(A) Illustration of a small cell cohort that adheres to a surface (-plane). The polarization field, , is defined on the contact surface with the adhesion plane. The magnitude of the polarization …
(A) Mean-squared displacement (MSD) for single-cell movements at different maximum cell polarity (stiffness parameters , ; average polarization field ; signaling radius ; cell-substrate …
(A–D) Role of substrate dissipation for cells of varying maximum cell polarity . The aspect ratio (A), the speed (B), and the persistence time (C) as a function of substrate dissipation …
(Stiffness parameters , ; average polarization field ; cell-substrate dissipation ; cell-substrate adhesion penalty ; cytoskeletal update rate ; independent simulations for each set …
(-cell systems; confinement radius ; area stiffness ; average polarization field ; signaling radius ; cytoskeletal update rate ; cell-cell adhesion ; cell-cell dissipation ; …
(-cell systems; confinement radius ; stiffness parameters , ; average polarization field ; maximum cell polarity ; signaling radius ; cytoskeletal update rate ; cell-cell adhesion ;…
(-cell systems; confinement radius ; stiffness parameters , ; average polarization field ; maximum cell polarity ; signaling radius ; cytoskeletal update rate ; cell-cell adhesion ;…
(-cell systems; confinement radius ; stiffness parameters , ; average polarization field ; maximum cell polarity ; signaling radius ; cytoskeletal update rate ; cell-cell adhesion ;…
(Stiffness parameters , ; average polarization field ; signaling radius ; cytoskeletal update rate ; cell-cell adhesion ; cell-cell dissipation ; cell-substrate dissipation ; cell-sub…
Cell monolayer expansion depends on the cell-cell dissipation, cell-substrate dissipation, and maximum cell polarity. (Initially a -cell system; stiffness parameters , ; average polarization …
(Initially a -cell system; stiffness parameters , ; average polarization field ; maximum cell polarity ; signaling radius ; cytoskeletal update rate ; cell-cell adhesion ; cell-cell …
Grid sites occupied by cell , i.e. its domain , are indicated in red colors. The cell’s membrane sites, , are indicated by the lighter red color, the cell’s immediate neighborhood, , is …
For ease of reference, grid rows have been numbered from to . Left (A): Solid black lines indicate cells’ membrane positions after acceptance of the respective elementary event; colors indicate …
(A) Adhesive energy contribution in a cyclic process, where a protrusion of source cell against target cell is followed by the inverse retraction event. Both events involve a third party cell , leading to net energy dissipation after the cyclic process has been completed. Protrusion: (i) Three pre-existing cell-cell contacts between and are torn apart (red dashed contacts); (ii) three new contacts between and are formed; (iii) the contact length between source cell and target cell increases by one unit of length. This implies . Retraction: (i) Three pre-existing cell-cell contacts between and are torn apart (red dashed contacts); (ii) three new contacts between and are formed; (iii) the contact length between source cell and target cell decreases by one unit of length. This implies . Altogether, this leads to , i.e. a (non-negative) dissipative contribution, whose magnitude depends on the dissipation matrix . (B) Shear viscosity due to cell-cell adhesion. Consider two rows of adhesive cells sliding past each other as indicated in the figure (left row of cells moves up by one grid site; colors indicate different cells). The associated adhesion energy change (per cell) reads , where denotes the number of cells sliding past each other, and where we assumed cells of like type, i.e. and (). The condition , Equation S15e, thus implies positive friction associated with cellular shear flows, whose magnitude is proportional to the number of cells sliding past each other. Note that this shear viscosity vanishes for , i.e. for zero dissipation matrix.
All source and parameter files are found in Source data 1.
Figure | Simulation code | Processing code | Parameters |
---|---|---|---|
Figure 2 | CPM_NoDivision | TrajectoryAnalysisSingle | single_Q |
Figure 2—figure supplement 1 (A-D) | CPM_NoDivision | TrajectoryAnalysisSingle | single_DQ |
Figure 2—figure supplement 1 (E-H) | CPM_NoDivision | TrajectoryAnalysisSingle | single_DM |
Figure 3 | CPM_NoDivision | TrajectoryAnalysisSingle | single_R |
Figure 4 | CPM_NoDivision | TrajectoryAnalysisCircularPattern | rotation_Q |
Figure 4—figure supplement 1 | CPM_NoDivision | TrajectoryAnalysisCircularPattern | rotation_N_R1 |
Figure 4—figure supplement 2 | CPM_NoDivision | TrajectoryAnalysisCircularPattern | rotation_N_R2 |
Figure 4—figure supplement 3 | CPM_NoDivision | TrajectoryAnalysisCircularPattern | rotation_N_R3 |
Figure 5 (A-D) | CPM_Division | wound_nodiv | |
Figure 5 (E-H) | CPM_Division | wound_div | |
Figure 5—figure supplement 1 (A-B) | CPM_Division_Supplement | FrontAnalysis | wound_div_A |
Figure 5—figure supplement 1 (C-D) | CPM_Division_Supplement | FrontAnalysis | wound_div_D |
Figure 5—figure supplement 1 (E, F) | CPM_Division_Supplement | FrontAnalysis | wound_div_Q |
Figure 6 (A-D) | CPM_Division | wound_div_fing_1.0 | |
Figure 6 (E-H) | CPM_Division | wound_div_fing_1.1 | |
Appendix 2—figure 1 | CPM_NoDivision | TrajectoryAnalysisSingle | single_A |
Simulation code, processing code and parameter files.