From qualitative data to correlation using deep generative networks: Demonstrating the relation of nuclear position with the arrangement of actin filaments.

The cell nucleus is a dynamic structure that changes locales during cellular processes such as proliferation, differentiation, or migration, and its mispositioning is a hallmark of several disorders. As with most mechanobiological activities of adherent cells, the repositioning and anchoring of the nucleus are presumed to be associated with the organization of the cytoskeleton, the network of protein filaments providing structural integrity to the cells. However, demonstrating this correlation between cytoskeleton organization and nuclear position requires the parameterization of the extraordinarily intricate cytoskeletal fiber arrangements. Here, we show that this parameterization and demonstration can be achieved outside the limits of human conceptualization, using generative network and raw microscope images, relying on machine-driven interpretation and selection of parameterizable features. The developed transformer-based architecture was able to generate high-quality, completed images of more than 8,000 cells, using only information on actin filaments, predicting the presence of a nucleus and its exact localization in more than 70 per cent of instances. Our results demonstrate one of the most basic principles of mechanobiology with a remarkable level of significance. They also highlight the role of deep learning as a powerful tool in biology beyond data augmentation and analysis, capable of interpreting-unconstrained by the principles of human reasoning-complex biological systems from qualitative data.

Introduction

Quantitative research methods involve measuring some predefined features of a representative population, gathering numerical data relative to such features, and statistically analyzing the data so that it may be generalized to a larger population or explain a particular phenomenon. While the aim of statistical analysis is to remove human bias from the scientific method, feature selection is a purely human process. As researchers, we select those features that can be measured, deem important, or believe useful in hypothesizing research outcomes. There is, however, an implicit preselection, because the possible features are in all cases limited to those we can define or at least conceptualize. In other words, we cannot measure what does not exist for us.

As the selection of measurables is a rational process, the scientific method has hitherto been unavoidably constrained by human interpretation and reasoning [1]. However, this has recently begun to change. Some deep neural networks trained on large datasets are known to develop an intrinsic understanding of images in a way that goes well beyond low-level features, capturing aspects that may not be obvious or conceptualizable in our interpretation of such images [2]. Here, we use that understanding developed by generative networks to interpret raw images of the arrangements of actin filaments in mammalian cells and demonstrate their relationship with the position of the nucleus. This correlation is commonly understood—or intuited—to exist since the mechanical interplay of both structures is known to have a major role in cell activities [3-8] and fate [9, 10], and their relative misplacement is a characteristic of cell malfunction and disease [11-14]. However, demonstrating it with statistical significance is limited by the impossibility of parameterizing the spaghetti-like arrangements of cytoskeletal fibers [15-17]. To avoid such parameterization, we shifted the analysis from the traditional measurement of the distinct features of each substructure (i.e., actin filaments and nuclei) to the isolation of all information related to each substructure in disjoint datasets and the use of the deep generative network to find, without manually created labels or human supervision, a deterministic relationship between the different information sets.

Results and discussion

The overall structure of the experimental design is presented in Fig 1. To build the paired datasets of nuclei and cytoskeletal fibers, the two substructures were fluorescently tagged with SyTOX Deep Red (660/682) and Alexa-Fluor 488 (490/519), respectively. The selection was based on the lack of overlapping absorptions at the primary emitting wavelengths of helium–neon (HeNe; 633 nm) and argon (Ar; 488 nm) lasers, avoiding any possible crosstalk between fluorophores. Altogether, 4,900 sets of paired images at a resolution of 300 pixels per inch were taken, each set containing an average of 20 cells. The paired dataset was randomly divided into training (80%) and test (20%) images. To find the nuclear position for a given cytoskeletal arrangement, we used a transformer-based architecture [18-20] based on the TFill network [21]. The architecture can be logically divided into three parts: (i) an encoder that takes the image of the cytoskeleton and successively embeds the two-dimensional (2D) image into high-dimensional, low-resolution feature representation; (ii) a transformer utilizes those high-dimensional features to model their dependencies with the high-dimensional features of the nuclei; and (iii) a decoder extracts those learned features in the high-dimensional space and transforms them to an image of nuclei (i.e., back to the low-dimensional, high-resolution space of common images). The results obtained were fed into a discriminator, which evaluated the proximity of the generated nuclei image to the real image and sent the results of that evaluation back to the network, training it further to improve the quality of the generated images. The auxiliary discriminator and the main generator stage a two-players-game, where two networks are trained simultaneously to compete against each other, one to generate increasingly realistic data (i.e., nuclei generation) and the other, the discriminator, improving its ability to differentiate real and generated data [22]. The iteration of this process enabled the network to identify relevant high-dimensional features in the cytoskeleton, enabling successful generation of the associated nucleus. During this process, the network was trained with qualitative data only, in the form of raw microscope images, without interpretation of the images, feature selection, or parameterization. The trained network was then used to generate the nuclei images corresponding to the test images of actin filaments. Thereafter, the images were segmented automatically, extracting the information on the number of nuclei and their diameter and position, and that information was compared with those of the real, or ground truth, nuclei.

Fig 1

Demonstration of a correlation between arrangements of actin filaments and nuclear position.

Actin filaments and nuclei information was isolated using non-overlapping fluorophores (Alexa Fluor 488 and SyTOX Deep Red). Then, 80% of the dataset of filaments was used as input to train a transformer-based network using the corresponding paired nuclei to evaluate the proximity to the real solution. The process iteration resulted in a fully trained network that was then used to generate the nuclei of the remaining 20% filament images of the dataset. The generated nuclei and their real counterparts were identified, and the coordinates of their centroids were determined to evaluate the network’s ability to predict the nuclear position using only actin filament arrangements.

The distinctiveness of the network we developed compared to other deep neural networks for image processing is that our objective was not the production of visually convincing images but of images with physiological significance, enabling the demonstration of dependencies between cellular substructures. Therefore, we eliminated image-refining steps aimed at improving appearance, common in other applications, using, for example, only a TFill-Coarse for image-to-image translation during training and testing. The encoder included a block of residual networks (ResNet, Fig 2A), enabling a fast and smooth flow of information across the network by avoiding training for irrelevant layers (i.e., not adding accuracy to the outcome) [23]. The encoded vectors obtained from the input images were then fed into the transformer layer (Fig 2B), whose focus was on accessing the long-range information related to the fibrillar organization in the entire cell. Using a self-attention mechanism, the transformer ensured that all regions of the image, regardless of their location relative to a nucleus, had equal opportunities of flowing through the network’s layers [21, 24]. In this way, we prevented the network’s bias toward finding an agreement between the predicted information and its immediate surrounding (preferred when filling in missing information in photorealistic images) [25] and encouraged agreement of the predicted nuclei with all information related to the fibrillar configuration. Finally, the feature maps were projected back into completed high-resolution images by the decoder and its upsampling layers.

Fig 2

Assessing the performance of TFill network and comparison with state-of-the-art generative models.

a, Encoder and Decoder layers comprise of a traditional convolutional neural network (CNN)-based ResNet block. b, The detailed architecture of the transformer encoder with self-attention mechanism. c, Reconstruction loss convergence as a function of iterations. d, Visual comparison of TFill generated nuclei images with trending image translation models. e, Quantitative comparison of TFill generated images with other image translation models using various metrics from computer vision (↓ Lower is better; ↑ Higher is better).

We used two distinctive loss functions during the training process. Since the targeted results, namely the nuclei, were relatively small compared to the background, we used a weighted reconstruction loss to correct the imbalance between the extensive dark background and the small, fluorescent nuclei [26]. This decision was taken after our initial attempts to predict nuclei, which were strongly biased toward the generation of black images, deemed “realistic” by the discriminator because of their proximity to the (mostly black) ground truth. By increasing the weight of the nuclei pixels (by an order of magnitude) in the calculation of the reconstruction loss, the system was encouraged to produce nuclei to achieve acceptable levels of “realism.” Then, an adversarial loss function [22] was used to evaluate the proximity of the generated nuclei images to real images of nuclei. This loss function was used and continuously refined by a discriminator trained to spot “fake” (i.e., generated) images of nuclei by comparison with the real images of nuclei. Concurrently, the generator was attempting to fool the discriminator by generating more realistic images while simultaneously minimizing the improving loss function.

The network training converged after 105 iterations (Fig 2C). The trained network was then used to generate the nuclei of the testing dataset. The photographic characteristics of the results were evaluated on multiple metrics, consisting of pixel-level ℓ1 loss curves, region-level Structural Similarity Index (SSIM) [27], and Peak Signal-to-Noise Ratio (PSNR) [28], image-feature-level Learned Perceptual Image Patch Similarity (LPIPS) [29], and dataset-feature-level Fréchet Inception Distance (FID) [30] (Additonal information in the Methods section). Despite the network architecture, which was designed for biological significance to the detriment of photorealism, the generation of images by the developed TFill network was on a par with those generated by state-of-the-art image translation networks geared toward realism, such as CycleGAN and pix2pix (Fig 2D and 2E) [31, 32]. It was not surprising with the structured paired dataset we used that the TFill-based network outperformed CycleGAN, which is conceived for mapping unpaired datasets. More interesting was the comparison with pix2pix, which is also explicitly designed to map paired images but focuses on photorealism [31]. Despite the different aims, both networks produced comparable metrics and realistic images. However, the TFill-based network showed a consistent output irrespective of the number of nuclei in the image, while pix2pix often generated noisy images and a recurrent “mosaic” artifact. Both effects were more frequent in images with many nuclei and were very likely introduced during the upscaling of the images to improve their quality. The performance of TFill (S1 Fig in S1 File) in generating photorealistic images, outdoing networks specifically built for this purpose, highlights the possible use of the presented architecture beyond the aim of this study, namely for predicting fluorescent labels, significantly reducing the processing time of biological samples [33].

In a further step, we evaluated the ability of the developed network to produce scientifically significant data, rather than just realistic images. We extracted the nuclear information using an automated segmentation system to determine and characterize the nuclei of the generated and real nuclei images. We also manually characterized a subset of 120 paired images as quality control for the automated characterization of the complete dataset. Overall, similar results were observed when the counting was done by automatic segmentation and matching or by manual analysis (Fig 3A). In the dataset of real images, 9,659 nuclei were isolated and characterized automatically, while 8,151 (84%) were detected on the synthetic dataset. Similarly, we manually counted 1,359 and 1,069 (i.e., 79%) nuclei in the ground truth and generated datasets, respectively. The 5% difference between automated and manual counting resulted from the different thresholds of complete nucleus used by a human and by the algorithm when counting nuclei at the edges of the images; whereas the human took an educated decision on when to consider a nucleus to fall within an image, the segmentation algorithm tended to detect and count all nuclei partially falling outside the image, resulting in additional counts. On the other hand, the approximately 20% difference between the total real nuclei and those generated by the network resulted from the independent sources of information used to produce the images of ground truth nuclei (i.e., from staining) and generated nuclei (i.e., from actin fibers). Those cases where the information on the actin fiber database was poor or missing resulted in a missing generated nucleus, while the real counterpart was properly stained and identified. This resistance of the network to produce nuclei without enough fiber information is a consequence of the deliberately conservative design of the network, which prioritized quality over quantity, in contrast with the usual “aggressive” approach of image-to-image translation neural networks, where finding a solution (or several) is the priority.

Fig 3

Positioning of nuclei generated from arrangements of actin filaments.

a, Results of the identification and matching of real and generated nuclei by an automatic counting of the whole generated dataset and by manual counting of a subset of images. Stained nuclei refer to those recorded directly using fluorescent microscopy. Generated nuclei are those produced by the neural network using actin filament arrangements. Matched nuclei are those generated at less than 4 μm of its real counterpart. b, Manual (left) and automatic (right) processing of the same image. In manual processing the profile of the nuclei is drawn to calculate the centroid and the nuclei matched by comparison with the real counterpart. On the other hand, the automatic processing automatically identified the nuclei and generated their bounding boxes, matching generated and real nuclei based on the maximization of the overlapping areas of the bounding boxes. c, Several examples of generated nuclei (red) and their corresponding real nuclei (blue). The first three images (green frame) correspond to nuclei generated within the average nuclear radius (4 μm) from their real position. The last image (red frame) corresponds to a mismatch, where the generated nucleus is too far from its real position (See S2 Fig in S1 File for full images; Bars are 20 μm). d, Example of a cell and the relative distance of 4 μm within the cytoplasm. The probability of randomly positioning the nucleus within the cytoplasm can be identified as the ratio of possible matched positions for the centroid (green area) with respect to all possible positions (orange area). Those possible positions of the centroid located at less than the nuclear radius from the edges of the cell (red area) are discarded under the premise that the nucleus cannot be positioned partially outside the cell (See S3 Fig in S1 File for further analysis of probabilities; Bar is 20 μm). e, Distribution of the distances of the generated nuclei respect their real position. 71% of the nuclei are situated at less than 4 μm of their real position. f, Distribution of distances of the generated nuclei considered matched (<4 μm). 40% of the matched nuclei are located at less than 1μm from their real position.

We then demonstrated the deterministic relationship between the nuclear position and the arrangement of actin filaments. We matched each generated nucleus with its real counterpart and calculated the Euclidean distance between their centroids. This was performed automatically by producing a bounding box for each identified nucleus, calculating the overlapping ratio (OR) of each bounding box of a generated nucleus with all those of real nuclei, and pairing them by maximizing the OR (Fig 3B). As before, we kept the manually processed subset as control. The bounding boxes were used to also calculate the centroid of each nucleus, which, in the case of generated nuclei, depend on the ability of the neural network to predict the right position and, to a lesser extent, the shape of the nucleus (Fig 3C, S2 Fig in S1 File) [34]. The neural network, using only cytoskeletal information, positioned 71 ± 1% (for a confidence interval (CI) of 95%) of the generated nuclei within the radius of the real nucleus (4 μm), and almost one out of three nuclei (29 ± 1%, for a CI of 95%) were generated at less than 1 μm from the center of the real nucleus (Fig 3D and 3E).

The consensus for biological experiments is to discard the null hypothesis for a p-value of < 0.05. In our experiments, the extreme level of confidence makes p values meaningless [35] (Additonal information in the Methods section). For example, given that the system has one out of 500 chances to randomly place the nucleus’s centroid at less than 4 μm of the correct position within the image (159.41×159.41 μm), the correct localization of 71% of the nuclei corresponds to a p-value of approximately 10−2170. Focusing the analysis on the location of the nucleus in the cell, rather than in the image, we would be assuming that the neural network somehow achieved the correct localization of the nuclei by developing: i) an understanding of the low-level characteristics of the filament arrangements (a feature conceptually similar to the limits or shape of the cell); ii) the understanding that the nuclei must be within those limits; and iii) the skills to predict the size and shape of the nuclei (Fig 3D). In such a situation, the problem would reduce in its last instance to the successful localization of the nucleus within the cytoplasm, a task that, in the most optimistic situation, can be randomly achieved in one out of two cases (S3 Fig in S1 File). This restrictive situation results in an equally negligible p = 6.6×10−130, yielding strong evidence against the null hypothesis (i.e., a random positioning of the nuclei within the cytoskeleton) and demonstrating, with overwhelming significance, one of the most basic principles of cell biology: the correlation between the position of the nucleus and the actin filaments.

Conclusion

In sum, to demonstrate the correlation between the position of the nucleus and the cytoskeleton in cells, we isolated the information about the substructures using non-overlapping fluorophores and laser lines. We developed an image-to-image translation algorithm based on a TFill network and trained it, using unparameterized images of actin filaments, to extract high-dimensional features relatable to nuclear information. The network’s success in accomplishing its task was measured by predicting several thousand nuclei from the arrangements of actin filaments. Seventy-one per cent of the nuclei were generated within the surface of the real nuclei, and almost half of those at less than 1 μm distant from their real position, demonstrating with astounding significance the hypothesis of a deterministic relation between the arrangements of the actin filaments and the position of the nucleus. This demonstration illustrates the ability to use deep neural networks, outside data analysis or augmentation, as a method to interpret reality beyond the limitations of human conceptualization, and, specifically, to extract features of systems with a complexity unsuitable for quantitative parameterization. Our results also evidence the conditions enabling a transition from a methodology in biology based on human analysis to methods of data acquisition focused on curating information for non-human interpretation.

Materials and methods

Cell culture

Mouse fibroblasts (NIH/3T3) (ATCC) were cultured and maintained in Dulbecco’s Modified Eagles Medium (high glucose DMEM, Nacalai Tesque) supplemented with 10% (v/v) Fetal Bovine Serum (FBS, Life Technologies) and 1% (v/v) Penicillin-Streptomycin mixed solution (Nacalai Tesque). Cells were incubated in normal physiological conditions (37°C, 5% CO2), passaged every three days, and their media was replenished every two days.

Fluorescence labelling

Upon confluence, the cells were trypsinized, centrifuged, and resuspended in fresh DMEM media at a concentration of 1 × 106 cells/ml. The cells were seeded on cover glass substrates (22 × 22 mm, thickness = 100 μm) at a seeding density of 20000 cells per substrate to ensure adequate spacing between the cells. All substrates were maintained in standard cell culture conditions (37°C, 5% CO2) for 24 hrs. The cell-seeded glass substrates were rinsed with Dulbecco’s Phosphate Buffered Saline (D-PBS) and fixed with 4% (w/v) Paraformaldehyde (PFA) (Merck Millipore) solution in D-PBS for 15 min. Samples were then washed three times (3X), 5 min each time, with D-PBS. Cells were permeabilized with 0.5% (v/v) Triton X-100 in D-PBS for 10 min and then washed 3X, 5 min each time, using D-PBS. Subsequently, the cells were blocked with 3% (w/v) bovine serum albumin (BSA, Gold Biotechnology) for 1 hr. Samples were stained with a 1:500 (v/v) dilution of Alexa-Fluor® 488 phalloidin (Life Technologies) for 30 min and washed 3X, 5 min each time, with D-PBS. Nuclei were stained with a 0.1 μM SyTOX™ Deep Red Nucleic Acid stain (Life Technologies) for 10 min, following which, the substrates were washed thoroughly with D-PBS to remove unbound stains. The coverslips were mounted (Fluoroshield mounting media, Abcam) and stored in the dark until further use.

Imaging

The images were acquired using a confocal microscope (Zeiss LSM 710) equipped with a 40× lens with numerical aperture 0.95 connected to Zen Black. Coverslips containing fixed cultured cells are mounted on top of a motorized stage. The microscope was programmed to acquire Z-stack images from a 25 x 25 square tile region (5.250 x 5.250 mm), thus acquiring a total of 625 image fields. The motorized stage can translate across x and y directions. The total thickness of each Z-stack was set to 20 μm, and images were acquired at an interval of 1 μm for each field. Two independent channels were acquired: Alexa Fluor 488 Phalloidin (Excitation (max): 495 nm, Emission (max): 518 nm) and SyTOX Deep Red (Excitation (max): 660 nm, Emission(max): 682 nm). During image acquisition, it was ensured that a stitching algorithm was not employed to facilitate the splitting of the large image area. A total of 4900 image pairs were collected across eight samples.

Dataset preparation

All acquired images were processed using Zen Blue Lite software. Images were first subjected to maximum intensity projection (MIP) to convert the 3D data into a single 2D image. It was ensured that all the features were visible in the single image plane. The large image area was split into two separate channels (Actin and Nuclei) and small, square image tiles, each of size 210 x 210 μm. The images were arranged into folders, each containing one Actin-Nucleus pair image data, using a custom-written Python script. 4900 image pairs were obtained and randomly divided into training (80% of the total dataset) and testing (20% of the total dataset) images.

Neural network–architecture

Our network architecture extends the TFill network from Zheng et al. We only used TFill-Coarse for image-to-image translation since this study focuses more on nuclei positioning than the realistic appearance generation [21]. Its architecture can be logically grouped into three parts: (i) an encoder that takes an image I ∈ ℝ3 as input and then successively embeds the 2D image into high-dimensional latent space thus yielding a low-resolution token representation z0; (ii) a transformer that captures long-range dependencies between encoded token representation and then outputs the global feature representation; (iii) and a decoder that takes the learned feature representation and generates all nuclei based on cell shapes. It gradually upsamples the low-resolution feature maps to high-resolution feature maps to achieve the original resolution images.

The transformer architecture was firstly introduced in Natural Language Processing (NLP) and later widely used in various computer vision (CV) tasks, such as scene classification, object detection, instance segmentation, image generation, and translation. A transformer encoder layer consists of a Multihead Self-Attention (MSA) and a Multilayer Perception (MLP) block. The MSA is applied to capture the long-range relationship between each token, while the MLP is responsible for further transforming the merged features from the MSA layers. Furthermore, to achieve the more complex features, the Layernorm (LN) is used before the MSA and MLP block for none-linear projection. They are expressed by: where z ∈ ℝ is the 1D sequence of N tokens x with C channels, E ∈ ℝ is the position embedding. z0 is the input sequence of the transformer while z is the sequence output in layer l.

The components of the neural network are illustrated in detail in Fig 2. Unlike the NLP that naturally treats each word as token [36] embedding for the 1D sequence, the visual image is in 2D without explicit word representation. Following the existing vision transformer [37-39] arch the CNN-based encoder embeds the 2D images as high-dimensional, low-resolution feature representations. The encoder is a ResNet-style convolutional neural network [40]. It is stacked with four repeated residual blocks. Each block consists of two convolutions, each followed by a leaky rectified linear unit with a leakage factor of 0.2 and a pixel-wise normalization. Besides, a skip connection is used to pass the information through a short path quickly. Each block is followed with a learned pooling operation with stride two to halve the resolution of the resulting feature map.

The transformer-based encoder consists of twelve transformer blocks. Each one can automatically capture the long-range dependencies between all locations in the feature maps. Furthermore, instead of the fixed weights in the CNN-based network, the transformer merges information using the input-dependent adaptive weightings, which are decided by the similarities between features. The decoder is an inverse operation of the encoder. It is applied to unfold the high-dimensional, low-resolution features into low-dimensional, high-resolution images. The decoder is also stacked with four repeated residual blocks as in the encoder. However, each block is followed with an upsampling layer to increase the resolution of feature maps. In parallel, the output layer is added after each block to get multilevel, multi-resolution outputs, where the output structure is inspired by StyleGAN v2 [41]. The multi-resolution outputs allow predication errors to quickly backpropagate to the previous encoders that can stabilize and speed up the training. Finally, an auxiliary discriminator using adversarial learning is applied to improve the generated image quality further [22]. We directly adopt the discriminator architecture from the latest StyleGAN v2 [41], which downsamples input images to 4×4 resolution, and then uses fully connected layers to judge them belong to “real(1)” or “fake(0)”. This encourages the generated results to match the distribution in the given data.

Loss functions

Weighted reconstruction loss

We first use pixel-weighted reconstruction loss to enable changing the influence of imbalanced nuclei and background ratios in the target image. The loss is defined as: where x is pixels in image domain Ω, Iout and Igt are the generated nucleus image and the corresponding ground truth respectively, M is the binary mask map where nucleus regions are labeled as “1,” and background pixels are labeled as “0”. Thus, the first term of the equation is related to the nuclei regions’ reconstruction, while the second term is for the background reconstruction. We use the L1 reconstruction loss for each matched pixel in the generated output and ground truth image.

In our images, most pixels belong to the black background. If we rebuild the original ground truth directly, the output will prefer to generate the black image on average. Therefore, we manually increase the weight of nuclei pixels using a factor α = 10, as compared with the black background pixels. To do this, we will enforce the model biases to the nuclei regions, resulting in a balance training.

Adversarial loss

We further introduce the adversarial loss to encourage the generated nuclei’s distribution to be closed to the nuclei’s distribution in the ground truth. Following the previous adversarial learning, we model this minimax game using an adversarial loss given by: where G is the generator and D is the discriminator, and Igt and Iin are the data from target ground truth sets and input sets. During the training, generator(G) and discriminator(D) parameters are updated alternately. The D is trained to distinguish between generated and ground truth images by maximizing the loss function above. At the same time, the G tries to fool the discriminator to generate more realistic images by minimizing the above loss function.

Neural network–evaluation

Fréchet inception distance (FID) [30]

This metric calculates the mean and variance distance between the feature vectors for ground truth and generated images. A low FID score indicates better performance.

Learned perceptual image patch similarity (LPIPS) [29]

This evaluates the diversity of generated images compared to its ground truth, and it is a state-of-the-art metric that correlates to human perceptual similarity. A lower LPIPS score indicates that the generated image is more realistic and similar to the ground truth.

Structural similarity index (SSIM) [27]

This metric computes the perceptual distance between a translated image and its corresponding ground truth based on three indices: luminance, contrast, and structure. The higher the SSIM score, the greater the similarity of the two images.

Peak signal-to-noise ratio (PSNR) [42]

PSNR calculates the differences in intensity between the ground truth and the generated image and is defined via the mean square error (MSE). A high PSNR score indicates that the intensity of both images is similar.

Comparison of nuclei count and positioning in real and generated images

The number of nuclei and their positioning were quantified using built-in functions in MATLAB (MathWorks, Natick, MA) [43]. The images were initially subjected to binarization via HSV thresholding. The properties of the nuclei were recorded from the thresholded images, and the nuclei were counted from the regionprops function. The function also provides information such as area, centroid, and bounding boxes around the nuclei region. We then filtered the segmented components with a minimum area of 50 pixels to eliminate noise due to thresholding deficiencies. In addition, poorly thresholded images were manually eliminated from further analysis since the goal is not to test for segmentation accuracy. 729 images out of 980 test images were used to calculate errors in nuclei count and positioning accuracy. The percentage error in nuclei detection was computed as follows: where Nuclei countGT indicates the number of nuclei in the ground truth and Nuclei countGen indicates the number of nuclei in the generated image. Subsequently, for every generated nucleus, the bounding box resulting from regionprops function was compared with that of ground truth to compute the overlap ratio using the MATLAB in-built function bboxOverlapRatio. The overlap ratio (OR) is an intersection over union metric (IoU), which was computed as follows: where BBGT and BBGen indicates the bounding boxes of ground truth and generated nuclei respectively. This is used to match generated nuclei centroids to ground truth nuclei centroids. Then, an error metric is computed as a Euclidean Distance (ED) between the two coordinates as follows:

We also use the Clopper and Pearson approach to establish 95% confidence intervals for all of the performance metrics in this study [44].

Distribution and probability of the nuclei position within the image and the cell

Statistical analysis is done by modeling the number of correct predictions made by the neural network using a binomial distribution, with a probability of success p for each prediction. Due to the very high number (n = 8151) of trials, a normal distribution is used to closely approximate the binomial. Based on 5785 correct predictions at the 4um distance, the 95% score confidence interval for p is computed to be 71.0+/-1.0%. Similarly, based on 2328 correct predictions at the 1um distance, the 95% score confidence interval for p is computed to be 28.6+/-1.0%.

To calculate the network’s success in predicting the correct position of the nuclei, we first calculated how successful any system would be doing it randomly. To do so, we define the ratio of “right positions” and “possible positions” on the area where the nucleus is generated (S3 Fig in S1 File). The correct positions are those within the nucleus area, taking 4 μm as the average radius for the cells employed in this study. This assumption is made based on the possible divergence of the centroid due to imaging and the different shapes of the real and generated nuclei. We calculated the ratio within the whole image as well as within the cell. To provide a realistic approximation and avoid an overrepresentation of possible positions, we impose the additional restriction that the whole nucleus must be inside the cell for the calculation. Therefore, those possible positions situated at a distance of less than a nuclear radius from the edges of the cell were discarded. To get realistic values, we first modeled cells as a circular entity based on the average radius in a confluent culture. Then, we repeated the same calculation for the images used in this study. In that case, the position ratios are strongly dependent on the cell geometry.

We calculated the ratios and associated p-values for several cells, including the two most extreme examples found. In one end are cells narrowly spread around the nucleus and with the cytoplasm distributed in several protrusions (S3C1 Fig in S1 File), strongly limiting the possible positions of the nucleus to the small central space. On the other extreme are cells uniformly spread and with short or inexistent protrusions (S3E Fig in S1 File), where the possible positions for the nucleus roughly cover the whole cytoplasm. We also repeated the same calculations using a threshold distance of 1 μm between the centroids of the real and predicted nuclei. In that case, the number of matched nuclei drops to almost half; however, the probability of correctly positioning it by chance also decreases dramatically, resulting in similarly low p-values.

All the p values reported in this study are negligible, and it makes no difference to have a p = 10−100 or 10−1000, since both are in a range of overwhelming statistical significance. In that situation, we find the confidence interval (reported in the main text) a much more informative way to report an error. Despite the absurdity of these negligible p values, we have included them as a comparison with the current standards in biology to highlight the power of the approach presented here. P values are a standard in biological and biomedical research, fields that struggle to achieve p values < 0.05, a thresholds that hardly ensure reproducibility of the results [45]. Here, however, analyzing a similar system, achieve p values that in the worst scenario are < 10−100., giving a clear picture of the quality of the demonstration compared to those currently accepted in biomedical studies.

This contains three additional figures on the performance of the generative network, the generation of nuclei, and the statistical analysis.

The cell image database used in this research is available in the supplementary file “NIH3T3_ImageDataset-20220519T022044Z-001.zip”. The network source code can be found at: https://github.com/JGFermart/NuclearPrediction.

(PDF)

Click here for additional data file.

Transfer Alert

This paper was transferred from another journal. As a result, its full editorial history (including decision letters, peer reviews and author responses) may not be present.

28 Apr 2022

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Florian Rehfeldt

Academic Editor

PLOS ONE

Journal Requirements:

When submitting your revision, we need you to address these additional requirements.

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and

https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf

2. Thank you for submitting the above manuscript to PLOS ONE. During our internal evaluation of the manuscript, we found significant text overlap between your submission and the following previously published work:

- https://www.researchgate.net/publication/335781725_Perspective_Dimensions_of_the_scientific_method

We would like to make you aware that copying extracts from previous publications, especially outside the methods section, word-for-word is unacceptable. In addition, the reproduction of text from published reports has implications for the copyright that may apply to the publications.

Please revise the manuscript to rephrase the duplicated text, cite your sources, and provide details as to how the current manuscript advances on previous work. Please note that further consideration is dependent on the submission of a manuscript that addresses these concerns about the overlap in text with published work.

We will carefully review your manuscript upon resubmission, so please ensure that your revision is thorough.

3. Thank you for stating the following in the Acknowledgments Section of your manuscript:

"The Singaporean Ministry of Education has supported this research through the MOE2018-T2-2-176 grant

to JGF."

We note that you have provided funding information that is not currently declared in your Funding Statement. However, funding information should not appear in the Acknowledgments section or other areas of your manuscript. We will only publish funding information present in the Funding Statement section of the online submission form.

Please remove any funding-related text from the manuscript and let us know how you would like to update your Funding Statement. Currently, your Funding Statement reads as follows:

"The Singaporean Ministry of Education has supported this research through the MOE2018-T2-2-176 grant to Javier G. Fernandez.The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript."

Please include your amended statements within your cover letter; we will change the online submission form on your behalf.

4. Please include captions for your Supporting Information files at the end of your manuscript, and update any in-text citations to match accordingly. Please see our Supporting Information guidelines for more information: http://journals.plos.org/plosone/s/supporting-information.

Additional Editor Comments:

Please address thoroughly the concerns raised by the reviewers. In particular the first major point from Reviewer 2 is absolutely crucial.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Partly

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: No

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The paper poses an interesting idea to use a encoder-transformer-decoder network to determine the nuclear positioning from cytoskeletal features. The approach, staining, training, and statistics is sound. Furthermore, raw images and documented code is available for the review.

I want to adress following issues:

Major:

- the autors acknowledge the importance of nuclear position and shape, yet fail to adress the nuclear shape, only using centroid, area and bounding box. The method and paper would greatly benefit from usage of nuclei shape and position in relation to cytoskeleton. Related to this, using the regionprops boundingbox results to calculate overlap of nuclei seems ill advised given nuclear shape differences

- the autors cite references from 1997 till 2012 to justify "mechanical interplay of both structures is known to have a

major role in cell activities[3-6] and fate[7]". There are several papers from 2017-2020 that have investigated this in detail. This papers also refute "correlation between cytoskeleton organization and nuclear position has not, to date, been demonstrated" from the abstract

- P.7 Reference missing. Since this is the reference where "components of the neural network are illustrated in detail", it is a major flaw

- several imaging folders in the ImageDataset are empty, for example Set_1420, Set_1436, Set_2577... The dataset thus contains only 497 sets of actin, nuclei and merged images instead of 611. The autors should either upload this data or remove the folders and correct the numbers given in the paper.

Minor:

- "poorly thresholded images were manually eliminated from further analysis" -> 1/4 of images have been removed, I fail to see how 1/4 could have been "poorly thresholded"?

- P.10 "main text) a much informative way to report an error" -> 'more' missing

- the code is given fully, however I needed to install several packages manually and had to do adjustments. However, I noticed the documentation within the code.

Reviewer #2: The authors of this study trained a neural network to predict location

of the cell nucleus from images of the cell actin cytoskeleton. The trained

system performes remarkably well. I have two major comments and a couple

of minor ones:

Major:

1) From actin images it is clear that the brightest actin arrays simply

alighn with cell edges, which is often the case. So roughly the actin image

outlines the cell perimeter. I am pretty sure the nucleus is located in the

geometric center of the cell, and so its location is only coincidentally

defined by actin; in reality it is defined by the cell shape. The authors

should address this problem somehow; otherwise, this study, though technically

good, is pointless.

2) The NN is not truly tested. Some tests would be very easy: use a few

chemical perturbations, like latrunculin, calyculin etc (there are more than

10 cheaply available). See if nuclear localization will still be predictable

from perturbed actin images without further training.

Minor:

1) there is no cell biological discussion of the vast literature on nuclear

positioning and actin localization; without it, it's hard to judge significance

of the results

2) the paper is written pretty densely; it would be good to see a few main

points described for laymen

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

19 May 2022

We want to thank the reviewers for their thoughtful and profound evaluation of our work. We have addressed all the technical comments and suggestions in the new version of the article and provided below a point-by-point response to those comments. However, the reviewers will find that some of the comments related to the results’ significance have not been fully addressed. This is not a neglection of the reviewers’ comments, which are educated and on point, but the result of keeping the article’s original focus —maintaining the scientific aim, despite its abstract nature and complexity, is central for us and one of the main drivers of submitting this work to a journal with a technically focused evaluation process (instead of perceived impact and significance).

As mentioned in our cover letter, our article’s main contribution is not in machine learning or biomechanics. Its main contribution is in epistemology. We believe that with the rise of ML and the development of “intelligent” systems, able to perform an inherently rational task as it is the interpretation of qualitative data, the traditional scientific method focused on human perception and reasoning is, for the first time, at a point requiring its revision to enable novel and less “human-centered” approaches to inquiry complex systems. The demonstration in our article that a correlation can be established without the need for a human interpretation or parametrization of a qualitative representation of the targeted system is an apparent proof of that. It is not arbitrary that our first reference is the “Dimensions of the scientific method” by Eberhard Voit.

We want to remark again that the lack of a proper response to the reviewer’s comments related to the perceived impact in the field of biomechanics must not be understood as contempt for their opinion. In the light of the comments, which centered on the article’s mechanobiological aspects, we realized that we succeeded in focusing the introduction, abstract, and conclusion simultaneously on the experimental design and the results. However, we failed to direct the reader to both aspects in the title. Therefore, in this new version, we have proposed changing the title to “From qualitative data to correlation using deep generative networks: Demonstrating the relation of nuclear position with the arrangement of actin filaments,” which we believe better matches the article’s content.

Review Comments to the Author

Reviewer #1: The paper poses an interesting idea to use a encoder-transformer-decoder network to determine the nuclear positioning from cytoskeletal features. The approach, staining, training, and statistics is sound. Furthermore, raw images and documented code is available for the review.

I want to adress following issues:

Major:

- the authors acknowledge the importance of nuclear position and shape, yet fail to address the nuclear shape, only using centroid, area and bounding box. The method and paper would greatly benefit from usage of nuclei shape and position in relation to cytoskeleton. Related to this, using the regionprops bounding box results to calculate overlap of nuclei seems ill advised given nuclear shape differences

We appreciate the reviewer’s comment. We often discussed the influence of the nuclear shape during the development of this study. We acknowledge the extreme relevance of the nuclear shape in mechanobiology and how it might be even more relevant than nuclear position to understand the triggering of specific cell mechanisms. This, however, was not the objective of this study, and we believe it is outside the scope of this paper. Additionally, our microscopy data, collected specifically for the objective of this study (location), would probably not allow us to perform such analysis due to the poor definition of the nuclear shape. We, however, specifically discuss the influence of the nuclear shape in our data (pages 4 and 5) since the centroid of the nuclei will change depending on the geometry. The consideration of the influence of the nuclear shape is also included in our “sanity check” performed with manually characterized data (Figure 3b, analysis in 3a), where the manually defined profile of the nuclei is compared with the automatically generated bounding boxes. We did not see that influence in the calculation of the centroid. We also highlight in the text the (necessary) prediction of the nuclear shape (not only the position) by the algorithm to achieve such results (page 13).

We appreciate how important it would be for the field to correlate the shape of the nucleus with the cytoskeleton arrangement. However, we believe that analysis is a different study outside the scope of this paper.

- the autors cite references from 1997 till 2012 to justify “mechanical interplay of both structures is known to have a major role in cell activities[3-6] and fate[7]”. There are several papers from 2017-2020 that have investigated this in detail. This papers also refute “correlation between cytoskeleton organization and nuclear position has not, to date, been demonstrated” from the abstract

We acknowledge a bias in our references toward those original studies that set the ground for the cytoskeleton-nucleus interactions. This comment on the lack of recent references agrees with a similar one from Reviewer 2.

We have revised the citations to include (five) more recent articles and corrected the wording in the abstract to avoid understating the field’s current state.

- P.7 Reference missing. Since this is the reference where “components of the neural network are illustrated in detail”, it is a major flaw .

We apologize for this error. We revised this article multiple times to avoid typos. However, due to the unusually strict format requirements for the initial submission in PLoS ONE, we had to rearrange several sections at the last minute. Because of that, we missed this broken link to the figure and got the error message instead. We have corrected it, and it now directs the reader to Figure 2. We thank the reviewer for such in detailed evaluation.

- several imaging folders in the ImageDataset are empty, for example Set_1420, Set_1436, Set_2577... The dataset thus contains only 497 sets of actin, nuclei and merged images instead of 611. The autors should either upload this data or remove the folders and correct the numbers given in the paper

We have corrected those. We are not sure why the database was incomplete, but our guess is that we hit some limit in either the file size or the length of the paths during the compression. We have updated the database. Please note that the database file must uncompress into 10Gb of data, while the fully trained model (also provided) is around 27Gb. Thank you for pointing out this major issue.

Dataset: https://www.dropbox.com/s/fqlvjrp5aitd1l6/NIH3T3_ImageDataset-20220519T022044Z-001.zip?dl=0

Fully trained model: https://www.dropbox.com/s/q779s51tqrbtdn4/Jyo%20-%20SUTD_Cell.zip?dl=0

Minor:

- “poorly thresholded images were manually eliminated from further analysis” -> 1/4 of images have been removed, I fail to see how 1/4 could have been “poorly thresholded”?

While the algorithm predicting nuclear position has been developed in-house from scratch, the segmentation system is based on existing tools and algorithms implemented in Matlab. Based on our experience, we are not surprised by a general-purpose thresholding algorithm failing 1 out of 4 times in a real scenario of a heterogeneous collection of microscope images of cells at about 70% convergence. A customized system could improve this performance, but since the current performance of the segmentation is more than enough to support the conclusions, we preferred to use standard tools rather than add a new and unrelated topic to the article, as it is the automatic segmentation of images.

- P.10 “main text) a much informative way to report an error” -> ‘more’ missing

Thanks, we changed it.

- the code is given fully, however I needed to install several packages manually and had to do adjustments. However, I noticed the documentation within the code.

We appreciate the comment. We cleaned, simplified, and documented the code to enable its easy use by others. We appreciate the independent test by the reviewer and the extra mile the reviewer went to test its accessibility to other researchers.

Reviewer #2: The authors of this study trained a neural network to predict location of the cell nucleus from images of the cell actin cytoskeleton. The trained system performes remarkably well. I have two major comments and a couple of minor ones:

Major:

1) From actin images it is clear that the brightest actin arrays simply alighn with cell edges, which is often the case. So roughly the actin image outlines the cell perimeter. I am pretty sure the nucleus is located in the geometric center of the cell, and so its location is only coincidentally defined by actin; in reality it is defined by the cell shape. The authors should address this problem somehow; otherwise, this study, though technically good, is pointless.

We agree on the possible mechanism the AI is using to predict the nucleus. We disagree that the achievement is pointless. As mentioned above, this is unsupervised training. The strategy found by the ML is, therefore, purely based on patterns developed by the ML in isolation from human concepts while working on qualitative data (microscope images). At no point do we provide to the algorithm the concept of cell, shape, filaments, or any other conceptualization of the images. All those concepts, rationalizable by our understanding of those images and others that the ML developed without a counterpart on our understanding of the images, are the key and uniqueness of this study. The ability to perform a non-human parametrization of a complex system and achieve a statistical correlation from qualitative data.

2) The NN is not truly tested. Some tests would be very easy: use a few chemical perturbations, like latrunculin, calyculin etc (there are more than cheaply available). See if nuclear localization will still be predictable from perturbed actin images without further training.

We share the interest in the topic with the reviewer, and we agree on further studies sprouting from this. In particular, the prediction of a disease of a specific cell-state based on nuclear dislocation. However, we believe the evidence strongly supports the paper’s conclusion and that the suggested experiments, while extremely interesting, move in a direction that is not compatible with the focus of this study.

Minor:

1) there is no cell biological discussion of the vast literature on nuclear positioning and actin localization; without it, it’s hard to judge significance of the results

The feedback on the age of the references used is common to both reviewers. We have updated the biomechanical citations to more recent ones, which we believe now give a more comprehensive picture of the field’s state. We appreciate the reviewers’ advice.

2) the paper is written pretty densely; it would be good to see a few main points described for laymen

We acknowledge the density of the article. However, it is worth noting that this article moves from experimental design to mechanobiology to machine learning and statistics. We feel it is impossible to elaborate on each field’s basics for non-experts without transforming the article into a sort of review. For example, for the authors in mechanobiology, the microscopy and biological explanations seem to be very basic, almost trivial when explaining the cytoskeleton. At the same time, the ML learning part seem too steep. We found that those in the field of ML feel the opposite, finding trivial the explanation of the work of an adversarial network and puzzling the explanation of mechanical principles of the cell or the non-overlapping fluorophores.

Submitted filename: Response To comments_2.pdf

Click here for additional data file.

23 Jun 2022

From qualitative data to correlation using deep generative networks: Demonstrating the relation of nuclear position with the arrangement of actin filaments

PONE-D-22-06274R1

Dear Dr. Fernandez,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Florian Rehfeldt

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The autors adressed all comments and made changes to most, and gave reasons to why the other comments were not adressed.

I would have liked to see nuclear positioning inorporated as well as a self-written script used for thresholding instead of a common MatLab skript. However, I can see why the autor deems this is as beyond the scope.

Reviewer #2: appropriate revisions...............................................................................................................................................................

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

**********

21 Jul 2022

PONE-D-22-06274R1

From qualitative data to correlation using deep generative networks: Demonstrating the relation of nuclear position with the arrangement of actin filaments

Dear Dr. Fernandez:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

If we can help with anything else, please email us at plosone@plos.org.

Thank you for submitting your work to PLOS ONE and supporting open access.

Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Dr. Florian Rehfeldt

Academic Editor

PLOS ONE