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The polarisation of cells and tissues is fundamental for tissue morphogenesisduring biological development and regeneration. A deeper understanding ofbiological polarity pattern formation can be gained from the consideration ofpattern reorganisation in response to an opposing instructive cue, which wehere consider by example of experimentally inducible body axis inversions inplanarian flatworms. Our dynamically diluted alignment model represents threeprocesses: entrainment of cell polarity by a global signal, local cell-cellcoupling aligning polarity among neighbours and cell turnover insertinginitially unpolarised cells. We show that a persistent global orienting signaldetermines the final mean polarity orientation in this stochastic model.Combining numerical and analytical approaches, we find that neighbour couplingretards polarity pattern reorganisation, whereas cell turnover accelerates it.We derive a formula for an effective neighbour coupling strength integratingboth effects and find that the time of polarity reorganisation depends linearlyon this effective parameter and no abrupt transitions are observed. This allowsto determine neighbour coupling strengths from experimental observations. Ourmodel is related to a dynamic $8$-Potts model with annealed site-dilution andmakes testable predictions regarding the polarisation of dynamic systems, suchas the planarian epithelium.

A Dynamically Diluted Alignment Model Reveals the Impact of Cell Turnover on the Plasticity of Tissue Polarity Patterns