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Pixel precise unsupervised detection of viral particle proliferation in cellular imaging data

Cellular and molecular imaging techniques and models have been developed to characterize single stages of viral proliferation after focal infection of cells in vitro. The fast and automatic classification of cell imaging data may prove helpful prior to any further comparison of representative experimental data to mathematical models of viral propagation in host cells. Here, we use computer generated images drawn from a reproduction of an imaging model from a previously published study of experimentally obtained cell imaging data representing progressive viral particle proliferation in host cell monolayers. Inspired by experimental time-based imaging data, here in this study viral particle increase in time is simulated by a one-by-one increase, across images, in black or gray single pixels representing dead or partially infected cells, and hypothetical remission by a one-by-one increase in white pixels coding for living cells in the original image model. The image simulations are submitted to unsupervised learning by a Self-Organizing Map (SOM) and the Quantization Error in the SOM output (SOM-QE) is used for automatic classification of the image simulations as a function of the represented extent of viral particle proliferation or cell recovery. Unsupervised classification by SOM-QE of 160 model images, each with more than three million pixels, is shown to provide a statistically reliable, pixel precise, and fast classification model that outperforms human computer-assisted image classification by RGB image mean computation. The automatic classification procedure proposed here provides a powerful approach to understand finely tuned mechanisms in the infection and proliferation of virus in cell lines in vitro or other cells.


Introduction
Viruses are cellular parasites that do not have a metabolism of their own. To proliferate, they must infect healthy host cells. To achieve this, virus particles are able to recognize and to bind specific receptor molecules on the cytoplasmic membranes of host cells, a process that is known as attachment. This interaction between viral particles and a host cell's membrane surface is mediated by proteins embedded within the viral envelope [1]. For example, the binding of viral envelope proteins to a host cell's surface structure in the case of the human immunodeficiency virus (HIV), which is a coronavirus, involves interaction between the surface protein gp120 and the CD4 receptor [2], a polypeptide that occurs almost exclusively in the membranes of T-helper cells (lymphocytes) and macrophages. This first step of the HIV replication cycle critically determines the ability of HIV to degrade the human immune system. In other cases, viral proteins may bind to cellular structures found on a larger variety of cell types.
Various tools for cellular and molecular imaging have been developed to characterize single intracellular stages of viral proliferation [1,3]. The high resolving power of electron microscopy (EM) permits studies at nanometer scale, providing direct images of viral proliferation (virion budding) on host cell membrane surfaces for diagnosis and research [4].
Scanning electron microscopy (SEM) in particular facilitates single cell analysis and comparison between cells by visualizing ultrastructual changes on membrane surfaces and structures harboring viral replication sites correlated with the progression or remission of the infectious process [2,4,5].
Immunocytochemistry [5,6] and cell viability imaging by color staining and other labeling techniques allow the study of spatial and temporal dynamics of virus spreading on host cell surfaces in vitro. Haseltine et al. [7] developed an imaging method that permits tracking the spread of focal infections using a combination of immunocytochemical labeling and step-by-step digital imaging. In their study, baby hamster kidney (BHK) cells were seeded on six well plates, grown as confluent monolayers and covered with a thin layer of agar. After piercing a small orifice in the agar, cell layers were infected by injecting 5 µl of virus VSVN1 inoculum at 1.6x10 7 infectious particles (i.e. a multiplicity of infection of 20) as described in [6,7]. Cells were subsequently fixed, and immunofluorescence labeled with an antibody against a viral glycoprotein on and within the infected cells. Images of ( Figure 1) were then acquired by epifluoresence microscopy at low magnification using a highresolution monochrome digital camera. to rule out any subjectivity of the analyst [5]. To ensure high-quality decision making in the evaluation of larger amounts of required. In addition, affordable precision software for an automatic classification of cell imaging data should combine high accuracy of classification with further advantages relative to speed, objectivity, and reproducibility of the quantifications. In our previous studies, we exploited functional properties such as sensitivity to spatial extent, intensity, and color of local image contrasts of the quantization error in the output of a Self-Organizing Map (SOM-QE) for unsupervised image classification as a function of the finest, often visible, clinically or functionally relevant variations in local contrast contents [8][9][10][11][12][13][14][15]. Regarding cell imaging data, the SOM-QE was successfully employed for fast unsupervised classification of SEM images of CD4 T-cells with varying extent of ultra-structural surface signals correlated with surface-localized single HIV-1 viral particle infection. It was shown that SOM-QE permits a fast automatic classification of sets of such SEM images as a function of ultra-structural signal changes that are invisible to the human eye. As pointed out in our previous studies, any imaging method currently available has its own limitations, including for SEM. It is important that all images from a series with presumed functional variations submitted to pixel precise analysis are identically scaled. SEM is meant to provide a 3D model of ultrastructural cell properties, however, the resulting images that are subject to any further analysis are in 2D, with a z-axis projecting into virtual depth. This leaves additional room for viewpoint-related errors, and it is necessary to ensure that images from a given time series are not only identically scaled in 2D, but are taken from one and the same 3D view of the cell, or any other structure, when submitted to analysis.
SOM-QE is also a powerful tool for the automatic classification of double-colorstaining based cell viability data, as shown previously in 96 image simulations [9]. SOM-QE consistently detects the smallest spatial changes in any of the local color signals [14,1]. These may reflect a systematic increase or decrease in theoretical cell viability below the expert visibility threshold. Signal detection experiments [9,11] have shown that clinically significant changes in the color or contrast of less than 10 pixels between two images of a series with clinical significance are impossible to detect, even by temporally unlimited expert visual inspection. SOM-QE detects any such changes in a consistent and statistically reliable manner, as shown in proof-of-concept studies demonstrating the selectivity of the metric to the spatial extent, the contrast intensity, the contrast polarity and the color of single-pixel changes in random-dot images containing millions of image pixels [12][13][14][15].
In the present study, we use the previously published cell imaging model by Haseltine et al. [7], described in all necessary detail here above. It is shown that the fast automatic classification by SOM-QE gives access to the earliest potential stages of viral propagation in host cells, which are detectable neither by visual inspection, nor by the imaging model per se.
The imaging model described in [7] was aimed at providing an age-segregating model for the time course, in terms of hours or days, of viral particle proliferation following focal infection of the cell monolayer. The original images from the reference study [7] quantize the sum of infected and dead cell concentrations, a continuous variable, onto an integer-valued intensity scale. A high resolution computer software reconstruction of one of the images from the reference study (see Figure 1), taken at a particular moment in time in the course of in vitro monolayer infection, was used as the ground truth image here. The model copy derived from the initial image is then used to simulate image sequences in theoretical time corresponding to seconds or minutes of the smallest possible infectious progression/recession of the virus in the cell monolayer. Viral particle growth with time is simulated by a one-by-one increase, across images. Black pixels indicate dead, gray pixels represent slightly infected, white pixels represent living cells in the original and the hypothetical image model.
The image simulations are then submitted to unsupervised learning by a Self-Organizing Map (SOM) and, as described previously [8][9][10][11][12][13][14][15], the Quantization Error in the SOM output (SOM-QE) is used for the automatic classification of the image simulations as a function of the represented extent of viral particle proliferation or cell recovery.  [7], where images of infected cells were generated at different times after focal infection of a cell monolayer. As described in [7], after focal infection in vitro, antibody labeling for viral glycoprotein, and detection by immunofluorescence microscopy, digital camera images of the infected monolayer region (circular image region) were generated. Contrast levels in the circular region represent relative amounts of living cell matter (white image pixels), progressing infection (image pixels in varying shades of gray), and dead cell matter (black image pixels). Images from top to bottom here correspond to times between 48 (top), 72 (middle) and 90 hours (bottom) of infection. Scale bars represent 1mm. The model image from which all image simulations for this study here were drawn is the top image of this figure.

Image simulations
A total number of 160 images were computer generated, using the single-pixel-level control functions in ADOBE Photoshop7, on the basis of a virtual copy of the first of the original images shown in Figure 1, which is a low resolution version of the high resolution ground truth image, shown in Figure 2, that was reconstructed for this study here prior to any further image simulations. Figure 2 shows the image state (ground truth) before any changes simulating further viral particle growth/recession were implemented. 159 further images were drawn directly from this high resolution computer model image to simulate the finest possible here, [13,13,13]  Single-pixel RGB increments simulate theoretical image data for hypothetical viral particle growth/recession in time. This is achieved by replacing, one by one, pixels indicating living cell matter (white) by pixels indicating different levels of infection (shades of gray) or dead cell matter (black). Cell recovery after a hypothetical treatment was simulated by replacing, one by one, image pixels indicating dead cell matter (black) by pixels indicating different levels of infection (shades of gray) or living cell matter (white).

Self-Organizing Map (SOM) and Quantization Error (QE)
The Self-Organizing Map (a prototype is graphically represented in Figure 3, for illustration) may be described formally as a nonlinear, ordered, smooth mapping of high-dimensional input data onto the elements of a regular, low-dimensional array [16]. It is assumed that the the trial-and-error method after testing the quality of the first guess, which is directly determined by the value of the resulting quantization error ; the lower this value, the better the first guess. It is worthwhile pointing out that the models were initialized by randomly picking vectors from the training image, called here the "original image". This allows the SOM to work on the original data without any prior assumptions about a level of organization within the data. This, however, requires to start with a wider neighborhood function and a bigger learning-rate factor than in procedures where initial values for model vectors are pre-selected [17]. The approach is economical in terms of computation times, which constitutes one of its major advantages for rapid change/no change detection on the basis of even larger sets of image data prior to any further human intervention or decision making.

Figure 3:
Representation of the SOM prototype with 16 models, indicated by the filled circles in the grey box. Each of these models is compared to the SOM input in an unsupervised winner-take-all learning process. Here in this study, the input vector corresponds to the RGB image pixel space. The model in the map best matching the SOM input will be a winner, and the parameters of the winning model will change towards further approaching the input. Parameters of models within close neighborhood of the winning model will also change, but to a lesser extent than those of the winner. At the end of training, each input space is associated with a model in the map. The difference between input vector and final winning model determines the quantization error (QE) in the SOM output.

Experimental procedure
The 160 images simulating viral particle growth by progressive one-by-one replacement, in the region inside the circle of infection, of white ("living cell matter") pixels by light gray, medium gray, dark gray or black ones, or cell recovery, following a hypothetical treatment specifically designed to enable cells to recover from the effects of infection, by progressive one-by-one replacement of black ("dead cell matter") pixels by light gray, medium gray, dark gray or white ones were fed into a single SOM. The training image for the SOM prior to analysis was the model image 'before any pixel change', shown in Figure

Descriptive analysis
The data in Figure 4

Discussion
The results from this study show that the unsupervised, self-organizing map-based automatic classification by SOM-QE [8][9][10][11][12][13][14][15] of cellular imaging models simulating viral proliferation in the cell [7], or cellular recovery after a specific hypothetical in vitro cell treatment in time with a single-pixel precision provides a statistically highly reliable classification model that by far outperforms human computer-assisted image classification in terms of the RGB image mean, for example, as demonstrated here. The linear models for SOM-QE increase or decrease as a function of local changes in single image pixel contrast reproduce the previously shown fine sensitivity of this neural network metric to changes in the contrast polarity and/or intensity of single pixels in several millions of image pixels [8][9][10][11][12][13][14][15]. The theoretical model images that were fed into SOM-QE analysis here each consist of more than three million pixels. The hypothetical timescale of the cell changes simulated by single-pixel changes between these high resolution images, for either viral progression or cell recovery, in either a single cell or in a monolayer of cells, may be estimated in seconds/minutes. With increasingly high resolution camera solutions, and images from a constant camera position taken every ten minutes and fed directly into a computer for SOM-QE analysis, cell biologists could become able to detect significant changes within cell monolayers or single cells within unprecedentedly short delays.
To provide a time course model for viral proliferation in terms of hours/days, the authors of the reference study [7] further reduced the complexity of information in their experimentally derived images, which had a considerably poorer resolution than our model image simulations here, by partitioning them into blocks of 20x20 pixels, which is not very precise, then averaging the pixels contained in each block. This reduction in image complexity was necessary to reduce the total number of pixels while retaining prominent features of the infection spread for further analysis by their own mathematical model. In the case of their largest image, this represented a reduction from roughly two million to five thousand pixels in their study [7]. Image reduction to deal with too much complexity always runs a risk of loss of potentially relevant information. Since SOM-QE provides pixel precision analysis of very large images, image data reduction is not required to reliably classify even the smallest local changes.
SOM-QE can also be applied to selected, particularly relevant image sections, or regions of interests (ROI), for analysis of single pixel changes whenever their spatial location in an image is a critical factor, as shown in some of our previous work [12]. Combining immunohistochemical data with digital imaging is definitely the way to go in the future. The exploitation of digital images in cancer diagnosis [18,19,20], for example, optimized by image segmentation methods capable of detection ROI automatically prior to further classification by SOM-QE, can provide objective analyses that make the difficult task of diagnosis more reliable and less time consuming for the human expert. Finally, in the current context of pandemic explosion of SARS-CoV, a particular class of coronavirus, there is hope that cellular imaging models, like the one described in [7], which inspired this study here, that account for in vitro coronavirus entry and proliferation mechanisms in cell lines or other cultured cells will allow for a better understanding of the infection process [21]. Rapid, nonexpensive, and swiftly implemented automatic image classification methods like the one proposed here could support the fast development of novel treatment strategies.

Conclusions
Digital image pixel RGB based models of viral proliferation after focal infection in vitro, or cell recovery in response to a specific treatment, may contain millions of image pixels that cannot be processed visually even by an experienced expert. The unsupervised self-organizing map based SOM-QE approach [8][9][10][11][12][13][14][15] is shown to provide a fast and statistically highly reliable classification model for the finest single pixel changes in image models containing several millions of pixels, simulating viral proliferation or cell recovery in terms of viral level reduction by progressive image pixel changes in contrast polarity and/or intensity. The classification method outperforms human computer-assisted image classification, is fast and economic, and can be applied to large imaging data prior to further mathematical modeling.