Researchers at The University of Texas at Austin and the University of California, Los Angeles, have created a new theoretical model that accurately describes how swarms of bacteria navigate their environment to locate and consume nutrients.

Microbes such as the common gut bacterium E. coli perform a process known as chemotaxis to detect microscopic nutrient gradients. The microbes "swim" or "crawl" through their surroundings, driven by rotating flagella, to chase gradients of chemical attractants until they reach a nutrient-rich location.

The researchers' new model, published in the journal Proceedings of the National Academy of Sciences, is the most accurate yet at predicting the dynamics of bacterial chemotaxis under various nutrient concentrations and viscosities—important factors that determine the swimming or crawling behavior of bacteria.

The findings help scientists better understand how bacteria find food at the microscale level and could lead to technological advances in the areas of biosensing, diagnostics and medicine.

"These microbes exhibit surprisingly rich behavior, and accurately predicting how they navigate a gradient is challenging," said Igor Aronson, a professor of mathematics at UT Austin and co-author of the paper. "Our simplified model allows researchers to compute the speed at which the microbes find food and compare the predictions with experiments, which could help optimize the process by which microbes find food or targets in the future. This has implications for applications in biotechnology, healthcare, and environmental remediation."

Bacterial chemotaxis is also linked to virulence. Microbes rely on the chemical gradient sensing in chemotaxis to locate and infect a host. E. coli, for example, uses chemotaxis to find nutrients and also to locate and infect mammalian intestines, the microbes' preferred habitat.

"The findings could lead to new antibiotics that hinder this navigational system in chemotaxis, preventing disease transmission," said Alexander V. Argun, a UCLA professor of mathematics and the other co-author of the paper.

The researchers note that previous mathematical models describing bacterial chemotaxis made a number of simplifying assumptions in their equations, which ultimately prevented them from matching the accuracy of experimental observations. In particular, previous models failed to account for an overdamped inertial effect that acts on the microbes, which slows down their dynamics.

"What the bacteria experience is similar to swimming in molasses," Aronson said. "The dynamics are very different from swimming through water, and most previous models did not take this into account."

The new theoretical model developed by Aronson and Argun incorporates the inertial effect along with several other realistic effects, such as the size and internal density of the bacteria, to greatly improve the model's accuracy in replicating experimental observations.

Argun also noted that some bacterial chemotaxis systems display a non-monotonic speed response, meaning that the speed of the microbes increases up to a maximum as the nutrient concentration increases, and then starts decreasing.

"This is different from what we see in most physical phenomena, where speed always increases as the driving force increases," Argun said. "Here, the swimming becomes less efficient at high nutrient concentrations due to 'over-signaling,' which our model is able to capture."

The researchers used their model to generate an accurate quantitative prediction for how the microbes' swimming speed changes as they adapt to nutrient scarcity, a prediction previously not available from analytical models.

"These mathematical models not only help us gain insights into nature, but they can also help us make predictions that can be tested experimentally," Aronson said. "This model should provide a better understanding of the role of chemotaxis in bacterial motility, ecology, and physiology."