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Index Introduction ................................................................................................................ 3
Chapter 1 .................................................................................................................... 4
Fluorescence Correlation Spectroscopy (FCS) .......................................................... 4
1.1 History ................................................................................................................. 4
1.2 Conceptual basis and theoretical background ...................................................... 6
1.2.1 “Burst” trace ..................................................................................................... 6
1.2.2 Point Spread Function ....................................................................................... 8
1.3 Fluorescence Correlation Spectroscopy............................................................. 10
1.3.1 Theory ............................................................................................................. 10
1.3.2 Processes which can be monitored by FCS .................................................... 16
1.3.3 Physical models for the autocorrelation function ........................................... 19
1.3.4 Statistical accuracy in FCS ............................................................................. 20
Chapter 2 .................................................................................................................. 23
Single-molecule fluorescence instrumentation ........................................................ 23
2.1 Introduction ........................................................................................................ 23
2.1.2 Optical arrangement for single-molecule detection ........................................ 26
2.1.3 Epi-fluorescence far-field microscopy............................................................ 26
2.1.4 The PSF in single-photon confocal epi-fluorescence illumination systems ... 30
2.1.5 Spectral discrimination ................................................................................... 32
2.1.6 Excitations sources ......................................................................................... 34
2.1.7 Microscope objective for single-molecule fluorescence detection ................. 36
2.2 Detectors for single-molecule fluorescence experiments .................................. 39
2.2.1 Point detectors ................................................................................................ 40
2.2.2 Imaging detectors ............................................................................................ 43
Chapter 3 .................................................................................................................. 46
Practical Training ..................................................................................................... 46
3.1 Introduction ........................................................................................................ 46
3.2 Lab overview ..................................................................................................... 46
2
3.3 Biological probes ........................................................................................... 47
3.4 Conformational dynamics of biopolymer ...................................................... 48
3.5 A quantum dots application: .......................................................................... 49
Immuno-Cytochemistry and Fluorescence in situ ............................................... 49
Hybridization ....................................................................................................... 49
Chapter 4 .................................................................................................................. 52
Experimental apparatus ....................................................................................... 52
4.1 Objective of the experiment ........................................................................... 52
4.2 Experimental setup ........................................................................................ 53
4.2.1 Liquid Cristal on Silicon (LCOS) spatial light modulator ...................... 54
4.2.2 The 32x32 SPAD Array .......................................................................... 56
4.2.3 Sample & Filters ..................................................................................... 59
Chapter 5 .................................................................................................................. 61
Experimental procedure and data analysis .......................................................... 61
5.1 Introduction .................................................................................................... 61
5.2 Alignment of the SPAD array ........................................................................ 63
5.3 Experimental measurement ........................................................................... 66
5.3.1 August experiments ................................................................................ 66
5.3.2 Data analysis ........................................................................................... 68
5.3.3 Point-Spread-Function (PSF) analysis .................................................... 76
5.3.4 November experiments ........................................................................... 78
Chapter 6 .................................................................................................................. 80
Conclusions and future prospective ..................................................................... 80
Bibliography ............................................................................................................ 82
3
Introduction
In order to complete the master in “ Nuclear and ionizing radiation technologies” I
spent the six months of the course’s practical part in the Laboratory of Prof. Shimon
Weiss at the University of California Los Angeles (UCLA). During my training period I
worked under the supervision of Dr. Xavier Michalet, on FCS (Fluorescence
Correlation Spectroscopy) measurement with two different kinds of SPAD arrays, a 8x1
and a 32x32 SPAD array both of them developed by the group of Prof. Sergio Cova at
the Politecnico di Milano. In particular I focused my efforts on the experiments with the
32x32 array, including experimental setup optimization, sample preparation and data
analysis.
The thesis is organized in the following way:
• In the Chapter 1 there is an introduction of FCS, history, conceptual basis
and physical model.
• In the Chapter 2 there is an overview in the instrumentation needed for FCS.
• In the Chapter 3 there is a presentation of the lab in which I spent my practical
training period.
• In the Chapter 4 there is the description of the experimental apparatus used
for the measures
• In the Chapter 5 there is the data analysis and the comments on the
experimental results.
• In the Chapter 6 there are the conclusion and the possible future prospective.
4
Chapter 1
Fluorescence Correlation Spectroscopy (FCS)
1.1 History
The understanding of the fluctuation-dissipation relationship in thermodynamics
has been a great achievement of statistical physics.
The theory of Brownian movement, presented by Einstein in one of his famous
1905 papers[1], not only established a macroscopic understanding of the consequence
of the existence of the atom, but also opened up a whole new area of research related to
the study of systems near equilibrium. The experimental support for this atomistic
theory came with Perrin’s observation of Brownian particles of mastic under a
microscope [2]. Macroscopic dynamical properties (the viscosity of the fluid) were
derived from microscopic fluctuations (the diffusion of the probe).
It is humbling to point out that, right at the beginning of the 20th century,
experimentalists had already figured out the importance of reducing the sample size and
using high-power microscopy to unravel atomic wonders.
The explicit formulation of the fluctuation-dissipation theorem states that the
dynamics governing the relaxation of a system out of equilibrium are embedded in the
equilibrium statistics.
In the spirit of this theory, Eigen and followers developed the temperature-jump
technique, where the relaxation of a system after thermal perturbation gives insight into
the thermodynamic equilibrium. Classically, the temperature jump is generated by
capacitance discharge of laser-pulse absorption, and the relaxation toward the
equilibrium is monitored by spectroscopy (e.g. UV absorption or circular dichroism).
Another perturbative technique has been introduced to measure the diffusion of
biomolecules.
5
Fluorescence recovery after photobleaching (FRAP), as its name implies, consist in
monitoring the dynamics of fluorescence restoration in a region after photolysis of the
dyes in this region, due to the diffusion of fluorescent molecules from neighboring
areas. This photodestructive method has been very successful in application to living
cells, specifically to analyze the dynamics of membrane trafficking.
A widely used method to study changes on a molecular scale (10-100 Angstrom) is
based on fluorescence resonance energy transfer (FRET): a transfer of the excitation
between two different fluorophores (donor and acceptor), whose corresponding
emission (donor) and absorption (acceptor) spectra overlap. The efficiency of energy
transfer depends strongly on the distance between the donor and the acceptor: hence one
can take advantage of FRET to follow the association of interacting molecules or to
monitor the distance between two sites within a macromolecule when labeled with two
appropriate dyes.
Fluorescence correlation spectroscopy (FCS) is an experimental technique
developed to study kinetic processes through the statistical analysis of equilibrium
fluctuations. A fluorescence signal is coupled to the different states of the system of
interest, so that spontaneous fluctuations in the system’s state generate variations in
fluorescence. The study of the autocorrelation function of fluctuations in fluorescence
emission gives information on the characteristic time scales and the relative weights of
different transitions in the system. Thus, with the appropriate model of the system
dynamics, different characteristic kinetic rates can be measured (for example
fluctuations in the number of fluorescent particles unravel the diffusion dynamics in the
sampling volume) [3].
Since its invention in 1972 by Madge et al [4], FCS has been used for various
applications, such as measuring: chemical rates of binding-unbinding reactions or
coefficient of translational and rotational diffusion. However, although the principal
ideas behind FCS as well as its main applications were already established at that stage,
the technique was initially poorly sensitive, requiring high concentrations of fluorescent
molecules. Its renaissance came in 1993 with the introduction of the confocal
illumination scheme in FCS by Rigler et al [5].
6
This work generated a lot of technical improvements, pushed the sensitivity of the
technique to the single-molecule level and led to a renewed interest in FCS. The
efficient detection of emitted photons extended the range of applications and allowed
one to probe the conformational fluctuations of biomolecules and the photodynamical
properties of fluorescent dyes.
FCS is a technique which relies on the fact that thermal noise, usually a source of
annoyance in an experimental measurement, can be used to obtain some information on
the system under study.
FCS corrects the shortcomings of its precursors, as it monitors the relaxation of
fluctuations around the equilibrium state in a non–invasive fashion. It relies on the
robust and specific signal provided by fluorescent particles to analyze their motions and
interactions. In combination with FRET, FCS further allows to probe the dynamics of
intra-molecular motion.
1.2 Conceptual basis and theoretical background
1.2.1 “Burst” trace
If the fluorescent analyte is allowed to flow or diffuse in and out of a small
excitation/collection volume defined by a focused laser beam, this gives rise to a
stochastic series of short-lived fluorescence bursts detected above the background noise
level (Figure 1.1). This type of experiment was one of the first used to demonstrate the
feasibility of fluorescence detection of single molecules in solution at room
temperature. However, despite the simplicity of the approach, the stochastic nature of
the data requires sophisticated analysis. Burst often consists of < 100 photons and the
data are therefore dominated by shot noise, in addition each molecule is able to take any
path through the excitation/collection volume which has a spatially dependent excitation
intensity and collection efficiency (also called instrument spread function, see
paragraph 2.1.4) , resulting in a range of burst widths and intensities [6].
7
Figure 1.1 This is the time trace for 10 seconds of beads measurement taken reading one of the 1024 pixel of the 32x32 SPAD array detector. “Bursts” corresponding to the bead diffusing through the focal volume are clearly visible. The burst duration is on the order of 10 ms.
The simplest approach to analyze such transient signal is often called burst analysis.
Burst analysis involves the straightforward counting of bursts, the quantification of the
number of photons in a burst, the length of the burst or the time between bursts
(recurrence time). It has been used quite widely, for example in high-throughput
screening and medical diagnostic applications.
The reliability of screening or identification assays using simple forms of burst
analysis has been improved by developing methods for the coincident detection of two
dye labels attached to a target molecule. In this way the properties of the particular
fluorescence bursts are of somewhat less concern as coincident bursts can be detected
with significantly more confidence, facilitating the discrimination of signals from
uncorrelated background events.
0200400600800
1000120014001600
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
coun
ts
time (ms)
Time trace pixel 24_16 beads
Time trace
8
1.2.2 Point Spread Function
The point spread function (PSF) is defined as the image of an infinitely small point
source of light originating in the specimen (object) space. Because the microscope
imaging system collects only a fraction of the light emitted by this point, it cannot focus
the light into a perfect point. Instead, the point appears widened and spread into a three-
dimensional diffraction pattern.
Depending upon the imaging mode being utilized (widefield, confocal, transmitted
light), the point-spread-function has a different and unique shape and contour. In a
confocal microscope, the shape of the point spread function resembles that of an oblong
ellipsoid of light surrounded by a flare of widening rings.
To describe the PSF in three dimensions, it is common to use a coordinate system
of three axes (x, y, and z) where x and y are parallel to the focal plane of the specimen
and z is parallel to the optical axis of the microscope. In this case, the PSF appears as a
set of concentric rings in the x-y plane (the so-called Airy disk which is commonly
referenced in texts on classical optical microscopy), and resembles an hourglass in the
x-z and y-z planes (Figure 1.2)
Figure 1.2 Surface plot of intensity in an Airy disk at the focal plane.
9
Figure 1.3. PSF mesured using a large area, single-pixel HPD, by recording the fluorescence emitted by a sub-
diffraction size bead scanned through the LCOS-generated spot. The 3 projections XY, XZ, YZ give an idea of the size and shape of the excitation spot. Since FCS measurements depend on excitation and emission PSFs, these measurements allow us to analyze the effect of the SPAD size on these measurements.
The PSF can be defined either theoretically by utilizing a mathematical model of
diffraction, or empirically by acquiring a three-dimensional image of a small fluorescent
bead (see Figure 1.3).
A theoretical PSF generally has axial and radial symmetry. In effect, the point
spread function is symmetric above and below the x-y plane (axial symmetry) and
rotationally about the z-axis (radial symmetry). An empirical point spread function can
deviate significantly from perfect symmetry (as in Figure 1.3). This deviation, more
commonly referred to as aberration, is produced by irregularities or misalignments in
any component of the imaging system optical train, especially the objective, but can
also occur with other components such as mirrors, beamsplitters, tube lenses, filters,
diaphragms, and apertures. The better the microscope alignment, the closer the
empirical PSF comes to its ideal symmetrical shape (there is also an effect due to laser
source, chromatic aberration, etc.).
The performance of both confocal and deconvolution microscopies depend on the PSF
being as close to the ideal case as possible.
10
1.3 Fluorescence Correlation Spectroscopy
1.3.1 Theory
The conceptual basis of FCS is illustrated in Figure 1.4 [7]. At equilibrium,
fluorescent molecules move through a small open region and/or undergo transitions
between different states with different fluorescent yields, resulting in temporal
fluctuations in the fluorescence measured from the region. The temporal autocorrelation
of the fluorescence fluctuations, which measures the average duration of a fluorescence
fluctuation, decays with time. The rate and shape of the decay of the autocorrelation
function provide information about the mechanisms and rates of the processes that
generate the fluorescence fluctuations. The amplitude of the autocorrelation function
provides information about the density (number) of fluorescent species in the sample
region.
Figure 1.4. Conceptual basis of FCS. At equilibrium, fluorescent molecules are transported by diffusion or
flow through an open region or undergo transitions between states of different fluorescent yields, giving rise to fluctuations in the measured fluorescence. The fluctuations δF(t) in the measured fluorescence F(t) from the average fluorescence ‹F› are autocorrelated as G(τ) (the normalized autocorrelation function of the intensity fluctuations). The autocorrelation function, which measures the average duration of a fluorescence fluctuation, decays with time τ: the rate and shape of decay are related to the mechanisms and rates of the processes that give rise to the fluorescence fluctuations. The magnitude of G(τ) is related to the number densities and relative fluorescence yield of different chemical species in the sample region.
Figure 1.6 Schematic representation of the principle of an autocorrelation calculation on a single molecule data set (top). A fluorescence burst (F(t)) is shifted by the integration time (lag time) then multiplied together, F(t)*F(t+lag time τ. The value of the autocorrelation function (G(The points shown are the actual overlap overlap integral is large whereas at longer lag times the overlap integral diminishes to zero. In this way the autocorrelation function contains information on the width on the featur
Autocorrelation curves are generally presented on semi
range of delay times is likely to span many order
autocorrelation function is approximately exponential in many cases and it
read off the approximate lifetime of the decay to get an indication of the timescale of
the measured fluctuations
The autocorrelation function
data shown in figure 1.5
fluctuation events, in this case the width
diffusion in and out of the volume.
Schematic representation of the principle of an autocorrelation calculation on a single molecule data set (top). A fluorescence burst (F(t)) is shifted by the integration time (lag time) τ. The original and shifted traces are
*F(t+τ), and the integrated area is stored as the value of the autocorrelation function at The value of the autocorrelation function (G(τ)) are then plotted on a logarithmic lag timescale (bottom).
The points shown are the actual overlap integrals (normalized) from the data shown (top). At short lag times the overlap integral is large whereas at longer lag times the overlap integral diminishes to zero. In this way the autocorrelation function contains information on the width on the feature in the data set.
Autocorrelation curves are generally presented on semi-logarithmic plots as the
range of delay times is likely to span many orders of magnitude: the shape
autocorrelation function is approximately exponential in many cases and it
read off the approximate lifetime of the decay to get an indication of the timescale of
measured fluctuations.
he autocorrelation function (ACF) for the type of raw single-
data shown in figure 1.5 can be used to obtain information about the timescale of the
events, in this case the width of the fluctuation (bursts) produced by
diffusion in and out of the volume.
12
Schematic representation of the principle of an autocorrelation calculation on a single molecule data
. The original and shifted traces are ), and the integrated area is stored as the value of the autocorrelation function at
)) are then plotted on a logarithmic lag timescale (bottom). integrals (normalized) from the data shown (top). At short lag times the
overlap integral is large whereas at longer lag times the overlap integral diminishes to zero. In this way the
logarithmic plots as the
of magnitude: the shape of the
autocorrelation function is approximately exponential in many cases and it is possible to
read off the approximate lifetime of the decay to get an indication of the timescale of
-molecule diffusion
information about the timescale of the
of the fluctuation (bursts) produced by
13
Note that the ACF is therefore built up from temporally similar signals of many
single-molecules.
Furthermore, the ACF may contain additional information on any other processes which
cause fluctuations on a time scale faster than the occupation times of molecules in the
volume.
Figure 1.7 Autocorrelation function for a 100 nm beads sample (aqueous solution), obtained using one of the
1024 pixel of the 32x32 SPAD Array of Politecnico di Milano.
Figure 1.7 shows the autocorrelation function calculated for a bead sample,
recorded using one channel of the 32x32 SPAD array used in our experiments . As
indicated in figure 1.6, a number of parameters can be extracted from the
autocorrelation function regardless of the mechanism of the fluctuations. The
amplitudes of the decay components give information about the relative strength of the
fluctuations; in the case shown in figure 1.7 we have only one diffusion component and
its amplitude provides a measure of the average number of molecules in the small
excitation/collection volume (proportional to the concentration). Additionally, the decay
rate of the processes gives an indication of the timescale of the processes that cause the
fluctuation.
In FCS of freely diffusing particles the primary fluctuations are due to the presence
or absence of a fluctuating species within the excitation/collection volume. However, in
typical FCS instrumentation a spatial inhomogeneity also exists in the
14
excitation/collection volume that leads to fluctuations without concentration changes.
Thus the amplitude of a given fluctuation is modulated by its position in the volume.
Fluctuations are therefore expressed as spatially weighted concentration changes
according to [6],
�����, �� ���������, �� �1.2�
where �����, �� is the concentration fluctuation and ���� is the excitation PSF convolved with the detection PSF.
Integration over the entire sample volume gives the total fluorescence signal
fluctuation and, assuming the existence of a single fluorescent species, the amplitude of
the fluorescence fluctuations is given by:
����� � ���������, �� ���. �1.3�
The total fluorescence signal is given by,
���� � ��������, �� ��� �1.4�
and the average fluorescence signal is thus:
������ ������ � ���� ���. �1.5�
Combining equations (1.1), (1.3) and (1.5) yields the fluorescence fluctuation
autocorrelation function ,
���� � ������������������, �����������, � � ���������� ������ ! ���� ���"# , �1.6�
15
where ������, �����������, � � ��� is referred to as the correlation function of a concentration fluctuation at some point �� at time t with the concentration fluctuation at a point ������ at some later time t + τ.
Equation (1.6) can be extended to a solution containing several different chemical
species by representing the fluorescence signal as the sum of different signals.
The particular case of G(0) represents the correlation of a molecule at ������ with a molecule at �� at the same instant. In a sample in which there are no long-range interactions, there is no spatial correlation and therefore fluctuations are only correlated
at the same instant at the same position (and all positions are equivalent). In this limit it
can be shown that equation (1.6) reduces to,
��0� & ������#�������# , �1.7�
where γ is a constant depending on the excitation and detection PSF (called emission
PSF) shape . Equation (1.7) then, is the relative mean square amplitude of fluctuations,
which for independent random molecular processes can be shown to be inversely
proportional to the average number of processes (). Thus,
��0� & 1() . �1.8�
a typical value of γ for common experimental geometries is ≈ 0.5 and depends on
���� and on the detection efficiency profile (emission PSF) with a weak dependence on sample volume shape.
Thus G(0) depends strongly on the number of fluorescent molecules in the sample
volume, and so FCS can probe sample concentration directly. This has been exploited in
a number of studies.
An interesting result of fluctuation analysis of this type is that it is not necessary to
have only single-molecule within the excitation PSF. In fact if, on average, a small
numbers of molecules are present in the PSF then temporal fluctuations in the
fluorescence signal will still be detected when one molecule enters or leaves the
volume; the fluctuations caused by a sing
Single-molecule sensitivity is only entirely lost if, when one molecule leaves the
volume (by diffusion or chemical reaction) it is immediately replaced by another, in
which case the fluctuations tend to zero. FCS is
single-molecule fluctuations over quite a broad range of concentration.
Experiments are, however, best performed in conditions where fluctuations are
maximized, that is, at or near
1.3.2 Processes which can be monitored by FCS
A number of common physical phenomena can affect and influence the
autocorrelation function of a diffusion single
1.1). They are summariz
Figure 1.8 Schematic of some of the processes diffusion experiment. White circle represent active fluorescent molecules (a) diffusion of a single labeled molecule in the inhomogeneous excitation volume, (b) triplet crossing causing intermittent fluorescence , (c) reversible binding with a second molecule that iconformational changes that induce changes in the amount of emitted fluorescence, and (e) photobleaching.
will still be detected when one molecule enters or leaves the
volume; the fluctuations caused by a single molecule are still being probed.
molecule sensitivity is only entirely lost if, when one molecule leaves the
volume (by diffusion or chemical reaction) it is immediately replaced by another, in
which case the fluctuations tend to zero. FCS is therefore, in principle, sensitive to
molecule fluctuations over quite a broad range of concentration.
Experiments are, however, best performed in conditions where fluctuations are
maximized, that is, at or near single-molecule concentrations (typically < 1 nM)
Processes which can be monitored by FCS
A number of common physical phenomena can affect and influence the
on of a diffusion single-molecule fluorescence experiment (figure
hey are summarized in figure 1.8 [6].
Schematic of some of the processes leading to fluctuations in a singleexperiment. White circle represent active fluorescent molecules (a) diffusion of a single labeled molecule in
the inhomogeneous excitation volume, (b) triplet crossing causing intermittent fluorescence , (c) reversible binding with a second molecule that is not fluorescent but quenches the fluorescence of the labeled molecule, (d) conformational changes that induce changes in the amount of emitted fluorescence, and (e) photobleaching.
16
will still be detected when one molecule enters or leaves the
le molecule are still being probed.
molecule sensitivity is only entirely lost if, when one molecule leaves the
volume (by diffusion or chemical reaction) it is immediately replaced by another, in
principle, sensitive to
molecule fluctuations over quite a broad range of concentration.
Experiments are, however, best performed in conditions where fluctuations are
cally < 1 nM).
Processes which can be monitored by FCS
A number of common physical phenomena can affect and influence the
ce experiment (figure
ctuations in a single-molecule fluorescence
experiment. White circle represent active fluorescent molecules (a) diffusion of a single labeled molecule in the inhomogeneous excitation volume, (b) triplet crossing causing intermittent fluorescence , (c) reversible binding
s not fluorescent but quenches the fluorescence of the labeled molecule, (d) conformational changes that induce changes in the amount of emitted fluorescence, and (e) photobleaching.
17
The main component which generally dominates the autocorrelation function is
diffusion (figure 1.8(a)). The Stokes-Einstein relation gives the translational diffusion
coefficient D of a particle in a viscous medium,
+ ,-. �1.9�
where k is the Boltzmann constant, T is the temperature in degrees K and f is the
friction coefficient for the particle in the fluid.
In the simple case of a spherical particles f is given by[6],
. 601� �1.10�
where 1 is the viscosity of the solvent and r the hydrodynamic radius (sometimes called the Stokes radius) of the sphere.
A typical diffusion time (the time taken to go across the PSF) for a small molecule
at room temperature in water is thus of the order 75µs (given a PSF radius of ≈ 250nm,
a solution viscosity of 1.04*10-3Nsm-2 at 293K and a molecular hydrodynamic radius of
10Å). Although this only represents the time taken to go across the PSF along the
shortest path it nevertheless gives an idea of the approximate timescale on which
diffusion processes will be observed in the autocorrelation function. Diffusion is rarely
the only source of fluctuation in FCS experiments. Triplet state blinking (figure 1.8(b))
modulates the fluorescence output of the molecule causing “blinking” on a
characteristic timescale of a few µs and therefore generates fluctuations that can be
observed in the autocorrelation function. In addition, the environment of the dye
molecule has been shown to greatly influence the photophysics and hence the measured
parameters as does excitation power.
The timescale of additional photo-induced transient states associated with inter-
molecular processes such as charge transfer reactions upon the binding of a dye to
another molecule have been shown to occur in the 10-100ns time regime (for example
R6G-DNA binding). Other molecular interactions (e.g. binding of a receptor-ligand
complex, figure 1.8(c) may result in slower fluctuations that can occur anywhere in the
autocorrelation function if the bind
fluorescence signal.
Many other mechanisms can influence FCS measurements and are difficult to
assign to a particular timescale. Photo
significant problem when working
Dynamic photobleaching of molecules to a permanent dark state is another and
problematic, especially at large excitation power
Consideration must also be
these photo-induced effects may occur as a function of the path they take through the
excitation volume, introducing another convoluted fluctuation.
Figure 1.9 [6] summarized the contributions of these common processes to the
autocorrelation function in an FCS experiment.
Figure 1.9 Diagram showing the temporal ranges of the processes that affect the autocorrelation of single molecule fluorescence data.
autocorrelation function if the binding event is reversible and modulates the
other mechanisms can influence FCS measurements and are difficult to
o a particular timescale. Photo-induced isomerization has been shown to be a
significant problem when working with particular dyes, for example Cy5.
Dynamic photobleaching of molecules to a permanent dark state is another and
problematic, especially at large excitation power (figure 1.8(e)).
Consideration must also be given to the inhomogeneous excitation
induced effects may occur as a function of the path they take through the
excitation volume, introducing another convoluted fluctuation.
summarized the contributions of these common processes to the
ion function in an FCS experiment.
Diagram showing the temporal ranges of the processes that affect the autocorrelation of single
18
ing event is reversible and modulates the
other mechanisms can influence FCS measurements and are difficult to
induced isomerization has been shown to be a
cular dyes, for example Cy5.
Dynamic photobleaching of molecules to a permanent dark state is another and can be
given to the inhomogeneous excitation profile – all of
induced effects may occur as a function of the path they take through the
summarized the contributions of these common processes to the
Diagram showing the temporal ranges of the processes that affect the autocorrelation of single
19
1.3.3 Physical models for the autocorrelation funct ion
There are a number of models that have been developed for FCS. Generally, in FCS
experiments the data are first processed to yield the autocorrelation function as
described earlier according to equation (1.1). Then a physical model which incorporates
descriptions of the sources of fluctuation is used to fit this function allowing the
physical parameters of interest to be determined. The simplest case is that of diffusional
motion of a fluorescent particle in and out of the PSF.
An analytical expression for the form of the autocorrelation function in the case of a
three-dimensional Gaussian PSF was developed by Aragon and Pecora[8].
���� 1() 21 ��
�3456 21 � ���34
56 #7 � +�
1() 21 ��
�3456 21 � �8#34
56 #7 � +� �1.11�
where () is the average number of fluorescent molecules within the PSF at any instant, and �3 9:;# 4+⁄ and �3� 9=# 4+⁄ are, respectively, the characteristic times of diffusion across and along the illuminated region. K=ωz/ωxy where ωz and ωxy are the
sizes of the beam waist in the direction of the propagation of light and in the
perpendicular direction, respectively (usually ωz > ωxy), assuming a Gaussian
illumination profile. DC is the value of the autocorrelation as τ→∞ (usually DC=1). τD
is called the molecular diffusion time (or correlation time) and is given for one-photon
excitation by,
�3 9>#
4+ �1.12�
where D is the translational diffusion coefficient. In particular, equation 1.12 refers
to the one-photon excitation case only. For a two excitation configuration the
denominator in equation (1.12) must be doubled.
20
As we could expect, the amplitude of the autocorrelation function is inversely
proportional to the average number of molecules in the sampling volume, since the
fluctuations �( ()⁄ in the number of molecules in the sampling volume are inversely proportional to ?() and since G(τ) is second order in the intensity of fluorescence.
Notice that in equation (1.11) each of the directions of translational motion brings
in a term (1 + t / τ)-1/2, so that for a two-dimensional diffusion in the xy plane we have,
���� 1()1
1 � � �3⁄ . �1.13�
In practice, equation (1.13) is also a good approximation to a 3D system with the
illumination conditions such that K2 >> 1 ( τD
21
There are two main sources for the fluctuations δn(t) in the number of detected
photons per sampling time. The first is the statistical nature of the system itself, i.e.
fluctuations in the number N of fluorescent molecules in the sampling volume due to
diffusion or chemical reactions. The relative fluctuations in photon counts due to this
source is related to the fluctuations in N: √AB� �( () ⁄ 1 ?()⁄ . These fluctuations contribute both to the signal G(τ) (as discussed above) and to the noise ?AB�������.
The second source of fluctuations δn(t) is the statistical nature of the photon
emission and detection processes, i.e. the fluctuations in the number of detected photons
per fluorescent molecule (shot noise). These fluctuations contribute to the noise only,
since the fluctuations at different time intervals are not correlated.
Shot noise depends on the total number of detected photons and its relative value is
?AB� �E��� EF⁄ 1 √EF⁄ 1 ?G()⁄ , where υ is an average number of detected photons per molecule per sampling interval.
In most experimental situations and definitely in most of the situations where the
FCS statistics is of concern, υ is small. For example, the typical diffusion time for a
simple dye molecule (e.g. Rhodamine 6G) in the FCS experiments is ≈ 100µs. Then
choosing a sampling time ≈ 1µs and taking the typical count rate of 30000 photons per
second per fluorescent molecule, we get υ ≈ 0.03.
For small values of υ and large (), the shot noise dominates the noise of the correlation function ?AB�������. Taking into account the fact that the shot noise is uncorrelated, the signal-to-noise ratio for the FCS measurement is,
@ (7 ����?AB� ������ H ����I()√- J I√- �1.14�
where T is the total number of accumulated sampling intervals ∆t ( T∆t is the total
duration of the experiment), and we made use of ���� J 1 ()⁄ . Is important to point the two main consequences of equation (1.14). First, as
previously mentioned, for () >> 1 the statistics of FCS is independent of the number of molecules per sampling volume and depends only on the photon count rate per molecule
and the total acquisition time.
22
Second, the S/N dependence on υ is stronger than the dependence on T, which means
for instance that is extremely important to optimize photon detection in the experiment
[1]. Finally, this expression also tells us that arbitrary S/N can be obtained by increasing
the measurement time. This is a crucial point in the context of this work, as this can
equivalently be obtained by accumulating the signal from multiple spots in parallel, thus
reducing the overall experiment duration.
23
Chapter 2
Single-molecule fluorescence instrumentation
2.1 Introduction
The instrumentation necessary to achieve single-molecule fluorescence detection is
relatively straightforward[6]. The main requirements are high optical efficiency
collection and a good signal-to-noise ratio. These are usually achieved by using high
numerical aperture microscope objectives and sensitive detectors such as SPAD (silicon
photon avalanche detector) or CCD (charge-coupled devices).
Optical detection of a single-molecule requires that its optical signal (usually
fluorescence) can be distinguished from the background light arising from other
molecules within the detection volume. This therefore implies that the optical system
must have a high throughput and detection efficiency and that background noise is
efficiently rejected. Generally, the detection of a single molecule is achieved either by
using very low sample concentrations or by immobilizing single-molecules on a surface
with a sparse density and combining either of these approaches with a very small
observation volume (< 0.1 fl). Even when such a small observation volume is used, one
generally still faces the problem of a relatively large background signal from many
solvent molecules, in comparison with the few fluorescence photons from the single
fluorescent molecule of interest. For example, in 0.1 fl water there are ≈ 109 water
molecules. If even a small amount of unwanted signal is emitted from these water
molecules and it overlaps the spectral region of the fluorescence of the single molecule
of interest, the signal-to-background ratio will make measurement impossible.
24
There are three primary sources of background noise:
1. Rayleigh scattering by the solvent molecules. This process result in a background
signal at the excitation wavelength that may leak through the optical detection
filters, which cannot provide 100% efficient rejection.
2. Raman scattering by the solvent molecules. This process result in a photon at both
higher and lower energy compared to the excitation light. However, since
fluorescence of the single molecule of interest will be at longer wavelengths than the
excitation, it is the Raman scattered light at lower energy (Stokes radiation) that is a
concern. Some of these Stokes scattered photons may overlap the detection filter
pass band and therefore contribute to the background signal.
3. Finally, a combination of fluorescence, Rayleigh and Raman scattering from
impurities in the solvent introduced by impurities in the buffer components or by
careless sample preparation.
In addition, the signal-to-noise ratio may also be affected by problems with the
instrumentation such as the stability of the light source, mechanical drift, detectors
noise, and non-linearity.
For a typical fluorescent dye molecule with a quantum yield of 0.8, we might
expect of the order 105-106 fluorescence photons per second to be detected if an
excitation flux of ≈ 100 kWcm-2 is used (i.e. 100 µW excitation power into an
observation volume of 250 nm diameter, an overall detection efficiency of 1%, visible
excitation and a fluorescence cross section of 4x10-16 cm2 for Rhodamine 6G). Even
without any impurities present, the background signal due to Raman and Rayleigh
scattering from the large number of solvent (water) molecules present would be many
orders of magnitude larger. Efficient methods for rejecting this background signal and
for detection of the few fluorescence photons are clearly essential [6].
The most trivial method is by reducing the size of the detection volume. This way,
we minimize the numbers of solvent molecules and therefore minimize the scattered
light.
25
Rayleigh scattered light removal is relatively easy as it is generally spectrally
distinct from the fluorescence emission. Similarly, a good laser excitation/dye emission
choice will allow the fluorescence signal from the molecule of interest to be separated
from Raman scattered light and the fluorescence from impurities by a suitable band-
pass filter (a filter with allows only certain wavelengths of light to be transmitted with
efficiency).
While the intensity of the Raman scattered light is low the large number of solvent
molecule in the volume makes this effect significant. For water (typically the highest
concentration solvent component) the inelastic Raman scattering causes a shift in the
scattered light that leads to a number of bands (due to, for example, the vibration along
O-H or H-O-H). The bands due to Raman scattering are typically expressed as the shift
in wavenumbers (cm-1) of scattering light with respect to the excitation light.
The relationship between wavenumber and wavelength is given by,
KBALEMNOL� PN56" 10QKBALRLES�T EN" �2.1�
For example, for the 532nm (laser used in our experiments) the wavenumber is
18797 cm-1. For water, 8 distinct Raman bands may be observed, the shift of the most
intense band is ≈ 3439 cm-1 and is relatively broad (a half width of around 400 cm-1),
the other bands are generally too weak to be observed. Thus for 532 nm excitation the
scattered light due to Raman shift will occur, principally, at 22236cm-1 (18797 - 3439)
or at a wavelength of ≈ 650 nm.
Since fluorescent dyes usually have quite broad emission spectra, narrow band pass
filters that reject the majority of the unwanted background signals can also reduce the
number of fluorescence photons reaching the detector. Minimizing the sample volume
and the use of appropriate filters are the two most important approaches to improving
the signal-to-noise ratio in single molecule fluorescence experiments.
26
2.1.2 Optical arrangement for single-molecule detec tion
A variety of optical arrangements have been chosen for single-molecule
fluorescence experiments. However, by far the most common approaches are the
confocal epifluorescence, multi-photon epifluorescence, and total internal reflection
geometries. The optical arrangement is mainly determined by the experimental design,
that is whether the molecules of interest are freely diffusing or are fixed in space. In
diffusion experiments, which have the benefit of being relatively simple to set up,
confocal or two-photon illumination is typically used.
2.1.3 Epi-fluorescence far-field microscopy
The epi-fluorescence (episcopic fluorescence) configuration (figure 2.1)[6] is
commonly encountered in microscopy. A single optical element is used to deliver the
excitation light to the sample and to collect the fluorescence emission. In general high
numerical aperture microscope objective is used. ‘One-photon’ excitation (i.e. the use of
excitation photons with energy matching the absorption transition in the fluorescent
molecule of interest) is the most commonly encountered excitation protocol. A
collimated laser beam is reflected off a dichroic mirror into the back-aperture of the
microscope objective. The light is focused to a diffraction-limited spot at the focal
plane, which is placed at the region of interest in the transparent sample (figure 2.2)[6].
The radius of the focused spot perpendicular to the direction of propagation can be
approximated by the half width at half maximum of the Airy disk intensity profile:
K~ 0.51V(W �2.2�
where λ is the wavelength of light used, and NA is the numerical aperture of the
objective lens. Using NA = 1.2 and λ =532nm gives an approximate focal spot diameter
of ≈ 450 nm.
27
Figure 2.1 Illustration of the inverted epi-fluorescence configuration. The excitation beam (grey, collimated or
parallel rays) is reflected towards the sample by a dichroic mirror (essentially a semi-transparent mirror) and focused at a point within the sample at the front focal plane of a microscope objective. In this example the same is represented as a fluid sitting on a thin glass coverslip, as is typical in these inverted configurations. A portion of fluorescence (and scattered excitation light) is collected by the same microscope objective (black rays). The fluorescence is transmitted through the dichroic mirror towards the detector while scattered excitation light is not transmitted but reflected (not shown) back toward the light source.
Figure 2.2 Close up of the excitation volume (not to scale) created by the epi-fluorescence configuration. A
collimated laser beam of width D is focused through a glass coverslip by a microscope objective and brought to a focus some distance above the glass/water interface. The depth of focus Z inside the sample is shown (defined, in this case, as twice the distance from the focal plane to the point at which the intensity has dropped by 1/e). The configuration results in spatial restriction of the beam diameter 2w in the direction perpendicular to the direction of propagation but does not restrict the beam in the direction of propagation.
It should be noted that this figure relates to a theoretical minimum (the diffraction
limit) and that rarely will this level of performance be reached due to a variety of optical
imperfections present in the optical system. Focal spot diameter of around 500nm -1µm
are more typical.
28
This focusing limits the extent of the region in the sample that is excited and
therefore limits the region in which fluorescence or scattering is generated. Some of the
fluorescence photons emitted by molecules in the excitation volume are collected by the
microscope objective and directed by the dichroic mirror to the detection arrangement.
Clearly, single-photon far-field excitation in this manner provides no spatial
reduction of the excitation/collection volume in the direction of propagation of the light
and so additional optics is required in the detection path to minimize this volume.
To achieve this, confocal detection is often employed (figure 2.3)[6].
Figure 2.3 Illustration of the principle of confocal detection to limit the collection volume in the direction of
the propagation of the excitation beam. Light emerging from near the focal plane (black spot) is collected and collimated by the microscope objective and then focused by a second lens to pass through an aperture and onto the detector. Light that originates from in front or behind the focal plane (grey spot) is out of focus at the aperture and only a small portion continues to the detector. The aperture is said to be confocal with the objective. (Optics delivering the excitation light have been omitted for clarity)
Confocal detection uses a small aperture (typically 25-50 µm in diameter ≈
M*Airy diameter, where M is the objective magnification) in the optical detection path.
The light collected by the microscope objective is focused onto this pinhole such that
only light collected from very close to the focal plane ( ≈ 0.5µm ) of the objective will
be transmitted through the pinhole.
29
Light originating from regions away from the focal plane of the objective will be
out of focus at the pinhole and will be rejected to a large extent and will not reach the
detector. The use of this confocal arrangement therefore does not restrict the volume of
excitation but does efficiently reduce the collection volume. The extent to which the
confocal approach is effective is a function of the pinhole size, microscope objective,
and the lens that is used to focus the light onto the pinhole. A common modification to
this principle is to use the point-like nature of some detectors to provide confocality
rather than adding a pinhole in the detection path. For example, the active area of a
single SPAD (silicon photon avalanche detector) that composes the 32x32 matrix of
SPAD used in our set-up, is circular and ≈ 20µm in diameter, which provides inherent
confocality when used with suitable focusing optics. The transmission efficiency of
modern microscope objective at visible wavelength is high, approaching 90%, but the
overall detection efficiency of the objective is a more complex issue.
The fluorescence from a single molecule is emitted in all directions. However the
microscope objective only collects the fluorescence from a solid angle defined by the
numerical aperture (NA = n*sin θ, where θ is the half angle of aperture and n is the
index of refraction of the sample medium).
Furthermore, when the dependence of the collection efficiency on the position of
the molecule within the focal volume is taken into account, the overall objective
detection efficiency at visible wavelength can be as low as 20%.
Although this may seem very low, this represents a practical limitation of using a
single microscope objective and this limitation exists for all forms of microscopy. It is
thus essential to optimize the efficiency of all other elements in the instrument.
Single-photon excitation in an epi-fluorescence configuration combined with
confocal detection provides the necessary spatial reduction of the collection volume that
is required to minimize the background noise, and has the added benefit of simplicity.
However, this approach has two distinct disadvantages. First, the excitation light is only
spatially restricted in one direction (perpendicular to the light path) and although
fluorescence from far outside the focal plane is rejected by the confocal detection
scheme, molecules in the larger excitation volume are continuously irradiated by this
simple arrangement. This causes unnecessary photobleaching of molecules that can
reduce the useful lifetime of the sample, particularly in solid samples.
30
Second the introduction of a pinhole (and associated optics, focusing lens) in the
detection path reduces the overall amount of fluorescence from the single molecule of
interest reaching the detector (in our case this is overcome using a detector with small
active area as discussed earlier).
In one-photon excitation a particular excitation wavelength is required for efficient
fluorescence emission, and generally the difference between this wavelength and the
peak emission wavelength shift (the Stokes shift) is small. Thus all dyes efficiently
excited at the same range of wavelength tend to have spectrally similar emission
wavelengths.
The PSF (more precisely, the convolution of the excitation and collection volumes)
for either one-photon (confocal) or two-photon geometries defines a volume in solution
that is approximately cylindrical, around 500 nm in diameter and 1 µm long (so a
volume of ≈ 0.2 fl) through which the molecules diffuse and are excited.
The configuration can also be used to take images of a surface if the detection volume is
placed at the coverslip/water interface (see figure 2.1 and 2.2) and scanned over the
sample surface.
2.1.4 The PSF in single-photon confocal epi-fluores cence
illumination systems
The instrument PSF is the mathematical function that describes the way in which
light is transformed as it passes through an optical system. In an imaging system the
image recorded by the detector is convoluted with the illumination, transmission and
detection properties of the particular instrument used. In a confocal system one might
first consider the shape of the volume created in solution from the laser beam focused
by the microscope objective, and determine the PSF that describes this volume. The
volume from which light is detected however is further restricted by the confocal
pinhole defining an emission PSF.
The convolution of both PSFs result is a combined pinhole-objective system PSF.
Furthermore, any lens, filter or detector may alter the apparent volume from which light
is detected. The convolution of all of these gives us the instrument PSF and so a
description of the excitation/detection volume through which molecules may pass.
31
The form of the PSF volume defined by a confocal geometry is therefore of crucial
importance for a range of fluctuation spectroscopy methods, in particular fluorescence
correlation spectroscopy (FCS). Fluctuation techniques generally rely on measuring the
photon count distribution for a signal detected from a single diffusing dye molecule.
This data is then largely stochastic, different signals being caused by diffusion
along random paths through the volume. Thus to enable a prediction of the resulting
data (for example, to calculate the expected photon count distribution or to determine a
diffusion rate) the sample volume must be well defined.
Despite this apparent complexity, it is perhaps surprising that a simple description
of the PSF for these microscopes has been widely applied in which the sample volume
is described by a three-dimensional Gaussian with a 1/e2 beam waist diameter 2ω0 and a
length 2z0 along the optical axis given by [6]:
X@�FFFFF���� X@�FFFFF�Y, Z, [� LY\ ]^ 2�Y# � Z#9># ^2[#[># _. �2.3�
This simple model has however some weaknesses; in particular, in many cases it
apparently does not describe the shape of volume accurately and can introduce artifacts
into FCS measurements that manifest as, for example, apparent additional species in the
solution. For confocal FCS the discussion of this issue has centered more around the
optimization of experimental conditions to achieve as near a three-dimensional
Gaussian PSF (as defined by equation 2.3) as possible. A detailed study by Hess and co-
workers[10] suggests that the near three-dimensional Gaussian PSF can be obtained by
careful illumination of the sample with a Gaussian laser beam underfilling (i.e. smaller
than the back aperture) of the microscope objective and by using a small confocal
aperture (in our case a point like nature of the SPAD detectors).
32
2.1.5 Spectral discrimination
Background signal rejection is critical for successful implementation of single-
molecule detection. We have discussed the origins of the background signal: Rayleigh
and Raman scattered light (from the sample, solvent and impurities) and extraneous
fluorescence (from impurities). We have already discussed the requirement to minimize
the excitation/collection volume to reduce these background signals. We will now
consider methods to “condition” the detected signal to remove background noise by
using spectral discrimination.
Spectral discrimination is the selection of certain wavelength (or energy) photons
using thin-film dielectric, glass or notch filters or diffraction gratings.
Glass color filters (or absorption filters – material showing differential wavelength
dependent absorption of light) are relatively inexpensive, easily cleaned, and have
optical properties that are stable over long periods of time. Their principal disadvantage
is to rely exclusively on absorption to reduce background signal. The amount of
background noise rejection therefore depends on the thickness of the filter, which in
turn affect the transmission of the fluorescence signal.
Furthermore, the glasses used for these filters can themselves be fluorescent which, in
the worst case, could generate a signal overlapping in wavelength with the desired
fluorescence signal, effectively reducing the overall signal-to-noise ratio. In general,
glass color filters are therefore not preferred for single-molecule fluorescence
experiments.
Thin-film interference filters are composed of thin films of dielectric material, each
approximately the thickness of the wavelength of light, layered in stack. The reflections
from the interfaces between the layers interfere constructively or destructively
depending on the wavelength of the light, the thickness of the layers, and the refractive
index of the layer material. Filters consisting of many stacked layers can be designed to
pass narrow wavelength bands (from a few nanometers wide band pass to tens of
nanometers wide) with transmission efficiencies of 80-95% at visible wavelengths.
Auto-fluorescence of these filters is low and the blocking of wavelength outside the
pass band can be very high (several order of magnitude lower transmission than in the
band pass).
33
However, like glass color filter, interference filter also suffer from a number of
disadvantages. The dielectric material forming the thin films tends to be quite soft,
which means that the filters are easily damaged and can degrade.
Single-molecule detection experiments usually incorporate three main type of thin-
film interference filters, often called excitation, dichroic, and emission filters (figure
2.4)[6]. Excitation filters may be required when broad emission wavelength lamps are
used, or even when laser sources are used to reject the unwanted luminescence or other
laser emission lines that might overlap with the detection wavelength range of the
experiment.
Figure 2.4 Illustration of the three filter types used in single molecule fluorescence experiments. a) The excitation filter selects the correct excitation wavelength from a multiple wavelength light source. b) The dichroic filter, through which the excitation light passes, reflects the returning emitted fluorescence from the sample separating it from most of the scattered excitation light which is re-transmitted. c) The emission filter removes much of the remaining scattered light and any unwanted fluorescence. The right-hand panels illustrate the transmission characteristic of typical examples of each filter.
34
Dichroic filters (or dichroic mirror) are generally used at angle of incidence of 45°
and are used to separate light into two (or more) color ranges. In single-molecule
instrumentation, these filters enable the use of the epifluorescence configuration
discussed previously.
Generally the excitation light is reflected by the dichroic and the back propagating
fluorescence from the sample is transmitted through the dichroic into the detection
pathway (or vice versa depending on whether the dichroic is long- or short- pass) while
the reflected or backscattered excitation light is transmitted through the filter back
towards the source and away from the detection path.
Since any filter is non-ideal it will transmit/reflect a portion of the unwanted
wavelength and so in single-molecule detection it is a matter of placing different types
of filters in series until sufficient blocking is achieved and the signal-to-noise ratio is
acceptable (acknowledging some loss of the desired signal with each filter addition).
The dichroic filter alone is rarely sufficient to provide the required spectral
discrimination and therefore emission filters are placed in front of the detector(s) to
reject light outside a desired band pass (or above or below a particular wavelength).
2.1.6 Excitations sources
The excitation source for single-molecule studies is chosen on the basis of the
excitation wavelength that is required, which in turns depends on the fluorophore to be
used. Since single-molecule detection requires a fluorophore with a high quantum yield,
by far the most commonly used are specifically designed fluorescent dyes. Although a
very broad range of these dyes is available, in general, the one chosen for single-
molecule fluorescence experiments have absorption bands in the blue-green region of
the spectrum because of the availability of laser excitation source in that region.
Laser with gain media such as argon ion (488 or 514nm) and Nd:YAG (532nm)
provide a stable and controllable source, are typically already polarized and have
collimated beams and Gaussian intensity profiles perpendicular to the direction of
propagation. Regardless of the excitation type or wavelength, the stability of the light
source is critical.
35
Any fluctuations in the fluorescence intensity from an analyte caused by
fluctuations in the output of the light source (or poor pointing stability of the beam) can
severely affect the results of experiments that rely on photon counting statistics such as
FCS, PCH and FRET.
Poor pointing stability (i.e. variation in the direction of laser beam) can also cause
changes in the excitation volume in confocal arrangements. Even if a perfect light
source, free from all intensity fluctuations, is incident on a detector then the output of
the detector (photon counts per given time interval) is not steady but exhibits
fluctuations within a Poisson distribution.
This is because the quantum mechanical nature of the interaction of a photon with a
detector leads to there being a statistical probability that the arrival of the photon results
in an output signal. Since single-molecule fluorescence detection involves the counting
of small numbers (< 200) of photons in short time interval (< ms), such inherent
fluctuations caused by the detection process can be the dominant source of noise in the
experiment. However, this phenomenon can also be used as a convenient test of the
stability of the instrumentation. If the scattered light or fluorescence from a
concentrated sample that does not induce variation in intensity is measured, then the
output of the detector should follow a Poisson distribution in counts per unit time
interval (figure 2.5)[6]. Any deviation from this (i.e. broader distribution ) indicates that
fluctuations are occurring over and above those induced by the stochastic nature of
photon detection and is indicative either of laser intensity fluctuation or shortcomings of
the instrumentation in term of mechanical stability.
36
Figure 2.5 Photon count histogram of an ideal scatteres placed at the laser focus. The collected photon count
distribution (circle normalized) is fitted exactly by a Poissonian function (line) indicating that there are no fluctuations in the detected signal arising from instability of the light source or other instrumentation.
2.1.7 Microscope objective for single-molecule fluo rescence
detection
The choice of the microscope objective is one of the most important issue in the
single-molecule detection system. In many experiments it is critical for the generation
of a small excitation volume. In epifluorescence geometries it also collects the
fluorescence from the sample. Microscope objective are compound lenses, consisting of
many individual elements. In general the design is intended to provide the required
magnification, a small focal spot, and, as far as possible, an aberration-free image with
high collection efficiency. As far as single-molecule fluorescence experiments are
concerned, the suitability of a microscope objective can be assessed by considering the
numerical aperture, the magnification, whether the objective is oil immersion or
designed to operate in air, and the degree of aberration correction.
37
The numerical aperture (NA) of an objective describes the solid angle over which
light is collected by the lens.
The NA is defined by[6],
(W E sin�c� �2.4�
where n is the refractive index of the imaging medium and µ is the half angle of the
solid cone defined by the collected light (figure 2.6)[6]. In microscopy, NA is important
because it indicates the resolving power of a lens. The size of the finest detail that can
be resolved is proportional to λ/NA, where λ is the wavelength of the light. A lens with
larger NA will be able to visualize finer detail than a lens with a smaller numerical
aperture, and also collect more light and will generally provide a brighter image.
Figure 2.6 (a) The numerical aperture of an objective is defined in terms of the half angle of the cone of rays
(µ). The effect of using an immersion oil is shown in (b) and (c) – peripheral rays which are refracted out of the cone defined by the numerical aperture when the space between the coverglass and objective is filled with air, propagate into the front lens of the objective when refraction is eliminated by filling the space with index matching oil.
38
In microscopes with an inverted design (the objective pointing upwards as in our
experiment) it is necessary to image through a thin coverglass. In this case when the
medium between the objective and coverslip is air (Figure 2.6 (b))[6], the numerical
aperture is limited to a value of ≈ 1 due to refraction at the coverslip – air interface. To
achieve a higher NA, an immersion objective is required. An oil immersion objective
has a high refractive index oil layer between the frontmost objective lens and the
coverglass (Figure 2.6(c)) where the oil and the coverglass are generally chosen to
match closely the refractive index of the objective. There are objectives with different
immersion fluids, but most commonly with water or oil, which have refractive index of
approximately 1.33 and 1.51, respectively. Water immersion objective are designed
(corrected)to image on aqueous sample through a number 1.5 coverslip (thickness ≈
170µm). They are preferable to oil immersion objective when imaging deep (≈ 10 µm)
in the sample, because of reduced aberration. Typically, in practice, water immersion
objective provide numerical apertures of up to 1.2 and oil objectives of up to 1.45. It
should be remembered that whatever the NA of the objective, the NA of the system is
(to an approximation) limited by the lowest refractive index substance between the
objective and sample. Thus a 1.45 NA objective, even when used with the correct
coverslip and immersion oil, would still have a reduced NA if the light as being focused
(or collected) through an aqueous solution, in other words if the specimen is not in
contact with the coverslip. For work in aqueous conditions where the sample is not in
contact with the coverslip (in diffusion experiments it is desirable to place the detection
volume several µm into the solution, to prevent artifact from molecules attached to the
nearby surface), the NA is effectively limited to a value close to the refractive index of
the solvent used (≈ 1.33 for water).
The NA can have a large effect on the collection efficiency of the objective. For
example, NAs of 1.45, 1.3, and 0.95 correspond to 40%, 26% and 10% of the total
possible sphere of collection around an objective. Thus small improvements in NA can
result in significantly more photons at the detector.
Optical aberrations can degrade the quality of images, change the light distribution
at the focus, reduce the resolving power, and increase the focal spot size (therefore
increasing the sample volume) of an objective.
39
The primary aberrations commonly experienced in microscopy are spherical, coma,
lateral and longitudinal chromatic, curvature of field, and astigmatism. Fortunately, high
NA objectives are often corrected for these aberrations to a great extent and they are
therefore not usually an issue from the point of view of single-molecule fluorescence
measurements.
2.2 Detectors for single-molecule fluorescence
experiments
The choice of detector is a critical stage in the development of a single-molecule
fluorescence experiment. In general the detector should fulfill the following requests:
1. high quantum efficiency (QE) over the spectral range of interest,
2. good linearity of quantum efficiency over the spectral range of interest,
3. sufficiently fast time response for the application,
4. low noise (i.e. low average dark count), permitting single-molecule
detection.
We will focus our discussion to detectors suitable for work in the visible and near-
infrared part of the optical spectrum: photomultiplier tubes (PMTs), avalanche
photodiodes (APDs), in particular single-photon avalanche diodes (SPADs) and
electron multiplying charge-coupled devices (EMCCDs).
These detectors may be divided in two categories. PMTs and SPADs (as well
APDs) are single point detectors, the single output of which is proportional (not for
SPADs and not PMTs used on single- photon counting mode) to the integrated light
intensity impinging on the detector area.
Such detectors can be used for fluctuation spectroscopy using light collected from a
point within the sample or the sample could be raster scanned to record and image.
CCDs are imaging detectors that contain an array of detector elements and the object
plane of the sample can be imaged directly onto the detector surface. The suitability of
each of these type of devices for a given single molecule spectroscopy application
depends on the way the devices work.
40
2.2.1 Point detectors
Point detectors are detectors which do not provide position information, but are not
necessarily of small dimension. For instance, most single-photon avalanche photodiodes
used in SMS have a sensitive area with a diameter of a few dozen to a couple hundred
micrometers, whereas photomultipliers have typically diameters of several millimeters.
This has some practical consequences for collection efficiency and design of the
detection path. As discussed before, point detectors are mostly used in a confocal setup
to detect photons emitted from a small volume excited in the sample. The smaller the
sensitive area, the lower the magnification of the collection optics needed to focus the
collected light onto this sensitive area, and the more difficult the alignment of the
detector for maximum detection efficiency[11].
As was just mentioned, there are two general types of point-detectors used for
single-molecule applications: photomultiplier tubes (PMT) and single-photon avalanche
photodiodes (SPAD). In both kinds of devices, each detected photon is first converted
into a charge carrier/s (photo-electron or electron-hole pair), which is/are then amplified
by several order of magnitude in a rapid avalanche process. The basic layout of a typical
PMT is illustrated in figure 2.7.
Figure 2.7 Illustration of the basic principle of operation of a PMT.
The photon strikes the photocathode, is absorbed and generates a photoelectron
with a certain quantum efficiency determined by the photocathode material. When a
photoelectron is produced it is accelerated towards the first dynode by the electric field
created by focusing electrode. The photoelectron strikes the first dynode and result in
the generation of secondary electrons (again with a certain efficiency), each of which is
41
accelerated in an electric field and strikes a subsequent dynode, generating further
secondary electrons. The process of amplification continues down the dynode chain
until the anode collects the electron emitted by the final dynode and an external circuit
detects this current. PMT’s often suffer from poor linearity in output current over a
large range of intensities, often have low quantum efficiency (typically < 25%) and also
a narrow spectral response. Dark current, generated when no light is falling on the
photocathode, due to thermionic emission of electron, is a source of noise in PMTs that
can be reduced by cooling. Multiplication noise (i.e. the variation in output signal for
any given single photon impinging on the photocathode due to the chain of probabilities
involved in the amplification process) is also an issue with PMTs at very low light level.
The single-photon avalanche diodes (SPADs) are semiconductor devices based on a
p-n junction reversed biased at a voltage (Va) higher than the breakdown voltage (Vb)
(figure 2.8). At this bias, the electric field is so high (higher than 3×105 V/cm) that a
single charge carrier injected in the depletion layer can trigger a self-sustaining
avalanche. The current rises swiftly (sub nanosecond rise-time) to a macroscopic steady
level, in the milliampere range. If the primary carrier is photo-generated, the leading
edge of the avalanche pulse marks (with picosecond time jitter) the arrival time of the
detected photon.
The current continues until the avalanche is quenched by lowering the bias voltage
Vd down to or below Vb : the lower electric field is not able any more to accelerate the
carriers to impact-ionize with lattice atoms, therefore current ceases. In order to be able
to detect another photon, the bias voltage must be raised again above breakdown[12].
Figure 2.8 Thin SPAD cross section
42
These operations require a suitable circuit, which has to:
1. sense the leading edge of the avalanche current;
2. generate a standard output pulse synchronous with the avalanche build-up;
3. quench the avalanche by lowering the bias down to the breakdown voltage;
4. restore the photodiode to the operative level. This circuit is usually referred to as
a quenching circuit.
The simplest quenching circuit is commonly called Passive Quenching Circuit and
composed of a single resistor in series to the SPAD. This experimental setup has been
employed since the early studies on the avalanche breakdown in junctions. The
avalanche current self-quenches simply because it develops a voltage drop across a
high-value ballast load (about 100 kΩ or more). After the quenching of the avalanche
current, the SPAD bias Vd slowly recovers to Va, and therefore the detector is ready to
be used again. A more advanced quenching scheme is called active quenching. In this
case a fast discriminator senses the steep onset of the avalanche current across a 50 Ω
resistor and provides a digital (CMOS, TTL, ECL, NIM) output pulse, synchronous
with the photon arrival time.
Besides photon-generated carriers, also thermally-generated carriers (through
generation-recombination processes within the semiconductor) can fire an avalanche
process. Therefore, it is possible to observe output pulses also when the SPAD is kept in
dark: the resulting average number of counts per second is called dark count rate and is
the key parameter in defining the detector noise.
It is worth noting that the reciprocal of the dark count rate defines the mean time
that the SPAD remains biased above breakdown before being triggered by an undesired
thermal generation. Therefore, in order to work as a single-photon detector, the SPAD
must be able to remain biased above breakdown for a sufficiently long time (e.g., longer
than few milliseconds, corresponding to a count rate of few kilo counts per second,
kcps).
43
Both APDs and SPADS are reverse biased semiconductor p-n junctions. However,
APDs are biased close to, but below the breakdown voltage of the semiconductor. This
high electric field provides an internal multiplication gain only on the order of few
hundreds, since the avalanche process is not diverging as in SPADs. The resulting
avalanche current intensity is linearly related to the optical signal intensity.
As mentioned in the previous paragraphs, the possibility to obtain for these
detector a very small size of their sensitive area (from ≈ 20 to ≈ 100 µm), offer the
advantage that they can also function as the confocal “aperture” in epifluorescence
microscope, removing the need for a pinhole and hence increasing the overall
detection efficiency. In addition, as will be discussed in the next chapter, the
possibility to build this devices in mono-dimensional or bi-dimensional array,
combined to the use of micro-lens array or spatial light modulator that generate an
array of excitation spot matching the SPAD array, make it possible to parallelize the
acquisition of the data in FCS measurement, resulting in a faster data acquisition
process.
2.2.2 Imaging detectors
Imaging detectors comprise a two dimensional array of typically micron scale
detector elements that can each be addressed by readout circuitry so that an image of the
sample can be acquired. A suitable optical arrangement must be used to image the
object onto the plane of the detector array. CCDs are by far the most common imaging
arrays; in these each detector element is formed from a charge storage device. Incident
photons generate charge carriers in each element which are accelerated and are stored
using an applied potential. The amount of charge stored in these “well” will thus be
proportional to the integrated light intensity that has fallen on that elements of the array.
Readout of the array is achieved by movement of the charge from each element of the
array to the next, either on an individual basis or line by line, as illustrated in figure 2.9.
The readout process is a limiting factor on the frame rate of CCD cameras.
This is determined by the speed of the electronics that move the charge, the time
required to clear out residual charge between exposures, and the speed of reading the
signal from the output register.
44
Figure 2.9 Schematic representation of the structure of a typical CCD. Elements are read out sequentially by
first moving charge downwards line by into an output register using a series of electrodes. This register is then read out one element at time and the signals amplified by an external electronic current amplifier. In the EMCCD system on-chip gain is provided before external amplification to lift even very low signals well above the read out noise floor.
To be suitable for single molecule detection a CCD should fulfill a number of
requirements: its spatial and temporal resolution should be appropriate to the
application, the quantum efficiency (QE) of converting photons arriving at the CCD
surface to charge generation is high, and the dynamic range (i.e. the range of input
intensities that can be accommodated) should be large. CCD quantum efficiency is
defined by the physical structure of the pixel elements and the electrodes as well as the
semiconductor material used. The QE also tend to be a strong function of temperature
and so all high-sensitivity CCD cameras are equipped with cooling as optimal operation
temperatures can be as low as -90°C.
The basic CCD detector is not suitable for fast frame rate, low light level
applications because of the frequency dependent read out noise (from electronic circuit
amplification) and gain must be introduced in order to render these devices capable of
single molecule detection. Intensified CCDs (ICCD) and electron multiplying CCDs
(EMCCD) are the two most common system that are used. ICCD were the first
development of CCDs intended to extend the detection sensitivity to near single
incident photon level.
45
They generally combine a micro channel plate (MCP, essentially an array of small
PMTs ) onto the front of the CCD array. These devices are however complex,
expensive, affected from noise dues, especially, from cross talk between MCP elements
on adjacent pixels and with finite lifetime. An alternative configuration is used in
EMCCD technology. The EMCCD uses an additional register between the output
register and the output amplifier, called the gain register (Figure 2.9). High potentials
applied to the
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