Fig. 7: Spatial patterns of cell density produce millimeter-scale activation patterns and kinematic waves.

A Left—phase diagram of qualitative behaviors of transceiver activation as a function of intrinsic proliferation rate (g) and initial cell density (r₀) for t = 2.7 days. Top right—Schematic of spatial pattern of density in a culture well, S = signaling, NS = non signaling. Bottom right—signal propagation simulation with initial condition of patterned cell density. Green represents the GFP concentration at steady-state [GFP]_SS. B, C In vitro density and signaling patterns. B Stitched epifluorescence micrographs of a culture well seeded with a sender:transceiver co-culture (1:100 ratio) in a spatial pattern of initial density (average of 2x) and imaged at 64 h of culture. Scale bar 2 mm. DAPI staining was used as a cell density readout (see Fig. S19B). Yellow box quantified in (C). C Fluorescence profiles showing the anti-correlated DAPI and GFP patterns, n = 1 profile shown. See Fig. S19 for the cell density pattern method. D, E In silico modeling predicts long-range kinematic waves over time. D Phase diagrams at three time-points with logarithmic y-axes. The density range between ρ_c^low and ρ_c^high (white dotted and dashed lines) is optimal for signaling. E Modeling results of signal propagation in a non-uniform cell density field. Green is [GFP]_SS. Between ρ_c^low and ρ_c^high (white dotted and dashed lines) is optimal for signaling. F, G Synthetic kinematic wave generated by a density pattern in vitro. F Epifluorescence micrographs of a culture well seeded with 1:100 senders:transceivers in a spatial pattern of density (average of 1x, i.e., 1250 c/mm²) and imaged daily. Green indicates activated transceivers, blue is correlated to cell number. Scale bar 2 mm. The yellow box region is quantified in (G). See Supplementary Movies 9–12 for time-lapse movie of this dataset, and Figs. S19 and 20 for more examples and details. G Spatial profile of GFP fluorescence in (F) over time. White dots show the mean wavefront position, which has a velocity of 0.67 ± 0.18 mm/day (mean ± s.d.). All experiments were repeated at least 3 times with similar results. Source data are provided as a Source Data file.