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Evaluating single molecule
detection methods for microarrays
with high dynamic range for
quantitative single cell analysis
Ali Salehi-Reyhani
Single molecule microarrays have been used in quantitative proteomics, in particular, single cell
analysis requiring high sensitivity and ultra-low limits of detection. In this paper, several image analysis
methods are evaluated for their ability to accurately enumerate single molecules bound to a microarray
spot. Crucially, protein abundance in single cells can vary signicantly and may span several orders
of magnitude. This poses a challenge to single molecule image analysis. In order to quantitatively
assess the performance of each method, synthetic image datasets are generated with known ground
truth whereby the number of single molecules varies over 5 orders of magnitude with a range of signal
to noise ratios. Experiments were performed on synthetic datasets whereby the number of single
molecules per spot corresponds to realistic single cell distributions whose ground truth summary
statistics are known. The methods of image analysis are assessed in their ability to accurately estimate
the distribution parameters. It is shown that super-resolution image analysis methods can signicantly
improve counting accuracy and better cope with single molecule congestion. The results highlight the
challenge posed by quantitative single cell analysis and the implications to performing such analyses
using microarray based approaches are discussed.
e need for quantitative information in systems biology has been the driving force of a number of analytical
techniques over the last decade or so, seeking to provide a fully resolved description of the underlying mech-
anisms at play. To quantify absolute numbers of biomolecules present in cells presents an enormous challenge.
Microarray technology has become a popular tool for highly parallel analyses of biological markers; arrays of
DNA, RNA, proteins, peptides, carbohydrates and other biomolecules are powerful research tools and play a criti-
cal role in biochemistry and molecular biology research. Microarrays are typically formed upon planar substrates,
such as a surface modied glass slide, comprising thousands of small spots, typically on the order of 100 µm in
diameter, where they react with specic analytes in a complex solution to perform a miniaturised bio-molecular
assay.
Fodor et al. lay the foundation for microarrays in 1991 by demonstrating a process to build an array of synthe-
sised peptides by sequentially depositing amino acid groups on a glass surface1. e substrate was functionalised
using a combination of photolabile chemical building blocks and photomasks to synthesise an array of 1024
peptides. e technology was subsequently used to construct oligonucleotide microarrays because of interest
in genome sequencing; nucleic acid synthesis was well known and the high throughput oered by microarrays
was appealing. Schena et al. used a robot to mechanically print spots of complementary DNA onto glass using a
quill-type metal pin2. Indeed, Schena’s technique has become the most widespread technique today in the prepa-
ration of protein microarrays.
Once sequencing the human genome was complete, attention focussed on the proteome and methods to study
it. e success of the microarray to genomic studies was not immediately replicated in protein microarrays owing
to the chemical complexity and diversity of the proteins themselves – proteins have a broad diversity of solubility,
tertiary structures and amino acid content. All aspects of protein microarrays, such as printing, surface chemistry,
geometry and capture probes, have undergone signicant development, and continue to do so.
Department Chemistry, Institute of Chemical Biology, Imperial College London, London, SW7 2AZ, UK.
Correspondence and requests for materials should be addressed to A.S.-R. (email: ali.salehi-reyhani@imperial.ac.uk)
Received: 4 October 2017
Accepted: 7 December 2017
Published: xx xx xxxx
OPEN
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Scientific REPORTS | (2017) 7:17957 | DOI:10.1038/s41598-017-18303-z
It would take over a decade for single cell analysis by microarray to be reported. Today, several approaches
to single cell protein analysis have been reported with the capability to sense and quantify protein species in a
highly complex or congested sample requiring no pre-separation stage3–6. Microarrays are compatible with the
microuidic format and, indeed, benets from the reduced volume environment in respect of the proportion of
the capture analyte that is bound7,8.
A number of optical techniques have been used to detect surface bound targets and conventional methods
predominantly employ uorescence slide scanners9. Image processing of such microarray scan data requires an
identication step to dissect an image into single spot sub-images, a segmentation step to identify spot shape and
classify pixels as either foreground, belonging to the spot, or background, and a step to extract signal intensity,
that may involve additional measures to limit non-biological variation of the data10. e estimation of true signal
is dicult for low-intensity spots and the desire to extend dynamic range to analyse targets at or near the limits of
detection motivated, in part, the development of single molecule detection methods; touted as the ultimate limit
in microarray performance sensitivity.
High resolution single molecule approaches to analysing microarrays have been greatly aided by the adop-
tion of evanescent wave-based techniques, such as total internal reection (TIRF) microscopy11–13. Hirscheld
was the rst to exploit evanescent wave excitation to optically detect single molecules14. More thorough surveys
of the eld and how it developed may be found elsewhere15–18. A crucial milestone in the development of single
molecule microarrays was achieved when Hesse et al. reported high resolution scanning over large scales at
high speed19. ey notably demonstrated an extended dynamic range using their methods, which signicantly
exceeded conventional microarray analysis.
Owing to their sensitivity and low limits of detection, single molecule microarray methods are well suited to
quantifying cellular constituents free of the cell and the ability to detect single biomarkers in liquid samples, par-
ticularly blood, can accelerate the discovery and use of more sensitive diagnostics. e enumeration of oncogenic
proteins expressed within cancer cells has been demonstrated using antibody-based capture spots and is capable
of detecting a little as 21 proteins from single cells4,20. Shirasaki et al. employed single molecule detection to
monitor in real-time the secretion of the cytokine interleukin 1β from a single cell21. Conventionally, such assays
require washing steps to remove unbound material prior to imaging. Single molecule microarrays imaged by
TIRF are able to simplify assays by avoiding such steps since only bound molecules are detected. Jain et al. showed
that employing single molecule methods enables the study of individual protein complexes and can help provide
information on complex stoichiometry22.
e identication of single molecules and their accurate enumeration is key in quantitative microarray anal-
ysis. Methods of spot detection in uorescence microscopy have been well reported; Izeddin et al. presented a
wavelet based algorithm that focussed on single molecule localisation23. Smal et al. performed a thorough survey
of techniques and quantitatively evaluated single molecule image analysis methods for peak detection24. However,
there is a paucity of reports that focus on the methods of image analysis for high-resolution single molecule
microarray data. e work of Mureşan et al. is an exception to this, wherein they report the detection of single
molecules based on undecimated wavelet transforms25. Using the detection results, an estimation of the number
of single molecules per spot could be made and could further discriminate between specic and non-specic
signal.
e determination of what constitutes a specic, or true, signal is not a simple task in single molecule imaging;
issues such as low signal to noise ratio (SNR), background estimation, impurities and variations in uorophore
labelling all contribute to errors. Methods of image analysis to detect single molecules are continually being
developed but are predominantly designed to analyse super-resolution cell microscopy data, whereby the focus
is generally toward single molecule localisation. Isolated uorophores may be localised to a precision well below
that of the diraction limit26; however, imaging single molecules in cells inevitably leads to the problem of con-
gestion where the target density in some structures is such that single molecules are no longer individually resolv-
able. Some super resolution microscopy techniques exploit the stochastic nature of photo-activatable uorophore
switching to image a subset of uorophores in an otherwise congested region; a complete molecular image is then
built up over time. Single molecule localisation microscopy (SMLM) is a proven bioanalytical tool and relies just
as heavily on switchable uorophores as it does on powerful algorithms to identify and estimate the positions of
single molecules. Many algorithms currently exist along with standardised data to benchmark implementations
that can provide guidance on which is most suitable for a particular application27,28.
In this work, methods of image analysis are assessed in their ability to accurately determine the number
of single molecules in high resolution images of microarray spots. Images were processed with wavelet based
transforms to enhance single molecule contrast or to denoise images. A concern when performing SMLM is
the ecient detection of a statistically sucient number of molecules for analysis. is needn’t be 100% of all
target molecules for SMLM whereas it certainly is the case when quantitatively enumerating targets bound to a
microarray spot. With this in mind, a super-resolution peak tting algorithm is also tested for its performance in
analysing microarray images. To evaluate methods, synthetic datasets were generated with known ground truth,
ranging from 100 to 1 × 107 molecules bound to a spot, equivalent to a density of molecules of 1.27 × 10−2 μm−2
to 1.27 × 103 μm−2. e density of single molecules per spot varied such that images are considered either to be i)
non-congested, where single molecules are sparse; ii) semi-congested, where the degree of overlap is signicant;
or iii) congested, where the density of single molecules is high and are no longer individually distinguishable.
It has been recently shown that the underlying mechanisms of gene expression may be uncovered from the
summary statistics of single cell distributions of protein abundance29. It is therefore important to measure these
distributions with sucient accuracy in order to capture subtle variations in behaviour as a cell or pathway is
stimulated or dysregulated. Synthetic datasets were generated whereby the number of single molecules per spot
corresponds to single cell distributions of protein abundance whose summary statistics are known. e distri-
bution parameters of which served as the ground truth to which the estimated distributions derived from single
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Scientific REPORTS | (2017) 7:17957 | DOI:10.1038/s41598-017-18303-z
molecule counts were compared. Finally, the image analysis methods are tested with experimental single mol-
ecule microarray data generated from a microuidic platform for the quantication of proteins with single cell
resolution.
Results
Single molecule image analysis. e performance of the detection methods was quantitatively evaluated
using synthetic image datasets (Fig.1). Single molecule detection rate, a measure of accuracy, was determined
as parameter settings were varied for synthetic images of varying image quality and number of single molecules.
Additionally, methods were compared to intensity thresholding without any pre-processing to reduce noise or
Figure 1. Synthetic single molecule image data. (a) e synthetic image shows a 10 × 5 test grid of single
molecules. From le to right, the signal to noise ratio of the single molecules in each column is 1, 2.5, 3, 4,
5, 6, 7.5, 10, 12.5, 15 and 20. e red arrows indicate each column and helps to identify low signal to noise
ratio single molecules. Scale bar is 5 μm. (b) Shown are exemplar images of simulated spots (SNR = 7.5). E ach
synthetic image is generated with a pre-dened number of single molecules randomly located inside a circular
area which is intended to mimic a microarray spot. e labels indicate the number of single molecules on
spot (102 molecules per spot is equivalent to a molecule density of 1.27 × 10−2 μm−2) and the dashed circle
in the lemost image indicates the extent of the microarray spot area. e bottom row of images are zoomed
in areas indicated by the red square in the top row. e scale bar for the top row of images is 20 µm, and 5 µm
for the bottom row. (c) Images are processed using the image analysis methods under assessment to detect
and enumerate the single molecules in each image; this is pre-dened and so the number of single molecules
‘counted’ by each method can be compared to the ground-truth to determine the accuracy as a function of
analysis method, number of single molecules per spot and signal to noise ratio of the molecules. (i) and (ii)
show exemplar results whereby the counting accuracy is <70% and >90%, respectively. e resolution of all
images is 0.26 μm per pixel.
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Scientific REPORTS | (2017) 7:17957 | DOI:10.1038/s41598-017-18303-z
enhance signal. e synthetic image datasets were each characterised by a SNR of the single molecules; SNR
values varied between 1 and 20. e detection rate is determined by comparing the ground truth to the count
number produced using each image analysis method. How the detection rate varies for each algorithm to an
increasing number of single molecules as a function of SNR is shown in Fig.2, for SNRs of 5, 7.5 and 10. (e
response to all SNRs is shown in FigureS2). For spots with a number of single molecules (NSM) that is low, their
density is such that they are spatially well separated and individually distinguishable. Due to the limited resolu-
tion of the microscope, as the NSM per spot increases, the likelihood of single molecules touching or overlapping
also increases such that they are identied as connected components or single structures; thereby underestimat-
ing the counted NSM.
Intensity thresholding alone (No Filter) fails for SNR ≤ 5 and accuracy only exceeds 80% for SNR ≥ 10 for
molecule density <0.127 (ISM < 1000 molecules per spot) i.e. non-congested spots. Processing with either the
Ricker (RW) or ‘a trous’ wavelet (ATW) signicantly enhances the accuracy in single molecule identication for
non-congested spots with low SNR and peak tting results in the best overall performance; however, there are
exceptions to this when comparing peak tting to processing with an ATW for SNR ≤ 4 (FigureS2).
For SNR ≥ 10, all methods performed to a satisfactory degree for molecule density <0.127 (NSM < 1000)
where accuracy exceeded 82.1%. e accuracy prole of each method for SNR ≥ 10 as molecule density increases
is typically sigmoidal; characterised by a fairly at response up to 0.1 μm−2 (NSM ~ 1000) beyond which accuracy
reduces sharply such that it drops below 30% for molecule density> 1 μm−2 (NSM > 104), regardless of image anal-
ysis method. e point at which the accuracy of an algorithm begins to sharply reduce represents the degree to
which it can identify overlapping single molecules as spots go from being non-congested to being semi-congested
then congested. It is not surprising that the non-peak tting methods perform similarly with regard to the point
at which accuracy falls as spots become semi-congested.
Analysing congested arrays. Protein abundance in single cells can span several orders of magnitude, and
due to cellular heterogeneity this can arise even for cells in a genetically identical population. e complication
to single molecule approaches when performing single cell analyses is that a suciently high cellular concentra-
tion of a protein in a subset of cells, for example, would result in some microarray spots becoming congested due
to the amount of analyte captured. Modifying the density of surface sites in a microarray to maintain a regime
whereby single molecules can be resolved has been previously suggested30. erefore, unless the distribution of
expected signal is suciently narrow, spots of varying density would be required on the same microarray and is
not necessarily the most straightforward approach. Furthermore, a reduction in the density of surface sites will
likely increase the limit of detection of a microarray assay, which is undesirable for single cell protein assays7.
Single molecules could by selectively identied in congested microarray data by photo-activated localisation
microscopy31 or by the detect and bleach strategy20. In the absence of more elaborate methods, an estimate of NSM
on congested microarray spots can be achieved by dividing the total integrated intensity by the average single
Figure 2. Non-congested arrays. e synthetic single molecule datasets are processed and the detection rate of
each single molecule image analysis method, or algorithm for short, is assessed as the pre-dened number of
single molecules in each image increases. Results show the performance of the algorithms to data with a signal
molecule signal to noise ratio of (a) 5, (b) 7.5 (solid lines) and 10 (dashed lines). When the number of single
molecules is low (<103 per image), the density of the single molecules in the microarray spot is relatively low
(<0.127 single molecules μm−2) and they can individually be distinguished. As the number of single molecules
per images increases, so does their density on spot, such that the degree of overlap becomes signicant and
accuracy drops as a result. e gure labels ‘No Filter’, ‘A Trous Wavelet’ and ‘Ricker Wavelet’ represent the
results of the intensity thresholding algorithms with either no lters or pre-processing, or pre-processing with
the ‘à trous’ or Ricker wavelet transforms, respectively. Similarly, the ‘PeakFit’ gure label represents the results
of the peak tting algorithm.
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molecule intensity. is strategy relies on the following experimental conditions: 1) the variation in the number of
uorescent labels per detection analyte is low; and 2) a low single molecule density, or non-congested, image may
be acquired to accurately estimate single molecule intensity (ISM). Single molecules will accumulate on capture
spots over time at a rate dened by the kinetics of binding. e second condition may be experimentally achieved
by imaging spots as a function of time or, in order to minimise photobleaching, once at a suciently early time
point and once when equilibrium has been achieved.
Single molecule intensity is rst estimated using the methods described above. For non-peak tting algo-
rithms, average single molecule intensity is estimated by summing thresholded pixel values and dividing by the
number of identied peaks. For the peak tting algorithm, each single molecule is t to an isotropic 2D Gaussian
prole which allows the full distribution of ISM to be determined per image; depending on which is more appro-
priate, an average or median ISM may be calculated. Images from the same datasets as above are intensity thresh-
olded based on the variation of the background pixel intensity (see Methods); to estimate NSM, the sum of the
surviving pixel values is divided by the average ISM. Figure3 shows the detection rate of the ‘congested’ image
analysis method when using such estimates of ISM for SNR of 5, 7.5 and 10 (see FigureS3 for responses to all SNR).
e variation in detection rate relates to how the accuracy to which ISM is estimated and the relative contri-
butions of the background and single molecules to pixel intensity when summed across the image. For low SNR,
intensity thresholding tends to identify more intense single molecules, systematically discriminating against low
intensity molecules thus positively skewing the distribution. In absolute terms, the total single molecule intensity
of these identied molecules is itself underestimated since there will be a proportion of the signal below threshold
that is lost. Of course, the process of thresholding is a balance between the rejection of background and preserva-
tion of signal intensity. As condence in background rejection increases (related to n) so does the amount of true
signal which is undesirably rejected. is poses less of a problem for digital counting but becomes an issue for
congested arrays as we must rely on an accurate estimate of single molecule intensity.
It is evident from Fig.3 that methods of analysis for congested spots were also applied to non-congested spots
(molecule density <1 μm−2, NSM <103). While in practice this would not be sensible, it does help us to under-
stand how inaccuracy arises in semi-congested and congested spots. For non-congested spots, the true count is
predominantly underestimated. In these spots, the density of single molecules is low and the relative contribution
of the background is high. Portions of each single molecule that fall below the threshold are discarded leading
to an underestimation of the total signal intensity on spot (Ispot). is, in addition to the overestimation of the
average ISM, leads to an overall underestimation of NSM per image, which is consistent for all algorithms analys-
ing non-congested spots. As single molecules accumulate, they will begin to raise the average intensity across
the spot. At some point the average intensity will exceed the threshold intensity. As single molecules are further
‘added’ to the spot, no proportion of a single molecule’s total intensity is any longer discarded by thresholding and
the increase in total spot intensity is equal to the total intensity of the additional single molecule. As NSM increases
in this regime, the detection rate will increase and accuracy improves. For very high NSM, the proportion of the
thresholded intensity to the total spot intensity decreases and the detection rate will plateaux. e detection rate
will tend toward a value which is the accuracy to which ISM is estimated.
Figure 3. Congested arrays. In congested images, the number of single molecules is estimated by dividing the
total array spot intensity by the average single molecule intensity, which is estimated using the single molecule
algorithms described above on non-congested images. Results show the performance of the algorithms to
data with a signal molecule signal to noise ratio of (a) 5, (b) 7.5 (solid lines) and 10 (dashed lines). e gure
labels ‘No Filter’, ‘A Trous Wavelet’ and ‘Ricker Wavelet’ represent the results when using estimates of average
single molecule intensity determined using the intensity thresholding algorithms with either no lters or pre-
processing, or pre-processing with the ‘à trous’ or Ricker wavelet transforms, respectively. Similarly, the ‘PeakFit’
gure label represents the results when using an estimate of average single molecule intensity determined using
the peak tting algorithm.
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In the cases of the intensity thresholding alone (No Filter) and the RW non-tting algorithms, the number
of molecules may be overestimated in some cases. is would arise due to the relative degrees by which Ispot and
ISM are under- and overestimated, respectively. is is suppressed when using the ATW as the process denoises
images and the eects due to the relative contribution of background intensity are suppressed. Peak tting allows
the 2D Gaussian prole of the single molecule to be known and therefore more reliably estimate the ISM. For
SNR ≥ 10 the accuracy ‘prole’ attens due to the relative contribution of the noise and any errors arising from
thresholding becomes relatively small.
Accurately measuring single cell distributions. Single molecule microarrays are well suited to quanti-
tative single cell analysis. Single cell protein abundance in a population of cells is well known to vary and datasets
will reect this information as a variation in the number of single molecules per microarray spot. Such data is
important for models of gene expression29,32 and therefore an accurate measure of this variation is obviously
desirable. With this goal in mind, synthetic datasets were generated whereby the number of single molecules
per spot within a dataset followed a gamma distribution with known shape and scale parameters. e gamma
distribution model is well known to faithfully describe cell to cell variation in protein expression33,34. e distri-
butions were formed by the same shape parameter (k = 2.0) and their scale parameter varied such that the distri-
butions were peaked in the non-congested (θ = 250 SMs, 3.18 × 10−2 μm−2), semi-congested (θ = 2.5 × 103 SMs,
0.318 μm−2) and congested (θ = 2.5 × 105 SMs, 31.8 μm−2) regimes. For each of the 3 distributions, datasets were
generated with dierent SNR, which varied from 5 to 20 (Figs4 and 5).
As a control to test the competence of the tting procedure, the ground truth distribution of known NSM is t-
ted alongside the counted NSM (Fig.4a). e shape and scale parameters were estimated by tting for all distribu-
tion datasets. For the non-congested datasets, it was possible that the counted distribution qualitatively resembled
the ground truth distribution. However, the tting parameters of these distributions would numerically dier
signicantly from the input ground truth parameters. In general, parameter estimates become more accurate as
SNR increases; however, for non-congested data there is a tendency to overestimate or underestimate the shape
and scale parameters, respectively (Fig.4b).
Here it is worth noting the relative performance of each algorithm in estimating NSM (Figs2 and 3) and in pro-
ducing data to estimate the parameters of a distribution (Fig.4b and c). When estimating the summary param-
eters of a gamma distribution, accuracy in the shape parameter may in some cases be prioritised over accuracy
in the scale parameter. Errors in scale will arise predominantly to the counting accuracy deviating from 100%,
whereas errors in shape will arise predominantly to non-linear ‘response’ in detection rate as evident in FigureS2
for low SNR. is is exemplied by the shape parameter being best estimated when the distribution is peaked
in the congested regime (Fig.4c); an inspection of the detection rate of the analysis of congested arrays (Fig.3)
shows a ‘at’ response over the range of values associated with the distribution (k = 2.0, θ = 2.5 × 105). Similarly,
an inspection of the detection rate of the single molecule analysis methods of non-congested arrays does show
a ‘at’ response, albeit a shallow negative gradient (Fig.2c). ese features are able to explain the apparent bias
observed when tting non-congested data (Fig.4b). It has been shown that in the case of single cell protein analy-
sis, microarrays may be calibrated using standard curves established using known concentrations of recombinant
proteins. Such calibration curves would factor out any errors in scale but would not be capable of correcting
errors in shape20. is exemplies the necessity for a high degree of accuracy over a wide dynamic range.
Analysing synthetic data distributed in both the non-congested and congested regimes is straightforward
whereas semi-congested data is more challenging as it is the region in which neither image analysis approach
is best suited. is is exemplied in FigureS4, where the analysis of such data fails to faithfully reproduce the
ground truth distribution. ere is a propensity for the intensity thresholding alone (No Filter) and the RW
non-tting algorithms to perform poorly in non-congested images at low SNR and to generally overestimate NSM
on congested spots at SNR > 5. Despite this, their estimation of spot and average single molecule intensity results,
serendipitously, when calculating NSM from total ISM, in more accurate estimations in non- and semi-congested
images. An argument based on the overall performance of both these approaches allows us to proceed in the
enumeration of semi-congested data with the ATW non-tting and peak tting image analysis methods, only.
e performance of the single molecule and congested image analysis methods were compared as the number of
single molecules per spot was increased through each of the 3 regimes, noting the point at which the performance
of the latter would exceed the former (Fig.5a). is crossing point would help decide what image data is analysed
with which method and is dictated by the density of single molecules on spot and the degree to which they are no
longer individually distinguishable. In practise this may be dicult to determine without some measure of the
proximity of single molecules to one another. Here, with the data presented it is justiable to simply determine
the numerically higher count as the more precise (Fig.5a) and represents a, somewhat, best case scenario when
applying these methods to real data. e semi-congested results in Fig.5b show that the combined approach ena-
bles an estimation of distribution parameters with ~90% accuracy for shape (ATW SNR ≥ 5) and scale (PeakFit
SNR ≥ 5).
e eect of varying the scale parameter and determining the response to other distribution types was not
tested.
Single cell data was acquired using a microuidic based single molecule microarray method4. MCF7 cells
are removed from culture and a single cell suspension is created. Cells are owed into a microuidic device
and isolated into individual analysis chambers; the chip used here comprised of 50 analysis chambers wherein
a single antibody capture spot is located. e protein p53 was captured using a suitable capture antibody. Since
p53 is unlabelled, a second detection antibody labelled with a uorophore is present in the solution which binds
to free p53 or the immobilised capture antibody-p53 complex at the surface. Spots are imaged by TIRF micros-
copy 90 min aer cells are optically lysed to ensure binding equilibrium had been reached. e basal expression
of p53 protein in MCF7 cells is such that captured protein on each spots typically results in a molecule density
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of <0.1 μm−2 and therefore suitable for the non-congested methods of analysis detailed above. Figure6 shows
the resultant distributions of counted single molecules from cells using each of the image analysis methods. e
distribution of the counts using peak tting algorithm is clearly dierent than those produced by the intensity
thresholding based methods. For example, the counted distribution of single molecules as a result of the RW
non-tting (k = 4.80 ± 0.94, θ = 27.9 ± 5.7) and peak tting algorithms (k = 6.51 ± 1.30, θ = 62.0 ± 12.8) are t
by a gamma distribution. Numerically, and visually by inspection of the ts in Fig.6, these are clearly dierent
Figure 4. Synthetic data to model single cell distributions. Synthetic image datasets are generated whereby
the number of single molecules in the microarray spot follows an asymmetric gamma distribution. (a) Shown
are the probability density function of histograms comparing the ground truth distribution (grey edges) of
pre-dened single molecule number to the single molecule counts estimated using the peak tting algorithm
(purple edges). Overlaid is the continuous gamma function (dashed black line; k = 2.0, θ = 250) from which
the ground truth distribution and image datasets are generated. e parameters tested here are such that the
gamma distribution is peaked in the (b) non-congested (k = 2.0, θ = 250) or (c) congested (k = 2.0, θ = 2.5 × 105)
regimes. Images were processed to estimate the number of single molecules, the distribution of which was
tted to estimate the parameters. e horizontal dashed black line indicates the ground truth parameter value.
e error bars for each data point indicate the standard error of tting. e grey rectangular region vertically
centred on the dashed line indicates the standard error of the t to the ground truth distribution values.
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counted single molecule distributions. e ground truth is unknown for the single cell single molecule image data
and therefore an absolute measure of accuracy for each of the image analysis methods is not possible. e results
from analysing the synthetic datasets would suggest that the peak tting algorithm is likely to be the most accu-
rate. By testing these methods of image analysis on experimental data with unknown ground truth the necessity
is further highlighted for a high accuracy to be maintained over a range of molecule densities on spot.
Discussion
e performance of a set of image analysis methods has been quantitatively assessed as applied to single molecule
microarrays. eir performance is assessed using realistic synthetic data with known ground truth over a wide
dynamic range and as SNR is varied; the absolute values of which are applicable to single cell protein analysis.
is study has highlighted the importance of accurate single molecule enumeration when analysing data upon
which quantitative models of systems biology increasingly relies. Synthetic datasets which serve to model the
wide dynamic range of single cell protein expression and cellular heterogeneity were analysed. e image analysis
method involving peak tting performed with the highest accuracy, overall.
e results presented here show that peak tting can maintain a detection rate in excess of 80% for molecule
densities approaching 0.3 μm−2 and with the accurate estimate of single molecule intensity can eectively exceed
103 μm−2 using the methods above. A number of approaches have been reported based on their ability to cope
with high density data. Originally used in astronomy to analyse crowded stellar elds35, methods that t popula-
tions of single molecules with multiple PSFs instead of just one can improve accuracy when detecting overlapping
molecules. Holden et al. implemented this in DAOSTORM36. Zhu et al. reported a sparse recovery technique
using compressed sensing and showed this could work with much higher molecule densities when compared
to DAOSTORM37. In summary, single molecule tting, DAOSTORM and compressed sensing were capable of
maintaining a detection rate of 80% or higher up to densities of ~0.5 μm−2, ~2 μm−2 and ~10 μm−2, respectively,
as estimated from published results using super resolution imaging systems36,37.
Figure 5. Synthetic data to model single cell distributions. Synthetic datasets are generated whereby the
number of single molecules in the microarray spot follows a gamma distribution with parameters such that
it is peaked in the semi-congested (k = 2.0, θ = 2.5 × 103) regime. (a) Image analysis methods best suited to
either non-congested or congested data were combined to maximise accuracy in this regime. (b) Results show
the accuracy in estimating distribution parameters when using the ‘à trous’ wavelet transform and peak tting
image analysis algorithms. e horizontal dashed black line indicates the ground truth parameter value. e
error bars for each t indicate the standard error of tting. e grey rectangular region vertically centred on the
dashed line indicates the standard error of the t to the ground truth distribution values.
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e density of single molecules is an important consideration to their reliable detection on microarray spots.
While strategies to alleviate this, such as the reduction of binding site density, have been proposed they are not
compatible with maintaining the requisite sensitivity necessary for measuring low abundance proteins in single
cells7. Certainly, the digitisation of peak detection enables single molecule counting to be more robust to system-
atic variation. e accuracy of congested data is more prone to variations in systematic parameters such as laser
intensity, emission collection eciency, detection camera, amongst other factors. Of course, the accuracy of data
in congested regions depends on the accurate measurement of single molecule intensity. e results quantitatively
show how this aects the accurate estimate of the number of single molecules bound to a congested spot. It must
be noted that in generating synthetic datasets, quenching was not taken into account and may be an issue for
microarray spots with suciently high binding site density.
An eective alternative to reduce congestion, would be to adopt the use of photo-switchable uorophores
and super-resolution microscopy methods such as photo-activated localisation microscopy (PALM) or stochas-
tic optical reconstruction microscopy (STORM). Although, if appropriately implemented, such methods are in
principle capable of eectively reducing imaged molecule density, there are a number of non-trivial challenges
which limit the accurate estimation of single molecule numbers. ese include photobleaching, uorophores
which are never activated and distinguishing the observation of the same uorophores in multiple consecutive or
non-consecutive frames. e detect and bleach (DAB) method has also been previously described to be capable
of regaining single molecule counting in densely occupied spots20. DAB works by dierencing subsequent frames
Figure 6. Testing experimental single cell data. (a) (i) Exemplar high-resolution image (0.26 μm per pixel)
centred on a single microarray spot. Fluorescent single molecules represent the capture antibody–protein–
detection antibody complex of a sandwich assay. e protein is p53 captured from MCF7 cells using a
microuidic based method of single cell analysis using single molecule microarrays. (ii) Shown is the image
in (i) processed with an overlay of detected single molecules. Scale bars are 20 μm. (b) e results of single
cell pulldowns (n = 50) are analysed. Shown are the probability density function of histograms of the single
molecule counts estimated using the image analysis methods under test. e dashed green and purple lines are
ts of a gamma function to the histograms produced using the intensity thresholding algorithm (pre-processing
with the Ricker wavelet transform) and the peak tting algorithm, respectively.
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Scientific REPORTS | (2017) 7:17957 | DOI:10.1038/s41598-017-18303-z
during continuous imaging of the spot and in the regime whereby molecular arrival or bleaching rate is low, single
molecules which bind and others that are irreversibly bleached will be sparse and individually identiable.
ere are ongoing public challenges that exist to evaluate and benchmark new and existing techniques, with
particular focus on localisation microscopy28. e methods of image analysis analysed here were assessed with
quantitative single cell analysis in mind.
Methods
Single molecule detection. Data sy nthesis. Simulation images are generated with randomly located sin-
gle molecules inside and outside a circular area which demarcates the microarray spot area. Each generated
dataset contains 65 512 × 512 pixel images: of which 55 are 512 × 512 pixel images that contain 10–107 randomly
located on-spot single molecules in addition to 100 randomly distributed single molecules; a further 10 images
contain 100 randomly distributed single molecules only and serve as background, or negative control, images. 11
datasets were generated with varying signal to noise ratios (1, 2.5, 3, 4, 5, 6, 7.5, 10, 12.5, 15 and 20). Each image
within a dataset are independent and represent dierent spots in a microarray. Each dataset is characterised by a
dierent SNR and is generated independently so the pre-dened number of single molecules in each image have
dierent coordinates.
Synthetic image parameters were selected to correspond with the microscope system reported in reference4.
To begin, the point spread function of the system was measured by imaging 100 nm uorescent beads (Invitrogen
Molecular Probes, FluoSpheres 540/560). Each simulated single molecule was generated using a 2D isotropic
Gaussian function where the width corresponds with the measure point spread function (equivalent to 1.6 pixels
in the 512 × 512 pixel image).
e resultant synthetic images are 512 × 512 pixel but to begin with a higher ‘super’ resolution 2560 × 2560
pixel image is generated. Uniformly distributed random numbers were used to generate single molecule coordi-
nates in each microarray spot in an image. e pixel intensity of the super resolution image was then binned using
a square 5 × 5 binning kernel to produce a 512 × 512 image. Larger binning kernels may be used to down sample
images to lower resolutions to simulate other microarray imaging systems25. Our single molecule imaging system
incorporates objective-type TIRF so noise such as that from immersion oil autouorescence and scatter from the
excitation laser are taken account of by adding a mean background intensity to each pixel. e excitation intensity
prole of our TIRF microscope system was imaged and normalised using the peak intensity. e simulated spot
images were then multiplied by the normalised laser prole image to better simulate real data. Poisson noise was
then applied. e signal-to-noise ratio (SNR) of the single molecules was dened as SNR = (S − B)/σ, where S is
the peak single molecule pixel intensity and B and σ are the average and standard deviation of background pixel
intensity, respectively.
To better capture systematic variations in microarray performance, spot diameter and capture density may be
varied to experimentally determined degrees. Here, to focus on errors arising from image analysis, the simulated
data is generated with no intra- or inter-spot variation in microarray spot quality. Microarray spots of constant
100 μm diameter are modelled. e modelled microarray spot is centred in a 512 pixel × 512 pixel image, with
pixel dimensions equivalent to a physical area of ~133 μm × 133 μm.
Synthetic single cell datasets. e resulting distribution when measuring the protein abundance per
single cell in a population of cells approximates the steady state protein abundance. To simulate single molecule
microarray data from single cell experiments, images were synthesised as above whereby the number of single
molecules on-spot were randomly generated from distributions with dened summary statistics. Datasets were
generated whereby asymmetric gamma distributions with identical shape parameters (k = 2.0) are peaked in the
non-congested (θ = 250 SMs), semi-congested (θ = 2.5 × 103 SMs) and congested (θ = 2.5 × 105 SMs) regimes and
were used to assess the counting algorithms performance in faithfully measuring these distributions.
Image Analysis. In summary, original images are eld attened, ltered then thresholded to produce images
from which peak counting is performed. e methods employed here are computationally fast and datasets are
typically processed within a few minutes.
Image ltering was performed using either the ‘à trous’ or Ricker wavelet transforms, which help to denoise
images and enhance the signal. e ‘à trous’ wavelet-based ltering technique is a 2D isotropic undecimated
wavelet transform38. e algorithm was implemented using the ‘ATrousJ_Filter’ plugin by Ihor Smal24 for ImageJ/
Fiji39 using a B-spline scaling function of third order. Each image is decomposed into planes of wavelet coe-
cients (see FigureS1). e rst plane contains high frequency components and the plane containing most of the
noise. e second and third planes contains structures best associated with single molecules whereas higher order
planes contain increasing lower spatial frequencies and are better associated with coarser image details.
e Ricker wavelet, also known as the Mexican hat wavelet owing to the shape of its 2D processing kernel,
is the application of a Laplacian of Gaussian to a 2D image (see FigureS1). is type of edge detection kernel is
an established method for object detection, such as single molecules and biological cells40,41. e algorithm was
implemented using the ‘Mexican Hat Filter’ plugin by Dimiter Prodanov for ImageJ/Fiji.
Single molecules were either detected by intensity thresholding or by tting peaks using a 2D Gaussian func-
tion. When intensity thresholding, pixel values were set to zero for pixels whose intensity value was less than
μ + nσ, where μ and σ are the mean and standard deviation of background pixel intensity, respectively, and n is
an integer which denes the probability that a pixel ‘belongs’ to a single molecule. Pixels that survive thresholding
are then retained based on cluster size, 4–36 pixel2, and circularity, greater than 0.5. e number of single mole-
cules is the number of remaining particles and the average single molecule intensity can be estimated.
To perform 2D Gaussian peak tting, algorithms were implemented using the GDSC plugin by Alex Herbert42
for ImageJ/Fiji. A PSF estimator rst determines by optimisation the average Gaussian parameters of the single
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Scientific REPORTS | (2017) 7:17957 | DOI:10.1038/s41598-017-18303-z
molecules from intensity peaks in the dataset by least squares tting. All peaks in each image are subsequently
tested against this Gaussian prole and only counted as single molecules if they fall within a precision threshold
for size and intensity. e total number of single molecules is simply the number of peaks in the image which
converge to the 2D Gaussian prole.
For images where the density of single molecules results in a signicant degree of overlap, single molecules
become dicult to individually distinguish. e number of single molecules is then estimated from dividing the
total intensity of a thresholded image by the average single molecule intensity.
Single Cell Analysis. Cell culture. MCF7 (ATCC) cells were cultured using high glucose Dulbecco’s
Modied Eagles Medium (DMEM; ermoFisher Scientic, UK) supplemented with 10% (v/v) foetal bovine
serum (FBS; ermoFisher Scientic, UK) in polystyrene asks in a 5% CO2 37 °C cell incubator. Suspensions of
single cells are prepared by detaching cells in culture using Accutase solution (Sigma, UK).
Single cell microarrays. A microfluidic based method was used to facilitate single cell protein analysis
based on previously reported work4. e PDMS microuidic chip is fabricated using well known methods of
so-lithography43. It is formed of a main channel through which single cell suspensions are owed to which an
array of analysis chambers (n = 50) are connected. Each analysis chamber has dimensions 300 μm × 300 μm × 35
μm resulting in an assay volume of 3.15 nL. e chip is sealed using a functionalised coverslip (Nexterion; Schott,
Europe) upon which an anti-p53 antibody (Enzo Life Sciences, UK) microarray is printed using an OmniGrid
Micro microarrayer (Digilab, UK). e microarray spotting solution contained the anti-p53 capture antibody
mixed 1:1 with a print buer formed of 3 × saline-sodium citrate buer, 1.5 M betaine supplemented with 0.01%
SDS; the nal concentration of antibody in the spotting solution was 0.5 mg mL−1. e spots are printed at dened
locations which allowed them to be aligned to the PDMS chip such that a single antibody spot is aligned to the
centre of each analysis chamber. e chip is lled with a solution of 0.25 μg mL−1 uorescent detection antibody
(anti-p53 DO1 labelled with Alexa Fluor 488; Santa Cruz, USA) with 4% bovine serum albumin in phosphate
buered saline.
Platform and procedure. e platform has been described in detail elsewhere4. An inverted microscope (Nikon
Ti-E; Nikon, Japan) forms the basis of the experimental platform. Single cells are individually isolated into analy-
sis chambers using an optical trap (1070 nm YLM-5 Ytterbium bre laser; IPG Photonics, UK). Once all analysis
chambers are occupied, single cell lysis is achieved optically by launching a high energy laser pulse (6 ns pulse
1064 nm Surelite SLI-10 Nd:YAG; Continuum, USA) into the medium immediately surrounding the cell. e
pulse produces an expanding cavitation bubble which shears the cell membrane allowing intracellular contents
to be released. Antibody spots are imaged using objective-based total internal reection uorescence (TIRF)
microscopy (488 nm Versalase; Laser 2000, UK) and an electron-multiplied CCD camera (IXON DU-897E;
Andor Technologies, Ireland). e acquired images are analysed using the methods above.
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Acknowledgements
is work was supported by an Imperial College Fellowship awarded to ASR.
Author Contributions
A.S.-R. conceived and designed the project, generated and analysed the data and wrote the paper.
Additional Information
Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-017-18303-z.
Competing Interests: e author declaresthat they have no competing interests.
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