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. 2011 Jul 8;6(7):e21960. doi: 10.1371/journal.pone.0021960

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Hoffmann et al.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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A: Radii and of cells i and j, respectively, the sum of their spherical cap heights and the radius of their contact area . B: Side view of cell i on substrate with full cell radius , substrate adhesion radius , and substrate cap height . Podium cone geometry with base radius , podium tip radius () and length of podium m. The length is measured from half to the center of the podium tip. C: podium position updates (contact guidance) in 2D. C1: shift of podium 1 of cell j away from podium 1 of cell i. C2: shift of podium 1 of cell k away from the body of cell i for small overlaps (analogously, for the spherical podium tip). C3: move of podium 1 of cell l towards the tangent line (T) of podium 2 of cell i if the overlapping podium exceeds the length of the tangent section (center of cell l to tangent point). The limiting line (L) between cases C2 and C3 is a spherical section. For small simulation step sizes and low cell densities C1 and C2 will generally suffice. Otherwise case C3 is employed to move a podium off another cell. However, full removal requires subsequent application of C1 or C2. and indicate the directional unit vector of podium 1 and 2 of cell i, respectively. The moved podia (cells j, k, l) are represented as their mid-line (dotted). Overlap between cells is defined by the intersection of this mid-line with the full podium of the respective resting cell (cell i) extended by the radius of the moved podium tip.

Inline graphic — A: Radii and of cells i and j, respectively, the sum of their spherical cap heights and the radius of their contact area . B: Side view of cell i on substrate with full cell radius , substrate adhesion radius , and substrate cap height . Podium cone geometry with base radius , podium tip radius () and length of podium m. The length is measured from half to the center of the podium tip. C: podium position updates (contact guidance) in 2D. C1: shift of podium 1 of cell j away from podium 1 of cell i. C2: shift of podium 1 of cell k away from the body of cell i for small overlaps (analogously, for the spherical podium tip). C3: move of podium 1 of cell l towards the tangent line (T) of podium 2 of cell i if the overlapping podium exceeds the length of the tangent section (center of cell l to tangent point). The limiting line (L) between cases C2 and C3 is a spherical section. For small simulation step sizes and low cell densities C1 and C2 will generally suffice. Otherwise case C3 is employed to move a podium off another cell. However, full removal requires subsequent application of C1 or C2. and indicate the directional unit vector of podium 1 and 2 of cell i, respectively. The moved podia (cells j, k, l) are represented as their mid-line (dotted). Overlap between cells is defined by the intersection of this mid-line with the full podium of the respective resting cell (cell i) extended by the radius of the moved podium tip.