The LyX User's Guide
Contents
1. kTPT The term ky ps is often neglected for the calculations but still remains a limiting factor for single molecule experiments Still the solution of the rate equation system is quite com plicated A less complex approach is the stationary case where the derivatives are set to 4 PS 4 Ps Pr 0 and the normalization condition is 1 ps Ps Pr If the photon emission rate is defined as R kioPs then R reads kio R 2 2 Kise k kictkise 1 i aay ea exc It is obvious that the photon emission R saturates for kexe kio 1 je 2 3 Rexc o Moreover if one introduces the saturation intensity Zs as 2 Ikr kio kic kisc kexc kr ag Kise the photon emission rate R can be rewritten as Is 2 4 1 I 2 2 Single molecule detection in solution In order to determine the fluorescence quantum yield f which relates the number of absorbed photons to the number of emitted photons the transition J 0 or at least I lt Is leads to Rol kio lo Ss kae kec f Pr 2 6 I A tket k f ee ho consists of radiative and non radiative components The fluorescence lifetime Tr is related Rexc 0 to the rate coefficients ki Kic and kisc and the fluorescence quantum yield p according to 1 P f 2 7 kio kic kise kio Based on this relations the fluorescence lifetime is an important parameter to characterize both TFI the in2. 21 F e 7 Graal Si 14 2 26 sp3 t e 2 26 with F as the fraction of molecules in the triplet state and tr as the mean duration of stay of the triplet state Additionally suggestions have been made to determine even rate constants as described in section 2 2 and photo induced back isomerization of dyes 106 107 facing the problem that with a large set of fitting parameters the accuracy of each parameter determination suffers Gennerich and Schild derived fitting functions for confined diffusion within neuronal dendrites which feature a diameter of less than 1 um and a length of tens of micrometers 31 30 For a more comprehensive review about the present use of FCS see reference 33 In contrast to the ACF which is calculated out of one intensity time trace it is often useful to determine the so called cross correlation function CCF which is calculated out of two intensity time traces Therefore the emitted beam of the fluorescent light is separated using a 50 50 beamsplitter and then focused on two detectors The definition for the CCF lai t 6la2 t 7 Gec t 14 Tay Uo yields the same fitting functions as described previously The advantage of using the CCF lies 2 27 in the fact that one can get rid of the effect of afterpulsing Afterpulsing is an intrinsic property of the detectors where the detection of a real photon can be followed by a detection of a virtual photon 21 113 and is furth
3. and beyond detection 2 After slightly defocussing the molecules in the z direction the imaged intensity patterns were used to determine the orientation of the molecules by applying an appropriate fitting model A similar pattern approach is described in reference 7 Instead of using slight defocussing different directions of incidence with linearly polarized light can be used for ori entation determination resulting in a shot noise limited angular resolution of 2 78 For the case of using highly symmetric single chromophores e g CdSe quantum dots Empedocles and coworkers demonstrated in 1999 that comparing the fluorescence intensity as a function of the polarization angle is sufficient for a three dimensional orientation determination 20 Several other publications deal with more complex excitation schemes Sick and coworkers used an annular illumination geometry approach where the inner part of the laser beam is cut off 91 Again the imaged intensity patterns can be attributed to different orientations with out loosing the spatial information as it occurs with the defocussing techniques H bner and coworkers used this scheme to determine the donor and acceptor transition dipoles in individ ual molecules which is crucial to reliable distance determination based on FRET 50 Forkey and coworkers used four different excitation polarizations in a total internal reflection scheme to measure the structural dynamics of the light chain d
4. is the total number of TCSPC channels The brackets indicate an averaging over an infinite number of measurements Moreover it can be shown assuming that photon detection i follows Poissonian statistics that with M j Pj the filter sets f n can be calculated according to P M aiag y at M diag wy 2 30 The L x L dimensional matrix consists of the diagonal elements I ne with j 1 L The i j independently from each other by measuring the two species in separate solutions The filter i j for verification of the filter sets according to approximation I a I is used for direct calculation The patterns p have to be measured sets f 4 and the corresponding patterns p form an orthonormal system which can be used Le fai Nf pee 2 31 j l In contrast to the normal procedure of calculating the auto correlation function where every photon is previously weighted with a factor of 1 the weighting factor in TRFCS is f Another useful application of TRFCS is the possibility of discriminating afterpulsing from the raw data 21 In avalanche photodiodes every absorbed photon can generate a photoelectron which then leads to further ionizations until the breakdown pulse occurs at the end This breakdown leads to the pulse which indicates the detection of a photon However if some of the charge carriers remain electronically trapped for a certain time they can be later on released by thermal excitation thereb
5. the acceptor absorption spectra The overlap integral is calculated as a function of the wavelength A z J i POJATA dA 2 10 with 4 A as the molar extinction coefficient of the acceptor and fp as the normalized emission spectrum of the donor f fp d 1 The energy transfer efficiency E can be either determined by the change in donor lifetime Tp p kf oy T gp Ka 5 1 72 2 11 kr pt K fret Ro TR D where Tp p represents the fluorescence lifetime in absence of the donor or by comparing the measured donor and acceptor intensities Jp and I as I PaA Ia yip The drawback of the second method is the incorporation of the donor and acceptor quantum 2 12 yields Pp and 4 and the detection efficiencies of both channels np and na for determining 11 Chapter 2 Single molecule spectroscopy fundamentals and beyond a D Accept c onor cceptor S4 D FRET L 4 mS 1 A ANN ANN Sop So a b high FRET 1 0 0 8 0 6 Lu 0 4 0 2 0 0 o Z amp W low FRET R nm Figure 2 4 a Simplified Jablonski diagram for FRET After absorbing a photon the energy in the ex cited state S1 p can be released directly by emitting a photon S1 So p or indirectly after a resonant energy transfer 15 S14 So a b Energy transfer efficiency E plotted as a function of R for Ro 4nm The transfer efficiency equals 50 at R 4nm c Schematic diagram of a protein labeled with a donor and an accept
6. 1 4Dt Gip t 1 1 2 19 ip t 1 z Z 2 19 for the two dimensional case of pure diffusion in the x y plane 1 4DT Gop t 1 1 r 2 20 N Wo and for the three dimensional case of pure diffusion 1 1 4Dt ADt G3p t 1 Les La N Wo Zo 2 21 where N represents the mean particle number in the detection volume and D the diffusion coefficient Defining the diffusion time for the one dimensional diffusion as P 2 2 22 P 4D l and for two and the three dimensional case as 2D 3D _ D 1D 2 23 the ratio between the diffusion time in the one dimensional case along z and in the three dimensional case is just the square of the structural parameter s which is defined as s zo wo and amounts to s 4 in a standard confocal microscope Therefore one can expect a 16 times longer Tp inside a small channel for one dimensional diffusion as compared to free bulk diffusion according to 2 2 2 iP Z0 _ 5S Wo D 4D 4D The ratio between the visually easier to access ACF decay half times 7 2 however is even 1618P 2 24 larger due to the different exponents of the diffusion terms Equations 2 19 and 2 21 can be expanded in order to determine the triplet parameters of the molecules 106 reading 1 is 4Dt 21 F e 7 LE 2 25 1 G T 1 1 1 7 7 ty IF or rather 15 Chapter 2 Single molecule spectroscopy fundamentals and beyond 1 Tt 1 4Dt 4Dt
7. 30 These dendrites are cellular extensions of the neurons where the majority of input to the neuron occurs They feature a thickness diameter of less than 1 um and a length of several tens of micrometers Other examples of reducing the effective detection volume are presented in the following 1 Cone shaped micro capillaries with an inner diameter of less than 1 um were used to confine the diffusion of single molecules 111 The flow of the conjugates was established using electrokinetic forces Due to the fact that the path of mo tion of the molecules is confined and thereby known the obtainable signal to noise ratio is increased compared with measurements in free solution 15 Sauer and coworker proposed the use of micro capillaries for DNA sequencing 84 2 Mesostructured molecular sieves were used to observe the translational diffusion of single terrylenediimide molecules 88 3 In recent years nanofluidic devices for single molecule detection fabricated by lithographic methods have gained more and more attention 64 This is mainly attributed to the availability of advanced lithographic techniques such as electron beam lithography reactive ion etching et cetera Han and coworkers reported on the separation of long DNA molecules using entropic trap arrays 38 and Foquet and coworkers showed the focal volume confinement by single fluidic channels featuring a channel width down to 350 nm 24 Even tough a reduction of the effective detect
8. Chapter 2 Single molecule spectroscopy fundamentals and beyond Overview In section 2 1 the photophysics of fluorescent molecules and the current state of knowledge in selected areas of single molecule spectroscopy SMS relevant to the scope of this thesis will be covered After giving a short overview of the history of single molecule detection SMD in solution in section 2 2 and discussing the scanning confocal optical microscopy SCOM and its scientific relevance in section 2 3 I will concentrate on several applications namely the single pair fluorescence resonance energy transfer spFRET in section 2 4 the fluorescence correlation spectroscopy FCS in section 2 5 and the 3D orientation determination of single molecules in section 2 6 Section 2 7 will deal with methods which have been suggested to geometrically confine molecules yielding smaller detection volumes 2 1 The photophysics of single molecules This section deals with the photophysics of single molecule experiments and follows the lines of references 77 99 112 The photophysics of fluorescent molecules is usually illustrated using a Jablonski diagram Figure 2 1 shows a simplified version of a three level system neglecting possible vibronic states By absorbing a photon from a laser source with a rate constant of kexc the molecule is excited from the ground state So to the first excited singlet state S1 The rate constant kexc is defined as Kexe OI h where o
9. angle of the incident laser light excludes light propagation trough the glass water interface However evanescent fields can enter the sample volume 42 93 The excitation volume is reduced by the fact that the penetration depth of the evanescent field in an aqueous solution is less than 200 nm SNOM Similar to TIRF the direct light propagation in a scanning near field optical micro scope is prevented and only evanescent fields can enter the volume of interest 5 In SNOM a tapered fiber tip with a diameter of less than 100 nm is covered with a metal at the side to fulfill this requirement Zero mode waveguides Zero mode waveguides consist of sub wavelength holes in a thin metal film deposited on a glass substrate Again the propagation of light through the metal film is forbidden and only evanescent fields occur within the holes 59 With this method observation volumes of zeptoliters 107 1 can be achieved Moreover Samiee and coworkers derived an empirical FCS model accounting for one dimensional diffusion within the tubes and used this technique to measure oligomerization of the bacteriophage repressor protein at micromolar concentrations 82 Besides reducing the excitation volume with the methods described above restricting the ac cessible space of the detectable diffusing fluorophores is another possible strategy for efficient single molecule detection An example from a biological system are dendrites of cultured neu rons 31
10. by M Minsky in 1955 he filled a patent instead of publishing a scientific publication the SCOM had become a versatile tool with well known properties in the field of fluorescence microscopy 103 Every confocal microscope is characterized by the use of the objective both for illumination of a focal volume and for detection out of the focal volume making the basic set up as simple as possible A schematic diagram of a state of the art SCOM as it is used for this work is shown in figure 2 2 The main principles of the set up will be discussed in this section whereas technical details will be discussed in section 3 2 The set up is used with pulsed lasers instead of continuous wave lasers to gain additional information about the fluorescent species such as the fluorescence lifetime The repetition rates of the lasers MHz range are adjusted to the fluorescence lifetime in such a way that the detection of a photon can be attributed to the last laser pulse If more than one laser is used at the same time the synchronized laser pulses alternate and are combined into one beam using a first dichroic mirror After adjusting the polarization by a 2 and a 4 filter the laser light is coupled into a polarization maintaining fiber in order to obtain a point source at the end of the fiber A lens or better an apochromatic objective with low magnification is used to obtain a parallel beam which than reaches the second dichroic mirror This dichroic mirror re
11. concentration of sample molecules is limited to less than one nanomol per liter to keep the probability of double occupancy low However systems that involve ligand binding or chemical change do often require micromolar or higher reagent concentrations 58 Unfortunately both limitations mostly interact with each other Reducing the effective excitation detection volume will lead to shortened transit times of the diffusing molecules The excitation detection volume can be reduced in two different ways One way is to reduce the excitation volume where different methods have been proposed STED The stimulated emission depletion was theoretically described by Hell and Wichmann 20 2 7 Geometrical confinement of diffusion in 1994 41 and gained a lot of attention after its experimental realization 40 53 This tech nique consists of a conventional confocal excitation spot which is overlapped with a STED spot featuring a central naught The STED spot is created by a pulsed laser with higher wavelength than the excitation wavelength and a A 2 wave plate in the center of the beam and efficiently depletes the first excited state of a fluorophore at high intensities in its accessible volume Therefore the effective excitation spot is drastically minimized to 0 67 attoliter 10718 1 and an optical resolution of around 30 nm can be obtained which is far beyond the diffraction limit TIRF In a total internal reflection fluorescence scheme a large
12. cular system at the same time within the focus of the confocal microscope Forster published in 1948 that a distance dependent non radiative energy transfer between two fluorophores can occur as long as two preconditions are fulfilled 28 1 the fluorophores are in close proximity lt 10 nm 2 the emission spectrum of the high energy fluorophore donor overlaps the absorption spectrum of the lower energy fluorophore acceptor Conventionally the used microscope consists of one laser for excitation pulsed or continuous operating mode of the donor and two photo diodes for a wavelength dependent detection of the donor and the acceptor emission respectively The energy transfer rate k between the excited states S1 p S1 4 can be expressed using kmp as the fluorescence rate constant of the donor in absence of the acceptor and r as the distance between the fluorophores according to 6 R fret ky 2 8 The distance of the fluorophores where the probability of energy transfer by a non radiative dipole dipole interaction from the donor to the acceptor is 50 is called the Forster radius Ro 6 K J A pK Ro K D 2 9 with x as the orientation factor K 2 3 for isotropic rotating systems p as the donor reading quantum yield in absence of the acceptor K as an constant K 8 8 107 mol n as the refractive index of the surrounding solution and J as the overlap integral of the donor emission spectra and
13. d in reference 23 Chapter 2 Single molecule spectroscopy fundamentals and beyond laser pulse gt gt photon m m TCSPC time ps start stop time 1 start stop time 2 time tag ns event 1 event 2 Figure 2 3 Principle of the time tagged time resolved TTTR data acquisition mode For every photon two times are stored a TCSPC time which counts the time between the last laser pulse and the detection of a photon with picosecond resolution and b the time tag of every photon on a continuous time trace with nanosecond resolution The fluorescence lifetime see chapter 2 1 of individual molecules can be calculated from the recorded TCSPC times and provides thereby a versatile tool for studying different photo physical phenomena local environment Strickler and Berg reported in 1962 that the fluorescence lifetime of a flu orophore is proportional to 1 n where n is the environmental refractive index 94 Thus the fluorescence lifetime can be used to probe the environmental conditions as for example described by Suhling and coworkers 96 They used the green fluorescent protein GFP as a probe in environments with different refractive indices adjusted by different concentrations of glycerol TRFCS The time resolved fluorescence correlation spectroscopy TRFCS can be used to sep arate the intensity of two fluorescent species as long as the fluorescent lifetimes of the species sufficiently differ 8 TRFCS is ex
14. er described in the next subsection Time resolved fluorescence correlation spectroscopy In 2002 Bohmer and coworkers introduced a new method for performing fluorescence corre lation spectroscopy by using the fluorescence lifetime to separate mixtures of different fluo rescent species 8 The method is called time resolved fluorescence correlation spectroscopy TRFCS In TCSPC see section 2 3 every photon is sorted into a channel according to its ar rival time after the laser pulse TCSPC time Let us assume a mixture of two species species A with a short fluorescence lifetime and species B with a sufficiently longer lifetime It is ob vious that photons which arrive shortly after the laser pulse are mainly emitted by species A whereas photons which arrive almost before the next pulse are mainly emitted by species B In fact every photon can be related to one of the species with a certain probability Generally the intensity J of each channel j can be written as B wit yA w pl 2 28 A B A B where w represents the overall number of photons and p the normalized probability of detecting photons within channel j of the respective species A and B If a mixture of two species in terms of Fluorescence Correlation Spectroscopy needs to be separated two filter sets f i A B have to be created in such a way that they fulfill L p K x fu pw 2 29 j l 16 2 5 Fluorescence correlation spectroscopy where L
15. flects the laser light to the overfilled objective overfilled the beam diameter of the laser is larger than the aperture of the objective which normally has a high numerical aperture and a high magnification to realize a small diffraction limited volume for the excitation of the fluorophores The objective itself is mounted to a piezo drive to change the position of the focal volume in the z direction To perform the scanning the whole sample holder can be moved by additional piezo drives in the x and or y direction Caused by the Stokes shift the excited fluorophores emit light with a higher wavelength which 2 3 Scanning confocal optical microscopy laser wm dichroic i mirror Figure 2 2 Schematic diagram of an advanced confocal microscope Two pulsed lasers with different emission wavelengths are used for interleaved excitation of the fluorophores The objective is used both for illumination of the focal volume and for detection out of the focal volume The avalanche photodiode is acting as a pin hole is collected by the objective and can now pass the second dichroic mirror Further on the wavelength range of the detected light can be either separated by a third dichroic mirror or tuned with different filter sets in order to get rid of remaining laser light or inelastic raman scattering Afterwards the light is focused by a lens onto the very small effective detection area of single photon counting modules avalanche ph
16. h repetition rate 82 Mhz for exciting the molecules The light was focused into a flow cell were the excitation of the Rhodamine 6G molecules occurred The fluorescence was collected by a microscope objective and then spatially filtered by a slit After passing an appropriate band pass filter the light was detected by a microchannel plate pho tomultiplier With this set up it was possible to reach sufficient signal to noise ratios even if the applied laser intensity was so high that the Rhodamine 6G molecules were photo bleached before traveling the whole way through the detection volume At the same time Rigler and Widengren published the detection of single Rhodamine 6G molecules using a confocal set up in a book chapter 81 The main advantage of the confocal set up was demonstrated in 1993 when Rigler and coworkers showed its superior performance in terms of the obtainable signal to noise ratio 80 One year later Eigen and Rigler expanded the range of applications by showing that the binding of a labeled DNA primer to a defined or undefined DNA sequence can be monitored by using fluorescence correlation spectroscopy 18 In 1996 Edman and coworkers showed that conformational transitions of single tetramethyl rhodaminemolecules linked to a DNA sequence can be resolved using single molecule time resolved detection 16 2 3 Scanning confocal optical microscopy Since the first description of a scanning confocal optical microscope SCOM
17. ion volume can be achieved with several methods it remains a challenge to combine reduced detection volumes with increased observation time 21
18. n which entered the volume the fluorescence signal was counted by a photomultiplier until a complete bleaching of the attached chromophores occurred In another publication Hirschfeld described the theoretical concept of time gated fluorescence detection using pulsed lasers which will be explained more in detail in section 2 3 and the pre bleaching of perturbing fluorescent compounds 44 Hirschfeld s con siderations can be summarized as follows 1 the excitation detection volume has to be as small as possible to discriminate the fluorescence from the molecule of interest from the background luminescence 2 SMD suffers from photo bleaching of fluorescent molecules 3 time gating may provide a tool for discrimination of different fluorescent species 4 quantum efficiencies and fluorescence lifetimes are important detection parameters 43 Interestingly already in 1976 Koppel and coworkers introduced a confocal detection scheme as it will be described in section 2 3 for studying the molecular and structural mobility of fluorescent probes without going to the single molecule level 55 It took almost 15 years until the detection of single fluorophores in solution was realized In 1990 Shera and coworkers successfully showed the detection of single Rhodamine 6G Chapter 2 Single molecule spectroscopy fundamentals and beyond molecules in solution 90 They used a mode locked frequency doubled Nd YAG laser with short pulses 70 ps and hig
19. of two structural domains In 1994 Xie and coworkers used two polarization directions 0 and 90 to show that dipole rotation is the origin of emission jumps in sulforhodamine 101 adsorbed on glass 110 A very accurate determination of the in plane dipole angle was demonstrated by Ha and coworkers in 1996 35 Single molecules were excited in the far field with linearly polarized light The polar ization angle y was continuously modulated in the millisecond range using an electro optical modulator Thus the detected emission signal can be plotted as a function of y Assuming that the emission signal Zem is a function of the absorption transition dipole T and the electrical 18 2 6 Orientation determination from 2 D to 3 D a Figure 2 6 a The orientation of a vector in spherical coordinates is fully determined by the polar angle 0 and the azimuthal angle b Polarization resolved techniques are using a projection of the transition dipole to determine the azimuthal angle Here a polarizing beamsplitter is used to divide the detectable light into its horizontal J 9 and vertical Ie 90 components field vector E according to lak lz E 2 34 the detected modulated intensity can be fitted using Tem locos Y Ipack 2 35 where Jo is the signal intensity and pack the background intensity Moreover this technique can resolve desorption and re adsorption of single molecules from and onto the coverslip bu
20. omain of brain myosin V with a time resolution of up to 20ms and without the need of any fitting procedure 25 Nearly at the same time Vacha and Kontani presented a set up combining a TIRF illumination scheme with epi fluorescence detection 101 They also achieved an orientation determination without ad ditional fitting procedures In 2004 Debarre and coworkers reported that so called out of plane molecules where the absorbing dipole coincides with the z axis can be detected more easily if amplitude and phase masking is applied to the input beam 12 In a theoretical work Fourkas predicted that comparing the fluorescent light intensities of three polarization directions would be sufficient to determine and 0 26 Even though a number of methods was proposed for a full three dimensional orientation de termination of the absorption emission dipole of single molecules yet no fast easy to use ap proach is available This problem will be addressed in chapter 5 2 7 Geometrical confinement of diffusion Single molecule detection of freely diffusing molecules suffers from two limitations First the transit time of the freely diffusing molecules through the confocal volume restricts the timescale of internal dynamics that can be explored It is obvious that the longer a single molecules stays within the confocal focus the more photons can be detected from that spe cific molecule Second in a typical single molecule experiment in solution the
21. or If the fluorophores are in close proximity for example folded protein the probability of the energy transfer is higher than in the case of a larger donor to acceptor distance unfolded protein the correction factor y as _ na a Np p However no pulsed laser set up is necessary if only intensities are analyzed 2 13 These considerations are summarized and visualized in figure 2 4 where a shows a simplified Jablonski diagram for FRET b the distance dependency of the energy transfer using equation 2 11 with Ro 4nm and c a doubly labeled protein whose potential conformational changes folded unfolded protein will change the observable energy transfer Schuler and coworkers demonstrated in 2002 that spFRET in solution can probe the energy surface of protein folding 87 86 In 2003 Rhoades and coworkers showed spFRET of immo bilized proteins 79 Newly developed single molecule techniques allow a time resolution on the nanosecond scale 71 For a recent review in the field of SMS protein folding unfolding see for example reference 66 Alternating Laser Excitation However spFRET using one laser for excitation as it has been described in the last section suffers from a number of drawbacks 51 First if a doubly labeled molecule donor and ac ceptor has an energy transfer efficiency close to unity high FRET this molecule can hardly be distinguished from a second molecule which is only labeled with an accep
22. oto diodes In this scheme the detectors are acting as pin holes and supress the light which is not originating from the focal plane of the microscope objective Time Correlated Single Photon Counting One of the major improvements in scanning confocal optical microscopy during the last decade was the availability of relatively cheap pulsed diode laser sources and fast hardware for detect ing the photons whose combination allows performing time correlated single photon counting TCSPC The TCSPC as it is used in this thesis works in the so called time tagged time resolved TTTR data acquisition mode which is sketched in figure 2 3 and described in more detail in reference 102 A pulsed laser with a sufficiently high repetition rate and a short pulse duration is used to excite a fluorescent molecule in the confocal volume The laser and the first timer are triggered by an external source providing the possibility to measure the TCSPC time between the arrival of a photon and the last laser pulse with a time resolution in the picosecond range The time resolution is given by the channel width of the hardware Additionally the time at which a photon is detected is recorded with a resolution on the nanosecond scale on a continuous time trace to obtain the information required for Fluorescence Correlation Spec troscopy see chapter 2 5 Even more sophisticated TCSPC techniques provide full correlation from a picosecond to second range as describe
23. oved by using pulsed interleaved lasers instead of a modulated continuous wave laser 69 Pulsed lasers with high repetition rates in the MHz range and pulse widths of around 0 5 ns allow to relate every detected photon to the last excita tion pulse as long as two requirements are fulfilled 1 the fluorescence lifetime is shorter than the time slice between two laser pulses and 2 the mean photon count rate is much smaller than 13 Chapter 2 Single molecule spectroscopy fundamentals and beyond S stoichiometry 0 E FRET efficiency 1 Figure 2 5 Schematic diagram of E S plot for one donor labeled two doubly labeled and one acceptor labeled species Without using the parameter S a distinction of two species with almost the same apparent energy transfer efficiency E would not be possible the repetition rate of the lasers The advantage of the last excitation scheme over that of ALEX is that one conserves the lifetime information of every detected photon 2 5 Fluorescence correlation spectroscopy In 1972 Magde and coworkers presented a new method to determine diffusion coefficients and particle concentrations from a detected fluctuating fluorescence signal 61 Two landmark publications followed in 1974 which described the concept more in detail 19 62 Fluorescence correlation spectroscopy FCS is based on the fluctuation l4 t of the de tectable time dependent fluorescence intensity J7 t around a mean value I4 e
24. plained in more detail in section 2 5 sp FRET If a donor molecule is closer than 10 nm to an acceptor molecule then the donor can transfer energy to the acceptor This process decreases the fluorescence lifetime of the donor and can thereby give a quantitative value for the energy transfer For further information see section 2 4 rotational mobility The rotational mobility of a fluorophore can be calculated from polariz ation resolved fluorescence decays 10 92 Thereby one can monitor the viscosity in the vicinity of the fluorophor or binding events which change the rotational mobility For further information see reference 56 For a more comprehensive review of the field see reference 95 It is obvious that TCSPC dramatically increases the number of accessible parameters to characterize single fluorophores and there nearby chemical physical and biological environment 2 4 Single pair fluorescence resonance energy transfer One of the most frequently used techniques in the area of single molecules is the single pair F rster resonance energy transfer or single pair fluorescence resonance energy transfer 10 2 4 Single pair fluorescence resonance energy transfer spFRET which allows the study of conformational changes of proteins with high accuracy and a resolution in the nanometer range 66 89 104 105 Here emphasized by the term single pair we are mainly interested in the detection of only one single mole
25. represents the absorption cross section of the molecule J the applied laser intensity and fiw the photon energy A molecule in the S state can undergo different relaxation processes e the singlet state S can relax to Sy by emitting a photon at a radiative rate constant k10 e S can relax to So by internal conversion with a non radiative rate constant kic e the molecule can bleach with a rate constant kp Chapter 2 Single molecule spectroscopy fundamentals and beyond S kyy AN T S ma Figure 2 1 Simplified Jablonski diagram showing the transition pathways for a fluorescent molecule The three level system consists of a ground state So an excited singlet state S and a triplet state 71 The rate constants k are explained in the text e S can undergo a spin forbidden intersystem crossing to the first triplet state T with non radiative rate constant kisec An occupied triplet state T can relax to S with the rate constant kr In most cases this process is non radiative for single fluorescent molecules Taking these relations into account one can formulate a system of differential equations which describes the occupancy of the different states as a function of time If the probability of occupancy for the i th state is given by p then the rate equation system reads d gee kexcPSo k10Ps KicPs kr Pr d qP kexePso Kiops KicPs KiscPs korps 2 1 d gP KiscPs
26. s the behavior of the auto correlation function Even if the mean diffusion time Tp remains unchanged the amplitude of the auto correlation function is getting smaller with increasing background luminescence As mentioned above the amplitude is inversely proportional to the number of apparent molecules 17 Chapter 2 Single molecule spectroscopy fundamentals and beyond within the focus Based on the work of Koppel in 1974 54 the following equation was derived by Milon and coworkers 67 in order to relate the calculated apparent number of molecules N to the real number of molecules N and the apparent number of molecules Nnoise given by the uncorrelated background according to N T Nnoise N NI 2 32 with background count rate per second IBe Nnoise N 2 33 count rate per molecule per second z I pg where Jgg is the estimated mean background intensity and the measured mean intensity If the presence of uncorrelated background cannot be completely neglected the real number of molecules N in the focus is always smaller than the calculated one without background correction 2 6 Orientation determination from 2 D to 3 D Beside using single molecules for spFRET as described in section 2 4 another unique feature of single molecules is their absorption and emission anisotropy due to the well defined tran sition dipole s for both processes allowing the determination of the molec
27. t suffers from the high number of photons which have to be detected in order to achieve suf ficient accuracy A more detailed description of the method can be found in reference 36 In 1997 Sase and coworkers resolved the axial rotation of sliding actin filaments by exciting the fluorophores with circularly light and separating the emitted fluorescence with a polarizing beamsplitter 83 Three dimensional orientation determination As mentioned above the determination of the full three dimensional orientation of single mole cules is much more sophisticated In the following several methods will be discussed which have been proposed in the literature Betzig and Chichester showed in 1993 that a near field scanning optical microscope can be used to determine the accurate position and the three dimensional orientation of single fluorophores 5 Unexpectedly the imaged molecules did not appear as identical peaks with comparable width but rather as a distribution of ellipsoidal and symmetric peaks or rings and arcs These patterns can be calculated for various orientations taking into account the interaction of the electric dipole of the molecule with the incident electromagnetic field from the aperture In 1999 Bartko and coworkers published a detection sheme using a confocal microscope operat ing in a total internal reflection mode between the sample air interface with CCD wide field 19 Chapter 2 Single molecule spectroscopy fundamentals
28. tion channels was recorded Integrating over a certain amount of alternation cycles led to four binned intensity traces a I ie intensity in the donor detection channel after excitation of the donor b pn intensity in the acceptor detection channel after excitation of the donor c ie intensity in the acceptor detection channel after excitation of the acceptor and d Tee intensity in the donor detection channel after excitation of the acceptor The calculation of the energy transfer efficiency E remains similar to equation 2 12 em D E 2e 2 14 pe ype exc exc with y as the correction factor mentioned previously However a new parameter S can be formulated which represents a donor acceptor D A stoichiometry according to Aem Dem S E Ipe Wp 2 1 5 g Aem Dem Dem Aem A Ioa t Ypes Hase HTa It can be shown that S is independent of E supporting material in reference 51 If a molecule is only donor labeled then S 1 because of D e x 0 and if a molecule is acceptor labeled only then S 0 because of lieve 1 El 0 Additionally as long as i a Then x ie EUA the stoichiometry of doubly labeled molecules is close to Sx0 5 whereas E remains dependent on the donor to acceptor distance Figure 2 5 shows a schematic diagram of an E vs S plot separating four different species using the stoichiometry parameter S and the energy transfer efficiency parameter E This excitation scheme can be further impr
29. tor The first 12 2 4 Single pair fluorescence resonance energy transfer one will show high intensities in the red detection channel and low intensities in the green one whereas for the second molecule there is a certain probability to excite the acceptor with the green laser this effect is known as crosstalk Therefore the second molecule will show a similar intensity behavior like the first one Second if a doubly labeled molecule has an energy transfer efficiency close to zero there might be no sufficient difference in the intensity traces to a molecule only labeled with a donor Third there is no possibility to quantitatively analyze the molecular interactions If there is an interaction in the form of Ma Lp M Lp where Mg represents an acceptor labeled macromolecule and Lp a donor labeled ligand the different species can not be resolved To overcome these drawbacks Kapanidis Lee and coworkers suggested in 2004 a new excita tion scheme called ALEX alternating laser excitation based on the use of two lasers instead of one 51 Each of the two lasers operating in the continuous wave mode was modulated by an electro optical modulator in association with a polarizer in such a way that an alternated excitation by either red or green laser light was achieved in order to excite the acceptor and the donor directly The alternation period Taz was in the us to ms range and during each excita tion cycle the number of photons in both detec
30. trinsic behavior of single molecules and the interactions between the molecule and its chemical and physical environment For applications see section 2 3 2 2 Single molecule detection in solution The main motivation of detecting single molecules is to circumvent the averaging effect of ensemble measurements For example if the overall fluorescence intensity from a sample con taining ten fluorescent particles is detected the potential presence of two different species with different brightness cannot be resolved The following section outlines the progress in the field of single molecule detection SMD starting from the first experiments which raised up a lot of requirements and notes for forthcoming single molecule experiments These considerations gave the starting signal for a very fast development in the field of SMD 104 The first detection of a multiply labeled single molecule was reported by Hirschfeld in 1976 42 He used proteins labeled with 80 100 chromophores which were excited by an Argon laser operating at a wavelength of 488 nm using a total internal reflection scheme In such a scheme the angle of the incident laser light is sufficiently large to reflect the laser light totally at the interface between cover glass and sample volume Only the evanescent field can enter the sample volume Therefore the small penetration depth of the evanescent field provided a exci tation detection volume of about 24 fl For each labeled protei
31. ule s orientation As shown in figure 2 6 a the orientation of a vector in spherical coordinates is fully deter mined by the polar angle and the azimuthal angle Whereas the determination of 0 is quite sophisticated the determination of is more straightforward Figure 2 6 b shows that by using a polarizing beamsplitter in front of two detectors the detectable light can be divided into its horizontal and vertical components However it has to be emphasized that the simple relation tang Ie o Ie 90 does not hold for using microscope objectives with high numerical aperture Historically the first polarization resolved techniques performed at single molecules were based on a different concept for orientation determination in steady state fluorescence polarization microscopy see reference 1 Instead of detecting polarization resolved inten sities the polarization of the laser light was modulated before exciting the single molecules Note that corresponds to the azimuthal angle of the emission transition dipole which does not coincide with the azimuthal angle of the absorption transition dipole in any case 36 In 1993 Giittler and coworkers published a method where the polarization of the laser light was changed with a 2 retardation plate 34 The polarized light was used to excite single pentacene molecules in a p terphenyl matrix The measured intensity is a function of the az imuthal angle and was used to show the existence
32. ven under equi librium conditions reading a t la 6la t 2 16 In the simplest case the fluctuation of the fluorescence signal is caused by the Brownian motion of a few fluorescent molecules in a sufficiently small detection volume It was shown by Rigler and coworkers that the convolution of the collimated laser beam and the collection efficiency function can be approximated by a three dimensional Gaussian with half axis wo and zo 80 2 2 2 1 x y z inex 2 a 5 2 17 Wo Zo which acts as the excitation detection focus Let us further assume that at the time t 0 a single fluorescent molecule is placed in the center of the focus Now if the following time in crement 7 is short enough so that the mean free pathway of the molecule is much smaller than the size of the focus there is a certain probability that the molecule remains within the focus at the measurement time t t T1 With this consideration it is obvious that the intensities detected in consecutive measurement intervals are related to each other Generally in FCS the 14 2 5 Fluorescence correlation spectroscopy fluctuating intensity is analyzed in terms of the intensity auto correlation function ACF Olg t dlg t t Ia A detailed derivation of the ACF can be found in the above mentioned references or in refer ences 46 112 The ACF for the one dimensional case of pure diffusion along the z axis reads 2 18 1
33. y starting a new chain of ionizations This will cause a new pulse at the detector output now generated by a virtual photon Due to the fact that FCS is sensitive for temporally related events afterpulsing causes decays in the auto correlation curve which often coincide with the decay of triplet states In contrast to the prior use of TRFCS where the fluorescence decay behavior of the two single species has to be known this problem is easier to solve Let us assume analogous to equation 2 28 that the measured intensity per channel is a superposition of two fractions namely the real data fraction A and the afterpulsing fraction B The probability for afterpulsing follows an exponential decay with a time constant large compared to the time between two laser pulses For this reason the probability pattern for B reads Mg j pa where L represents the total number of TCSPC channels For the 4 j normalization it follows that M4 po 1 I Min I The calculation of the filter sets is straightforward using equation 2 30 and taking I i x Ij calculation of p the minimum value of 7 is substracted from every measured 7 After the Influence of uncorrelated background If the diffusion of single molecules is confined to host materials this may cause additional uncorrelated background luminescence Either caused by the material itself or by adsorption of probe molecules onto the host material the background influence
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