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1 ENERGY TRANSFER Submission deadline of December Total number of points = = 119 Name: FRET Max Real 5,1 A 3 B 3 C 3 5,2 A 3 B 3 C 4 5,3 A 15 B 5 C 8 D 6 5,4 A 3 B 5 C 5 5,5 30 5,6 A 5 B 10 C 5 D 3 SUM (MAX) % 119 This page must be the first page of your solutions! 1

2 PCR 3.1 (9) You have one A molecule and three variants of D molecule (D1, D2, D3). For all possible pairs the spectral overlapping is the same, the distance between D and A is the same in all pairs. The donors have the following characteristics: D1: fluorescence lifetime 1 = 2 ns, fluorescence quantum yield 1 = 0.25 D2: fluorescence lifetime 2 = 0.4 ns, fluorescence quantum yield 2 = 0.1 D3: fluorescence lifetime 3 = 3 ns, fluorescence quantum yield 1 = 0.5 a) (3) List the pairs in the order of increasing of the energy transfer rate (k FRET ) Write the dependence k FRET on and b) (3) List the pairs in the order of increasing of the Förster radius (R 0 ) Write the dependence R 0 on and c) (3) List the pairs in the order of increasing of the efficiency of FRET ( ) Write the dependence of on and PCR 3.2. (10) Energy transfer rate, k ET a) (3) Does k ET depend on radiative lifetime ( 0 ) of the donor? If so, write the equation. b) (3) Does k ET depend on radiative lifetime of the acceptor? If so, write the equation. c) (4) How does k ET depend on transition dipole moments of the donor ( D ) and the acceptor ( A )? 2

3 PCR 3.3. (34) Spectral overlap Absorption and fluorescence spectra of a donor (D) and an acceptor (A) molecule are given at the Figure. The fluorescence spectra are normalized: F d 1 wholespectrum Fluorescence quantum yield D in the absence of A is 0.5. Fluorescence quantum yield of A is 1. The solvent is water (n=1.33) a) (15) Calculate R 0 for energy transfer from D to A in solution (averaged over all orientations). In order to calculate the overlapping integral approximate the spectra in the spectral overlapping region by straight lines. b) (5) Do you expect to have any energy transfer from D to A if the distance between molecules is 10 nm? If so, estimate the transfer efficiency. c) (8) The concentration of D in a frozen solution is 10-4 mol/l. Estimate the concentration of A in the same solution in order to have 50% energy transferred from D to A? d) (6) You have a 50/50 mixture of D and A in the sample. With probability of 50% excited D transfers its energy to the acceptor. 1) Draw the shape of the absorption spectrum of the sample (use the graphs provided below). The relative amplitudes of the peaks should reflect the reality! 2) Draw the shape of the fluorescence spectrum if excitation = 650 nm 3) Draw the shape of the fluorescence spectrum if excitation = 500 nm In all the cases excitation intensity is the same. Your graphs should reflect the fluorescence intensities that you can compare cases 2 and 3. 3

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5 PCR 3.4 (13) D A a) (3) Tell which of those DA pairs have zero energy transfer efficiency (consider orientations only). b) (5) Calculate 2 for all pairs c) (5) Calculate efficiency of energy transfer for the first pair if the distance between the molecules is 6 nm and R 0 for random orientations is 5 nm. PCR 3.5 (30) You have a nanostructure shown at the figure. The acceptor molecule is placed in the center of a 2-dimentional array of donor molecules. The donor molecules are excited by light. The fluorescence yield of the acceptor molecule is zero, so it works as a fluorescence quencher. The position of every acceptor molecule is given by r and (polar coordinates, see the picture). Neglect the discontinuity of the sample, in other words, assume that the size of the molecules and the distance between them are much smaller than 10 nm, which is R 0 for headto-tail oriented D and A Donors a) Obtain analytical expression for R 0 of energy transfer from A to D as a function of angle. b) Using this expression draw the area in the sample within which the donor molecules are quenched with probability more than 50%. D Acceptor A r R 0 ( ) =? 5

6 PCR 3.6. (23) Electron and Energy transfer Both energy transfer and electron transfer can lead to fluorescence quenching of a donor molecule in a DA pair if A is not fluorescent a) (5) Compare dependences of the quenching rates on distances between D and A for the two mechanisms b) (10) What are the typical values of D-A distances when electron transfer can compete with fluorescence decay of the donor? Fluorescence decay time of D without A is about 10 ns. Use the equation for the electron transfer rate with the following parameters: H AB = 0.5 ev T=300K =1 ev =30 nm -1 for the rest assume the most favorable condition in the Marcus theory of electron transfer. c) (5) What are typical values of D-A distances when Energy transfer can compete with fluorescence decay of the donor? Take typical values of the Förster radius for good DA pairs for your estimation. d) (3) For the DA pair with the intermolecular distance of 3 nm A quenches fluorescence of D very efficiently. Based on your answers in a) and b) tell the most probable mechanism of the quenching (electron or energy transfer?) 6