Figure 3. A mathematical model suggests constraints for the emergence and organization of cells in complimentary metabolic states.

(A) Processes, based on experimental data, incorporated into developing a simple mathematical model to simulate colony development. The dark and light cells are appropriately colored, and the parameters incorporated are resource production (σ), diffusion parameters for the resource (D), consumption of the resource (µ), and fast or slow rates of division (α or γ), based on resource or amino acid consumption. (B) The spatial distribution of cells is reduced to a grid like lattice within the model, to allow coarse graining of the location of cells across a colony. The rules for cell division and expansion incorporate the ability to consume existing nutrients in the medium, produce a resource and/or consume a produced resource, and a threshold amount of resource build up before utilization. (C) A flow-chart of the algorithm used in the mathematical model. The decision making process in the algorithm, incorporating all the elements described in panels (A) and (B) is illustrated. Also see Figure 3—figure supplement 1A–C and Materials and methods. (D) A simulation of the development of a wild-type colony, based on the default model developed. The inset shows an image of a real wild-type colony (same brightfield image used in Figure 1B), which has developed for an equivalent time (~6 days). Also see Figure 3—figure supplement 1A–C and Video 1. (E) A simulation of colony development using the model, where key parameters have been altered. (i) The sharing of a produced resource is restricted. (ii) The ability to switch from a dark to a light state is restricted. (iii) Light cells produce a resource taken up by dark cells is included. Note that in all three scenarios the colony size remains small, and fairly static. Also see Figure 3—figure supplement 2A–D and Videos 2, 3 and 4.

Figure 3—figure supplement 1. Effects on the colony as we change individual parameters used in the model.

(A) Changing the diffusion constant (D [L²T⁻¹]) of the resource in the medium. The diffusion constant used to simulate the left panel colony is 100 times smaller than the default colony (middle panel). The right panel colony was simulated with a very large effective diffusion constant. To get this fast diffusion, the total available resource was uniformly redistributed over the grid between every two time steps. Thus, every grid location had the same level of resource before the cells consume or produce it, as if the resource diffused very quickly over the grid. (B) Changing the growth rate of the cells. g_d and g_l are growth rate parameters of the dark and light cells respectively. The light cells grow four times faster than the dark cells in all cases. The middle panel colony is the default colony. g_d = 0.01. The one on the left has half the growth rate and the one on the right has twice the growth rate in comparison. (C) Changing the resource (R) produced by the dark cells. The light cells consume resource at a fixed rate if available. The middle panel has R = 0.07. The left colony simulation has half the produced value and the right colony simulation has double the produced value. All colony simulations were started with 1257 grids (each containing ~100 cells), of which 99% were dark cells, and were run for 750 time steps.

Figure 3—figure supplement 2. Reproducibility of the model, under different scenarios.

Since the colony simulations have elements of stochasticity present in the model, presented are a few replicate colonies from independent simulation. These showcase crucial and reproducible aspects of the different conditions explored in Figure 3D and Figure 3E. (A) three wild-type colonies generated with the default parameter set. The common features are a circular centre with mostly light cells, an annular region with dark cells and a few light cells, and the colony periphery with mostly light cells. (B) three replicate colonies with the ‘no sharing’ condition. The dark cells do not produce any shared resource. The final colonies have mostly dark cells as the number of light cells doesn't change. (C) three replicate colonies with the ‘no switching’ condition. If there are a few light cells at the periphery, they can consume the shared resource produced by the dark cells and grow into the empty space. However, the centre of the colonies has mostly dark cells. (D) three replicate colonies with the ‘wrong sharing’ condition (sharing of a resource made by light cells, taken up by dark cells), which are similar to the ‘no sharing’ condition.