Functional hyperspectral imaging captures subtle details of cell metabolism in olfactory neurosphere cells, disease-specific models of neurodegenerative disorders

Hyperspectral imaging uses spectral and spatial image information for target detection and classification. In this work hyperspectral autofluorescence imaging was applied to patient olfactory neurosphere-derived cells, a cell model of a human metabolic disease MELAS (mitochondrial myopathy, encephalomyopathy, lactic acidosis, stroke-like syndrome). By using an endogenous source of contrast subtle metabolic variations have been detected between living cells in their full morphological context which made it possible to distinguish healthy from diseased cells before and after therapy. Cellular maps of native fluorophores, flavins, bound and free NADH and retinoids unveiled subtle metabolic signatures and helped uncover significant cell subpopulations, in particular a subpopulation with compromised mitochondrial function. Taken together, our results demonstrate that multispectral spectral imaging provides a new non-invasive method to investigate neurodegenerative and other disease models, and it paves the way for novel cellular characterisation in health, disease and during treatment, with proper account of intrinsic cellular heterogeneity.


Introduction
Olfactory neurosphere (ONS) cells are easily accessible, patientderived models of neurological disease [1]. They are harvested from the human olfactory mucosa, the organ of smell in the nose, which regenerates throughout life. This neural tissue is accessible in human adults and it demonstrates disease-dependent cell biology alterations in Alzheimer's and Parkinson's diseases, Rett syndrome, fragile X syndrome, schizophrenia, MELAS and other diseases [2][3][4][5][6][7][8]. The analysis of such cells provides new routes for the understanding of the pathogenesis of complex neurodegenerative conditions. Relative to other tissue neurons exhibit intense metabolic demands, therefore impairment of cellular metabolism accompanies many neurodegenerative diseases. Thus new methods are required to characterise and quantify metabolism of neural and other cells and tissue on a single cell level. Such methods are important for accurate early diagnosis, treatment monitoring and the development of therapies.
Here we report the application of hyperspectral autofluorescence analysis to functional, metabolic imaging of patient-derived ONS cells suffering from the mitochondriopathy MELAS. MELAS syndrome is commonly attributed to the m.3243A N G mitochondrial DNA (mtDNA) point mutation within the MT-TL1 gene [28][29][30][31]. This mutation is thought to disrupt respiratory chain complex assembly as reflected by impaired mitochondrial protein synthesis [28] and reduced mitochondrial respiratory chain enzyme activities [29]. Mitochondrial dysfunction follows, with studies reporting reduced mitochondrial membrane potential, with a parallel increase in reactive oxygen species production leading to reduced ATP production [32] and induction of mitochondrial permeability [29]. Cellular damage is apparent too, with increased glycolytic rate, impaired NADH response, decreased glucose oxidation and increased lactate production [31]. This defective oxidative metabolic state is thought to influence the clinical expression of disease. Because highly metabolic cells such as myocytes and neurons are highly dependent on efficient mitochondrial function, the percentage of mutant mtDNA relative to wild-type mtDNA known as the "mutational load" is important for determining whether the cell will be affected by the mutation or not. This poorly understood phenomenon known as heteroplasmy, the existence of both wild-type and mutant mtDNA within a cell or tissue is unique to mitochondriopathies. Earlier studies have demonstrated that high mutational load is detrimental to metabolism. Thus the analysis method that is able to yield quantitative insights concerning metabolism of individual live cells as well as their populations is a valuable tool to improve the understanding of this and other mitochondrial diseases. This work demonstrates that a simple hyperspectral imaging system coupled to a conventional wide-field microscope and high content analysis of the images provides novel insights into cell metabolic signatures, their heterogeneity and MELAS disease biology.
This study examines the effect of MELAS mutational load and the shift in heteroplasmy due to galactose treatment on cell metabolism. To this aim we have cultured ONS cells from both control and MELAS patients with greatly varying low (11%) and high (44%) mutational loads. We have subsequently exposed them to galactosesupplemented medium which has been shown to cause a reduction in mutational load [33,34]. The cells were imaged to observe their autofluorescence characteristics. Throughout this work, hyperspectral autofluorescence images of live cells have been obtained at a number of excitation wavelength ranges between 334 and 495 nm (each approximately 10 nm wide). The emission is detected in the range 570 nm-605 nm. More details are described in the Methods section and in Supplementary Material S1-S5.

Hyperspectral imaging can distinguish MELAS patients from healthy controls and sheds light on the effectiveness of galactose treatment
We present the results of hyperspectral autofluorescence characterisation of the ONS cells with low (11%) and high (44%) mutational loads of the m.3243A N G MELAS mutation ("MELAS ONS cells") and corresponding control cells (control 1 for 11% and control 2 for 44% MELAS mutational load, respectively). Hyperspectral data correlations have been removed by using PCA as described in Supplementary Material Section S4. Subsequently, average cell spectra (represented here by single data points) have been plotted in a two-dimensional spectral space produced by the linear discriminant analysis (LDA, see Supplementary Material S4). These are presented in Fig. 1 a where the axes represent the directions onto which the cellular data have been projected by LDA. The LDA optimally separates the three groups of cells: healthy cells from both controls 1 and 2, 11% mutant MELAS and 44% mutant MELAS cells.
Clear separation of clusters observed in Fig. 1 a indicates that the cells from MELAS patients can be distinguished from control cells. Moreover, the cells from two different MELAS patients also form different clusters, thus all three cell classes are well separated. To statistically analyse the cluster separations, a second LDA projection of cell data was carried out [35]. For this new projection, two classes of cells were chosen at a time, and their average spectra were projected onto a common line. This approach visualises cell distributions by histograms ( Fig. 1 b-g). We found that every pair of classes selected among control, MELAS, MELAS galactose treated cell classes gave p-values in the Kolmogorov-Smirnov test of less than 10 −12 , consistently with Fig. 1 a [36,37]. The Kolmogorov-Smirnov test if passed with p b 0.05 allows us to reject the null hypothesis that the samples are drawn from the same distribution.
The multispectral autofluorescence analysis of cells that have undergone galactose treatment to reduce mutational load is shown in Fig. 1 a. In this figure, the clusters of MELAS treated cells are located between the control population and the MELAS population. The histograms produced by pairwise LDA projections are significantly different as shown in Fig. 1 d-g. Thus multispectral imaging makes it possible to distinguish MELAS ONS cells from control cells and also quantifies the response of such cells to pharmacological interventions.

Mapping of key fluorophores in cells
In order to shed light on biochemistry of the ONS cells we decomposed the spectral images of the cells under investigation into five most significant spectral components representing the most prominent fluorophore groups. This analysis uses an unsupervised unmixing approach (see Methods and Supplementary Material Section S4.2 for details). The resulting component (endmember) spectra are shown in Fig. 2 a-e (44% MELAS). The corresponding data for 11% MELAS are shown in Sup. Fig S2. The endmember spectra are found to closely correspond to the spectra of bound (red shifted) flavins, FAD and/or spectrally similar FMN, A2E, bound NADH, free NADH, and lipofuscin, the most abundant cellular fluorophores according to the literature [15]. All groups of cells had significant contributions of free and bound NADH as well as A2E and lipofuscin. The fifth spectral component was different in 11% MELAS and 44% MELAS cells. We found FAD/FMN in the group of 11% MELAS, 11% treated and control 1 ONS cells but bound flavins were prominent in the group of 44% MELAS, 44% MELAS treated and control 2 ONS cells.
To verify our assignment we carried out colocalisation analysis of autofluorescence endmembers with organelle stained images (Sup. Figs. S3, S4). An adaptive algorithm was used to correct for cell motion occurring between autofluorescence imaging and subsequent organelle (mitochondria and lysosome) staining. The image correlations between the endmembers and individual stains are displayed in Sup. Fig. S4 indicating (a) high degree of colocalisation between (bound) flavins and stained mitochondria; (b) the absence of colocalisation between free NADH bound NADH (correlation coefficient r of 0.17); (c) strong colocalisation of bound NADH and the mitochondria, with the values of r between 0.62 and 0.9; and (d) co-localisation of retinoids with the lysosomes and mitochondria.
Finally, we explored whether the identified fluorophores appropriately respond to chemical interventions. To this aim we applied several known fluorescence quenchers including (a) sodium borohydride which reduces free NAD + to fluorescent NADH and reduces fluorescent flavins thus quenching their fluorescence; (b) acrylamide which quenches flavins; and (c) FCCP and rotenone, both specifically quenching NADH [38,39]. Their effect on the fluorescence intensity is shown in Sup. Fig. S5. Fig. S6 shows a comparison of hyperspectral unmixing with fluorescence lifetime imaging (FLIM) in cells treated with H 2 O 2 where we observed similar trends.
Our approach produced cellular maps of each of the five key fluorophore groups within the examined cells. These are shown in  well. Statistically significant trends in average fluorophore intensities in all examined cells are shown in Sup. Fig. S7. These data indicate that MELAS ONS cells present a fluorophore profile that reflects altered metabolism, different to control ONS cells, while galactose treatment appears to modify the fluorophore profile of the treated MELAS cells.

Identification of cell subpopulations
We used our automated algorithm described in Methods to search for cell subpopulations by looking for clustering of fluorophore abundances. All combinations of features have been tested and scored in terms of how well they clustered indicating subpopulation coincidence. This was done for all features shown to have definite one-dimensional subpopulations.
Interestingly, we found two uneven well-separated subpopulations for 11% MELAS (red and blue symbols, Fig. 3 a), and two similar size equally well-separated subpopulations for 44% MELAS (yellow and green symbols, Fig. 3 b). Statistical analysis of these and other subpopulations before and after galactose treatment is shown in Sup. Fig. S8. We also draw attention to the behaviour of the optical redox ratio, in particular the ratio of flavins to bound NADH (Sup. Fig. S8) showing clear subpopulations in MELAS ONS cells. These subpopulations disappear after galactose treatment. The ratio of free to bound NADH which is a relative measure of glycolysis and several other features also shows clear subpopulations (Sup. Fig. S8).

Biochemical differences between the examined cell groups
Sup. Fig. S9 summarises the results of biochemical characterisation of the examined cell groups. It shows that the biochemistry of MELAS cells is significantly altered compared to healthy controls. For example the ATP production and MTMP in MELAS cells are lower than in healthy controls, while the levels of lactate and SOX are elevated. These values return closer to those in control cells after treatment. These results are consistent with significant differences observed in the autofluorescence properties of these cell groups.

Hyperspectral imaging enables differentiation of cell groups
Hyperspectral analysis to differentiate cell groups enables to statistically establish that MELAS ONS cells differ from control cells. The ONS cells from each MELAS patient before and after galactose treatment can also be distinguished (Fig. 1 a). This is consistent with earlier studies showing that galactose treatment enhances mitochondrial metabolism. We and others have shown improved mitochondrial function with exposure of diseased cells to galactose by shifting the mutational load of diseased cells [33,34]. The mechanism by which cells shift in mutational load is unknown, however, selective apoptosis in combination with cell proliferation and mitophagy for surviving cells may reduce the mutational load of cells.
The method presented here produces p-values for the hypothesis that the two cell groups are different. It is also robust with respect to reproducibility and the same results have been obtained in repetitive cell experiments from different cell passages carried out four months apart (data not shown). These results also show that hyperspectral analysis of cellular autofluorescence is sensitive enough to monitor functional treatment response of ONS cells from single individuals.

Hyperspectral imaging enables biochemically sensitive functional imaging of cells
In addition to cell classifications, our hyperspectral dataset provides detailed insights into cell biochemistry. The fluorescence of unlabelled cells is produced by endogenous fluorophores including NADH and NAD(P)H, riboflavin and flavin-coenzymes including FAD and FMN, retinol and other retinoids including components of lipofuscin, pyridoxine, vitamin B12, vitamin D, ceroid, cytochromes, vitamin K, tryptophan, tyrosine, phenylalanine, kynurenine and porphyrins, as well as the complexes of these fluorescent molecules with proteins [19,20,26,[41][42][43][44][45][46][47]. Among these fluorophores protein-bound and free NAD(P)H produces a significant part of the fluorescence signal responding to excitation in the 330-390 nm wavelength range. Flavins are prominent in the longer wavelength range (excitation peaks at 360 nm and at 440-450 nm, emission in the range 450-600 nm) with parts of their spectra well separated from the NAD(P)H group. Retinoids, especially retinol can also be observed, in particular lipofuscin and A2E tend to be highly visible [19,20,41]. Previous studies of autofluorescence in cells indicate the absence of fluorophore quenching; this means that fluorophore concentration is proportional to fluorescence intensity. In particular, a linear correlation has been shown between total NADH content determined biochemically and NADH fluorescence, [42,43]. The total NADH concentration is typically in 100 μM range [44]. Other fluorophores listed here are less abundant, for example flavins are present in cells at~50 μM [45], and the most abundant retinoid, retinol at 1-2 μM concentrations. Retinoic acid, anhydroretinol and retinal have lower concentrations; all are below the onset of concentration quenching [26], while lipofuscin can form highly concentrated granules.
Unlike in other works [14] our spectra have sufficient spectral resolution to differentiate between unbound and protein-bound forms of NADH, whose spectrum is blue-shifted by 20 nm compared to free NADH [46,47]. However we are unable to differentiate between NADH and NADPH, thus the NADH components in this work (free or bound) represents both NADH and NADPH fluorescence [26]. The bound flavin component represents the majority of the cellular flavins' fluorescence produced by the mitochondrial lipoamide dehydrogenase (LipDH) and electron transfer flavoprotein (ETF), but also any other bound flavins. The shape of the bound flavin excitation spectrum observed here is similar to that of aqueous solution of riboflavin, with a red shift by 50 nm by the effect of protein binding [38,[48][49][50]. We have been able to separately identify FAD, but it could not be separated from spectrally similar FMN [14]. In the retinoid group, the A2E has also been separately identified, while the spectrally similar retinoids [51,52] (retinol, retinoic acid, cellular retinol-binding proteins (CRBPs), and cellular retinoic acid-binding proteins (CRABPs)) have been merged with lipofuscin.

Trends in fluorophore content
Here, we discuss the trends observed in various cellular characteristics between control, MELAS and MELAS treated cells. We first discuss the fluorophore content presented in Fig. S7 which shows that the 44% MELAS cells show significantly more bound flavin fluorescence than the controls. The 11% MELAS cells seem to contain mostly FAD/FMN instead of bound flavins and the increase of FAD/FMN in MELAS cells is much less pronounced. Mitochondriopathies often lead to accumulation of reduced forms of FAD, NADH and FMN, as they cannot bind to the respiratory chain proteins [53]. In mitochondriopathies such as MELAS which affects assembly of respiratory chain proteins, it is expected that at high mutational loads (such as 44%), we would find reduced forms of FAD and FMN (all flavins) present at higher levels when compared to control cells. However, at lower mutational loads (such as 11%) this effect is expected to be less pronounced, because the assembly of proteins may not be as disrupted as it is at higher mutational loads. The build-up of reactive oxygen species also confirmed in our experiment (Fig. S9) may change the flavin redox balance and increase flavin fluorescence.
The trends in free and bound NADH content in the examined cells are complicated, with 44% MELAS cells showing a slight increase of bound NADH compared to controls (Fig. S7), while 11% MELAS cells show slightly less bound NADH and slightly more free NADH than the respective control cells. These complex trends need to be reconciled with widely reported increase in NADH fluorescence in more glycolytic cells [11]. However this increase has been reported only in cells with intact, functioning mitochondria. While MELAS ONS cells do exhibit higher levels of glycolysis than control cells (Fig. S9), they may have decreased mitochondrial numbers at certain mutational loads. In such cells, the amount of NADH present under glycolysis conditions may depend upon the overall cytosolic pool size of NAD + and NADH, and may bear no simple relation to the amount of NADH in the control cells. The relatively higher levels of bound NADH in 44% than in 11% MELAS cells (Fig. S9) could be consistent with a higher mitochondrial activity combined with a smaller mitochondrial mass, resulting in a similar ATP production, with a slightly reduced production of lactate, and a much higher superoxide generation.

Discussion of specific cell subpopulations
Here we discuss cell populations visualised by scatterplots in Fig. 3 and those statistically analysed in Fig. S8. For 44% MELAS, Fig. 3 b shows two distinctive populations with different metabolic profiles (yellow and green symbols) where the "blue" cells have a generally higher ratio of free to bound NADH, and they also have a higher average lipofuscin. These cells constitute~41% of the total, consistent with 44% mutational loading, and they form a completely separated cluster. Fig. 3 a displays subpopulations uncovered in 11% MELAS ONS cells (red and blue symbols). These two populations have similar characteristics as those in 44% MELAS. Cells in the small cluster comprising 7% cells (red symbols) has a high ratio of free NADH to bound NADH and a majority of cells (blue symbols) have a much lower free to bound NADH ratio. The red cells have comparatively high levels of lipofuscin. We do not know at this point whether these metabolically different "red" and "yellow" cells are carrying the mutations; this should be investigated further.
The behaviour of subpopulations before and after treatment is shown in Fig. S8. This figure shows the plots of bound flavin versus bound NADH content for control, 44% MELAS and 44% MELAS treated cells. We can see here that control cells form two fairly tight populations, with bound flavins' abundance varying in the range of 0.2 to 2.2. In contrast, the MELAS cells form very distinctive populations, one with low bound flavins (between 0 and 3) and a group of cells which could be still mutated with an unusually high bound flavin content (between 5 and 20). After treatment, the high bound flavins' group completely disappears and the remaining cells form a single population spreading over the same region of abundances as the control cells. Sup. Fig. S8 also shows the populations with respect to the free and bound NADH content. Again, we observe two well-defined subpopulations in control cells. The MELAS cells also show two populations, one of which has a much higher free NADH content that the control cells. After treatment only a single population is observed. Sup. Fig. S8 shows similar trends in the fluorophore ratios, again displaying clear subpopulations in most cases. These subpopulations are particularly pronounced in MELAS cells for bound flavins to bound NADH ratio. These subpopulations are associated with varying levels of metabolic activity.
The data in Fig. 3 and Sup. Fig. S8 are consistent with the view that MELAS cells in this patient belong to two distinctive classes. Thus our data shed light on the hypothesis that MELAS is a disease which affects cells to a different degree as opposed to the alternative hypothesis that all cells are similar and characterised by a certain proportion of defective mitochondria in each. Distinguishing between these two hypotheses is significant for the design of patients' treatment regimens.

Conclusions
Originally developed for remote sensing, this work expands the hyperspectral approach to the fields of medicine and cell biology in areas utilising fluorescence microscopy. It yields quantitative and straightforward interpretation of physiological processes in living tissues similar to multiphoton fluorescence and/or FLIM but without the complexity and cost of a multiphoton FLIM imaging system. The use of single photon fluorescence at comparatively low excitation irradiances (in the order of 10 3 W/cm 2 ) from light emitting diodes makes this method compatible with in-vivo use.
We demonstrated that hyperspectral or multispectral imaging provides richly detailed information about living cells which allows to test hypotheses about similarity or otherwise of cell distributions and about the effects of chemical interventions, in this case galactose treatment.
We have been able to unambiguously decompose cellular autofluorescence into contributions from several most abundant fluorophores present in those cells, generate cellular maps and provide statistical information about cellular abundances of these fluorophores. Although we have not included here detailed analysis cellular distribution of these fluorophores, this method can be naturally extended to provide combined morphological and chemical cellular features.
The information about average content of the most abundant fluorophores in each individual cell obtained in our method bears some similarity to flow cytometry measurements. Hundreds of cells can be analysed in each experiment mostly automatically and there is scope for full automation. This approach has allowed to identify biologically and functionally distinguishable cell subpopulations of potential biological significance. Overall, our results indicate that hyperspectral imaging provides new windows into biological functions of individual living cells, and it can detect and quantify their metabolic activity. Our approach combined with high content data mining of cell images has provided novel insights into the MELAS disease which is characterised by genetically determined mitochondrial dysfunction. We have shown that the new method can help assess the disease status and the effectiveness of therapy. Olfactory neurosphere cells investigated here are regarded as disease-specific models of neuronal disorders [1]. Using this method it will be possible to analyse impairment of metabolic function in these diseases. Thus hyperspectral analysis presented here may help to better understand a broad range of diseases affecting metabolism including neuronal degeneration.

Methods
See Supplementary Material for expanded description of methods.

Primary cell culture
In this study we used cells from the MELAS patient-derived olfactory-derived neurospheres (ONS) with varying levels of mutational load (11% and 44%) generated from olfactory primary cultures. To prepare these ONS, nasal biopsies were carried out and harvested cells were expanded and subcultured as described in more details in Supplementary Material S1. All biopsy tissues were obtained with informed written consent of the patients and the study carried out under a protocol that was approved by the ethics committees of the Royal North Shore Hospital and the University of Sydney, according to the guidelines of the National Health and Medical Research Council of Australia. Cells from control subjects were harvested and treated in the same fashion. The MELAS cells were subjected to galactose-supplemented, glucosefree media (starvation) over a period of 4 days. We present data from three different cell passages.

Microscopic imaging
Imaging was carried out on cells having an approximately constant cell density. Each cell sample was prepared and imaged in duplicate. Altogether, over 1500 cells were imaged in this study, between 350 and 400 for each patient (more details in Supplementary Material S2 and S3).

Mitochondrial parameter assays
Cells were carefully characterised biologically by a variety of methods. In particular we measured mutational load by standard radiolabelled ("hot-finish") PCR/RFLP analysis, carried out the citrate synthase assay for the determination of mitochondrial mass, and measured the level of lactate, ATP, mitochondrial superoxide generation (SOX), and mitochondrial transmembrane potential by flow cytometry. All cells were also imaged by laser scanning microscopy, with Green Mitotracker, Red Lysotracker and Blue ER-Tracker staining (see Supplementary Material S2 for more details).

Hyperspectral measurements technique
Our method uses fluorescence of native fluorophores commonly found in cells. In our approach the images of live cells are obtained by an Andor IXON camera under illumination at a number of selected bands of excitation wavelengths (here, centred at 334, 365,385,395,405,415,425,435,455,475,495 nm, each about 10 nm wide). The emission is measured with a 532 nm long pass dichroic mirror together with a 587 nm bandpass filter (35 nm bandwidth), in the range 570 nm-605 nm. The spectra obtained in this way are excitation spectra. This selection of excitation-emission channels with optimised exposure times enables to capture images with sufficient signal to noise ratio for accurate unmixing of multiple cellular fluorophores. This includes free and bound NADH whose spectra have tails in the 570-605 nm range, however these compounds produce a significant proportion of the autofluorescence signal at 334 nm excitation wavelength. Optical powers at the objective ranged from 0.1 μW at 334 nm excitation to 102 μW at 475 nm. These measurements yield fluorescence excitation spectra measured at each pixel for all images of cells coming from all patients. These spectra are further corrected for instrumental response. A "background" reference image of a culture dish with a medium is also taken and subtracted from all images with cells.

Data analysis method for differentiation of cell groups
The original pixel spectra containing intensity and wavelength information are represented as vectors in an n-dimensional spectral space whose coordinates are intensities at each of the n excitation wavelength (here, n = 11). This dataset contains significant correlations, as cell images at adjacent wavelengths are very similar; this is first removed by using a covariance matrix calculated from the data (see Supplementary Material S4 for mathematical details). Further, we calculate average cell spectra. The method of linear discriminant analysis (LDA) [35] is then employed, in order to establish whether these average spectra from biologically identifiable classes of cells form well separated clusters. In this method we first choose the m cell classes and by using LDA we project the original n-dimensional spectral space and the data points representing the average spectra of our cells onto a new, lowerdimensional space. Its dimension is given by the number of groups of cell classes to be distinguished less1. For convenience of presentation, in this work we have been using three classes of cells, so that after LDA the spectra of these cells can be depicted as points on two dimensional plots. This two-dimensional spectral space produced by LDA is referred to as the "canonical spectral space". Its basis vectors are orthogonal, and aligned with the axes in our relevant figures.
The LDA method ensures that the new space is optimised to provide the best degree of separation between selected cell classes (such as, for example, cells from different patients). Finally, to quantify the distinctiveness between selected pairs of cell clusters we perform the LDA analysis again, on each pair of cell cluster data projecting them onto a one-dimensional line. The Kolmogorov-Smirnov statistical test is then applied to gauge and compare the similarity of the pair of clusters. We also calculate the maximum Fisher statistical distance, a measure of cluster closeness which is sensitive to cluster means and takes account of the data dispersion.
We add that the data for additional cells and/or patients or data produced by other authors may be plotted together with our data. Although there is no mathematical certainty that optimum separation will be achieved for such blended datasets, a clear separation may often be achieved in the case when class distinction results are statistically strong with small p-values.

Data analysis method to determine fluorophore abundance
We are assuming that the observed spectra are a linear combination of fundamental spectra originating from particular substances, called endmembers. ThisN number of endmember spectra Xis weighted by an abundance coefficient vector f such that an observed spectrum Z p which is given by Eq. (1): where e is the residual, or noise, not explained by the mixture of endmembers.
The problem of finding the endmembers has a simple geometrical interpretation. The spectra of all individual pixels in cells represent a certain cluster in an N dimensional space. The cluster is contained within a convex hull called a simplex and each pixel spectrum point within this simplex represents a linear combination of the spectra represented by the extreme points (vertices) of that simplex. These vertex spectra are chosen to be endmembers. See Supplementary Material Section S4.2 for more details about identifying endmembers.
In order to find the best simplex representing the data points two conditions need to be satisfied: that the coefficients of the abundance vector are all positive and that they add to unity. To identify that best simplex we minimised the least squares error between the target spectra and the product of our abundance vector multiplied by the endmember spectra, for the entire set of data. The corresponding endmembers spectra are shown in Fig. 2 and Sup. Fig. S1. These are identified to measured reference spectra of known fluorescent compounds in cells and/or to their spectra reported in the literature. Fit errors are typically being between 5 and 10%, due to the presence of other less abundant and unidentified residue spectra.

Data analysis method to detect cell subpopulations
In order to characterise subpopulations in the examined cells we first specify K, the number of subpopulations we wish to find in each data group (K = 2 in the presented analysis). Then for all groups within all variables, the data undergo an unsupervised mixture model. The non-deterministic algorithm is used to break the data into potential subpopulations. Each produced solution goes through selection criteria so that only the highest scoring solution per data group is selected. The criteria are that each of the subpopulations must be N 30% of the whole dataset, the subpopulations must have a statistical separation greater than 1, and they must pass a Kolmogorov-Smirnov test with p b 0.05. The mixture model returns only the subpopulation means and covariance, so in order to classify the data points in one of the K subpopulations we used a Naive Bayes classifier. The method reproducibly finds subpopulations that agree with intuition when looking at the histograms. Boxplots are used to give an overview of data and a visualisation has been created to display groups of data with subpopulations. The width of the subpopulation boxes is proportional to their size, to allow some inference power across groups.

Competing financial interests
Authors have no competing financial interests.

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