Mathematical modelling of motility regulation in Myxococcus xanthus

Myxococcus xanthus, referred to as a 'social bacterium', demonstrates unique behaviors such as coordinated motility, cooperative feeding, and multicellular structure formation. Its complex social behaviors and developmental processes make M. xanthus a model organism for studying bacterial social behaviors and their underlying mechanisms. Much of the social behavior of M. xanthus hinges on coordination of cell motility among bacteria in close proximity. M. xanthus moves on moist solid surfaces, using its Adventurous (A)-motility and Social (S)-motility systems. A striking feature of M. xanthus motility is the periodic reversal of its direction of movement. The reversal frequency is influenced by chemical and mechanical cues in the surrounding environment. The modulation of the reversal frequency upon physical contact between cells is believed to be a key factor in the bacterium's social behaviors, especially in the formation of complex patterns and structures within the cell population.

Here I utilized mathematical modeling to study the motility regulation in M. xanthus, focusing on contact-dependent reversal control, mechanosensing response and impact of motility regulation in solitary (single-cell) predation. My goal is to provide experiment-guiding theories and hypotheses for M. xanthus motility regulation, which is essential to fully understand the social behaviors in this bacterium.

In Chapter 2, I developed a single-cell model based on a hypothesis that the motility regulation in M. xanthus is mediated by the interplay between the cell polarity regulation pathway and the A-motility machinery. The aim of this model is to elucidate the cellular mechanism governing contact-dependent motility coordination among cells and to understand how contact-dependent responses at the single-cell level contribute to population-level patterns. This model suggests that the A-motility machinery of M. xanthus potentially serves as a 'mechanosensor' that transduces mechanical cues in the environment into a reversal modulation signal.

Chapter 3 addresses a puzzling observation: cells with A-motility alone (A+S−) show a dependence of reversal frequency on substrate stiffness that is opposite to what is observed in wild-type cells that possess both motility systems. Specifically, A+S− cells reverse less frequently on harder substrates, whereas wild-type cells reverse more frequently. To elucidate this perplexing phenomenon, I refined the single-cell model developed in Chapter 2 to study the mechanosensing behaviors with or without S-motility. The base model was sufficient to explain the mechanosensing response in A+S− cells. I then proposed possible interactions between the A-motility and S-motility systems that could explain the contrasting responses to substrate stiffness when S-motility is present or absent. This provides a testable prediction for future experimental investigations. The model suggests that the A-motility system in M. xanthus functions as a central hub of mechanosensing-based reversal control, modulating cell reversal in response to environmental mechanical cues.

In Chapter 4, I constructed an agent-based model to investigate the optimal motility strategies for nutrient consumption by M. xanthus during its solitary predation. For different nutrient source types and their uptake latencies, the model identifies 'explore', 'inch', and 'fast explore' as the three most effective motility strategies. Variability in velocity and cell reversal period changes the optimal strategies from 'explore' mode to 'revisit' mode and to 'speed-controlled explore' mode, respectively, for massive remains of prey nutrient sources with moderate uptake latency. The experimental observation that solitary M. xanthus cells combined the 'revisit' and 'inch' mode—as predicted by the model for nutrient acquisition respectively from prey remains and macromolecules—suggests that some of the dead preys may not release its cellular contents immediately and that release of molecular nutrients may require multiple digestion cycles. This model provides insights into the functional role of complex motility regulation in M. xanthus during solitary predation.