  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.
