Dynamic scaling analysis of two-dimensional cell colony fronts in a gel medium: A biological system approaching a quenched Kardar-Parisi-Zhang universality

The interfacial two-dimensional spreading dynamics of quasilinear Vero cell colony fronts in methylcellulose (MC)-containing culture medium, under a constant average front displacement velocity regime, was investigated. Under comparable experimental conditions, the average colony front displacement velocity becomes lower than that reported for a standard culture medium. Initially, the presence of MC in the medium hinders both the colony spreading, due to a gradual change in the average size and shape of cells and their distribution in the colony, and the cell motility in the gelled medium. Furthermore, at longer culture times enlarged cells appear at random in the border region of the colony. These cells behave as obstacles (pinning sites) for the displacement of smaller cells towards the colony front. The dynamic scaling analysis of rough fronts yields the set of exponents $\alpha =0.63\pm 0.04,\beta =0.75\pm 0.05$, and $z=0.84\pm 0.05$, which is close to that expected for a quenched Kardar-Parisi-Zhang model.

Figure 1

Images of a quasilinear colony front region for different growth times after fixing and staining: (a) 2400 min; (b) 19 600 min. Black dots correspond to cell nuclei.

Figure 2

Average colony front height versus growth time. Symbols correspond to different experiments.

Figure 3

Sequential images of a quasilinear colony front region taken at (a) $t=14595$ min and (b) $t=20$ 370 min. The coarse trajectory displacement of regular cells around a cluster of enlarged ones during growth is indicated by the arrows.

Figure 4

Colony front roughness versus growth time log-log plot. Data from different colonies have been binned.

Figure 5

Colony front roughness versus colony growth time log-log plots for different front widths $l$, as indicated. Straight lines with slopes 0.33 and 0.75 are displayed to guide the eye. Inset: Corresponding $t_s$ versus $l_s$ log-log plot.

Figure 6

Colony (a) front roughness versus front width $l$ and (b) $S(k,t)$ versus $k$ log-log plots for different colony growth times. The line with slope $-2.26$ (i.e., $\langle {\alpha }_S\rangle =0.63$) is a guide for the eye. Data have been binned.

Figure 7

Log-log plots of Family-Vicsek scaling relationships at various growth times as indicated. Data have been binned.