Quantitative Colocalisation Imaging: Concepts,
Measurements, and Pitfalls
Martin Oheim and Dongdong Li
Abstract Many questions in cell biology and biophysics involve the quantitation of
the colocalisation of proteins tagged with different fluorophores and their interaction.
However, the incomplete separation of the different colour channels due to the
presence of autofluorescence, along with cross-excitation and emission ‘bleed-through’
of one colour channel into the other, all combine to render the interpretation of multi-
band images ambiguous. Traditionally often used in a qualitative manner by simply
overlaying fluorescence images (‘red plus green equals yellow’), multicolour fluo-
rescence is increasingly moving away from static dual-colour images towards more
quantitative studies involving the investigation of dynamical three-dimensional
interaction of proteins tagged with different fluorophores in live cells. Quantifying
fluorescence resonance energy transfer efficiency, fluorescence complementation
and colour merging following photoactivation or photoswitching provide related
examples in which quantitative image analysis of multicolour fluorescence is
required. Despite its widespread use, reliable standards for evaluating the degree
of spectral overlap in multicolour fluorescence and calculating quantitative colo-
calisation estimates are missing. In this chapter, using a number of intuitive yet
practical examples, we discuss the factors that affect image quality and study their
impact on the measured degree of colocalisation. We equally compare different
pixel-based and object-based descriptors for analysing colocalisation of spectrally
separate fluorescence. Finally, we discuss the use of spectral imaging and linear
unmixing to study the presence in a ‘mixed pixel’ of spectrally overlapping fluoro-
phores and discuss how this technique can be used to provide quantitative colocali-
sation information in more complex experimental scenarios in which classic dual- or
triple-colour fluorescence would produce erroneous results.
During the past 15 years there has been a remarkable growth in the use of fluores-
cence imaging in biological microscopy. This development has been largely driven
by the generation and widespread use of fluorescent protein chimeras (reviewed in
S.L. Shorte and F. Frischknecht (eds.), Imaging Cellular and Molecular Biological Functions.
© Springer 2007
118 M. Oheim and D. Li
Shaner et al. 2005; Giepmans2006). Also, three-dimensional imaging at the subcel-
lular level has become possible for many researchers with the broad availability of
confocal and two-photon-excited fluorescence (2PEF) microscopes to many labo-
ratories and imaging platforms. After the identification of the key molecules and
signalling pathways, many questions in cell biology and cell biophysics concern
where and when these molecules interact (Schultz et al. 2005). As a consequence,
microscopic multicolour imaging is moving away from classical confocal immun-
ofluorescence (Miyashita 2004) towards studies that typically involve the quantifi-
cation of the dynamics of the three-dimensional expression and –ideally – interaction
of proteins tagged with different fluorophores in live cells. Information on molecu-
lar interaction could be derived by adding information derived from fluorescence
resonance energy transfer (FRET) (Jares-Erijman and Jovin 2003), fluorescence
complementation assays (Kerppola 2006), or colour merging following photoacti-
vation or photoswitching (Betzig et al. 2006; Chudakov et al. 2006; Hess et al.
2006). Thus, larger and highly dimensional data sets must be handled.
Colocalisation studies using fluorescence imaging represent a powerful method
for exploring putative associations between molecules and their targeting to discrete
intracellular compartments. Ideally, several spectrally well-distinct fluorophores
would be specifically addressed to their molecular-scale targets and imaged into
distinct, spectrally separated detection channels so that the fluorescence intensity in
each channel would contain spatial and concentration information exclusively
derived from one fluorophore. These images could then be pseudocolour-coded
displayed side by side or overlaid and the amount of colocalisation could be esti-
mated from these intensity maps. Red and green equals yellow. The estimation of
protein expression and colocalisation can be broken down to two steps: first, the
selective labelling with and imaging of different fluorophores, followed by the
quantification of their colocalisation from multicolour images. Both of these steps
are based on hypotheses, for example that all collected fluorescence originates from
endogenous label, and rely on the correct expression and subcellular targeting of
fusion proteins, the existence of only negligible cross-talk between acquisition
channels, or the linearity and spatial homogeneity of the analysed images.
In a real experiment, however, every one of the underlying assumptions is
probably violated to some extent. Two simple questions arise:
1. To what extent are the spatial, spectral, and (to a lesser degree) temporal images
2. How can we quantify the degree of colocalisation from such fluorescence images?
The aim of this chapter is to discuss the problems associated with the different
techniques for dual-colour imaging and quantifying colocalisation and to evaluate their
respective performance and limitations. Considering the microscope as a linear imaging
device, we can describe the image of an arbitrary object as the linear superposition
of point images of different intensity. We therefore restrict our discussion to imaging
(subresolution) point objects. The generalisation to extended objects is straightforward.
The chapter is organised as follows: we first (Sect. 5.1.1) introduce a synthetic yet
realistic dual-colour example that we will use throughout this chapter to study the
5 Quantitative Colocalisation Imaging 119
impact of different image parameters on the colocalisation estimate and to evaluate
different strategies to quantify colocalisation. This example has the virtue that we can
know and control the true amount of colocalisation between probes and can vary their
degree of spectral overlap and relative brightness, vary the image noise and background
offset in a controlled manner, and study their impact on the colocalisation estimate.
In Sect. 5.1.2, we stress the importance of matching dyes, filters, and intermediate
optical components by regarding (Box 5.1) step by step the process of choosing
appropriate combinations in a realistic experiment. Box 5.2 offers a swift review of
optical sectioning techniques that can improve the colocalisation detection.
Box 5.1 Tracing spectral throughput along the excitation and emission
The goal of dual-colour fluorescence microscopy is to simultaneously map
the location and dynamics of two fluorescent vesicle markers from a dual-
colour image pair. Multicolour maps are only as good as the raw images that
are used to calculate them.
We here develop a simple rationale to chose optimal filters for a given
fluorophore pair and to estimate the cross-talk that is engendered by filter
mismatch. A more complete treatment can be found as an online resource on
the Oheim laboratory Web site (Oheim et al. 2007). In the simplest case of
only two fluorophores and negligible (or spatially and spectrally uniform)
background, the fluorophore separation only depends on their excitation and
emission spectral overlap and the filter bands used to isolate them. Neglecting
higher-order effects (fluorophore saturation, self-absorption, aggregate forma-
tion and quenching, bleaching), the measured intensity (in analogue/digital
[A/D] units) of a fluorophore on a microscopic image depends linearly on
1. The fluorophore spectral extinction e(l), which describes the probability of
absorbing a photon at wavelength l and is typically given as e × Fabs (l),
where e is the molar extinction coefficient (mostly but not always specified
at peak absorption) and Fabs (l) is the fluorophore absorption spectrum, with
the peak absorption normalised to 1. e is of the order of 61,000 mol−1 cm−1
for pEGFP-N1 (Clontech) and 48,000 mol−1 cm−1 for FM4-64 (Invitrogen).
The curves for Fabs (l) are given in Fig. 5.6b. We next trace along the micro-
scope light path (Fig. 5.6a, inset), starting from the light source1, the fraction
of the excitation light (black line) that is transmitted by the intermediate
optical components and reaches the sample to excite the fluorophores.
1 The black line is the normalised experimental spectral distribution of the excitation light source
used – here, a TILL polychrome II with about 20-nm excitation bandwidth. Alternatively, one could
substitute here the transmission spectrum of an emission bandpass filter multiplied with the spectral
emission of the Xe or Hg arc lamp.
120 M. Oheim and D. Li
Box 5.1 (continued)
Next, the dashed blue line shows the reflectance (1 minus transmission,
neglecting absorption) of the primary dichroic beamsplitter.
2. The fluorescence quantum yield f of a fluorophore defines the probability of
an excited molecule relaxing to the ground state by emitting a fluorescence
photon. The probability of emitting a photon at wavelength l is obtained by
multiplying f with the normalised (Ú Fem (l) d l = 1) fluorescence emission
spectrum Fem (l). f = 0.60 for enhanced-green fluorescent protein (EGFP;
Patterson et al. 1997). In the absence of specific information for FM4-64 in
lipid membranes (Bill Betz, Denise Lo Invitrogen, personal communica-
tions), we equally assumed 0.6 for FM4-64 (Table 5.1). The product eφ is
sometimes referred to as the fluorophore brightness. The most absorptive
fluorophores absorb more than 2 orders of magnitude more efficiently than
the least. This is in stark contrast to the quantum efficiency, which typically
falls in the range from 0.25 to 0.9 for most useful fluorophores, so they will
not differ by more than a factor of 3–4 at most. As a result, f will be of sec-
ondary importance in determining brightness.
Table 5.1 Spectroscopic properties of enhanced-green fluorescent protein (EGFP) and
ε (mol−1 cm)−1
50 mM HEPES, pH 7.5
Measured in CHCl3
HEPES N-(2-hydroxyethyl)piperazine-N´-ethanesulfonic acid
λex, peak (nm)
λem, peak (nm)
48,000 734 0.6c
a Cubitt et al. (1999)
b Patterson et al. (1997)
c FM dyes are almost non-fluorescent in water, but their quantum yield increases about 350
times when they partition into a hydrophobic environment. (Henkel et al. 1996). The actual
φ value in a lipid is hard to determine, as the concentration is typically not known. We
therefore simply assumed that FM4-64 and EGFP have the same quantum efficiency.
3. The fluorophore concentration c, in moles per litre, or its density, e.g. for
4. The camera exposure or, more generally, detector integration time.
5. The fluorescence excitation volume (related to the objective optical
depth, along the z-axis and illuminated area (xy), and thus to the numerical
aperture (NA); however, not in two-photon-excited fluorescence).
6. The fraction of fluorescence collected (i.e. the solid angle covered by the
7. The fluorescence collection volume (in the case of confocal apertures or
directional-emission detection; Axelrod 2001).
8. The A/D unit, i.e. the number of counts per detected electron/pixel.
5 Quantitative Colocalisation Imaging 121
9. Light flux (illumination intensity) and detector response (detector quantum
We consider here a single-excitation side-by-side projection of two colour-
channel images (Fig. 5.6a, inset); we only compare the relative contribution of
isomolar EGFP and FM4-64 to each colour-channel image, ceterum paribus.
Given the narrow spectral width of the excitation, we neglected the spectral
profile of the light source, which is set unity for all l. To estimate cross-excita-
tion, we multiply for each dye the spectral profile of the excitation light source,
the dichroic reflectance (i.e., 1 minus its transmittance, neglecting absorption)
and e × Fabs (l) (Fig. 5.6b, bottom). Integration over λ shows that – under these
conditions – EGFP is 1.3-fold more efficiently excited than FM4-64. Stated
otherwise, the (intentional) cross-excitation is 43% (FM4-64) versus 57%
(EGFP), so both fluorophores are excited with (roughly) equal efficiency.
On the emission side, to calculate bleed-through we proceed similarly by trac-
ing back the transmitted fluorescence through both microscope detection arms.
Hence, to calculate the contribution of each fluorophore to the ‘red’ and ‘green’
colour image we consecutively multiply their fluorescence emission spectra with
f and the transmission curve of the primary dichroic mirror, the transmission (for
the ‘red’ channel) and reflection (for the ‘green’ channel) of the secondary dich-
roic mirror (Fig. 5.6a, inset), and, for each channel, the transmission curves of the
respective emission bandpass filters. The corresponding curves are shown in Fig.
5.6c (top). Again, we neglected the transmission spectrum of the microscope
intermediate optics as well as the spectral response of the detector, which we
assume to be uniform in the wavelength range studied. The result is illustrated in
the bottom panel of Fig. 5.6c, and integration over l yields a 4% estimate of the
contamination of the green-detection channel with FM4-64 signal and of less than
0.01% EGFP detected in the red colour channel.
Finally, the total cross-talk between the red and green channels is given by
multiplying the excitation cross-talk and emission bleed-through and dividing
through the sum of these products for both fluorophores (Oheim et al. 2007).
In the specific case of 488-nm excitation and simultaneous dual-emission
imaging of FM4-64 and EGFP, we obtain that 99.98% of the signal detected
in the red channel comes from FM4-64 and 96.85% of the signal detected in
the green channel results from EGFP.
Thus, from the spectral separability analysis we expect that both EGFP and
FM4-64 largely dominate the green- and red-detection channels, respectively,
with only negligible cross-talk.
To facilitate the comparison of colocalisation data across different studies and
to evaluate the error of the colocalisation estimate, it should be good practice to
explicitly state the amount of cross-talk between the different detection channels
used. The spectral separability index defined here offers a convenient criterion
for evaluating and comparing multicolour data sets (Oheim et al. 2007).
122 M. Oheim and D. Li
Box 5.2 Optical sectioning techniques to lower image background and increase
Confocal microscopy is a well-established optical sectioning technique that
is based on the observation that a point source of excitation light (illumina-
tion pinhole) can be used to create a diffraction-limited focus in the speci-
men plane, which in turn corresponds to a confocal spot in the image plane.
Thus, in-focus light at locations different from the illuminated spot as well
as out-of-focus signal can be effi ciently rejected by placing a small pinhole
(roughly of the diameter of the Airy disc) in the confocal image plane. To cre-
ate an image, the spot is scanned with respect to the specimen, in biological
confocal microscopy typically by scanning the beam angle in the objective
pupil. Although it (slightly) increases resolution and (substantially) reduces
background, confocal microscopy is not particularly well suited for live-cell
imaging, because – as most generated fl uorescence is rejected at the confocal
aperture – it makes very ineffi cient use of excitation photons.
Multiphoton excitation fl uorescence (MPEF) microscopy is a laser-scanning
technique as well. Here, the improved image contrast and background rejection
are achieved by restricting the fl uorescence excitation volume, rather than the
fl uorescence collection volume as in confocal microscopy. The technique is
based on the near-simultaneous non-linear absorption of two or more photons
that combine their energies to excite a fl uorophore from the ground state to
the fi rst excited state. MPEF is restricted to a tiny volume near the focus, be-
cause high photon densities are required for the phenomenon of multiphoton
absorption (one way to think about this is to realise that the trajectories of
multiple photons must cross the excited molecule simultaneously). MPEF
uses infrared light to excite ultraviolet (three-photon excited fl uorescence) or
visible (2PEF) fl uorescence. This, together with the broad 2PEF absorption
spectra (compared with one-photon excited fl uorescence), and the availability
of the entire visible-wavelength range for fl uorescence detection, permits
effi cient fi ltering and facilitates multiband recordings.
Total internal reflection fluorescence microscopy (TIRFM) is a light-
confinement technique that exploits the phenomenon of total internal refl ection
of a light (in most instances, a laser) beam at a dielectric interface to generate
a thin (approximately λ/5), exponentially decaying evanescent fi eld that skims
the lower-refractive-index medium. This near-fi eld perturbation can be used
to create a near- surface fl uorescence excitation. When cells are grown on the
dielectric boundary (i.e. the glass–water interface) only fl uorophores in a thin
near- membrane space are excited, whereas the bulk of the cell is spared from
fl uorescence excitation and photobleaching. Owing to its extremely low back-
ground, evanescent-fi eld microscopy is often used when studying single-fl uoro-
phore photodynamics. Because the image is restricted to a thin section, TIRFM
is typically used in conjunction with epifl uorescence excitation.
5 Quantitative Colocalisation Imaging 123
Deconvolution. Within the approximation of linear imaging theory, each point
of the object can be described as a point-source of light that gives – depending
on its intensity and precise focal position – rise to a shifted and weighted copy
of the point-spread function (PSF). Conversely, with knowledge of the experi-
mental PSF, the information contained in a three-dimensional image stack can
– in principle – be used to back-calculate the initial fl uorophore distribution
that produced the blurred diffraction-limited image. Although the reassign-
ment of detected photons to their original location is – in principle – possible,
the mathematical algorithms to solve this ‘inverse problem’ are fairly noise
sensitive and are somewhat notorious in generating artefacts. In laboratory
practice, three-dimensional image restauration by ‘deblurring’ is often outper-
formed by confocal imaging.
Reversible saturable optical fl uorescence transition (RESOLFT) concepts.
Contrary to what one might expect from the optical diffraction limit, fl uores-
cence microscopy is in principle capable of unlimited resolution. The nec-
essary elements are spatially structured illumination light and a non-linear
dependence of the fl uorescence emission rate on the illumination intensity.
In saturated structured-illumination microscopy, the non-linearity arises from
saturation of the excited state (Gustafsson 2005). The diffraction barrier has
equally been broken by a saturated depletion of the marker’s fl uorescent state
by stimulated emission (Willig et al. 2006),but this approach requires pico-
second laser pulses of gigawatt per square centimetre intensity. With use of
much smaller intensities, subdiffraction resolution can be achieved from re-
versible photoswitching of a marker protein between a fl uorescence-activated
and a non-activated state, whereby one of the transitions is accomplished by
means of a spatial intensity distribution featuring a zero (Betzig et al. 2006;
Hofmann et al. 2005).
Section 5.2 revisits these examples to review different semiquantitative (colour
merging, Sect. 5.2.1), pixel-based (Sect. 5.2.2), and object-based colocalisation
estimates (Sect. 5.2.3) and discusses their performance. Box 5.3 extends the calcu-
lation of colocalisation coefficients to fluorophore abundance maps rather than flu-
orescence images. These maps are generated as a result of spectral imaging and
linear unmixing (SILU) techniques in which the presence and relative contribution
of fluorescent probes are analysed from a set of spectral images that is overdeter-
mined, i.e., contains more planes than the sample contains fluorophores. We have
recently introduced a variant of this technique specifically adapted for classifying
resolution-limited point objects containing multiple fluorophores in live cells
(Nadrigny et al. 2006).
124 M. Oheim and D. Li
Box 5.3 Multispectral and hyperspectral imaging
In addition to sequential or synchronous multiband recordings, many com-
mercial laser scanning microscopes now permit multispectral or ‘hyper’-spectral
detection. Spectral detectors are based on a dispersion element (prism, grat-
ing) and the parallel detection of a range of wavelength, either on a linear
photodiode array (Zeiss) or on an arrangement of multiple photomultiplier
tubes with movable entry slits (Leica). These instruments generate a fl exibil-
ity that fi lter-based multichannel acquisition cannot offer. Spectral imaging
devices have the advantage over earlier integrative (photometric) devices of
providing – for each pixel – spectral and localisation information in addition
to fl uorescence intensities.
Because microscope images are diffraction-limited, neighbouring pixels
of fl uorescent objects are not independent; therefore, object-based approach-
es to quantify colocalisation can take into account a priori knowledge of the
imaged object. An advantage of such object-based colocalisation analysis is
that one can make use of additional information, e.g. the size and shape of
the subcellular object under study, or of correlations between neighbouring
pixels (Nadrigny et al. 2006).
When thinking in terms of multidimensional histograms (Sect. 5.2.3),
we can view linear unmixing as a projection of each spectral pixel vector
onto an orthonormal basis. Thus, instead of parameterising the spectral vec-
tor in terms of N fl uorescence detection channels, its coordinates are given in
terms of a set of k (pure) fl uorophore vectors. Already with a surprisingly low
number of spectrally overlapping detection bands (Neher and Neher 2004a)
spectral imaging and linear unmixing permits fi ngerprinting the expression of
spectrally overlapping fl uorescent proteins on single secretory vesicles in the
presence of a spectrally broad autofl uorescence. By making use of statistical
tools and the knowledge of the microscope’s PSF, this technique provides a
robust alternative to error-prone dual-colour or triple-colour colocalisation
studies in live cells (Nadrigny et al. 2006).
Most of the arguments used throughout this chapter rely on multiple-emission
detection but symmetrically apply to experiments using multiple excitation wave-
lengths instead. We also note that although the optimal separation of fluorophore
signal often requires both multiple-excitation and multiple-emission fluorescence
imaging, we focus here on multiple-emission detection.
5.1.1 One Fluorophore, One Image?
Multicolour displays showing overlaid multichannel fluorescence images are
increasingly being used in the cell and neurobiological literature to illustrate
5 Quantitative Colocalisation Imaging 125
molecular colocalisation and interaction. It is generally assumed that one
fluorescence channel contains a specific signal, exclusively related to one fluoro-
phore, and that images are comparable among different acquisition channels.
Figure legends will typically read ‘a Confocal fluorescence images of a … cell
coexpressing a molecule X – enhanced-green fluorescent protein (EGFP) chimera
(top), and protein Y fused to monomeric red fluorescent protein (mRFP, bottom).
b Time series of EGFP (top) and mRFP images (bottom) reveals an increase in
colocalisation after stimulation. c Pseudocolour overlay of EGFP and mRFP
images. Note the increase in yellow indicating colocalisation (arrowheads)…’ or
similar. Often, the precise experimental conditions (illumination, filter and detec-
tion settings, fluorophore variants used, etc.) are not very explicit and controls are
omitted. The critical evaluation of colocalisation data requires more information
than is often given. The major problems encountered with quantitative multicol-
our microscopy are well identified. Their relative importance, however, can vary
from one microscope to another, from one experiment to another, and probably
even from one batch of cells to another, depending, e.g., on the level of protein
expression, autofluorescence in the preparation, or detector noise. For each com-
bination of fluorophores imaged, it is important to quantify to what degree the
different detection bands really contain independent and fluorophore-specific
information. Also, although it might appear tedious and time-consuming, under-
standing the physical limitations of what can be achieved with a given combina-
tion of flurophores, filters, and optical components is a useful exercise that lays
the grounds for sensible instrument use. We stress this point specifically having
the engineers and researchers in mind who are responsible for and run shared
facilities and imaging platforms and can guide less experienced users to make
126.96.36.199 Spectral Overlap
Organic fluorophores typically display broad absorption bands that lead to considerable
cross-excitation. Cross-excitation quantifies the amount of (usually unwanted2)
excitation of fluorophores other than the one to be excited by this wavelength band.
On the emission side, the problem is typically called bleed-through and relates to
the amount of fluorescence that originates from other fluorophores detected in the
fluorescence channel designed to view one specific fluorophore. Often, it is
accentuated over cross-excitation because fluorescence tails off into the red owing
to the decay into higher vibrational levels of the S1 state and thermalisation of the
excess vibrational energy, solvent effects, excited-state reactions, complex formation,
or energy transfer. The total cross-talk will be proportional to the product of cross-
excitation and bleed-through (Box 5.1).
2 Special cases in which excitation cross-talk and emission bleed-through are not only tolerated but
intentionally wanted are dual-colour emission detection with simultaneous excitation of two dyes
emitting in different fluorescence bands, or dual-colour excitation with single-emission detection.
126 M. Oheim and D. Li
The ever-increasing generation of new fluorescent protein colour variants
(reviewed in Shaner et al. 2005) and the expanding family of genetically encoded
indicators (Griesbeck 2004) have not removed but rather accentuated the problem
of fluorophore separation in multicolour fluorescence microscopy. Although a
broader range of monomeric fluorescent proteins is becoming available, the
choice of spectrally well separated variants is still very restricted. Also, for each
new fusion protein and expression system, the specific targeting and lack of
retention in the endoplasmic reticulum must be verified individually. For
example, Hirrlinger et al. (2005) recently demonstrated that the formation of flu-
orescent precipitates limits the use of the spectrally attractive red-emitting reef
coral proteins in transgenic animals. Those fluorescent proteins that work best
have considerable overlap and cannot be separated using specific filter sets
(Nadrigny et al. 2006; Zimmermann 2005).
We display in Fig. 5.1a two synthetic in-focus fluorophore maps. True fluorophore
locations are represented by cross hairs (green) and circles (red), respectively. To
model image formation, we convolved this high-resolution fluorophore map with an
(experimentally determined interpolated high-resolution) point-spread function (PSF)
of an objective with a numerical aperture (NA) of 1.45 and resampled the resulting
diffraction-limited image with a pixelated imaging detector (Fig. 5.1b).The resulting
red and green images were low-pass-filtered (1 µm−1) and the low-pass-filtered image
was subtracted from the original image to remove high-frequency noise. The result
was thresholded to exclude background, and binarised. We estimated the colocali-
sation in the red channel (index 1), by calculating the degree of overlap of the two
binary masks of the dual-colour image relative to the red binary image squared
(Lynch et al. 1991),
( , )
( , )
w x y w
w x y
w x y
w x y
and the sum runs over all pixels (x,y).
above a threshold t1. We chose t1=t2 but the threshold levels for the red (index
1) and green (index 2) channels can (in principle) be chosen independently.
w1(x,y) and w2(x,y) are the pixel values of the red and green images, respectively.
rbin measures the fraction of pixels on the green binary image that are equally
present on the red binary image, relative to the total area of red pixels. We
chose the somewhat bulky notation to allow for later generalisation (see below).
255Σw1*(x,y) is the number of pixels
5 Quantitative Colocalisation Imaging 127
Fig. 5.1 Influence of cross-talk on colocalisation determination. a Artificially generated in-focus
dual-colour images. To generate synthetic red and green high-resolution matrices 30 100-nm-
diameter ‘fluorophores’ of each colour were placed on a grid of 50 nm. Red squares and green
cross hairs indicate the ‘true’ particle positions. The actual degree of colocalisation was set as
50%, i.e. 15 particles colocalised, indicated by the overlap of both indicators, and the others were
randomly distributed. Both high-resolution matrices were sequentially convolved with the exper-
imental point-spread function (PSF), sampled by a low-resolution matrix with a pixel size of
200 nm, and shot noise was added to each pixel of the low-resolution matrix following a Poisson
process. Inset: ‘High-resolution’ PSF. The experimental PSF determined by imaging a 93-nm
fluorescent bead with an oil-immersion objective with a numerical aperture of 1.45 was radially
averaged, interpolated, and resampled on a 50-nm grid. The line profile shows a linear cross-section
of the interpolated in-focus PSF. b Green- and red-channel images and their pseudocolour overlap
in the absence of spectral cross-talk. c Introduction of cross-talk. For clarity, only the cross-talk
from the green channel into the red channel is evaluated. The cross-talk ratio is the amount of
green fluorescence signal added to the red channel. An example (cross-talk ratio 0.5) is shown.
d Increasing cross-talk adds a false colocalisation that can largely outnumber the ‘true’ amount of
colocalisation. Colocalisation of 36% was estimated from the cross-talk-free fluorescent image
pair using an object-based algorithm (see text for details)
128 M. Oheim and D. Li
Colocalisation in the green channel is estimated similarly, by dividing through
Σ[w2*(x,y)]2 instead. Owing to its use of binary image masks rbin underestimates
the true amount of colocalisation (36 vs. 50%), because even for a perfect match
the added noise makes it impossible to delineate the real shape of the object.
Thresholding favours the selection of high-intensity pixels, so the true particle
size is underestimated when binarising the images and so is rbin. See Sect. 52 for
alternative descriptors of colocalisation.
What happens if we increase the cross-talk between both images? Figure 5.1c
displays the red- and green-channel images and their pseudocolour overlay that
result when increasing the fraction of the ‘green’ image leaking into the ‘red’
image. Whereas rbin found 36% colocalisation on the original image pair, increasing
the cross-talk ratio adds a false apparent colocalisation that can largely outnumber
the true amount of overlap (Fig. 5.1d).
188.8.131.52 Low Signal
In order to provide meaningful estimates for fluorophore colocalisation, the
fluorescence signal has to stick out of the image noise. In live-cell imaging, the
sensitivity of the sample to high-intensity illumination (photodamage) and the loss
of signal upon prolonged fluorophore excitation (photobleaching) often prescribe
low excitation intensities. The resulting lower signal as well as the intrinsically
dimmer fluorescence of fluorescent proteins (when compared with the commonly
used organic fluorophores) requires additional precaution as to the interpretation of
multicolour images. It might even be necessary to go back to fixed samples and use
antibodies against the fluorescent proteins used so as to amplify the detectable sig-
nal above the noise level of the detector, however at the expense of losing quantita-
tive intensity information (Martinez-Arca et al. 2003). Figure 5.2a shows, for the
same image pair as shown previously, the effect of increasing the noise relative to
a fixed signal in the green channel. The ‘red’ image is always the same, and we
have assumed zero cross-talk between the two channels. Figure 5.2b displays the
evolution of rbin when the ‘green’ image fades away in the image noise. When
always using the same fractional intensity for thresholding, the colocalisation
becomes less and less apparent with increasing image noise, because fewer and
fewer pixels remain after binarisation. However, other measures of colocalisation
(Sect. 5.2) produce a different and even the opposite result. Median filtering
(Demandolx and Davoust 1997) and deconvolution (Landmann 2002; Li et al.
2004) are two techniques that enhance the signal-to-noise ratio and colocalisation
detection (not shown).
184.108.40.206 Three-Dimensional Spatial Resolution
Do two objects truly colocalise or do their images simply blur one into the other
because the image resolution is low? Diffraction blurs the three-dimensional image
5 Quantitative Colocalisation Imaging 129
of the object. In focus, subresolution objects appear with an apparent size much
bigger than the true biological object given by the Airy disc, i.e. the in-focus plane
of the three-dimensional PSF of the microscope (Fig. 5.1a, inset). Also, the microscope
spatial resolution is not isotropic but is degraded along the microscope optical axis.
Together with chromatic aberrations, diffraction results in spreading out a point
object on the microscopic image, thereby creating a false apparent overlap between
the images of proximal but not colocalised objects.
Until now, we have assumed that all objects were located in focus (z = 0) and the
microscope had a perfect optical sectioning capacity. However, the objective will
collect fluorescence from objects located above and below the nominal focal plane.
These objects will contribute not with their in-focus image but with their respective
(blurred) off-focus plane of the PSF. The spread of signal across multiple optical
sections presents a significant source of false-positive artefact in the measurement
of colocalisation (Fig. 5.3). To examine the effect of out-of-focus fluorescence on
the colocalisation estimate, we moved the synthetic point objects to a random off-
focus position drawn from a Gaussian distribution with mean dz and the width
given by the approximately 1.9 µm effective depth of field of a NA-1.45 objective.
Figure 5.3 shows an in-focus fluorescence image pair, along with the corresponding
Fig. 5.2 Effect of decreasing the signal-to-noise ratio (SNR) in the green channel on colocalisation
estimates. The ‘red’ image is always the same. In contrast, the noise was increased in the green
channel for a constant signal of 500 counts. a Superimposed images of red- and green-channel
images with different SNR levels as indicated. b Colocalisation is underestimated at low SNR. The
amount of ‘true’ colocalisation in the absence of image noise is about 35% when using the object-
based descriptor (Eq. 5.1) for estimating colocalisation. A minimal SNR is required to obtain reliable
130 M. Oheim and D. Li
image in which we randomly introduced a mean defocus of 0.6 µm in both image
channels. We equally plot the evolution of rbin when increasing defocus from zero
to 0.1, 0.2, 0.4, 0.6, or 0.8 µm. The amount of false-positive colocalisation resulting
from overlapping Airy patterns for dz = 0, and the effect resulting from the super-
position of spatially unrelated signal give rise to an increasing false-positive
colocalisation. Wide-field microscopy is only little suited for colocalisation analy-
sis, because it suffers from out-of-focus blur. Image restoration by deconvolution
can – in part – compensate for this problem, but is very sensitive to image noise
and can generate bright pixels or grainy artefacts that are mistaken for fluorescent
objects (Landmann 2002).
The impact of lateral resolution on the apparent colocalisation of in-focus objects
is illustrated in Fig. 5.4. We investigated this effect by placing red particles of
2r1=100-nm diameter and green particles of increasing size 2r2 randomly in the
object plane, respecting their mutual size exclusion, i.e. the interparticle distance is
r1 + r2 or bigger. For object sizes below or close to the optical resolution, the
estimated false-positive colocalisation is low and roughly constant. With increasing
Fig. 5.3 Defocus results in false-positive colocalisation. Randomly distributed fluorophores were
created for both channels. The colocalisation is low for the in-focus image pair, consistent with
the small amount of random overlap resulting from the overlap of Airy patterns of proximal
particles in the red and green channels. Moving objects slightly out of focus increases the apparent
colocalisation and produces false positives (see text for details)
5 Quantitative Colocalisation Imaging 131
object size, rbin (relative to the bigger-particle green image) slightly decreases,
because the boundary effect becomes less and less prominent relative to the
increasing green pixel area. As expected from the asymmetric three-dimensional
resolution, rbin is more sensitive to the axial than to the lateral resolution.
Fig. 5.4 The object size affects the colocalisation estimate. a Thirty red and green particles of 100-nm
size each were created and randomly distributed in focus, respecting their mutual size exclusion, i.e. no
two particle centres could get any closer than rred + rgreen, here 200 nm. The images were then blurred by
convolution with the experimental PSF, Poisson noise was added, and the colocalisation was estimated
as before. We then increased the diameter of green objects while keeping the red object size constant at
100 nm. The leftmost panel shows an example for 1-µm object size. b The size with which objects appear
on fluorescence images is of critical importance in cases involving objects of near-resolution size.
Evolution of the colocalisation estimate when using the red or the green channel as a reference (cf. Eq.
5.1a). The (false) apparent colocalisation rises with particle size in the red channel, because the number
of pixels in which red and green overlap increases (owing to the bigger and bigger size of the green
objects) while always dividing through a constant area or red pixels. Not the almost constant colocalisa-
tion estimate for particles with a size below or close to the optical resolution limit. In contrast, the
colocalisation estimate is nearly constant when dividing the green and red overlap area by the con-
comitantly rising total area of green pixels. The slight drop results from the fact that the blurred edge
creating the false overlap roughly grows as rgreen, whereas the reference area grows as rgreen