Single Molecule Spectroscopy with Confocal Microscopy

P.D. Zoon
Universiteit van Amsterdam

Contents

1  Introduction into SMD and SMS
    1.1  Basic Principles of Single Molecule Spectroscopy
    1.2  Single Molecule Spectroscopy at Low Temperatures
    1.3  Room Temperature Single Molecule Spectroscopy
    1.4  Single Quantum System
2  Typical Sample Preparation
3  Confocal Microscopy
    3.1  Introduction into Confocal Microscopy
    3.2  Detailed Description Confocal Setup
        3.2.1  Dichroic mirror
        3.2.2  Microscope Objective
        3.2.3  Pinhole
        3.2.4  Scanning Stage
        3.2.5  Detectors
4  Two Photon Excitation
5  Examples
    5.1  Dendritic Multi Chromophoric System
    5.2  Green Fluorescent Protein (GFP)
    5.3  Vesicles
    5.4  Fluorescence Resonance Energy Transfer (FRET) as a sensor for Ca2+

1  Introduction into SMD and SMS

One of the greatest challenges for chemists and biologists was the imaging of a single-molecule. Ever since the discovery of the microscope by van Leeuwenhoek around 1680, biologists have used this instrument to take a look at cells. Quite soon technical improvements showed that there is a certain limit to which an object can be magnified. The resolution of a light microscope is given by the radius of the Airy disc:


dx =  0.61◊l
NA
(1)

with l the wavelenght of the light and NA the numerical aperture of the optical element. Under the best conditions, with violet light at a wavelenght of 400 nm and a numerical aperture of 1.4, a resolution of just below 200 nm can be obtained. This is small enough to look at whole cells and large organelles like the nucleus or the mitochondria. It does not come close to study things at a molecular level. So when we talk about single molecule spectroscopy or detection, the molecule itself is too small to be observed directly. It is actually the photons which are absorbed and emitted, from a single molecule, which are detected. When talking about single molecule detection (SMD) and single molecule spectroscopy (SMS), the question arises: Why look at single molecules?

When looking at a single molecule level, information can be obtained that otherwise would disappear in the ensemble average. Statistical information of how a band in a (many-molecule) spectrum is made up can be gained now. This can be illustrated by the following example: a patient is taking a drug on day one, it is working for 100%, but one week later the drug is only working for 50%. Is the reason for this that only 50% of the molecules is active fully and 50% is completely inactive or is 100% of the molecules active but only with an activeness of 50% ? Maybe even more complicated statistical distributions are in order to solve this problem. It is not possible to answer this question when one looks at many-molecule spectra because there is always be ensemble averaging, but when one looks at a lot of different single molecules (one at a time) the many-molecule spectrum can be reconstructed from the single molecule occurrence-histograms (see figure 1 ).

reconstruct.jpg

Figure 1: Single molecule occurrences provide extra information about distribution statistics and can be reconstructed to give the many-molecule emission band.

So single-molecule detection gives extra statistical information and allows the exploration of "hidden" heterogeneity in complex materials (like polymer films and glasses) as well as direct observation of dynamical state changes arising from photophysics and photochemistry. For instance when examining green fluorescent protein (GFP) at a single-molecule level it was found that GFP shows a remarkable blinking of fluorescence (see below). From a spectroscopical point of view the challenge is also great: it is spectroscopy at it's ultimate sensitivity. To see 1.66 10-26 moles of molecules (1.66 yoctomole), in other words the inverse of Avogadro’s number.

A single molecule can be used as a reporter of its local nano-environment, that is, of exact constellation of functional groups, atoms, ions, electrostatic charge and/or other influences in its immediate vicinity. Thus, SMS might also give insight into preferentially solvation with polymer matrices.

Ideally a molecule used in SMS has a high quantum yield and a high photostability, so that almost every absorbed photon will give an emission photon and that the molecule can go trough as many cycles as possible before an irreversible photo-product is formed (photo-bleaching). Another interesting feature of SMS, is the use of single molecules as source for single photons. Single photon sources are very much in need since the use of quantum cryptography. In quantum cryptography a single photon is given a certain polarization direction, when the polarization of the photon is not known it is impossible the retrieve without altering the polarization.

In this report we will discuss (shortly) how SMS was done historically, how it is usually done today and what kind of different techniques there are. Subsequently we will focus on the confocal microscope setup and we will conclude with some examples of SMS done with confocal microscopy.

1.1  Basic Principles of Single Molecule Spectroscopy

To put it simple, to achieve SMS at any temperature, one must (a) guarantee that only one molecule is in resonance in the volume probed by the laser, (b) provide that the signal-to noise ratio (SNR) for the single-molecule signal is greater than the background for reasonable averaging time. Guaranteeing that only one molecule is present in the detection volume is generally achieved by dilution. For example, at room temperature one needs to work with roughly 10-10 mole/liter concentration with a probed volume of about 10mm3. Achieving the required SNR is be done by several methods:

To obtain a large a signal as possible, one needs a combination of small focal volume, large absorption cross-section, high photo-stability, weak bottle necks into dark states such as triplet states, operation below saturation of the molecular absorption and a high fluorescence quantum yield if fluorescence is detected. For absorption methods, achieving a low noise level from background effects follows careful reduction of residual signals and operation at a power level sufficient to reduce the relative contribution from laser shot noise. For fluorescence methods, one has to rigoursly exclude fluorescent impurities, minimize the volume probed to avoid Raman scattering and reject any scattered radiation at the pumping wavelenght.

1.2  Single Molecule Spectroscopy at Low Temperatures

The first reports on single molecule detection were done in polymer matrices at very low temperatures (1.5 K). The reports about this experiments are very physical in nature and focus a lot of attention on zero-phonon transitions and line widths. These early experiments show that the detection of single molecules is possible and that there is a lot of new information to gain from single molecule experiments. High resolution spectroscopy of single molecules in solid matrices at low temperatures yielded a variety of new observations: direct observation of spectral diffusion (spectral shifting) of a single molecule due to spontaneous changes of the surrounding environment, light induced spectral shift, Markovian dynamics and photon anti-bunching [1,2]. One of the first systems studied was pentacene on p-terphenyl, this system has weak enough hole burning so that it could be used as a model system for single-molecule spectroscopy. In these early experiments for this system a lifetime-limited homogeneous line width of 7.8 ± 0.2 MHz was observed [3]. This line width is the minimum value allowed by the lifetime of the S1 excited state of 24ns, which is in good comparison with photon-echo measurements on ensembles. Such narrow single molecule lines are wonderful for the spectroscopist: many detailed studies of the local environment can be performed, because these narrow lines are much more sensitive to perturbations than broad ones. Spectral shifts of single-molecule line shapes are common in many systems. They are not restricted to certain crystalline hosts, but appear also in almost all polymers [4].

1.3  Room Temperature Single Molecule Spectroscopy

The requirements of severe background reduction, high detection efficiency and spatially selective imaging necessary for single molecules detection are achieved by several ways of microscopy as shown in figure 2.

types.jpgFigure 2: Four experimental approaches to detect single molecules: a) near-field microscopy, b) confocal microscopy, c) wide-field microscopy and d) total internal reflection (dark-field) microscopy . From [5].

Near-field microscopy (figure 2a) has the smallest illumination volume (approx. 105 nm3). This is facilitated by subwavelength illumination through a small aperture optical-fibre probe. A superior lateral optical response of 70 nm on a single molecule can be obtained, which results in accuracy down to a few nm. The small excitation volume also allows independent observation of more closely packed molecules on a surface. As result of the evanescent characteristic of the near-field excitation, only molecules within the first few tenths of nanometers away from the surface are efficiently excited, which can be useful for the detection of individual molecules on te surface of cell membranes. Due to technological obstacles, fabrication and the need of a metallic probe near the molecule, the focus is now shifted towards the more flexible, far-field methods, such as confocal and wide-field microscopy. The detection volume of a confocal microscope is in the order of 108 nm3,so the minimal distance between molecules should be at least 0.5 mm. Because of the larger detection volume also more background noise is gathered, so further background reduction is necessary. Confocal excitation has a less complicated setup and more practical freedom to use sample chambers for liquid immersion or pressure control. In both figure 2a and b the detector is confocally aligned with the excitation volume. For imaging the sample must be scanned through the excitation volume, which should contain maximum one molecule at the time. This is an important difference between bright-field (figure 2c) and dark-field (figure 2d), in which a large part of the sample is illuminated and several molecules are excited at the same time. Again the excitation volume is larger so the background is even larger for the bright-field method. This can be circumvented in dark-field microscopy, where the axial depth of excitation volume is strongly reduced by making use of the evanescence field formed at a refractive index interface in a total internal reflection geometry (figure 2d). Dark- and bright-field approaches are particularly suited to investigate the behavior of several molecules at the same time, but have the drawback of a lower time resolution as compared to confocal or near-field methods.

For experiments hoping to find useful biological information, it is important to have an aqueous environment. In water a molecule can move a mean squared distance of ~ 300 mm2 in one second due to Brownian motion. This clearly poses a problem if one wants to observe only one molecule. The target molecule will move ut of the focal spot due to the Brownian motion. The best way to overcome this problem is to fixate, or anchor, the desired molecule.

In 1996, partial immobilization of molecules was achieved using water filled pores of poly(acrylamide) gels, this technique has been demonstrated for for organic dye molecules [6] as well as for green fluorescent protein [7]. Poly(acrylamide)gels are widely used for separation techniques, are not only suitable as an immobilizing matrix. They can also be studied themselves by using the diffusion of of the embedded dye molecules as a probe for the local gel environment. Excitation and detection of single nile red molecules in poly(acrylamide) gels by total internal reflection (TIR) microscopy allowed the measurement of the three dimensional motion pathways for the first time [6]. Another problem is that at room temperature the absorption cross-section of typical dyes is orders of magnitude smaller than at cryogenic temperatures, 10-16 vs 10-10 cm-2 respectively. So the ability to absorb a photon greatly reduces at room temperature. Finally at room temperature also the photo-bleaching increases, at room temperature photobleaching occurs after absorbing roughly 106-107 photons, limiting the observation time of a single molecule to a few seconds.

1.4  Single Quantum System

At the single molecule level a single molecule can be seen as a single quantum system as has been shown be various people [4,8]. This also means that some particular effects can be observed which are specifically linked to a single quantum system. Not all of these effects are as commonly observed as others: spectral diffusion, photon-bunching en anti-bunching, (dynamic) stark shifts, markovian dynamics. For all experiments photon bunching and anti-bunching is observed so a brief explanation will be given here.

In figure 3 a schematic representation of photon bunching and anti-bunching can be seen. For a simple three level system containing S0, S1 and T1 the system can emit photons by going from S0->S1->S0 until intersystem crossing occurs. So a certain amount of photons is emitted in a bunch before a dark period, with an average length equal to the triplet lifetime, occurs. Within one bunch the emitted photons from a single quantum system are expected to anti-bunch, which means that the photons space themselves out in time. Or in other words the probability for two photons to arrive at the detector at them same time is zero. For a single molecule, anti-bunching is easy to understand as follows. After emission of a photon, the molecule has returned to the groundstate and cannot emit a second photon immediately. A time on the order of of the inverse of the Rabi frequency1 must elapse before the probability of emission of a second photon is appreciable. This corresponds more or less with one fluorescence lifetime [9].

bunching.jpg

Figure 3: Schematic representation of the temporal behavior of photon emission form a single molecule showing (a) photon bunching on the scale of the triplet lifetime and (b) anti-bunching on the scale of the inverse of the Rabi frequency. From [4]

2  Typical Sample Preparation

Samples for single molecule measurements are typically prepared according to a recipe similar to this one:

The samples are prepared by spincoating solutions of the target molecule in chloroform (5 ◊10-10M) containing 3mg/ml polyvinylbutyral (PVB, or another polymer) on a cover glass at 4000 rpm to yield thin polymer films (20-40nm thick) containing on average 0.2 molecules per mm-2. The sample preparation includes careful cleaning of the glassware used for the sample preparation as well as subsequent cleaning of the cover glasses by sonification in acetone, sodium hydroxide (10%) solution, MilliQ water and spectrophotometric grade ethanol [10].

3  Confocal Microscopy

In 1957 Marvin Minsky 'discovered' the confocal principle. The invention of Minsky remained largely unnoticed, probably due to the absence of strong light sources and computers to handle the large amounts of data. After the patent had expired the confocal microscope was reinvented at two different places, at the same time. In Oxford, Sheppard developed a theory of light of image formation of what he called a Type 2, scanning microscope. At the same time the dutch physicist Brakenhoff applied this principle in 1979 in a light microscope and he built the first practical confocal microscope. The idea was to develop a better version of the light microscope, which would also be able to do three-dimensional imaging (of biological specimen). This first lead to the use of electron microscopy, but in electron microscopy the samples have to be sliced and dehydrated. So the three-dimensional information gets (partly) lost. Confocal microscopy turned out to be a good complementary form. After the actual imaging of the three-dimensional chromatin distribution in the neuroblastoma nuclei by Brakenhoff et al [11], confocal microscopy was generally accepted as a technique in biological research.

3.1  Introduction into Confocal Microscopy

In figure 4 the setup of a schematic representation of a (simple) confocal microscope can bee seen.
setup.jpg

Figure 4: Schematic representation of a (simple) confocal microscope setup. From http://www.microscopyu.com

Confocal (fluorescence) microscopy is a microscopic technique that provides true three dimensional imaging and resolution. The 3D resolution is attained by designing a microscope in such a way that all the light which is not coming from an in-focus plane is being blocked or removed afterwards. The way to achieve this is by putting a pinhole in front of the detector (see figure4). In this way all the light originating from an in-focus plane will pass freely through the pinhole, whereas light coming from a out-of focus plane will largely be blocked by the pinhole. The light coming from the laser passes an (excitation) pinhole and is reflected by a dichroic mirror and focused by a microscope objective to a small spot on the sample. A dichroic mirror has the property that it reflects one wavelenght while transmitting others (a more detailed description of the different elements in the confocal setup will be discussed in the next section). Specific dichroic mirrors can be made for the relevant wavelenght regions of excitation and emission. When the sample is excited, it will start to emit light in a random direction. A fraction of the emitted photons is collected by the microscope objective and imaged onto the detector. By putting a pinhole in front of the detector blurring form out-of focus planes is greatly reduced. The position of this pinhole is such that it is in a conjugate plane with both the plane of focus of the microscope objective and the point of the excitation of the laser, which is defined by the excitation pinhole. The effect of blocking out the ou-ofg focus contributions is also known as optical sectioning. It permits the imaging of separate (axial) slices within the specimen. The size of the pinhole, of course, determines how much background reduction can be realized. Considerations concerning to the size of the pinhole will be discussed in the next section. For a specific setting of the microscope only a single point in the sample is imaged at one time. In other words, confocal microscopy is serial technique rather than a parallel one. To obtain a single optical section some kind of scanning is required. There are two different ways in which this can be done: sample scanning and laser scanning. With sample scanning the beam is kept stationary and the sample is moved, while in laser scanning the sample is kept fixed and the laser beam is moved. Nowadays laser scanning is the preferred way of scanning, because a lot of biological samples are used. Cells are very flexible objects so when they move a lot of blurring will occur. Laser scanning is usually denoted as CSLM: Confocal Scanning Laser Microscopy.

3.2  Detailed Description Confocal Setup

In the next section a more detailed description of some of the elements used in a confocal setup will be discussed. For a in-detail description of a time resolved confocal setup with a high sensitivity look at reference readers are pointed at [12]. Generally an inverted microscope is used in confocal microscopy, which mean that the objective is under the sample insted of above. Usually the sample illumination and the collection of the emitted photons occurs both through the same objective.

3.2.1  Dichroic mirror

A dichroic mirror is a mirror which reflects one wavelenght and transmits another wavelenght. It helps filtering out residual excitation light and facilitates the collection and excitation through the same objective. The mirror usually has a fixed angle in which it has to be placed gain the optimal reflective and transmissive properties. When working with polarized light the properties of the mirror have to be checked in respect with the polarization direction of the light (p, s). Usually the manufacturer will give these properties or the mirror is specially coated so that the difference between polarization directions will negligible.

3.2.2  Microscope Objective

The most important part of the microscope is the objective. This is responsible for the magnification of the substrate and the focusing of the laser beam. The numerical aperture is a measure for the optical resolution and the light sensitivity of the lens and is defined as follows:
NA = n sinq
(2)
In which NA is the numerical aperture, n the refractive index of the medium between lens and sample and q half the angle subtended by the lens at its focus. The concept of numerical aperture is closely related to that of the focal-ratio or f-number. In a simple lens the f-number is the ratio between the lens' focal length and the its clear aperture ∆ (effective diameter). f-number = f/¯. The relation between f-number and NA is :
NA = sinq = ¯/2f.
(3)

As mentioned before the objective is used for both illumination and light collection of the sample, the quality of the confocal setup is generally determined by the quality of the objective (see figure 4). There can be several types optical aberrations caused by a lens: spherical aberration, coma, field curvature distortion, longitudinal and lateral chromatic aberration and chromatic magnification difference. Not all of these aberrations can easily be overcome and a complete explanation can be found elsewhere [13,14]. The objectives are divided in several categories with respect to their optical aberration correction namely: achromat, apochromat, fluorite, planachromat and planapochromat.

Achromatic lenses are only corrected in the green/yellow part of the spectrum. This type of lens is relatively inexpensive. It shows red and blue colorations at the edge of the spot and loses sharpness and shows blurring when going form the center towards the edge of the spot.

Apochromatic lenses are chromatically corrected for three wavelengths and match Abbe's sine condition2 for two wavelenghts and do not show the the colorations loss of sharpness and blurring at the edge of the spot. They usually have a higher NA (compared with achromat) and a slightly smaller working distance (working distance is defined as the free working range of the objective before its lowest structural element means contact with either the object or the coverglass)

Fluorite lenses are in between achromatic and apochromatic with respect to aberration correction, but have less lenses and therefore have a slightly higher contrast, which makes ideal for use in fluorescence microscopy.

Planachromat lenses are the corrected in the same way as achromat lenses but have an additional flat field correction.

Planapochromat are corrected in the same way as apochromat lenses but also contain additional flat field correction, which makes them the ideal objective to be used in single molecule detection. There are also some specialistic objectives like Zeiss' ultrafluor, which has chromatic correction from the UV up to he visible region of the spectrum, and Nikon's CF (color-free), which has plana(po)chromatic correction and produce intermediate images without chromatic magnification differences over the image field. Another important thing to keep in mind is that the focal length is related to the pinhole size; a long focal length allows one to use a larger pinhole, which makes the outlining of the setup a lot easier.

3.2.3  Pinhole

The pinhole is an important component which has impact on both the axial and the lateral resolution of the microscope. The pinhole is a very small hole, usually with a diameter 10 to100 mm, that in single molecule detection mainly serves to minimize the detection volume to increases the SNR. A smaller pinhole results in a smaller detection volume, and thus in a lower background, but also transmits fewer signals to the detector. In practice the pinhole should have approximately the same diameter as the FWHM (full width at half maximum) of the Airy diffraction pattern generated by the lens at the pinhole's position (intermediate image plane). For example, assuming a diffraction limited focusing and magnification of 100 then the pinhole diameter should be about 50 to 100 mm. This results in a detection volume of 1 femtoliter. Precision pinholes are offered in a wide range of different sizes and different materials. They are made by laser drilling of stainless steel org gold-coated copper substrates. Complete sets of pinholes are offered by different manufacturers. In these sets, each pinhole is individually mounted and marked with its diameter. To reduce light reflection black pinholes are also available. To allow comfortable positioning with micrometer resolution, the pinhole should be mounted on a precision xy-stage. To obtain the best long term stability it is better to fix the stage to the body of the microscope.

3.2.4  Scanning Stage

As discussed before, to obtain a complete two-dimensional image of the sample, either the sample or the beam have to be scanned. Sample scanning is from a practical point of view not so good (slow scan speed, wobbling of liquid samples) so here the focus will be on the beam scanning equipment. Because the scan is demagnified by the objective lens, the mechanic tolerance of beam scanning systems are less critical than those for sample scanning. Usually feedback-stabilized vibrating mirrors which can scan at a frequency of up to 1 kHz per scan line. They can achieve scan rates of 0.1 to 30 Hz per image. In an epi-illumination system, the collected light is descanned by passing the same scan mirrors as the excitation light before being focused on the fixed detector. As in conventional microscopy, the image size of a beam scanning a confocal microscope is limited to the field of view of the objective lens used. All single beam CLSM's suffer from the limitations inherent to serial data collection; namely the necessity to compromise between the rate of image acquisition, spatial resolution of the raster scan and the signal-to-noise ratio. So the usefulness of a fast beam scanning system is controversial, since at low fluorescence levels, data acquisition may become limited by the achievable photon emission rates per pixel. For a high resolution confocal microscope the lateral scan resolution is about 50 to 100 nm and the axial scan resolution 200 to 400nm. Thus a 2D image of 25◊25 mm 2 with a 50 nm scan step size will already contain 500◊500 pixels. Generally 105 to 106 photons will be emitted per second by a single molecule and, with a desired peak number of 100 photons per pixel for the center position of the molecule, a scan rate of 100 ms has to met. The detected photons are usually registered and stored as time-tagged (TT) or time tagged time resolved data(TTTR). An intensity and/or lifetime image is subsequently calculated from these stored photon data after the scan. This means that there has to be a perfect synchronization between scan motion and time tagging of the detected photons. This rather difficult to realize on a software basis, so therefore direct hardware based synchronization between scanning and data acquisition is recommended, as implemented for the PI P-527 series from PicoQuant, berlin. The scanner driver is used directly from the TCSPC (time correlated single photon counting) board. it uses the time-tag clock to drive a scan-stage/mirror scanner, making sure that there is a perfect synchronization with the TTTR photon data acquisition. The initial scanner settings and scan range as well as the time per pixel are downloaded via a serial protocol. For a block diagram of the driver hardware see [15].

3.2.5  Detectors

There are a lot of different detectors used for collecting the emitted photons all which have their own specific advantages and disadvantages. A short description will be given here with regard for the use in single molecule measurements, where one has the need for high detection/quantum efficiency and low noise generation. Mainly three types of detectors are used commonly: Photo Multiplier Tube (PMT), Charged Coupled Device (CCD) and Avalanche Photo Diode (APD).

Table 1: Specifications different photo-detectors commonly used or single molecule spectroscopy. Photo Multiplier Tube (PMT), Avalanche Photo Diode (APD), Charge Coupled Device (CCD).
PMT APD CCD
Range 200-800 nmf 200-900 nm 200-900 nm*
Quantum Yield:
Blue 30% 45% 40%
Green-yellow 30% 60-70% 85%
Red 20% 80% 70%
when operated at -20 ∞C
*back illuminated with unichrome 200-350; backilluminated with VIS/AR 350-900 nm

A schematic representation of a PMT and APD are shown in figure 5.

detectors.jpg

Figure 5: Schematic representation of the make up of a avalanche diode (left) and a photomultiplier tube (right). For the working of the detector see the text. From http://micro.magnet.fsu.edu

A photodiode works as follows. A photon hits the SiO2 and an electron-hole pair is released, if the light energy is higher than the band gap energy. At room temperature this is 1.12 eV for SiO2 at room temperature so it is sensitive for wavelenghts shorter than 1100nm. This sensitivity is commonly expressed in terms of photosensitivity S (A/W) and quantum efficiency QE (%). The photosensitivity is the photo-current divided by the incident radiant power, expressed in A/W. The quantum efficiency is he ratio of the electron-hole pairs generated versus the number of the incident photons. The two terms give the following relation for the quantum efficiency of a photodiode:

QE =  S ◊1240
l
◊100(%)
(4)

With l, the wavelenght in nm and S, the photosensitivity in A/W. When electron-hole pairs are generated in the depletion region of a photodiode with a reverse voltage applied to the PN junction, the electrons drift towards the anode while the holes drift towards the cathode, due to the electric field developed across the PN junction. The drift speed of these electron-hole pairs or carriers depends on the electric field strength. However when the electric field is raised to a certain point the carriers are more likely to collide with the crystal lattice, so that their drift speed becomes saturated in at an average speed. This starts to occur when the electric field is in the order of magnitude of about 104 V/cm, and the saturated drift speed at this point is about 107 cm/s. If the the reverse voltages is increased even more some of the carriers which have escaped the collision with the crystal lattice will have a large energy. When these carriers collide with the crystal lattice, ionization in which new electron-pairs are generated takes place. These electron pairs then create additional electron-hole pairs just like a chain reaction. This phenomenon is referred to as avalanche multiplication of the photo-current. As more and more electrons are accelerated in this avalanche process, a space charge will be built up and the effective accelerating potential will be reduced. At some point the electrons lose more energy to friction than they gain by (electric) acceleration and therefore do not reach energies high enough for ionization. Generally there are two types of APD's: deep diffusion type and reach-through structure. Because in the deep-diffusion type the n-layer is much deeper than the p-layer, electrons produced in the n-layer multiply more readily than holes. This in turn leads to reduced dark current, which is mostly generated by holes. The disadvantage is that only light absorbed in the p-layer leads to effective multiplication, so that is the region with the lowest field. As a result the response time is in the order of 10-30 ns. Some photons can be absorbed in the wide n-layer and are therefore multiplied less than maximal, so there is a fairly large contribution of random shot noise due to different levels of multiplication. In APD's with a Reach-through structure, there is a very narrow junction and multiplication takes place at the back end of the device. Most of the thickness of this device consists of low doped silicon or germanium, in which the field strength is quite low. In this system the photons that have been absorbed only take picoseconds to reach the acceleration junction. Since almost no photons are absorbed in the multiplication area, variations in gain are nearly eliminated. All electrons, once the 'reached through' to the p-n junction, undergo the same acceleration and therefore the same multiplication. This device offers high-speed response and low noise, it is also more expensive. The dark current of a photodiode is is depend on the reverse bias voltage amd will grow larger with increasing bias voltage. Noise in a photodiode can take two forms. First is the shot noise of the dark current, which results form the statistical uncertainty in the arrival rate of the photons. Thus shot noise is present in all signals and is given by:

Idark =
÷
 
2qidarkB
 
(5)
Where Idark is rms noise current, q is the electron charge, idark is the dark signal current and B is the frequency bandwidth of the detector-amplifier combination. The second form is the thermal noise of the shunt resistance, also known as Johnson noise. It is given by:
IRsh =   ÷
 4kTB
Rsh
 
(6)
Where IRsh is rms noise current resulting from Johnson noise, k is the boltzmann constant, T the absolute temperature of the photodiode and Rsh is the shunt resistance of the photodiode. The shot noise will dominate in photo-conductive operation, while the Johnson noise will dominate in photo-voltaic mode. Because APD's always operate in photo-conductive mode, its noise takes the same form as the photodiode darkness current shot, with the addition of two terms:
Isignal =
÷
 
2q(isignal+idark)M2FB
 
(7)
where Isignal is the photon-generated signal before gain. For applications with strong light signals, the shot noise performance of the detector is more important than the detector dark noise and the amplifier noise.

snr.jpg

Figure 6: Signal-to-Noise Ratio of an APD (blue), PMT (Red) and a photodiode (green) at different light levels. Reconstructed from [16]. Type numbers correspond to Hamatsu parts

When the light level is very low or the signal is of short duration solid state detectors often do not have a high enough SNR to preform the necessary measurement. PMT's are well suited for this kind of situations. It is possible to economically construct PMT's with very high surface areas. By doing so the amount of light collected can be increased.

A typical photomultiplier tube (PMT) consists of a photoemissive cathode (photocathode) followed by focusing electrodes, an electron multiplier and electron collector (anode) in a vacuum tube. When light hits the photocathode, the photocathode emits photoelectrons into the vacuum. These photoelectrons are then directed by the focusing electrodes towards the electron multiplier where electrons are multiplied by a secondary emission process. In short the photo-electron hits a dynode plate where another electron will be released these two will hit another plate giving rise to the multiplication process. Because of secondary emission multiplication, PMT's provide extremely high sensitivity and exceptionally low noise when compared to other photosensitive devices currently used to detect radiant energy in the ultraviolet and visible regions. The photomultiplier tube also features fast time response and a choice of large photosensitive areas. By changing the material of the photocathode the quantum efficiency can be tweaked into a certain wavelenght area.

Photomultipliers have an almost noise free gain as high as 106, with a small noise factor F of 1.4 to 1.6. An APD will have an F 2.0 to 4.0. The vey large gain of the PMT often means that the noise of an external amplifier can be neglected. Often PMT's are not considered because designers believe that the quantum efficiency or the high voltage (1000V) will complicate the design. This is not longer a problem: new photocathode materials are now available with quantum efficiencies of 30 to 40% in some regions of the spectrum. There are also PMT modules available that operate at less than 15V dc. The applications in which a PMT, APD or a photodiode can be used, are summarized below:

In absorption spectroscopy the detector has to be able to see a very small difference between a reference signal and the sample signal. So a the detector has to see a small change in a signal that is so large that the amplifier noise is not important. Gain in the detector is not necessary; however the detector has to have a large SNR to detect the very small changes. In this case a photodiode or a photodiode area is the best choice.

When looking at fluoresceing samples the PMT traditionally used as detector. With a lot of focus now on fluorescence labeling in cells, there now is a desire to look at fluorescence in the red and infrared. The signal coming from a sample is approximately 1ms with 100,000 photons. Amplifier noise makes this signal too small for a photodiode. The gain of a PMT is well suited to this light level in UV-visible region of the spectrum, but for longer wavelenghts the quantum efficiency is too small. The APD has a high quantum efficiency in this region and enough gain to offer good performance, making it a good choice for this application.

4  Two Photon Excitation

In contrast to conventional confocal microscopy with one-photon excitation, two photon excitation results in a small excitation volume, allowing the minimization of photo-damage of the sample and the discrimination of background signals to [17]. One has to take care though that through non-linear effects, with high laser powers severe photo-damage may occur. Two-photon excitation permits deeper penetartion for thick biological samples. Because near-IR radiation doesn't harm cells as much as more blue irradiation, higher laser powers can be used to deeper penetrate the sample. The SNR and spatial resolution reported by S·nchez et al [17] are of comparable size as found in one-photon excitation experiments. A sample of Rhodamine B (RhB) was prepared in the following way: a solution of 10-9 M of RhB in methanol was prepared and 20 ml was spin coated at 5000 rpm onto glass slidess. Below saturation the fluorescence count is found to be [17]:
Cf µ  qKs(2) NA4 <P>2
ltf
(8)
where q is the fluorescence quantum efficiency; K is the fluorescence detection efficiency; s2 is the two-photon absorption cross section (in m4s/photon); NA is the numerical aperture of the objective lens; <P> is the average excitation power (in W) at the sample; l is the wavelength; t is the pulse width and f is the repetition rate of the pulse train. The main conclusions from this experiment are that it is possible to image fluorescence of single molecules at room temperature by two-photon excitation with femtosecond pulses with more or less the same characteristics and sensitivity as found for one-photon excitation. An interesting observation was that with two-photon excitation the photo-bleaching rate was twice as fast as for one-photon excitation. This could however be depending on the molecule studied and the wavelenght used. Some of the bleached molecules reappeared after being in the dark for several hours, which hints to a reversible photo chemical reaction. Sonnleitner et al did similar experiments on supported lipid membranes with tertamethyl rhodamine as chromophore [18]. They come to he same conclusion as SanchÈz. It is possible to image single molecules with two-photon excitation. By applying two-photon excitation, the excitation wavelenght is in the near-infrared and the background luminescence is much lower in this spectral region. Hence, there will be a much larger SNR. For reasons mentioned above excitation in the red and near IR are very much appreciated, this does lead to a large reduction in possible chromophores and standard dyes. By applying two photon excitation, the excitation can be still be done in the red part of the spectrum and the standard blue/green active dyes and chromophores can still be used. With the two photon cross section of rhodamine B (which is of similar structure as the dye used) at 800 nm, s(2) = 153 ◊10-50 cm-4s/photon the calculated probability, p, for excitation of the fluorophore per laser pulse is, well below the saturation value (p = 1):
p =  0.588
2
s(2)t Ê
Ë		  1
Rt
 l
hc
Iill ˆ
¯		 2

 
= 0.0071
(9)
with h is Planck's constant and l = 800 nm the excitation wavelenght, R = 80 MHz is the repitition rate and t = 160 fs is the pulse width of the laser system, and Iill = 1000 kWcm-2. The theoretical fluorescence signal Ftheo from a single molecule as calculated from equation 9 is:
Ftheo = Q hdet pR = 4.8  cnts   ms-1
(10)
when the quantum efficiency of the fluorophore Q = 0.23 and the detection efficiency of the apparatus used hdet = 3.7%, is taken into account. The value found for Ftheo is corroborates well with both the experimental value from the single molecule as well as that of the high concentration data. It was also found that when the laser intensity was increased above 1400 kW/cm2 the signal strength decreased rapidly, this is probably due to higher photo-bleaching processes.

5  Examples

In the next sections some typical examples for single molecule spectroscopy will be presented. The ability to track and identify single molecules plays a very important part in biology and gene expression today. Proteins can now be followed in real-time through-out the cell by applying fluorescent labeling. One of the most important labels used in biological systems at the moment is green fluorescent protein.

5.1  Dendritic Multi Chromophoric System

Dendrimers have drawn a lot of attention because of their highly branched structures capable of being used as building blocks for photonic devices. Several reports on dendrimers have been published in different areas such as guest-host chemistry, analytical chemistry, catalysis, biology and opto-electronics. Dendrimers can also be used to mimic the photo-synthetic light harvesting antenna system. Different types of dendrict and related chromophore assemblies have been designed and investigated to harvest light energy. A lot of work in this field has been done on dendritic systems containing multiple chromophoric sites by the group of de Schryver and Hofkens at the Catholic Univeristy of Leuven in Belgium [19,20,21,22,23,24,10,25,9,26]. In this section a short resume of the work and the most important findings will be given.

In figure 7 the structures of a second generation dendrimer and a model compound containing the same chromophore can be seen.

dendritic.jpg

Figure 7: (a) structure of the second generation dendrimer and (b) structure of the model compound. The important feature of this polyphenylene dendrimer is that it does not absorb light above 450 nm, due to the out fo plane twisting between the different phenyl units. As a chromophore perylenecarboximide was introduced (R) because of its photostability, high absorption coefficient e = 38000 M-1cm-1  at  490  nm and its high fluorescence quantum yield (ff = 0.95). From [21].

The dendrimer synthesis serves as a way to obtain well-defined number of chromophores in a confined volume-element. Not only the amount of chromophores can easily be controlled, but also the interactions between the different chromophore can be governed be changing the structure of the branches to which the chromophores are attached or by attaching the branches to different cores. The chromophores in each branch of dendrimer allow the interactions of the branches, conformational distortions as well as excitation energy transfer or electron transfer among the chromophores to be probed. One of the questions that was adressed with single molecule spectroscopy of this systems was wether there is a transition from single-molecule behavior (discrete on/off jumps in fluorescence intensity of one chromophore) to ensemble behavior (exponential bleaching of the fluorescence intensity). The system shown in figure 7a, although containing eight chromophores, still behaves as a single emitting quantum system, showing collective on/off behavior similar to the on/off behavior reported for molecules with only one chromophore. Collective effects as seen for this multi-chromophoric system were also observed for natural light-harvesting antenna systems and a multichromophoric polymer system. The former system contains a well-defined number of chromophores that are arranged in a orderly fashion by the surrounding protein. it is believed that these collective effects are related to excited state energy transfer processes occuring in the multichromophoric antenna systems. Typical fluorescence intensity trajectories (transients)- that is, fluorescence intensity of a singe molecule as function of time- for the model compound can be seen in figure 8 .

transient.jpg

Figure 8: Transients of the model compound excited at 488 nm (intensity of 350 W/cm2 at the sample) in a 30-nm thin PVB film. (a) 60% of the transients show a one-step photobleaching behavior and no other features. (b) 35% of the transients show one or more off periods (intensity drops to the background level). The inset is a zoom of the second off period in the depicted transient. The off time in this case is 35 ms. (c) 5% of the transients of the model compound show different intensity levels. From [21]

Sixty percent of the investigated transient for this model compound show a one step bleaching, as can be expected for a single chromophore. In 35% of the transients, the fluorescence drops to the background level (see inset figure 8b) for periods ranging from 5 to 1200 ms before irreversible photobleaching occurs. The drops in intensity are often referred to as off-times. These off-times can result form several processes. Often they are related to the occupation of a triplet state. As shown in other articles a triplet lifetime can be calculated from these of times if one presumes a simple three-level system consisting of a ground state, the first singlet excited state and the first triplet excited state [27]. When fitting the distributions of the off-times from this model, taking in account this model, a triplet lifetime of 110 ms is found. This value is an upper limit as lifetimes shorter than the bin times will not be observed. In figure 9 the transients of the second generation dendrimer (g2) can be seen.

transient-g2.jpg

Figure 9: Transients of the dendrimer g2 excited at 488 nm (intensity of 350 W/cm2 at the sample) in a 30-nm thin PVB film (a, b). (a) Transient recorded with linear polarized excitiation light. Several off periods as well as levels can be seen in the transient. (b) Transient recorded with circular polarized excitation light, hence sampling all eight chromophores in the dendrimer. The inset is a zoom in the first high level of the transient. Both low levels and off levels of different duration can be seen. The transient shows a long duration low level (500 s) before it finally photobleaches. From [21]

The transients of the second generation dendrimer show more levels and jumps and longer survival times (time of irradiation before irreversible photobleaching occurs) when compared to the model compound. The model compound survives on average 70 s and 1.5 105 photons are detected when excited with linear polarized light, g2 has an average survival time of 280 s and 7.9 105 photons are detected. When using circular polarized light at the same wavelenght and same excitation power a mean survival time of 450 s and 11 105 detected photons are found. The difference in photons detected between the two polarization conditions can be explained by assuming that the average z-orientation of the sampled molecules is similar for the two polarization conditions. In the case of circular polarized light, all eight chromophores will be sampled, while in the case of linear polarized light, only a fraction of the the eight chromophores will contribute to the absorption. The longer survival time can be explained on the basis of sampling all chromophores versus addressing only some of the chromophores. If the eight chromophores of g2 absorb and emit independently of each other, one would expect mainly jumps between close lying intensity levels. The fluorescence transients of g2 show reversible jumps between a high level and a low level or the off level. The transients recorded using circular polarized light, exciting all eight chromophores of the dendrimer, show reversible jumps between high and off level (see inset figure 9b). The duration of the off-states varies from a few milliseconds in the beginning to several hundreds of milliseconds at the end of the transient. Off states in later parts of the transient can last for several seconds or tens of seconds. All eight chromophores being in the off state simultaneously is an implausible explanation for the collective on/off behavior in the transients. Another explanation could be that the eight chromophores are strongly coupled and hence act as a single quantum system. If a single quantum system goes to an off state, like the triplet state this would be the explanation for the collective behavior observed for g2. The absorption spectra of the model compound and g2 do not differ much, so the hypothesis of a single quantum system cannot be supported. Coulombic interaction is also possible in the excited state and there is a difference in fluorescence properties as expressed in the reduced fluorescence quantum yield, the emission spectra and a more complex time-behavior for g2 when compared with the model compound [28]. The chromophores are within the Fˆrtser radius of singlet energy transfer. This implies that the fluorescence will occur from the chromophoric site that is lowest in energy and hence acts as a trapping site from which the fluorescence will occur. From this, the off states have to be explained on the basis of dark deactivation channels that are opened via the energetically lowest chromophoric site. The exact nature of all the deactivation channels is at the moment not fully understood. For this dendritic system the triplet state of the energetically lowest chromophoric site is one of the possible candidates. Excitation energy transfer from the first singlet exciyed state too the first triplet state resulting in the singlet ground state and a higher lying triplet state is a spin allowed process. It might occur in multichromophoric systems such as g2 if the rate constant of energy trabsfer is high enough. The good overlap between the triplet absorption spectrum of g2 and the emission spectra of both the model and g2 supports this hypothesis. The relaxation of the higher triplet state to the first triplet state is a very fast, spin-allowed non-radiative process. The competition between singlet/triplet energy transfer and the fluorescence from the S1 can then account for the occurrence of both off-levels within the binning time. A similar mechanism, involving singlet-triplet annihilation, is already reported for the multichromophoric allophycocyanine system. Triplet lifetimes of several seconds are unlikely, other deactivation channels for the long off times at the end of the transient need to be considered.

Collective or cooperative effects were found in this dendritic system, these effects are known to occur in in J-aggregates, antenna systems of bacteria and in conjugated polymers. These effects are related to the process of energy transfer and exciton coupling. The observation of collective on/off jumps of all eight different chromophores can be explained by singlet-triplet energy transfer.

5.2  Green Fluorescent Protein (GFP)

Lately the green fluorescent protein (GFP) of the jellyfish Aequorea victoria has become one of the most important fluorescent labels in biology[29]. The fluorescing chromophore in GFP is 4-(p-hydroybenzylidene)-imidazolidin-5-one which is formed in a posttranslational cyclization reaction from the three amino acids Serine65, tYrosine66, Glycine67 (in short S65Y66G67). This sequence is part of an a-helix that penetrates a barrel like structure of b-strands which shield the chromophore from external environment. The structure of GFP and the chromophore along with the absorption spectrum (and the spectrum of GFP mutant E222Q) can be seen in figure 10. The photophysics of this protein is governed by a complicated equilibrium between the neutral and the anionic form (which is deprotonated) of Glycine (see figure 11).

gfp.jpg

Figure 10: A) 3 dimensional bucket like structure of GFP with the chromophore shielded in the middle. B) The absorption spectrum of wild type GFP (wt-GFP) shows two bands: around 396 nm caused by the neutral from and one around 476nm which is caused by the anionic form (dashed line). The absorption spectrum of GFP mutant E222Q shows only one band around 476nm (full line). By replacing the glutamic acid (E) for glutamine (Q) the acidity around the chromophore is lowered and therefore the anionic form is stabilized.

Both forms are easily distinguished from their absorption spectra (see figure 10b). In the wild type (wt) the absorption bands of the neutral an the anionic chromophore are centered at 396 nm and 476 nm respectively. Excitation of wt-GFP at 396 nm leads to a fluorescence emission at 508 nm which is virtually indistinguishable from the fluorescence at 476 nm [29]. Ultrafast spectroscopy experiments showed that this emission behave can be explained by excited state deprotonation. The reason why GFP became such a popular probe in biological experiments is that is is a auto-fluorescing protein, which means that it does not require external co-factors to fluoresce and that it is relatively straightforward to code for. A lot of different variants and mutants are made from the wild-type, so that the fluorescence can be shifted towards other wavelenghts like YFP and CFP (yellow and cyan fluorescent protein). The longest emitting wavelenght obtained by modification of GFP is 529 nm for e-YFP (enhanced yellow fluorescent protein). To continue to measure at even longer wavelenghts a lot of research is now going on into a new red fluorescent protein from a coral of the Discosoma genus, dubbed DsRed [30].

GFP_cycle.jpg

Figure 11: Structure of the chromophore in GFP in its protonated form, with some important amino acids. From [31]

When examining single copies of GFP immobilized in aerated aqueous polymers Dickson et al discovered repeated cycles of fluorescent emission on a time-scale of several seconds, since then called blinking [7]. This observation is not possible to make in bulk samples, since the dark periods will be averaged out. By excitation at 488 nm the molecule will fluoresce and return to the groundstate, eventually the molecule will reached a long-lived dark state.The term dark-states as use here, denotes any state which either does not absorb at the excitation wavelenght or which upon excitation doe not lead to a fluorescence emission. In a simple organic dye molecule this could for instance be intersystemcrossing to the triplet state. The exact nature of this dark state remains unknown for now. The individual GFP molecules from this long-lived dark state will can be switched back to the original emissive state by irradiation at 405 nm.

The first thing that is generally done when looking at single molecules of GFP is modifying it such a way that only the long wavelenght absorption band remains. When only one band is present a much larger SNR can be reached. In this case preferably the longer wavelenght should remain because when exciting in the (near) UV the background noise to increases and can cause the sample to degrade (when for instance one is looking at a cell). It is also noteworthy that chromophores with lower excitation energies seem to be more photo-stable, in general. So for this purpose the mutant E222Q was prepared, by substituting glutamic acid with glutamine at position 222 the backbone of the protein stays the same, but by removing the acid group the anionic form of the chromophore gets stabilized. When looking at the spectrum in figure 10b the solid line of E222Q shows only absorption at 488 nm, so only the anionic form is present. When Dickson et al irradiated the sample with 405 nm, most of the initial fluorescence returned, hinting to the possibility that the the chromophore is neutrally present in the long-lived dark state.

This observation inspired Jung et al to do simultaneous two color excitation experiments [32,33,34,31]. So Jung et al excited E222Q with as main excitation wavelenght 496 nm and they used 407 nm light as an additional color (also for the other mutants they examined). Switching on the 407 nm wavelenght showed a maximum increase of 120% in signal intensity at a pH of 10. High pH values were chosen to avoid any contribution from external protonation processes. When taking time depend traces, it was obvious that the (the neutral) RH state of the chromophore is not the long-lived dark state. So these two-color experiments unfortunately yield no concluding evidence about the exact nature of this long-lived dark state. These two color experiments can be used however, to suppress the background signal and to visualize molecules that are otherwise hard to detect due to insufficient SNR. Since not all mutants show the increase in intensity when adding the second color illumination, also discrimination between different GFP labels, which have similar excitation and emission spectra, can made in this way.

5.3  Vesicles

Living systems usually carry out their biochemical reactions with the cellullar compartments defined by a phospholipid bilayer boundary. A good way to mimic this environment is to use vesicles, which can be made in various sizes ranging from femto liters (10-15 liters) to zeptoliters(10-21 liters). The vesicles can be precisely positioned and manipulated in solution by optical trapping, they can also be attached to a glass-surface by means of a linking agent [35]. Chiu et al prepared unilamellar vesicles between 50 nanometer and 50 micrometer in diameter from different types of phospholipids by applying a new type of rota-evaporative technique [36].The laser power used in this experiment is not high enough to induce membrane damage, especially in the visible region where the bi-layer lacks the absorption features; the integrity of the vesicles also highly depends on buffer conditions as pH and ionic strength. Since there is very limited volume inside the vesicles, the initial number of substrate molecules is limited and typically becomes largely depleted during the course of a reaction. By using micro-manipulator-controlled ultramicorelectrodes for electro-poration and electro-fusion Chiu et al were able to use the lipid bilayer as a partition between the reactants [37]. By using the the ultra-micro electrodes they were able to break down the membrane bilayer through electric field mediated membrane pore formation and membrane fusion. Since the initial stages of electro-fusion and electro-poration are similar. Fusion pores are being generated in the process. To see if any leakage would limit the utility of this technique, fluorescent molecules were encapsulated in the vesicles and the fluorescence was monitored before and after fusion of the vesicles. No leakage was observed. To demonstrate that two different components would mix after fusion, two vesicles, each containing a different fluorescent dye were fused. To perform two-color mixing in fluorescence, the contents of the merged vesicle simultaneously excited at two different wavelenghts. The emitted photons were collected and separated into their respective color channels and then detected by two CCD cameras. Figure 12 shows the fusion between a vesicle containing carboxyrhodamine-6G (green fluorescence) and one containing TOTO-3-intercalated 15-mer DNA (red fluorescence) to yield a fused vesicle that appears orange.

vesicles.jpg

Figure 12: Fluorescence color mixing. Fusion of two vesicles, each containing a dye whose fluorescence is at a different color: 20 mM carboxyrhodamine-6G (top vesicle) and 20mM TOTO-3&nbspinteintercalated 15-mer DNA (bottom vesicle). (A) and (C) are bright-field images taken before and after fusion; (B) and (D) are the corresponding fluorescence images. Images before (E) and after (G) electrofusion (about 75 kV/cm; 10 ms) of a 10 mM fluo-3–containing vesicle (left) and a 10 mM Ca21-containing vesicle (right) are shown under bright-field illumination in a buffer solution containing 10 mM Hepes and 140 mM NaCl (pH 7.4). Corresponding fluorescence images are shown in (F) and (H). The fluo-3 solution encapsulated in the liposomes and the extraliposomal solution were titrated with EGTA to reduce background fluorescence. The vesicles were initially immobilized on poly-L-lysine–coated borosilicate cover slips, followed by rinsing with Ca21-free buffer solution. From [37]

Figure 12(E to H) shows a reaction carried out inside the vesicles, one of which holds fluo-3 (10 mM) and the other Ca2+ (10 mM). Before fusion (G) no fluorescence was detected from the Ca2+ vesicle, a small fluorescence in the background was observed in the vesicle with fluo-3. Binding of Ca2+ to fluo-3 increases the fluorescence quantum yield of this chelator by about 40-fold. In figure (H), this enhancement is clearly visible after the vesicles were merged. This technique offers the opportunity to probe the dynamics of chemical reactions in spatially confined nano-environments.

5.4  Fluorescence Resonance Energy Transfer (FRET) as a sensor for Ca2+

One study in the Moerner laboratory focused on cameleon YC2.1 complex, whose structure is based upon a cyan emitting GFP (CFP) by the calmodulin Ca2+-binding protein and a calmodulin-binding peptide (M13) (see figure 13a).

fret.jpg

Figure 13: a) Schematic representation of the structure of cameleon and the change in FRET upon binding and unbinding of Ca2+ ions. b) histograms of the energy transfer efficiency measured for for single molecules of cameleon in agarose gels, at three different Ca2+ ion concentrations. For more details see ref [38].

If Ca2+ ions are bound , the construct forms a more compact shape, leading to a higher efficiency of excitation transfer from the donor CFP to the acceptor YFP. The degree of FRET in cameleon is therefore a sensitive reporter of the concentration of Ca2+ in solution and cells. Analysis of single-molecule signals from the cameleon YC2.1 complex diluted in aqueous agarose gels allowed retrieval of several interesting features of energy transfer between donor and acceptor mutants of the construct as a function of the calcium concentration in the medium. The energy transfer efficiency distribution deduced from single-molecule confocal fluorescence signals shows an increased width at the Ca2+ dissociation constant concentration 13b. This observation is constant with the ligand binding kinetics, whose time scale at intermediate calcium concentration is close to our measurement time scale (20-200ms). The complex dynamics of the fluctuations were examined using a combination of autocorrelation and cross-correlation in conjunction with polarization measurements. Besides reorientation fluctuations of the two dipoles that seem to occur slowly compared to the emission time scale but fast compared to the integration time. slower variations in the energy transfer between the tow GFP mutants were observed. Both negative and positive cross correlations in the donor and the acceptor emission signals were present, the former related to the energy transfer process, the latter caused by other perturbations of the donor and acceptor emission.

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Footnotes:

1The Rabi frequency is defined by the scalar product of the transition dipole moment and the exciting electric field amplitude divided by Plank's constant: [(2m12 Elaser)/h], where 1 and 2 denote the ground and excited states, respectively

2Abbe deduced the reason why definition was reduced with the reduction of aperture size of a lens. Today we know the phenomena as the diffraction effect. He calculated how to build a lens without spherical aberration by combining geometry and specially formulated optical glass. He also explained the phenomenom of coma. The correction for coma today is the application of Abbe's sine condition. Further, Abbe is responsible for introducing fluorite into lens design to correct for chromatic aberration. The culmination of research in the elimination of chromatic aberration lead Abbe to the development of apo-chromatic lenses. From http://www.mir.com.my/rb/photography/htmls/contax_history/history1.htm

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On 18 Dec 2002, 16:54.

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