Fig 1.
Summary chart of the investigation of the influence of cell shape on cell polarization gradients.
From left to right; schematic overview of cell polarization (top) Unstimulated cell (bottom) Following stimulation (e.g. mechanical or biochemical) of a cell, active Rho GTPases redistribute such that regions of high active Rac and Cdc42 represent the front while the back is associated with regions of a high amount of active Rho as suggested by [4]. We implemented the computational model of Marée et al. [4] on the shapes used by Jiang et al. [14] to investigate the influence of cell shape on polarization, including the effect of polarization direction, polarization strength, size, shape and aspect ratio.
Fig 2.
Schematic overview of the Rho GTPase model adapted from [4].
The f parameter corresponds to the feedback between Rho GTPases and PIs. In this study, we set the f parameter to 0.4.
Table 1.
Parameter values for the polarization model, same as Marée et al. [4].
Fig 3.
Initial active Cdc42 condition and geometry for the polarization model.
Spatial distribution of active Cdc42 at 1s for all shapes (initial polarization). The black arrow indicates the initial polarization direction.
Table 2.
Initial concentration of each species as implemented in the VCell model.
Fig 4.
Spatiotemporal evolution of the patterns of active Rho GTPases and PIPs in a teardrop-shaped cell.
Regions where the active Rho GTPase and PIP concentration is above a particular value (see scale bar) are colored white. The black arrow indicates the initial direction of polarization.
Fig 5.
Initial polarization direction influences active Cdc42 patterns.
The following initial polarization directions were tested: L-R (left-right), R-L (right-left), U-D (up-down). The turning arrow indicates which patterns turn from an up-down initial polarization pattern to a left-right. The polarization patterns represent the active Cdc42 concentration. Regions where the active Cdc42 concentration is above 3 μM are colored white.
Fig 6.
Initial polarization direction in combination with the initial polarization strength and duration influences the reverse polarization pattern.
L-R (left-right), R-L (right-left), U-D (up-down) initial polarization directions. The turning arrow indicates which patterns turn from an up-down initial polarization pattern to a left-right. The polarization patterns represent the active Cdc42 concentration. Regions where the active Cdc42 concentration is above 3 μM are colored white. Constant (cons.) slope of 0.05, intercept (interc.) values: low = 1.6, high = 3. Constant intercept of 2.6, slope values: low = 0.025, high = 0.1.
Fig 7.
Cell shape influences cell polarization patterns.
A) Temporal evolution of maximal Cdc42 for a cell stimulated in the L-R direction. B) Spatial evolution of Cdc42 concentration for a cell stimulated in the L-R direction at 30s. The concentrations are measured on the main axis, as shown in the inset. C) Temporal evolution of maximal Cdc42 for a cell stimulated in the R-L direction. D) Spatial evolution of Cdc42 concentration for a cell stimulated in the R-L direction at 30s. The concentrations are measured on the main axis, as shown in the inset, where the x-coordinate is determined from left to right.
Fig 8.
Cell size and aspect ratio affect polarization patterns.
A) Polarization patterns of active Cdc42 at different aspect ratios for the teardrop. L: length, W: width. 1000s simulation time. B) Summary plot showing six main polarization patterns for the teardrop, rectangle (or square) and circle (or ellipse). The terms “shorter” and “longer” refer to the cell size along a particular (initial or new) axis with respect to the other axis. “Polarization” refers to a polarization pattern such that the maximum of Cdc42 is at one end of the cell, while the minimum is at the opposite end. “Reverse polarization” refers to the shifting of the maximum such that it is no longer situated at the one of the extremities of the cell. The “initial” axis refers to the axis along which we initially polarize the cell (L-R), while the “new” axis refers to the main axis perpendicular to the initial axis. The initial polarization direction is left-right, as indicated by the black arrow. Regions where the active Cdc42 concentration is above 8 μM are colored white.
Fig 9.
1D parameter space exploration for the circle and the teardrop.
The black arrow represents the initial polarization direction, the standard polarization scheme was used. The polarization patterns represent the active Cdc42 concentration. Regions where the active Cdc42 concentration is above 3 μM are colored white.
Fig 10.
Phase diagram showing how the polarization model behaves with changes in n, a1 and dcdc42 for the circle and the teardrop.
The standard polarization scheme was used. The grey phase represents a uniform concentration, the green phase represents reverse polarization and the red phase represents normal polarization. The points represent the sampling points for which simulations were run to observe the system behavior.