Figure 6

Figure 6

An NSC lattice model captures NSC population dynamics

(A) Model lineage flowchart. γ: transition rates; P_qq, P_qp, and P_pp: probabilities for (as)symmetric aNSC divisions; dashed line: lateral inhibition (LI) of aNPs on NSC activation (see also Figures S5G–S5K’’ and Methods Figure S1).

(B and B’) Snapshot of the lattice (B) and (B’) examples of activation (purple arrowhead), division (black star), and differentiation (orange arrowhead) (Video S2).

(C and D) Average cell proportions (C) and (D) percentages of cell fates following cell division in sets of 18 simulations with and without LI versus in vivo.

(E–E’’’) Dynamics and spatial correlations from the NSC lattice model with (top) and without (bottom) aNP-driven LI.

(E) Stable cell numbers and proportions over time, matching experimental data. Bold line: mean; shaded area: range; n = 18 simulations..

(E’) Snapshots of the lattice at 1 time step from a simulation of 500 time steps. Red arrowheads: aNSCs neighboring aNPs.

(E’’ and E’’’) Besag’s L function of aNSCs relative to one another (E’’) and to aNPs (E’’’). Results of a representative simulation are shown (1 from each model). L_(simul)(r) (red lines): simulated values; L_(H0,mean)(r) (black dotted lines): means under the random labeling null hypothesis; r: mean cell diameter (distance is measured from cell’s center); gray regions: 95% confidence envelopes. Red arrowhead to the dispersion of aNSCs from aNPs at a range of 1- to 2-cell diameter with LI. Cutoff for p values in E’’’ = 0.05.