Fig 1.
Overview of our approach and experimental material.
(A) The outline of our method. By applying image processing techniques and the CNN method, the cell outline and SFs can be extracted from the original microscopic images. The extracted outline and SFs will be sent into the diffusion model so that the network can understand the transformation from cell outlines to SFs. (B) Schematic of cell culture. The cells are cultured on the glass substrate, and the SFs can be visualized by fluorescently-labeled phalloidin. Scale bars are 20 μm.
Fig 2.
CNN method for the SFs segmentation.
(A) Preparation of training data. By utilizing the augmentation methods, the original 50 images are increased to 2000 for the CNN network to be trained. (B) The CNN network (U2-Net) is trained with the augmented SFs data. After sufficient training, the network can automatically segment the SFs from microscopic images.
Fig 3.
Generating SFs from cell shapes using the diffusion model.
(A) Schematic of the diffusion model showing the forward process of turning SF images into Gaussian noise and the reverse denoising process of transforming Gaussian noise into SF images under a certain cell contour condition. (B) Architecture of the neural network used to predict noise added to SF data in the forward diffusion process under the cell contour condition. After training, the network can generate SF data from random noise based on the input cell contour.
Fig 4.
SF segmentation accuracy using CNN method.
(A) Accuracy comparison of SF segmentation results using our CNN method and the filament sensor. The box plots describe the minimum, first quartile, median, third quartile, and maximum. (B) False negative rate (FNR) and (C) False positive rate (FPR) of SF segmentation results using our CNN method and the filament sensor, with lower values indicating better performance. (D) Visualization of SF segmentation results using our CNN method and the filament sensor.
Fig 5.
Predicted SFs based on the diffusion model.
(A) Comparison of real (ground truth) SF images and predicted SF region from the diffusion model. The contour P shows the probability of the SF localization. (B) ROC curve and the corresponding AUC score for each threshold Pth value. The ROC curve illustrates the FPR (false positive rate) versus the TPR (true positive rate) of the prediction. (C) A sample image explaining the data preparation for the ROC analysis. The image is separated into 64 × 64 grids, and each grid is categorized as the SF region (pink) if any of the pixels inside the grid are pixels with SF (white). (D) Error of predicted SF length ℓredict and direction from the diffusion model. (E) Comparison of ground truth SF length ℓreal and predicted SF length lpredict, with the dashed line indicating equal values. (F) Comparison of ground truth SF direction
and predicted SF direction
, with the dashed line indicating equal values.
Fig 6.
Quantitative analysis of the relation between predicted SF dynamics and cell morphologies.
(A) Probability distribution function of the angle differences between cell direction ψ and SF direction in both ground truth data and predicted data from the diffusion model. (B) Relationship between SF length and cell area in both ground truth data and predicted data. (C) Correlation between ground truth SF order parameter S and predicted SF order parameter S from the diffusion model, and cell aspect ratio, divided into 5 intervals. The box plots describe the minimum, first quartile, median, third quartile and maximum. (D) Correlation between cell circularity and SF order parameter in both ground truth data and predicted data.
Fig 7.
Correlation between local cell curvature, SF intensity and cell contractile force.
(A) Visualization of the local curvature values along the cell contour. (B) Visualization of local SF intensity on cell contour. (C) A negative correlation between cell curvature value and SF intensity for a single cell contour. (D) A correlation between the SF intensity and the SF probability P. The correlation 0.87 is calucated from 1293 cells, while 500 points are randamly ploted for a clear visualization. (E) Schematic representation of the cell from (A), depicting line tension λ and surface tension σ, with their relationship determined by the curvature radius R. (F) The contractile force measured using the WFM method. (G) Positive correlation between curvature and force, and (H) negative correlation between the SF probability P and force. The correlations were calculated for each point on the cell contour (360 images). For a clear visualization, 2000 points are randomly selected.
Fig 8.
Results from generated SFs comparing with previous studies.
(A) Probability P of SFs under rectangular constraints predicted by the diffusion model, and a scale bar is 20 μm. (B) Relationship between simulated SF order parameter and constraint area aspect ratio, compared with results from a previous study (marked as ▽) [19]. The box plots describe the minimum, first quartile, median, third quartile and maximum.
Fig 9.
Results from the virtual experiment using the diffusion model.
(A) Comparison of generated SFs with geometrical constraints of aspect ratio (AR = 1 and 3) to experimental results of HFF-1 cells with comparable geometry constraints. The cells in the experimental group have aspect ratios of 1.1 and 2.8, and areas of 1.83 × 103 μm2 and 1.88 × 103 μm2, which are similar to the morphology conditions during the virtual experiments. Scale bars represent 20 μm. (B) Relationship between distance from the geometrically constrained edge r* and probability of generating SFs Pmean for three cases of aspect ratio (AR = 1, 3 and 5). (C,D) Probability distribution function (PDF) of the probability of generating SFs P with a constraint of (C) AR = 1 and (D) AR = 3. (E) Standard deviation σP of P decreases as constraint aspect ratio increases.