GAME OF COORDINATION FOR BACTERIAL PATTERN FORMATION: A FINITE AUTOMATA MODELLING

Bacterial colonies in nature are often required to evolve under harsh and hostile environmental growth conditions. In order to do so, bacteria work as a social formation and employ intricate communication capabilities to exchange information and interact cooperatively to form highly complex colonies, equipped with higher capabilities for adaptation to the environmental challenges. These colonies that could be observed as intricate spatial patterns are essentially the manifestation of bacterial self-organization resulting from such cooperative behavior. The information required by the bacteria for giving rise to the observed self-organized complex pattern formation is generated through cooperative interactions, depending on and in response to the available growth conditions. Bacterial self-organization and colony formation, thus, appears as an instance of a social network, essentially created through communicative interactions. In this paper, we use concepts from game theory and informatics to describe the emergence of self-organization and consequent pattern formation through communicative cooperation in Bacillus subtilis colonies. The emergence of cooperative regime is modelled as an Assurance game, with the bacterial colonies as individual players. The game is played iteratively through cooperative communication, and mediated by exchange of information about the local environment between the different bacterial colonies comprising the system. The iteration causes the interactive system to grow and produce beautiful complex spatial patterns signaling the emergence of self-organization. As a formal description of the game, we model the emergence of this cooperative behavior as finite deterministic automata, whose transition function is informed by the Assurance game pay-off.