Stressed bacteria have developed cooperative strategies to cope with unfavorable growth conditions and to replicate. In this paper, we describe experimentally the effects of stressing bacteria using antibiotic stress, nutritional stress and substrate stress. We find that the cooperative communications between bacteria in the colony are manifested as fascinating complex spatial patterns. We then describe a modeling of this experimentally observed cooperative behavior of the bacteria colony from the perspective of complexity. The inter-bacterial interactions that give rise to the spatial patterns are viewed as an emergent phenomenon, with the interactions being modeled as a Prisoner’s dilemma game. We obtain deterministic finite automata that model the interactions, and derive both, a context-free as well as a context-sensitive grammar describing the bacterial interactions and consequent evolution over discrete time.

Interacting groups of motile organisms form complex systems that offer a rich repository for studying and learning about various interesting facets of complexity. These organisms may exhibit characteristic patterns of self-organized collective behavior, forming spatial aggregation (Gros, 2008; and Mitchell, 2009).

In this paper, we study an interacting colony of bacteria as a typification of complexity. A single bacterium can be treated as a complex molecule which interacts with its environment, communicates with other individuals, replicates and undergoes evolution and mutation. When millions of bacteria act collectively as a group (as is the case in any bacterial colony), a large variety of different, fascinating spatial patterns emerge as a result of games played by the individual bacteria colony with its neighbors as well as with the environment. These patterns are the emergent result of local interactions (interactions within the neighborhood of each individual colony) through exchange and processing of information over discrete time, and environmental conditions, and can be usefully viewed as being programmed by the particular way the bacteria in question interact as well as by the particular way these bacteria respond to environmental signals (Ben-Jacob, 1997; Ben-Jacob et al., 2004; and Krawezyk et al., 2004).

In nature, bacterial colonies may often experience hostile, challenging environmental conditions that may not offer optimal factors for growth and evolution of the colonies. Evolving populations of bacteria (and therefore bacterial colonies) carry and mediate information via games played by them locally. Each colony would receive a finite set of input information or signal from its neighbors (and therefore, as well as the environment) in the form of strategies played by the neighboring colony in the game. This input set decides the transition of the colony to the next state in discrete time step, producing a final set (the next generation). Bacterial colonies therefore could be thought of as finite state machines. To cope with environmental stress, the aggregation of colonies or finite state machines, which essentially form a complex system through the mechanism of information processing, develop extensive cooperative behavior. These cooperative behaviors could be modelled as payoffs of games played between the colonies mentioned in the above paragraph, to share available resources usefully via transmission of information between them, and evolve. These stressed bacterial colonies exhibit emergence and self-organization, two of the essential signatures of a complex system, and produce fascinating spatially complex patterns of aggregation, manifesting the complexity of information transfer and processing (Doudoroff et al., 1957; Shapiro, 1988; Ben-Jacob et al., 1998 and 2000a; Lacasta et al., 1999; and Mitchell, 2009).

Our objective in this paper is to model the cooperative behavior of such stressed bacterial colonies which emerges as a self-organized system through information processing, by using Deterministic Finite Automata (DFA), since automatic structures could be a suitable modeling tool to study such informatics (Papadimitriou and Lewis, 1997; and Hopcroft et al., 2006).

Environmental Sciences Journal, SWAT Hydrological Model, Upper Bernam River Basin, Malaysia, Soil and Water Assessment Tool, Geographic Information System, Water Resources, Remote Sensing Technology, Agricultural Research Service, Universal Soil Loss Equation, GIS Database, Landsat Thematic Mapper Imageries, Meteorological Data, Government Departments.