Fig 1.
Description of cell parameters and simulation model.
(a) The depicted snapshot illustrates a simulation box, showcasing 16 interacting cells interconnected by springs. The electric field within this model is oriented along the positive x-axis. Each cell is colored by the angle formed between the x-axis and the cell’s major axis. (b) A cell exposed to field E estimates the direction of the field and polarizes (changes its polarity direction ) towards its estimate. A cell’s precision
in detecting the electric field direction, depends on its orientation angle
, where
is the shortest angle between the cell’s longitudinal axis (green line) and the x-axis (orange line). With this definition,
will be between
and
. (c) Cell precision
as a function of cell orientation for different values of intrinsic (
) and anisotropic (
) variances. Cells oriented horizontally (
) have the lowest precision and cells with vertical orientation (
) have the highest precision. (d) A diagram illustrating the tendency of a cell, with its long axis represented by a green line, to align with neighboring cells, whose long axes are depicted with purple lines. (e) A diagram depicting the tendency of a cell to align its orientation, illustrated by a green line, perpendicularly to the cell’s average velocity. The orientation orthogonal to the velocity is represented by a blue line. (f) The graph presents the temporal evolution of the average directionality of cell groups across 40 simulations, with shaded areas representing the standard deviations calculated over these simulations. Each simulation featured 64 cells. The red arrow spans the final 5 hours and we report the mean over this period as the final steady state directionality.
Fig 2.
The average directionality for various combinations of isotropic
and anisotropic
variances and alignment rates to velocity.
Isotropic component () changes across rows (top to bottom) and anisotropic component (
) across rows (left to right) with specific values shown at right side and bottom of the figure (i.e. the panel (f) show directionalities for
). The averages are over 40 simulations at the interaction strength of k = 0.2
. For each simulation the reported directionality is the steady state average over the final 5 hours of simulation as shown in Fig 1f. Results for different values of alignment rates to average velocity are color coded
rad/min (black),
rad/min (purple), and
rad/min (orange). The averaging time T for velocity is set to 1h, and the number of cells N was set to 4, 16, 32, 48, 64, and 96. The shaded areas represent standard errors, although they may not be easily discernible due to their small size.
Fig 3.
Cell orientations and directionalities as a function of velocity averaging time.
In the left column, the absolute value of the cell orientation angle is presented, while the right column displays the directionality. The reported values represent averages across 40 simulations of 64 cells conducted with an interaction strength of k = 0.2 and
. The shaded areas represent standard errors of the mean.
Fig 4.
Effect of rates of alignment to velocity () and neighbors (
) on directionality (a), absolute value of orientation angle (b), and order parameter (c).
Each grid value represents an average result over 40 simulations conducted with 64 cells at the interaction strength of k = 0.2 with an averaging time T = 1 h with colorbars indicating corresponding numeric values. Example simulation snapshots for alignment rate tuples of (i),
rad/min,
rad/min; (ii),
rad/min,
rad/min; (iii),
rad/min,
rad/min; (iv),
rad/min,
rad/min; (v),
rad/min,
rad/min; (vi),
rad/min,
rad/min, also shown in panel c. Cells are colored according to their orientation shown on the colorbar. For all simulations
and
.
Fig 5.
Dependence of directionality on cell-cell adhesion.
(a) Velocity (top row) and directionality (bottom row) as a function of cell count for different (color coded) spring constants. (b) Directionality for different combinations of isotropic variance and interaction strength k (left). The arrow indicates a linear path of concurrent variations of
and k resulting decreasing directionality shown on the right figure. Here
. (c) Directionality for different combinations of alignment rate to velocity
and interaction strength k (left). The arrow indicates a linear path of concurrent variations of
and k resulting decreasing directionality shown on the right figure. Here
. The reported values represent averages across 40 simulations with 64 cells
. Where applicable the shaded areas represent standard errors of the mean.