Disruption of microbial communication yields a two-dimensional percolation transition

Computation in bacterial communities

Bacteria across many scales are involved in a dynamic process of information exchange to coordinate activity and community structure within large and diverse populations. The molecular components bacteria use to communicate have been discovered and characterized, and recent efforts have begun to understand the potential for bacterial signal exchange to gather information from the environment and coordinate collective behaviors. Such computations made by bacteria to coordinate the action of a population of cells in response to information gathered by a multitude of inputs is a form of collective intelligence. These computations must be robust to fluctuations in both biological, chemical, and physical parameters as well as to operate with energetic efficiency. Given these constraints, what are the limits of computation by bacterial populations and what strategies have evolved to ensure bacterial communities efficiently work together? Here the current understanding of information exchange and collective decision making that occur in microbial populations will be reviewed. Looking toward the future, we consider how a deeper understanding of bacterial computation will inform future direction in microbiology, biotechnology, and biophysics.

Phase transitions, percolation, fracture of materials, and deep learning

Percolation and fracture propagation in disordered solids represent two important problems in science and engineering that are characterized by phase transitions: loss of macroscopic connectivity at the percolation threshold p_{c} and formation of a macroscopic fracture network at the incipient fracture point (IFP). Percolation also represents the fracture problem in the limit of very strong disorder. An important unsolved problem is accurate prediction of physical properties of systems undergoing such transitions, given limited data far from the transition point. There is currently no theoretical method that can use limited data for a region far from a transition point p_{c} or the IFP and predict the physical properties all the way to that point, including their location. We present a deep neural network (DNN) for predicting such properties of two- and three-dimensional systems and in particular their percolation probability, the threshold p_{c}, the elastic moduli, and the universal Poisson ratio at p_{c}. All the predictions are in excellent agreement with the data. In particular, the DNN predicts correctly p_{c}, even though the training data were for the state of the systems far from p_{c}. This opens up the possibility of using the DNN for predicting physical properties of many types of disordered materials that undergo phase transformation, for which limited data are available for only far from the transition point.

Spatially propagating activation of quorum sensing in Vibrio fischeri and the transition to low population density

Bacteria communicate by secreting and detecting diffusible small molecule signals or pheromones. Using the local concentrations of these signals to regulate gene expression, individual cells can synchronize changes in phenotype population-wide, a behavior known as quorum sensing (QS). In unstirred media, the interplay between diffusion of signals, bacterial growth, and regulatory feedback can generate complex spatial and temporal patterns of expression of QS-controlled genes. Here we identify the parameters that allow a local signal to trigger a self-sustaining, traveling activation of QS behavior. Using the natural bioluminescence of wild-type Vibrio fischeri as a readout of its lux QS system, we measure the induction of a spreading QS response by a localized triggering stimulus in unstirred media. Our data show that a QS response propagates outward, sustained by positive feedback in synthesis of the diffusible signal, and that this response occurs only if the triggering stimulus exceeds a critical threshold. We also test how the autonomous or untriggered activation of the V. fischeri QS pathway changes at very low initial population densities. At the lowest population densities, clusters of cells do not transition to a self-sensing behavior, but rather remain in communication via signal diffusion until they reach sufficiently large size that their own growth slows. Our data, which are reproduced by simple growth and diffusion simulations, indicate that in part owing to bacterial growth behavior, natural QS systems can be characterized by long distance communication through signal diffusion even in very heterogeneous and spatially dispersed populations.

Spiral Wave Propagation in Communities with Spatially Correlated Heterogeneity

Many multicellular communities propagate signals in a directed manner via excitable waves. Cell-to-cell heterogeneity is a ubiquitous feature of multicellular communities, but the effects of heterogeneity on wave propagation are still unclear. Here, we use a minimal FitzHugh-Nagumo-type model to investigate excitable wave propagation in a two-dimensional heterogeneous community. The model shows three dynamic regimes in which waves either propagate directionally, die out, or spiral indefinitely, and we characterize how these regimes depend on the heterogeneity parameters. We find that in some parameter regimes, spatial correlations in the heterogeneity enhance directional propagation and suppress spiraling. However, in other regimes, spatial correlations promote spiraling, a surprising feature that we explain by demonstrating that these spirals form by a second, distinct mechanism. Finally, we characterize the dynamics using techniques from percolation theory. Despite the fact that percolation theory does not completely describe the dynamics quantitatively because it neglects the details of the excitable propagation, we find that it accounts for the transitions between the dynamic regimes and the general dependency of the spiral period on the heterogeneity and thus provides important insights. Our results reveal that the spatial structure of cell-to-cell heterogeneity can have important consequences for signal propagation in cellular communities.

Statistics of correlated percolation in a bacterial community

Signal propagation over long distances is a ubiquitous feature of multicellular communities, but cell-to-cell variability can cause propagation to be highly heterogeneous. Simple models of signal propagation in heterogenous media, such as percolation theory, can potentially provide a quantitative understanding of these processes, but it is unclear whether these simple models properly capture the complexities of multicellular systems. We recently discovered that in biofilms of the bacterium Bacillus subtilis, the propagation of an electrical signal is statistically consistent with percolation theory, and yet it is reasonable to suspect that key features of this system go beyond the simple assumptions of basic percolation theory. Indeed, we find here that the probability for a cell to signal is not independent from other cells as assumed in percolation theory, but instead is correlated with its nearby neighbors. We develop a mechanistic model, in which correlated signaling emerges from cell division, phenotypic inheritance, and cell displacement, that reproduces the experimentally observed correlations. We find that the correlations do not significantly affect the spatial statistics, which we rationalize using a renormalization argument. Moreover, the fraction of signaling cells is not constant in space, as assumed in percolation theory, but instead varies within and across biofilms. We find that this feature lowers the fraction of signaling cells at which one observes the characteristic power-law statistics of cluster sizes, consistent with our experimental results. We validate the model using a mutant biofilm whose signaling probability decays along the propagation direction. Our results reveal key statistical features of a correlated signaling process in a multicellular community. More broadly, our results identify extensions to percolation theory that do or do not alter its predictions and may be more appropriate for biological systems.

Percolation in a reduced equilibrium model of planar cell polarity

Planar cell polarity (PCP) is a biological phenomenon where a large number of cells get polarized and coordinatedly align in a plane. PCP is an example of self-organization through local and global interactions between cells. In this work, we have used a lattice-based spin model for PCP that mimics the alignment of cells through local interactions. We have investigated the equilibrium behavior of this model. In this model, alignment of cells leads to the formation of clusters of aligned cells, and such clustering exhibits percolation transition. Even though the alignment of a cell in this model depends upon its neighbors, finite-size scaling analysis shows that this model belongs to the universality class of simple two-dimensional random percolation.

A neural network model predicts community-level signaling states in a diverse microbial community

Signal crosstalk within biological communication networks is common, and such crosstalk can have unexpected consequences for decision making in heterogeneous communities of cells. Here we examined crosstalk within a bacterial community composed of five strains of Bacillus subtilis, with each strain producing a variant of the quorum sensing peptide ComX. In isolation, each strain produced one variant of the ComX signal to induce expression of genes associated with bacterial competence. When strains were combined, a mixture of ComX variants was produced resulting in variable levels of gene expression. To examine gene regulation in mixed communities, we implemented a neural network model. Experimental quantification of asymmetric crosstalk between pairs of strains parametrized the model, enabling the accurate prediction of activity within the full five-strain network. Unlike the single strain system in which quorum sensing activated upon exceeding a threshold concentration of the signal, crosstalk within the five-strain community resulted in multiple community-level quorum sensing states, each with a unique combination of quorum sensing activation among the five strains. Quorum sensing activity of the strains within the community was influenced by the combination and ratio of strains as well as community dynamics. The community-level signaling state was altered through an external signal perturbation, and the output state depended on the timing of the perturbation. Given the ubiquity of signal crosstalk in diverse microbial communities, the application of such neural network models will increase accuracy of predicting activity within microbial consortia and enable new strategies for control and design of bacterial signaling networks.