Fig 1.
(A) The model bacteria’s “genotype” consists of a toxin production “gene”, a resistance “gene”, a toxin production rate πT and a response threshold θ. Bacteria regulating their toxin production and/or resistance only express these genes if the local concentration of the density cue exceeds the cell’s response threshold. Expression of the toxin, resistance, and response to the cue come at a fitness cost. (B) The model consists of three coupled 2D lattices, which hold the bacteria, the density cue concentration and the toxin concentration. Bacteria locally compete for unoccupied space to reproduce. All cells have a natural death rate. For cells that are not resistant the death rate increases linearly with the local toxin concentration. All bacteria produce the cue, while the toxin is produced only by bacteria that express their toxin gene. The toxin and density cue diffuse and are degraded at fixed rates.
Table 1.
Model parameters.
Fig 2.
Types of KRS-systems that evolved in a fixed, densely populated habitat.
Simulations were initialised with bacteria with random genotypes, and then run until evolutionary steady state was reached. Out of the 2000 simulations in the parameter sweep, 228 resulted in a KRS-system. (A) In 206 runs killer cells (genotype (On, On)), resistant cells (genotype (Off, On)) and sensitive cells (genotype (Off, Off)) coexisted, but no regulation evolved. (B) In 22 runs regulation did evolve, and in most of these (17 runs) coexistence was found between cells that regulate their toxin production but constitutively expresses resistance (genotype (Reg, On)), non-regulating resistant cells (genotype (Off, On)), and sensitive cells (genotype (Off, Off)). Parameter values for the example runs shown here are: (A) Lcue = 3.7, Ltox = 16.5, ,
, CR = 0.12, and CC = 0.07; (B) Lcue = 6, Ltox = 6,
,
, CR = 0.1, and CC = 0.02.
Fig 3.
Parameter conditions for the evolution of regulation.
The distribution of parameter values for simulations that yielded KRS-dynamics without regulation (n = 206) and those that yielded KRS-dynamics with regulation (n = 22). In simulations that resulted in the evolution of regulation, the spatial range of the cue and the response costs were lower, while the toxin production costs were higher. Results of 2-sided t-tests with Bonferroni-correction for multiple testing: **: p < 10−6, *: p < 10−3, n.s.: not significant.
Fig 4.
Model dynamics of a run in which density-dependent toxin regulation evolved.
(A) Snapshot of the simulation lattice. KRS-dynamics emerge with sensitive cells (genotype (Off, Off), blue), resistant cells (genotype (Off, On), white) and regulating killer cells (genotype (Reg, On), orange). The latter switch between two phenotypes: toxin producing (dark orange) and resistant (light orange). See also S1 Video. (B) Toxin production rate in the (Reg, On)-cells over time. Cells were initialised with a toxin production rate sampled at random between 0 and 1. Over time, a mean value of πT ≈ 0.8 is selected. (C) Distribution of response threshold values in (Reg, On)-cells over time, plotted against a background distribution of the cue concentration sensed by these (Reg, On)-cells. Response threshold values around θ = 0.875 are selected. The selected response threshold values tend to be higher than the median cue concentration sensed by regulating cells, indicating that at any time only a minority of cells produces toxin.
Fig 5.
Model dynamics under a serial-transfer regime.
The simulation was initialised with cells with random genotypes. Every 500 time steps, a random sample of 1000 cells from the current population was transferred to a new, empty lattice (“fresh medium”). (A, B) Abundance of genotypes over time on long (panel A) and short (panel B) time scales. Since the number of cells varies greatly within each transfer cycle, in panel A only the genotype abundances observed at the end of each cycle are plotted. The evolved population mainly consists of three genotypes: sensitives (genotype (Off, Off)), regulating resistants (genotype (Off, Reg)), and regulating killers, that also regulate their resistance (genotype (Reg, Reg)). (C) Snapshots of a small part of the simulation lattice showing colony growth between two transfers. Early on, (Off, Off)-, (Off, Reg)- and (Reg, Reg)-cells all express the sensitive phenotype. As the size of the colonies increases, the phenotype of cells in the interior of (Off, Reg)- and (Reg, Reg)-colonies switches to resistant, and in the case of (Reg, Reg)-cells after τdelay time steps to toxin producing. Cells on colony edges remain sensitive, allowing the colony to grow rapidly. See also S2 Video. Parameter values: Lcue = 6, Ltox = 6, ,
, CR = 0.1, and CC = 0.02.
Fig 6.
Density cue concentration profile of expanding colonies and the evolved response threshold values of (Reg, Reg)-cells.
(A) Colonies were grown from a single (Reg, Reg)-cell to characterise the radial density cue concentration profile of an expanding colony. Measured values from the simulations correspond well to the analytical approximation (see S2 Text). (B) Distribution of the evolved response threshold values in (Reg, Reg)-cells at the end of the simulation (time = 600, 000), plotted against the background of the cue concentration sensed by these cells at the end of a transfer cycle (i.e. when the population approaches carrying capacity) for five replicate simulations. The evolved response threshold values vary somewhat between replicates, but are always lower than the cue concentration at local carrying capacity (grey distributions) and higher than the maximum of the cue concentration at the edge of a growing colony. Hence, cells on the colony edge never express their toxin production and resistance genes, while cells in the colony interior and at the interface between colonies (where local cell density is close to carrying capacity) are resistant and do produce toxin.