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Time Correlated Single Photon Counting (TCSPC): Examples Prof. C. Altucci Corso di Fisica Atomica Molecolare e Spettroscopia a.a. 2014-2015 Laurea Magistrale in Fisica PhD School in Physics 1 What do we mean by Fluorophore “lifetime”? Absroptiona dn emission are relative to populations of molecular species. Generally, single molecule properties are deduced by the measured ensemble response. For a population of excited fluorophores we can write the rate equation: * dn() t kn*() t dt describing the variation per unit time of the number of molecules in the excited state at the time t 2 The solution is: * () t )e x p (-kt) n n(0 * The lifetime is equal to k -1 The lifetime is then the time needed for the excited molecules to decay at 1/e (36.8%) of the initial value. t=0 is the end of the excitation pulse. * n (t) t / e * n (0) 3 The decay constant k stands for the sum of the constants related to all possible decay channels. k = kf + ki + kx + kET + …= kf + knr •kf fluorescence decay, •ki internal conversion decay, •kx inter-system crossing decay, •kET energy-transfer decay, •knr all non-radiative decays 4 Non-radiative processes: • Isolated molecules in “gas-phase” undergo only internal conversion or inter-system crossing • In the condensed phase additional mechanisms have to be accounted for due to interactions with the micro-environment: chemical reactions in the excited state, energy transfer, … Coumarine in ethanol has a 4 ns lifetime Isoalloxazine in water has a 4.5 ns lifetime Lifetime of Tryptophan in proteins vary from ~0.1 ns to ~8 ns 5 The radiative lifetime r = kf-1 is nearly constant for a given molecule The overall fluorescence lifetime = k-1 = (kf + knr)-1 depends on the micro-environment surrounding through knr. Quantum yield for fluorescence: k k f QY f k k f nrk r It is proportional to fluorescence lifetime The addition of a further decay path, non-radiative, increases knr and decreases and thus QY. The fluorescnce intensity is proportional to n*(t), I (t) = kf n*(t) 6 The Stokes shift consists in the fluorescence to occur with a photon energy smaller (larger wavelength) than that of the excitation radiation The emission spectra or substantially independent on the excitation wavelength. The excess energy is rapidly dissipated (10-12 s). The mirror rule. 7 Diffusion times in solution. The excess energy is quickly dissipated (10-12 s): x2=2D. For example: for oxygen in water D 2.510-5 cm2/s, if the fluorephore lifetime is 10 ns we obtain x 70 Å which is comparable with the thickness of a biological membrane or with the linear size of a protein. Absorption spectroscopy gives info of the ground state structure. Fluorescence/Emission spectroscopy gives info on the excited state structure. 8 Let’s focus on TCSPC. How to measure the fluorescence lifetime? Time domain The real fluorescence decay is a convolution with the excitation pulse profile IR() t I() t P () t The measured fluorescence decay decadimento di fluorescenza misurato ism a convolution the overall system response Molecules are excited by a short pulse (ideally a function) at t = 0. The intensity of the fluorescence decay is usually measured by the Time Correlated Single Photon Counting (TCSPC) I(t) =ex p(-t/τ) It ( ) I ( t ) R ( t ) M R It ( ) I ( t )P ( t ) R ( t ) I ( t )i ( t ) M R E F The system response function iREF is typically measured as the response to the “direct” excitation pulse. 9 Steady-state and time-resolved regimes While steady-state fluorescence measurements are simple, nanosecond time-resolved measurements typically require complex and expensive instrumentation. Given the relationship between steady-state and time-resolved measurements, what is the value of these more complex measurements? It turns out that much of the molecular information available from fluorescence is lost during the time averaging process. 10 Time domain I ( t ) [ e x p (tτ -/) ] i ( t ) M R E F I(t) parameters are usually obtained by a non-linear best-fit combined to a deconvolution. The deconvolution is not required when the excitation pulse is much shorter than the lifetime to measure and/or when we do not need a high accuracy in the lifetime determination. 11 Mono-exponential decay It ()ex p ( t/) Multi-exponential (at least two distinct lifetimes) t It ie i i A similar analysis is performed in case of multi-dim. Decay to extract the lifetimes τi and the weights αi. Increasing the number of parameters in the fitting procedure reults in increasing the risk of numerical artifacts (more than 3 lifetimes are not recommended). Alternatively, the Method of Maximum Entropy can be used to analyze distributions of lifetimes. Esposito R., Altucci C., Velotta R., Analysis of Simulated Fluorescence Intensities Decays by a New Maximum Entropy Method Algorithm, Journal of Fluorescence, 23, 203-211, 2012 ∑ αi Mean lifetime – the time that a molecules spends in its excited state as an average over the molecular ensemble τ m= i τi ∑ αi i 12 Time Correlated Single Photon Counting (TCSPC) Simple experimental set-up for fluorescence decay measurements with TCSPC. Measurement of start-stop times in time-resolved fluorescence measurement with TCSPC. Histogram of start-stop times in time-resolved fluorescence measurement with TCSPC. 13 Glucose Oxidase Red: FAD cofactors bound deep inside the enzyme. FAD (Flavine Adenine Dinucleotide) * The active site where glucose binds just above the FAD. This enzyme, like many other proteins, is covered with carbohydrate chains, shown in green. It is produced by a mould species , the Aspergillus Niger 60 x 52 x 37 Å 14 Flavin Adenine Dinucleotide (FAD) Flavine “Open” configuration “Stacked” configuration Fluorescent site Adenine 15 Reaction induced by Glucose Glucose oxidation and FAD reduction Glucose + GOD (FAD+) gluconic acid + GOD (FADH2) GOD (FADH2) + O2 H2O2 + GOD (FAD+) (1) (2) Unlike other enzymes GOD needs an external agent (O2) to complete the cycle (this allows one to control the reduced FAD concentration) 16 Experimental set-up GOD GOD+Glu Diode laser l= 404 nm rep. rate= 40 MHz <P>= 1 mW width=80 ps IRF~120 ps Bandpass Filter @520nm FWHM:10nm Microscope objective Sample (stirring cell) 17 Effect of Glucose GOD+GLU 1 mM A01 32.0 0.310 3 01 339 4 ps A02 100.0 0.310 3 02 3106 21 ps signal (arb. units) GOD + GLU 1mM GOD 100 2 red 0.27 10 0 2000 4000 6000 time (ps) GOD GOD+GLU FAD in oxidized form FAD in reduced form (due to Glucose) GOD A01 7.0 0.1 10 3 01 10.7 1.0 ps A02 72.0 0.2 10 3 02 2911 14 ps 2 red 0.28 18 Free FAD Lifetime (conformational effects) GOD+glu GOD The experiment with acid and basic buffers shed light on the FAD conformation in GOD! 19 Estimation of the features for sensors (preliminary results in sol-gel) amp2/(amp1+amp2) (arb. units) Assuming Michaelis-Menten behaviour S ES S K M 0 2 4 6 8 10 12 [GLU]mM 14 16 18 20 22 A1 C S A1 A2 S K M KM 1.7 0.4 mM C 0.59 0.03 20 21 Another example: 5-Benzyluracil A Model System for DNA-Protein cross-link UV LASER Pulse @ 258 nm 5-benzyluracil (5BU) Dynamics and Photocyclization of 5-benzyluracil 5,6-benzyluracil (5,6BU) take a brick from DNA side (Uracil) and a part from the protein side (benzene) and study their interaction and dynamics induced by UV light. Sun, G.; Fecko, C. J.; Nicewonger, R. B.; Webb, W. W.; Begley, T. P., “DNA-protein cross-linking: model systems for pyrimidine-aromatic amino acid cross-linking.” Org. Lett. 2006, 8, 681–3 22 TCSPC Results Decay Constants: τ1= 50 ± 5 ps Counts 1000 τ2= 1.6 ± 0.2 ns 100 Fitting function: 10 6 7 8 9 10 time (ns) 𝒇 𝒕 = 𝑨𝟏 𝑰𝑹𝑭 𝒕 ⊗ 𝑬𝒙𝒑(− 𝒕 𝒕 ) + 𝑨𝟐 𝑰𝑹𝑭 𝒕 ⊗ 𝑬𝒙𝒑(− ) 𝝉𝟏 𝝉𝟐 23