Supplementary Information from A dynamically diluted alignment model reveals the impact of cell turnover on the plasticity of tissue polarity patterns

Supplementary Information to Hoffmann, Voss-Böhme, Rink and Brusch 2017: “A Dynamically Diluted Alignment Model Reveals the Impact of Cell Turnover on the Plasticity of Tissue Polarity Patterns” with detailed derivations of equations that are used in the main text, a table summarising all variable names and notations and additional results in 7 supplementary figures: Fig.S1, Lattice size effects. Fig.S2, Effects of de-novo polarisation rate beta on the time of minimal order. Fig.S3, Statistical robustness of time of minimal order. Fig.S4, Bistability of mean-field ODE system for very high neighbour coupling strength. Fig.S5, Time of minimal order for vanishing neighbour coupling strength. Fig.S6, Time of minimal order collapses to linear function of the effective neighbour coupling strength. Fig.S7, Effects of coupling strength to global signal epsilon_s on the time of minimal order

Original research data: time of minimal order in sampled trajectories of the dynamically diluted alignment model from A dynamically diluted alignment model reveals the impact of cell turnover on the plasticity of tissue polarity patterns

Time of minimal order data measured from sampled trajectories of the dynamically diluted alignment model (main text eqs. (4), (6) and (7)), using a variant of the stochastic simulation algorithm that is adapted to Interacting Particle Systems [Klauß and Voss-Böhme (2008)]. Columns are simulation ID, de-novo polarisation rate beta, cell replacement rate delta, neighbour coupling strength epsilon_n, effective neighbour coupling strength epsilon_n_eff (which is a function of beta, delta and epsilon_n), coupling strength to global signal epsilon_s, lattice size in x- and y- direction, boundary condition in x- and y-direction, components s_x and s_y of the global signal vector, end time of the simulation, time interval of simulation logging, time of minimal order (the observable). There are data of 25 simulations with different random number series for each parameter combination

Supplementary Movie from A dynamically diluted alignment model reveals the impact of cell turnover on the plasticity of tissue polarity patterns

Typical simulation run of the IPS model on a 100-by-100 lattice with periodic boundary conditions. The movie covers 1 time unit in the non-dimensionalised model time; time resolution of visualisation is 0.001. See main text figure 2C for colour code. The bottom left detail of the same simulation is shown in main text figure 3A, subpanels a-d, for times 0.05, 0.2, 0.5, 0.8, and its analysis is shown in main text figure 3B. Parameters are neighbour coupling strength epsilon_n=4.5, cell replacement rate delta=0.2, de-novo polarisation rate beta=1 and coupling strength to global signal epsilon_s=1, the global signal s=(1,0) points to the right