Model and numerical implementation details.

<p><b>Figure A</b>: (a) Supracellular front-rear axes arrangement probabilities for enhanced binding (<i>k</i><sub>on</sub>) and/or unbinding (<i>k</i><sub>off</sub>) rates of Rho GTPases at the cell-cell junction. The number and box color represent the outcome probability. The numbers along the axes indicate the amplification factor, while the label indicates the rate and cell affected. Modifications in cell 1 are shown along the y-axis, and cell 2 along the x-axis. The color outline corresponds to the interaction motif in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1012216#pcbi.1012216.g003" target="_blank">Fig 3c</a>. White asterisks mark parameter choices where no modifications are made in one of the doublet cells yet supracellular outcome is successful. (b) Doublet simulation in supracellular arrangement. <b>Figure B</b>: Parameter sweeps for concentration dependent intercellular regulation of Rho GTPase rates. Outcome probability for co-alignment (bottom) and supracellular (top) arrangement are indicated by the number and box color. Outlined boxes highlight over 70% likeliness, and the color corresponds to a motif in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1012216#pcbi.1012216.g003" target="_blank">Fig 3c</a>. Dashed outlines mean not successful outcomes but previously identified as successful in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1012216#pcbi.1012216.g003" target="_blank">Fig 3</a>. <b>Figure C</b>: Probabilities of supracellular arrangement projected onto a 3D parameter space exploration with (a) the additive F-actin network growth rate constants as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1012216#pcbi.1012216.e005" target="_blank">Eq 5</a> and (b) concentration dependent network growth rate constants in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1012216#pcbi.1012216.e006" target="_blank">Eq 6</a>. The constants can take on positive, zero, or negative values. White asterisks indicate regions where mutual excitation-inhibition of the same type of F-actin structures did not produce successful outcomes for supracellular arrangement. <b>Figure D</b>: A directional bias is imposed on cell 2 due to an external stimulus which modified the dynamics of both polarity proteins Rac and Rho. Probabilities for leader-follower (supracellular) arrangement of the polarity axes of the doublet with intercellular coupling of (a) Rho GTPases (a) or (b) F-actin structures. The outlined boxes indicate over 70% likeliness for the arrangement. The color of the box outline matches the cell-cell interaction schematic in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1012216#pcbi.1012216.g003" target="_blank">Fig 3c</a>. <b>Figure E</b>: Single cell simulation outputs for modified couplings between Rho and bundled actomyosin network (B). (a) Top: schematic of the one-sided coupled model: only Rac proteins and the branched actin network engage in mutual local positive feedback. Bottom: we introduce additional positive feedback from Rho molecules to bundled network. (b) Schematic of the negative feedback from bundled network to Rho molecules but positive feedback from Rho to bundled network. (c) Schematic of the negative feedback from branched network (A) to Rho molecules, with positive feedback from Rho to bundled network. <b>Table A</b>: Definition and values of parameters for the mechanochemical polarity model. <b>Table B</b>: Pathways of communication between a pair of cells and the probability of a supracellular arrangement (S.), co-alignment (Co-A.), collision (C.), misalignment (Mis.), or non-polarized (N.P.) arrangement. <b>Table C</b>: Doublet polarity outcome probabilities for a subset of cell-cell coupling pathways, where cell 2 is assumed to have more responsive GTP activity over the entire domain, either through increased binding rate of Rac and/or Rho. The outcome probabilities are listed for supracellular (S.), co-alignment (Co.-A.), collision (C.), misalignment (Mis.), or non-polarized (N.P.) arrangements. <b>Table D</b>: Doublet polarity outcome probabilities for a subset of cell-cell coupling pathways, where cell 2 is assumed to have faster actin assembly dynamics over the entire domain, either through increased growth rate of branched and/or bundled network. The outcome probabilities are listed for supracellular (S.), co-alignment (Co.-A.), collision (C.), misalignment (Mis.), or non-polarized (N.P.) arrangements. <b>Table E</b>: Doublet polarity outcome probabilities for a switch in orientation of the external stimulus. For 0 ≤ <i>t</i> ≤ 5 seconds, cell 2 receives the external stimulus, but for 5 < <i>t</i> ≤ 100 seconds, cell 1 receives the stimulus in a new direction. A few cell-cell coupling pathways are tested, and the outcome likeliness is reported for doublet polarization in the new direction of the external signal (S.P.) and co-alignment arrangement (Co.-A.). <b>Table F</b>: Pathways of communication between four cells in a linear arrangement and the probability of the cells polarizing in same direction (L/R), supracellular (S.) or co-alignment (Co-A.) arrangement. <b>Table G</b>: Pathways of communication between four cells in a square arrangement and the probability of the cells polarizing in a supracellular (S.) or co-alignment (Co-A.) arrangement. Table H: Co-alignment and non-polarized (N.P.) outcomes for 100 model realizations with variations in the size of the cell-cell coupling region (as a fraction of an individual cell’s perimeter). For the intercellular coupling, 5 different biochemical or structural interaction motifs are screened.</p> <p>(PDF)</p>