A Dynamic Network Formation Model for Understanding Bacterial Self-Organization Into Micro-Colonies

We propose a general parametrizable model to capture the dynamic interaction among bacteria in the formation of micro-colonies. Micro-colonies represent the first social step towards the formation of structured multicellular communities known as bacterial biofilms, which protect the bacteria against antimicrobials. In our model, bacteria can form links in the form of intercellular adhesins (such as polysaccharides) to collaborate in the production of resources that are fundamental to protect them against antimicrobials. Since maintaining a link can be costly, we assume that each bacterium forms and maintains a link only if the benefit received from the link is larger than the cost, and we formalize the interaction among bacteria as a dynamic network formation game. We rigorously characterize some of the key properties of the network evolution depending on the parameters of the system. In particular, we derive the parameters under which it is guaranteed that all bacteria will join micro- colonies and the parameters under which it is guaranteed that some bacteria will not join micro-colonies. Importantly, our study does not only characterize the properties of networks emerging in equilibrium, but it also provides important insights on how the network dynamically evolves and on how the formation history impacts the emerging networks in equilibrium. This analysis can be used to develop methods to influence on-the-fly the evolution of the network, and such methods can be useful to treat or prevent biofilm-related diseases.