Fluorescence Lifetimes Martin Hof Radek Mach The Jablonski

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 S 2 Radiationless decay knd > 1010 s-1 ki ~ 106 1012 s-1 Inter-system crossing kx ~ 104 – 1012 s-1 S 1 kx ~ 10 -1 – 105 s-1 Absorption Fluorescence kf ~ 107 – 109 s-1 T 1 Phosphorescence kph < 106 s-1 S 0 • 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: k 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: k and describes the decrease in excited molecules at all further times. Integration gives: k 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:

The deexcitation rate k is the sum of the rates of all possible deexcitation pathways: k = kf + ki + kx + k. ET + …= kf + knr kf is the rate of fluorescence, ki the rate of internal conversion and vibrational relaxation, kx the rate of intersystem crossing, k. ET 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 27 ns bound to t. RNA 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. 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 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) 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.

Time (or pulsed) domain Ideal single-exponential decay of fluorescence intensity (excited by a d-pulse at t = 0) The real fluorescence decay is a convolution with the profile of the excitation pulse The measured fluorescence decay is a convolution of the real decay with the response of the detection The instrument response function i. REF 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) An analogous analysis is performed in the case of multi-exponential decay to extract lifetimes i and fractions ai. 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

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: ü the charging is triggered by photon arrival and stopped by the excitation pulse ü 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 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 distribution: Specifically: After many (NE) excitation cycles, Ni counts will be detected in the i-th interval Low intensities are used in TCSPC, therefore wi << 1 and: 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. 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 5000 U Time-correlated single photon counting instrument equipped with a LED short pulse diode excitation source. = 4. 1 ns c 2 = 1. 023 56 ps/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 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 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 of equations for a single-exponential decay: considering the harmonic excitation: we assume a solution in the form: 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.

Frequency (harmonic) domain – general expressions An integral transform of the fluorescence decay I(t) gives: 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 E 1 I A D S V I C C 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 I A D S V I C C Rho Strong fluorescence E 1 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.

E 2 Hydrophobicity – sensing with lifetime sensitive dyes 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 Fluorescence intensity Fluorescence lifetime exc = 467 nm 100×, 1. 3 N. A. oil immersion 300 × 300 pixels acquisition time: 2 ms/pixel Lifetime distribution