The territorial nature of aggression in biofilms

Abstract

Microbial conflicts have a particularly aggressive nature. In addition to other chemical, mechanical, and biological weapons in their repertoire, bacteria have evolved bacteriocins, which are narrow-spectrum toxins that kill closely related strains. Bacterial cells are known to frequently use their arsenal while competing against each other for nutrients and space. This stands in contrast with the animal world, where conflicts over resources and mating opportunities are far less lethal, and get commonly resolved via ritualized fighting or "limited war" tactics. Prevalence of aggression in microbial communities is usually explained as due to their limited ability to resolve conflicts via signaling as well as their limited ability to pull out from conflicts due to the sessile nature of their life within biofilms. We use an approach that combines Evolutionary Game Theory (EGT) and Individual-based Modeling (IbM) to investigate the origins of aggression in microbial conflicts. In order to understand how the spatial mode of growth affects the cost of a fight, we compare the growth dynamics emerging from engaging in aggression in a well-mixed system to a spatially structured system. To this end, a mathematical model is constructed for the competition between two bacterial strains where each strain produces a diffusible toxin to which the other strain is sensitive. It is observed that in the biofilm growth mode, starting from a mixed layer of two strains, mutual aggression gives rise to an exceedingly high level of spatial segregation, which in turn reduces the cost of aggression on both strains compared to when the same competition occurs in a well-mixed culture. Another observation is that the transition from a mixed layer to segregated growth is characterized by a switch in the overall growth dynamics. An increased "lag time" is observed in the overall population growth curve that is associated with the earlier stages of growth, when each strain is still experiencing the inhibiting effect of the toxin produced by its competitor. Afterwards, an exponential phase of growth kicks in once the competing strains start segregating from each other. The emerging "lag time" arises from the spiteful interactions between the two strains rather than acclimation of cells' internal physiology. Our analysis highlights the territorial nature of microbial conflicts as the key driver to their elevated levels of aggression as it increases the benefit-to-cost ratio of participating in antagonistic interactions.

Keywords: aggression; bacteriocins; biofilms; evolutionary game theory (EGT); individual based modeling.

Figure 1

(A) An illustrative diagram (Hashem and Van Impe, 2022a,b) of a competition between two constitutive toxin producers, where each strain is immune to its own toxin, growing together on the same nutrient. The diagram depicts two biological species, P₁ and P₂, each denoted by a square, and three chemical species, N, T₁, and T₂, each denoted by a circle and representing the common nutrient and the toxins produced by P₁ and P₂, respectively. The consumption of N as well as the production of T₁ and T₂ are denoted by solid lines, while the inhibiting effects of T₁ and T₂ on P₂ and P₁, respectively, are denoted by dashed lines. (B) An illustration of the microbial life cycle model: a metapopulation of the two strains P₁ and P₂ is assumed to grow in a finite number of separate patches. The model consists of (i) an initialization step: all patches are seeded with the bacterial strains, (ii) a growth step: the growth dynamics is simulated in each patch separately until the population levels of all strains reach a steady state, and (iii) a mixing step: all patches are mixed with each other and the new composition of the metapopulation is used to initialize a new cycle of the model.

Figure 2

The evolution of the biomass density of the two bacterial strains in time, under the scenarios of (i) symmetric aggression (red): both strains produce toxins, by setting the toxin investment fraction, f, for both of them to 0.1 (ii) asymmetric aggression (blue): one of the strains, P₁, produce a toxin, f = 0.1, while the other fully invests in growth, f = 0 and (iii) No toxin production (green): the two strains do not produce toxins and both fully invest in growth, f = 0 for both strains. (A) At low toxin lethality. (B) At high toxin lethality.

Figure 3

Pairwise invasibility plots for the competition between two constitutive toxin producing strains under different conditions. The green areas are where a mutant toxin production strategy, f_mut, fares better than a resident toxin production strategy, f_res. And thus can spread in the population. A resident strategy is said to be evolutionary stable if it can not be invaded by any mutant. (A) High toxin lethality/high initial nutrient concentration [N(t = 0) = 10⁴ mg l⁻¹, K_T = 15 × 10⁻⁴ l mg toxin⁻¹ h⁻¹]: here, producing toxin can be advantageous up to a certain extent. When the two strains are producing toxin at an optimal investment rate f^*, lying here at the center of the graph, no mutant can fare better. (B) At low toxin lethality/ low initial nutrient concentration parameter region [N(t = 0) = 10³ mg l⁻¹ K${}_T=1.5\times 10^{-4}$ l mg toxin⁻¹ h⁻¹: in such conditions producing toxin is disadvantageous to the producing strain. Hence in a population in which the strains are attacking each other using an investment in toxin production, f_res, any mutant with lower level of toxin production, f_mut < f_res, will fare better. The graph shows that the only strategy that is evolutionary stable lies at the origin: when the two strains are not producing toxins at all. (C) The pairwise invasibility plot when multiple evolutionary stable growth strategies exist [N(t = 0) = 10³ mg l⁻¹, $K_T=13\times 10^{-4}$ l mg toxin⁻¹ h⁻¹]. Here, both no toxin production and toxin production at an optimal investment rate are evolutionary stable.

Figure 4

A parameter map showing the optimal, evolutionary stable, growth strategy (aggressive vs. no toxin production) under different combinations of toxin killing rate and initial nutrient concentration. For a constitutive toxin producer, aggression is favored as the initial nutrient concentration and the toxin lethality increase. Peaceful growth conversely is the optimal growth strategy when nutrients are more limited and the toxin is less lethal. A third, narrower, parameter region exists which is characterized by the existence of multiple evolutionary stable growth strategies.

Figure 5

While the spatial mode of growth significantly reduce the cost endured in the mutual aggression scenario due to the resulting spatial segregation, the outcomes of other scenarios are not significantly altered from the well-mixed growth setting. (A) No aggression: competition between two non toxin producers in the biofilm mode of growth. Starting from an initial mixed layer of cells, the two strains grow together to form a mixed biofilm with little linage segregation. (B) Asymmetric aggression: competition between a toxin producing strain (red) and a non toxin producing strain (blue), in spatial settings. The constitutive toxin producer come to dominate the competition at early stage, leading to the elimination of the non toxin producing strain.

Figure 6

An individual-based model of a competition between two toxin producing strains, growing together as a biofilm starting from an initial mixed layer of cells. The two strains gradually segregate into two distinct clusters. The cells lying at the clusters' boundaries are experiencing negative growth, due to the toxins' effect, and the further a cell lies from the clusters' boundaries, the lower the damage it suffers.

Figure 7

(A) The average fitness of two strains engaging in mutual aggression, relative to their fitness in the no aggression scenario, in case of a spatial vs. well-mixed mode of growth, at different toxin lethalities, using three different models of mixed growth as a benchmark. Besides the initial simple mixed growth model, two additional mixed growth models have been created within the IbM environment. In Mixed growth(IbM)I, the spatial mixing effect is induced by randomizing the positions of the cells after each iteration, while in Mixed growth(IbM)II the concentrations of the toxins are made to be uniform at the horizontal direction by replacing the toxin concentration at each spatial point in each row of the environment grid by the average value of the toxins' concentration in the row to which the spatial point belongs. (B) The effect of mutual aggression on the lag phase of a microbial community: the growth curves of the overall population in case of (i) mutual aggression scenario (red) and (ii) No aggression (black) for two strains growing together in a spatial settings as a biofilm. The duration of the lag phase is defined here as the intersection of the maximum slope at the exponential phase with the horizontal asymptote at the initial population level, shown with the dotted lines.

Figure 8

(A) The competition between two toxin producing strains at low toxins diffusivities in a grid of 1, 200 × 200μm. The low toxin diffusivity, increases its effectiveness, resulting in clusters with sharp, well-defined, boundaries. (B) Competition between two toxin producing strains, at high toxins diffusivities in a grid of 1, 200 × 200μm, where D_T is set to 10 times the nominal value. The high toxin diffusivity reduces its effectiveness as it gets more quickly diluted, resulting in a more uniform growth with less defined boundaries between the two spatially segregated strains. (C) The average fitness of the two strains engaging in mutual aggression, relative to their fitness in the no aggression scenario, under low and high diffusivities.