Quorum sensing as a mechanism to harness the wisdom of the crowds

Abstract

Bacteria release and sense small molecules called autoinducers in a process known as quorum sensing. The prevailing interpretation of quorum sensing is that by sensing autoinducer concentrations, bacteria estimate population density to regulate the expression of functions that are only beneficial when carried out by a sufficiently large number of cells. However, a major challenge to this interpretation is that the concentration of autoinducers strongly depends on the environment, often rendering autoinducer-based estimates of cell density unreliable. Here we propose an alternative interpretation of quorum sensing, where bacteria, by releasing and sensing autoinducers, harness social interactions to sense the environment as a collective. Using a computational model we show that this functionality can explain the evolution of quorum sensing and arises from individuals improving their estimation accuracy by pooling many imperfect estimates - analogous to the 'wisdom of the crowds' in decision theory. Importantly, our model reconciles the observed dependence of quorum sensing on both population density and the environment and explains why several quorum sensing systems regulate the production of private goods.

Fig. 1. Model structure.

a Internally, every cell has the simplest gene network of positive feedback regulation, where A promotes its own transcription. This network is parameterized as a bistable system with two stable equilibria separated by an unstable equilibrium in the midpoint between both (Fig. S1). Bacteria can also exchange A with the extracellular environment by passive diffusion through the membrane at a rate proportional to the evolvable parameter c. b At each timestep, the intracellular concentration of A is updated for every cell, and the extracellular concentration of A is updated according to a diffusion process with diffusion constant D over the 2-D grid (bacteria occupy the whole 2-D grid, but only 3 cells are shown for illustration). The sizes of the yellow halo illustrate different scenarios: (bottom) a cell with c = 0 that does not exchange A with the extracellular environment; (center) a cell that either has a low value of c or lives in an environment where diffusivity D is low; (top) a cell with a high value of c, or that lives in an environment with high diffusivity. c The environment experienced by each cell on the grid fluctuates randomly between two states, E_ON and E_OFF. In generations when the environment is in the E_ON state, bacteria maximize their fitness by expressing A at a high level, whereas in the E_OFF state, fitness is maximal when A is produced at a low basal level. The fitness of every cell is calculated at the end of every generation as the difference between its level of expression of A and the optimal level of expression given the environmental state, averaged over the entire generation. d The grid is repopulated such that every individual has the chance of reproducing with a probability proportional to its fitness and its descendants are placed at or in adjacent locations to its position in the grid. This is illustrated for a single high fitness parent and its offspring (fitness increases from green to white). The full grid is repopulated every generation but for illustration only the offspring of one cell is shown.

Fig. 2. Evolution of quorum sensing as a collective sensing mechanism.

a Evolution of the communication parameter c across time in a single evolutionary simulation. b Genetic composition of the bacteria located in a single arbitrary row of the two-dimensional grid tracked through evolutionary time. Although few cells with increased values of c emerge in the first 100 generations, they are mostly surrounded by cells with c = 0 and do not benefit from cell-cell communication. At ~500 generations, the number of cells with c > 0 increases and there are successive sweeps of higher values of c. c Mean c (top) and mean population fitness (bottom) across 2500 generations in 200 replicate evolutionary simulations showing that the rapid spread of communication through the population is associated with a rapid increase in the benefit of collective sensing arising once there is a minimum degree of communication in the population. When the mean c exceeds 0.1, most cells are communicating to the extent that they can correctly determine the state of the environment and mean fitness approaches 1.0. Thereafter, and due to the sigmoidal shape of the fitness function, evolving higher c has a marginal effect on fitness. The gene regulatory network is parameterized as shown in Fig. S1 and the rest of parameters are E_OFF = 10, E_ON = 80, σ_OFF = 25, σ_ON = 50, D = 0.5, µ = 0.001, ∂ = 0.03, s = 0.8 and x = 20.

Fig. 3. Quorum sensing, local interactions and the role of environmental diffusion.

a Genetic composition of two populations (shown in the two-dimensional 50 × 50 grid) that start with a subpopulation of communicators (light blue, c = 0.1) surrounded by non-communicators (dark blue, c = 0) across 40 generations of selection. In the top populations, the offspring of a cell is placed randomly on the grid, whereas in the bottom populations, offspring occupy a position close to their mother cell. Random placement of offspring leads to the extinction of communicating cells because bacteria with high c only benefit from collective sensing if there are other communicators nearby. b Individual fitness values in two populations of non-communicators (c = 0) that contain a subpopulation of communicators (c = 0.1, shown by the red square). When environmental diffusion is low (D = 0.5), the subpopulation of communicators benefits from collective sensing, whereas at high environmental diffusion (D = 50), communicating cells are coupled with non-communicators and any fitness benefit of collective sensing disappears. Fitness values are calculated after one generation in an E_ON environment. A similar pattern is observed in an E_OFF environment. c Cumulative distribution of the time to evolution of communication in three scenarios: (green) biologically-inspired scenario presented in Fig. 2, where the offspring of a cell remain nearby and bacteria interact locally; (red) same scenario as Fig. 2 except the offspring of a cell are randomly placed over the spatial grid after reproduction; (blue) same scenario as Fig. 2 except the rate D of diffusion in the extracellular environment is high so bacteria have a long interaction range. 100 simulations are shown per condition and we assume that communication evolves when the mean c exceeds 0.1 (Fig. 2c). For all panels, unless indicated otherwise, parameters are as in Fig. 2. Note that the evolution of collective sensing is further hindered if, in addition to high environmental diffusion or random placement of the offspring, the mutational stepsize is large; in either case, we failed to observe the evolution of collective sensing in 7000 generations for 50 replicate simulations with ∂ = 0.1.

Fig. 4. Evolution of quorum sensing in spatially heterogeneous environments.

a (Top) Example of the spatial domains (green vs. gray reflecting E_OFF vs. E_ON or vice versa) featuring contrasting environmental states in a single evolutionary simulation with high spatial heterogeneity. The yellow halo represents the neighborhood of interaction of a focal cell; the size of this neighborhood depends on the rate of environmental diffusivity D. (bottom) Mean c across 4000 generations in 100 replicate evolutionary simulations with high spatial environmental heterogeneity. The evolution of cell-to-cell communication is hindered because communicating cells receive conflicting information from individuals experiencing a different environmental state. Panel (b) (top and bottom) shows results for a scenario with low environmental heterogeneity. Cell-to-cell communication evolves in all simulations. Panel (c) (top) reflects a scenario with low spatial heterogeneity and a high rate of environmental diffusivity (D = 50), as illustrated by the large size of the yellow halo. Despite coarse spatial heterogeneity, high diffusion increases the coupling between cells experiencing different environmental states, generally undermining the information value of the external autoinducer signal. As a result, cell-to-cell communication evolves in only a fraction of the simulations (bottom) and takes on average longer to evolve than in a spatially homogeneous environment. For all panels, unless indicated otherwise, parameters are as in Fig. 2.