Morphodynamics of a growing microbial colony driven by cell death

Bacterial cells can often self-organize into multicellular structures with complex spatiotemporal morphology. In this work, we study the spatiotemporal dynamics of a growing microbial colony in the presence of cell death. We present an individual-based model of nonmotile bacterial cells which grow and proliferate by consuming diffusing nutrients on a semisolid two-dimensional surface. The colony spreads by growth forces and sliding motility of cells and undergoes cell death followed by subsequent disintegration of the dead cells in the medium. We model cell death by considering two possible situations: In one of the cases, cell death occurs in response to the limitation of local nutrients, while the other case corresponds to an active death process, known as apoptotic or programmed cell death. We demonstrate how the colony morphology is influenced by the presence of cell death. Our results show that cell death facilitates transitions from roughly circular to highly branched structures at the periphery of an expanding colony. Interestingly, our results also reveal that for the colonies which are growing in higher initial nutrient concentrations, cell death occurs much earlier compared to the colonies which are growing in lower initial nutrient concentrations. This work provides new insights into the branched patterning of growing bacterial colonies as a consequence of complex interplay among the biochemical and mechanical effects.

Figure 1

Snapshot of colonies (alive+dead) in absence and in presence of cell death for a cutoff $\epsilon =0.2$. For both the cases of nutrient-limited death and apoptotic death, value of the rate of cell death is $k_d=0.01$ and rate of lysis of the dead cells is $k_{\mathrm{lys}}=0.002$. Shown here is the snapshot of a simulated colony in case of nutrient-limited cell death, which occurs when local nutrient concentration crosses a threshold value of $C_{\mathrm{thresh}}=0.001$. The color bar shows the variation of concentrations from low (blue) to high (yellow); black corresponds to a zero value.

Figure 2

Spatiotemporal morphology of the growing colonies with respect to time in presence and absence of cell death. For both the cases of nutrient-limited death and programmed cell death, the rate of cell death is $k_d=0.001$. Shown here are the snapshots of a simulated colony which occurs for a threshold concentration of the local nutrient level $C_{\mathrm{thresh}}=0.001$ in the case of nutrient-limited cell death. Programmed cell death occurs randomly without any concentration threshold of the nutrient concentration. Here alive cells are represented by spherocylinders (cyan) and dead and disintegrated cells are depicted in the form of tiny red dots. All the other parameters are chosen to be same as given in the Table 1.

Figure 3

(a) Plot of effective radius of the growing colonies with respect to time. (b) Plot of the speed of the colony with respect to time. The blue curve (with filled squares) corresponds to no-death situation, whereas the magenta (with filled circles) and orange (with filled triangles) curves correspond to nutrient-limited and programmed cell death, respectively. Rate of nutrient-limited and programmed cell death is $k_d=0.001$ and all the other parameters are same as given in the Table 1.

Figure 4

Roughness parameter ${\sigma }_f$, which is determined by calculating the variance in radius of the peripheral bacterial cells of the expanding colonies with respect to time for (a) no death (filled blue squares), nutrient-dependent death (filled magenta circles), and programmed cell death (filled orange triangles). The cell death rate is taken as $k_d=0.001$. (b) Plot of averaged values of roughness parameter ${\sigma }_f$ from multiple realizations of simulation trajectories as a function of death rate $k_d$ for programmed cell death (orange curve with empty triangles) and nutrient-dependent cell death (magenta curve with empty squares). All the other parameters are same as given in the Table 1.

Figure 5

Plot of square root of covered area of the live cells of the expanding colony with respect to time. The red curve with filled squares corresponds to the case of programmed cell death, whereas the blue curve with filled circles and the magenta curve with filled triangles (which are basically indistinguishable) correspond to the cases of delayed and continuous production of nutrient by the dead cells during programmed death, respectively. For all three cases, the death rate is taken as $k_d=0.001$. All the other parameters are the same as given in the Table 1.

Figure 6

Roughness parameter ${\sigma }_f$ of the expanding colonies with respect to the time. The black curve with crosses corresponds to the case of no death ($k_d=0.0$) in the colony; the red curve with triangles for programmed cell death ($k_d=0.001$) with low repulsive coefficients of dead cells ($E_d={10}^4$) without cell lysis ($k_{\mathrm{lys}}=0.0$) and removal; the orange curve with circles corresponds to the case of programmed cell death ($k_d=0.001$) with low elastic repulsive coefficient of dead cells ($E_d={10}^4$) and their removal from the system ($k_{\mathrm{lys}}=1.0$); and the purple diamond curve shows the case where dead cells have same repulsive coefficient as alive cells ($E_d=E=3\times {10}^5$) but undergoes lysis ($k_{\mathrm{lys}}=1.0$) and removal from the growing colony. The rate of cell death is $k_d=0.001$ and all the other parameters are kept same as given in the Table 1.

Figure 7

Effect of initial nutrient concentration ($C_0$) on initiation of cell death in case of nutrient-dependent death. (a) Plot of total number of alive cells with respect to time for different $C_0\mathrm{s}$. (b) Plot of total number of dead cells with respect to time for different $C_0\mathrm{s}$. The onset of cell death is represented by $T_d$. All the other parameters are kept as given in Table 1 in the corresponding simulations.