SIAM News Blog

Understanding Bacterial Communication via Quorum Sensing

By Lina Sorg

Many species of bacteria utilize a communication system called quorum sensing (QS) to detect and respond to cell population density, which subsequently informs and coordinates their behavior. Gene regulation forms the basis of QS, during which bacteria produce and release chemical signaling molecules called autoinducers that traverse the environment and provide cells with necessary information (see Figure 1). The bacteria then use this information to control other mechanisms within the cells and make substantial lifestyle changes. For example, QS in Vibrio fischeri—a type of marine bacterium—causes luminescence. In the soil bacterium Pseudomonas putida, it generates a biofilm and influences soil processes. And in Pseudomonas aeruginosa—a common bacterium in soil and water—it causes disease.

Figure 1. During quorum sensing (QS), bacteria produce and release chemical signaling molecules called autoinducers that traverse the environment and provide cells with necessary information. Figure courtesy of Christina Kuttler.
Despite their diversity, all of these applications are governed by similar mechanisms. “How can we view this from a mathematical point of view to better understand behavior?” Christina Kuttler of Technische Universität München asked. During a minisymposium presentation at the 2023 SIAM Conference on Computational Science and Engineering, which is currently taking place in Amsterdam, the Netherlands, Kuttler explored bacterial communication and QS from both a mathematical and biological perspective. She began by reducing a gene regulation system to one single ordinary differential equation (ODE). The resulting simplified system exhibits bistability and has two stable equilibrium states: a resting state and an activated state. “Bistability also helps to stabilize the system against small perturbations,” Kuttler said.

However, several possibilities exist for negative feedback on different levels: within the gene regulatory system, during QS-governed degradation of the signal molecule, and during QS-governed detachment of bacteria (see Figure 2). Kuttler then discussed an experiment with P. putida in a batch culture—a closed culture system with limited nutrients—that measures bacterial density and the concentration of homoserine lactone (HSL), a class of signaling molecule. She noted that HSL concentration exhibits a rapid, unexpected decrease after the initial expected increase and wonders whether increased abiotic degradation is responsible.

After accounting for this occurrence in her original model, Kuttler exhibited a delay QS model of P. putida (with constant delay) wherein QS controls the production of lactonase: a metalloenzyme that targets and inactivates HSL production and degrades the autoinducers. She fit this delay differential equation model to experimental data. Because the original simplified ODE cannot sufficiently handle the heterogenous spatial distribution of cells that often occurs in biofilm, Kuttler created a simple partial differential equation model that combines bacterial density with a one-dimensional spread in space. Here she used the Fisher equation for bacteria and revealed that a traveling wave connects the QS upregulated stationary state with the QS downregulated stationary state.

Figure 2. Positive versus negative feedback. Figure courtesy of the Amoeba Sisters.
Next, Kuttler focused specifically on pathogenicity. “Another interesting question is of course how to include treatment, and one classical treatment is antibiotics,” she said. To address this query, Kuttler considered the use of antibiotics under several conditions. She examined the QS system as a simplified reaction-diffusion model inside a given area — an approach that falls above the single-cell level but below the biofilm level and accounts for the generation of autoinducers and lactonase in the bacterial colonies (represented by a normal distribution around their centers). Though the model is somewhat rough, she wanted to get it to a point where she could run a working simulation.

Kuttler then presented the resulting simulation in a simplistic, hybrid setting over the course of 12, 24, and 36 hours. Without antibiotics treatment, logistical growth occurs in the colonies’ radius and stochastic generation of new colonies ensues. The presence of antibiotics initially reduces colony growth and lowers bacteria levels, but new colonization—and new bacteria—eventually come to pass.

While this simplistic simulation allows for quick calculations and an efficient albeit rudimentary overview, researchers still have much to learn about the interactions between bacterial behavior, QS, and antibiotics. “Hybrid approaches may be useful, as bacteria and bacterial colonies may be better described as discrete objects, whereas small molecules in large numbers are better as continuous variables, Kuttler said.

Lina Sorg is the managing editor of SIAM News.
blog comments powered by Disqus