A minimal model for simulating tissue extension during morphogenesis based on anisotropic cell adhesion

Morphogenesis relies on the ability of tissues to undergo large-scale deformations. An important example of this is convergent extension, where tissues extend along an axis and contract along a perpendicular one to form elongated structures in an embryo. This shows that this process can be explained by applying the differential adhesion hypothesis to the case of a single cell type with anisotropic adhesive properties. The article first presents a theoretical derivation showing that a difference in the density of binding sites along the cell membrane naturally leads to the energy-minimized state in which cells align and the tissue extends. The article then implements the theory in a minimal numerical model where cells are represented as dimer (domino) tiles on a two-dimensional square lattice. By employing a stochastic displacement algorithm, our simulations demonstrate that the anisotropic differential adhesion is sufficient to trigger cell alignment followed by tissue extension, illustrating how complex morphogenetic processes can emerge from generic physical principles.

Minimalni model za simulacijo ekstenzije tkiva med morfogenezo na osnovi anizotropne celične adhezije

Morfogeneza temelji na sposobnosti tkiv, da se podvržejo velikim deformacijam. Pomemben primer je konvergentna ekstenzija, pri kateri se tkiva podaljšajo vzdolž neke osi, se obenem skrčijo v smeri pravokotno na to os ter na ta način v zarodku oblikujejo podolgovate strukture. Članek kaže, da je ta proces mogoče razložiti z uporabo hipoteze o diferencialni adheziji na primeru enega tipa celic z anizotropnimi adhezijskimi lastnostmi. Članek najprej predstavi teoretično izpeljavo, ki pokaže, da pod pogojem različne gostote vezavnih mest vzdolž membrane celice težijo v stanje minimalne energije, v katerem celice uskladijo orientacijo, tkivo pa se podaljša. Na podlagi teorije je nato implementiran minimalni model, v katerem so celice predstavljene kot dimeri (domine) na dvodimenzionalni kvadratni mreži. Z uporabo algoritma za stohastične premike simulacije pokažejo, da je anizotropna diferencialna adhezija dovolj, da povzroči poravnavo celic in podaljšanje tkiva. S tem je ponazorjeno, kako lahko kompleksni morfogenetski procesi izhajajo iz splošnih fizikalnih načel.