A continuous-discrete model of cell contraction incorporating actin and intermediate filaments

Figure 1. Model specifications (A) Schematic illustration of the model before deformation. Cytoplasm containing major (blue) and minor (red) fibers, representing actin filaments (AFs) and intermediate filaments (IFs), respectively. (B) Schematic representation of the deformed cell resulting from the forces exerted by AFs. (C) Arrangement of actin filaments near focal adhesions, cell cortex, and within cytoplasm (adapted from de Rooij et al.31). (D) Relative position of fibrous actin and vimentin intermediate filaments (adapted from Wu et al.32).

Figure 2. Model predictions (A) Similar to the finite element approach, the domain is discretized using a triangular mesh (B) Initial distribution of major and minor fibers. New arrangement of (C) major and (D) minor fibers after cell deformation. Insets show the force applied to a piece of plasma membrane by the cytoplasmic and cortical components of major and minor fibers. (E) Overlay of major and minor fibers. (F) Simple mechanical model and parameters of the contour model. (G) Distribution of mean strain within the domain, solid lines show the direction of the major principal strain in each element. (H) Accumulative average displacement and (I) rotation of major and minor fibers.

Figure 3. Comparison of model predictions with experimental data (A) Cells are cultured on a collagen I grid. F-actin was stained using Phalloidin and is shown in red, while paxillin labeling is shown in green (adapted from Tabdanov et al.46). (B) A triangular mesh was used to discretize the polygon representing cells. (C) Initial distribution of major and minor fibers over the undeformed domain. Focal adhesions are shown in green. (D) New arrangement of major and (E) minor fibers after cell deformation. (F) Overlay of major and minor fibers. Dash line depicts the experimental periphery of the cell. (G) Quantitative comparison of the radius of curvature of membrane segments in simulation and experimental data. R denotes the pairwise linear correlation coefficient. (H) Spatial distribution of actin and intermediate filaments within the cell, classified into three regions based on their relative distance from the nucleus: [0–1/3], [1/3–2/3], and [2/3–1]. (Upper error bars represent SD. p values were calculated using Student’s t test.).

Figure 4. Comparison of model predictions with experimental data (A) Circular isotropic arrangement of fibronectin dots. (B) Filamentous actin in the cell cultured on the isotropic pattern. (C) Model’s prediction displaying the new arrangement of major and minor fibers after cell deformation. (D) Quantitative comparison of the radius of curvature of membrane segments in simulation and experimental data. (E) Spatial distribution of actin and intermediate filaments in the simulated and experimental cells. Filaments are grouped based on their relative distance to the nucleus. (F) Circular anisotropic arrangement of fibronectin dashes and dots. (G) Filamentous actin in the cell cultured on the anisotropic pattern. (H) Model’s prediction displaying the new arrangement of major and minor fibers after cell deformation. (I) Quantitative comparison of the radius of curvature of membrane segments in simulation and experimental data. (J) Spatial distribution of actin and intermediate filaments in the simulated and experimental cells. Filaments are grouped based on their relative distance to the nucleus. Dash line depicts the experimental periphery of the cell. Panels a, b, f, and g were adapted from…

Figure 5. Comparison of model predictions with experimental data (A) NIH3T3cells, cultured on a fibronectin-coated plastic dish, were stained for F-actin and paxillin (Data adapted from Carter et al.48). (B) A polygon resembling the cell with a triangular mesh was used in the model. Constraints are depicted by green dots. (C) The initial distribution of major and minor fibers. (D) Predictions of the model show the accumulation of major fibers in the vicinity of the constraints and in the cytoplasmic region. Dash line depicts the experimental periphery of the cell. (E) Quantitative comparison of the radius of curvature of membrane segments in simulation and experimental data. (F) Spatial distribution of actin and intermediate filaments in the simulated and experimental cells. Filaments are grouped based on their relative distance to the nucleus. (Upper error bars represent SD. p values were calculated using Student’s t test.).

Figure 6. Comparison of model predictions with experimental data (A) Fibroblasts, cultured on glass, were stained for F-actin, vimentin, and paxillin (Data taken from Swoger et al.49). (B) A polygon resembling the cell with a triangular mesh was used in the model. Constraints are depicted by green dots. (C) The initial distribution of major and minor fibers. (D) Predictions of the model show the relative configuration of major and minor fibers within the cellular domain. Black dash-line represents the experimental periphery of the cell. (E) Quantitative comparison of the radius of curvature of membrane segments in simulation and experimental data. (F) Spatial distribution of actin and intermediate filaments in the simulated and experimental cells. Filaments are grouped based on their relative distance to the nucleus. (Upper error bars represent SD. p values were calculated using Student’s t test.).