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Fig. 5 Single and multicellular models of Her6 protein expression with normal and altered protein stability. (A) Model 1: a stochastic single-cell model that explicitly models mRNA and protein. αp and αm are protein and mRNA synthesis rates, respectively, and μp and μm are the degradation rates. Hauto is the Hill function used for the direct repressive action of Her6 protein on its own mRNA production, which has an associated time delay (Table S1). (B) Model 2: the same as Model 1 but extended to a multicellular model. Cells are coupled bidirectionally with a repressive Hill function, HLI, that has an associated time delay and represents Notch-Delta lateral inhibition signalling. For all simulations, both models were run as a hexagonal grid of 10 rows by 6 columns. (C) Her6 expression from Model 2 run with a parameter set contained within the accepted optimiser parameter sets. Each row corresponds to a different protein degradation rate (indicated on the left, ranging between 1× and 1.1×). The first column shows the time-series of every cell for the full simulation. The second column shows histograms of Her6 abundance taken from the second half of the simulations. The third column shows the final time point of each simulation plotted on a hexagonal grid in which colour indicates Her6 expression in each cell (lighter colours indicate higher expression). (D) Time series coefficient of variation (CVt) plotted at normal and 1.1× degradation. For normal degradation rate, median CVt=0.30 (white dot), and for 1.1× degradation, median CVt=0.61. Kruskal–Wallis statistical test showed a significant difference in the distributions, P=1.3×10−20. (E) Median temporal period for each parameter set. Median period was 141 h in both cases. Kruskal–Wallis statistical test showed no significant difference in the distributions, P=0.55. (F) Median coherence for each parameter set. Median coherence for normal degradation was 0.36, and for 1.1× degradation coherence was 0.58. Kruskal–Wallis statistical test showed a significant difference in the distributions, P=1.5×10−8. ***P≤0.001; ****P≤0.0001. ns, not significant