Table 1 Model algorithm components and resulting model properties

From: Modeling epithelial deformation and cell rearrangement in response to external forces during Zebrafish epiboly

Algorithm components

Simulation behaviors

 

Bond remodeling

Remodeling algorithm

Force regulation

Cell division

Viscoelasticity

Tissue integrity

Synchrony

Cell rearrangement

Edge Straightness

1. Living zebrafish embryos

    

+

+

+

+

⇧

2. Simplistic model: fixed bonds

–

 

–

–

–

+

+

–

⇩

3. Dynamic model: bond remodeling

+

R

–

–

–

–

–

+

⇩

4. Model 1 (viscoelastic: constrained geometry)

+

EM

–

–

+

+

–

+

⇧a

+

+

+

–

+

⇧a

5. Model 2 (regulated: force feedback)

+

EM

+

–

+

+

+

+

⇧

+

+

+

+

+

⇧

  1. Line 1 represents the properties of living embryos we would like our model to replicate. Subsequent lines represent different versions of our model, including different combinations of algorithm components, and the resulting model properties.
  2. Algorithm components
  3. In the simplistic model with fixed bonds (line 2), bonded cell-cell relationships are fixed; and the applied force on any marginal EVL cell depends only on the length of the cell’s leading edge (force per unit length of edge held everywhere uniform). Bond remodeling (line 3) adds stochastic, dynamic breaking of bonds and formation of new ones. Remodeling is either purely random (R), or uses an energy minimization (EM) acceptance criterion with a bond-angle constraint (lines 4 and 5). Cell division, when enabled, occurs uniformly until 55% epiboly and then ceases. Under force regulation (Model 2), the force applied to each particle takes into account the polar angle of the cell’s position, i.e., the cell’s progress toward the vegetal pole (force per unit length of edge is higher for lagging regions of leading edge).
  4. Simulation behaviors
  5. Viscoelasticity:
  6. − elastic; after deformation, tissue is unstable and experiences drastic recoil when applied tension is released.
  7. + viscoelastoplastic; tissue accommodates deformation and internal reorganization without tearing; after deformation, tissue is stable in its final configuration, and experiences only weak and localized recoil after applied tension is released.
  8. Tissue integrity:
  9. − tears and holes develop.
  10. + tissue integrity maintained; absence of tearing or holes.
  11. Synchrony:
  12. – leading edge becomes lopsided; different regions converge on pole at different rates.
  13. + all regions of leading edge converge on pole in synchrony; edge remains centered on the pole.
  14. Cell rearrangement: absent (–) or present (+).
  15. Edge straightness: Increasing (⇧) or decreasing (⇩) as epiboly proceeds.
  16. a Edge straightens through most of epiboly but becomes distorted at the later stages.
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