data for two rhodamine isomers (5’ and 6’) linked to the peptide

C C

V

S

AD N

I

I

D

RhoRho Rho

C C

I

I

D

N

A

D

S

V

Weak fluorescenceStrong fluorescence

E1

0 2 4 6 8 10 12 14

0

1x104

2x104

3x104

4x104

5x104

Fre

qu

en

cy [

cps]

Lifetime [ns]

fluorescence lifetime image of a part of a membrane of a living hepatocyte cell stained with the dye NBD (7-nitrobenz-2-oxa-1,3-diazole) → lifetime is depending on the hydrophobicity of the environment

exc = 467 nm100×, 1.3 N.A. oil immersion300 × 300 pixels

acquisition time: 2 ms/pixel

Fluorescence intensity Fluorescence lifetime Lifetime distribution

Hydrophobicity – sensing with lifetime sensitive dyes

E2

Acknowledgement

The course was inspired by courses of:

Prof. David M. J ameson, Ph.D.

Prof. RNDr. J aromír Plášek, Csc.

Prof. William Reusch

Financial support from the grant:

FRVŠ 33/119970