Evolving cellular automata for diversity generation and pattern recognition: deterministic versus random strategy

Microbiological systems evolve to fulfil their tasks with maximal efficiency. Modelling efforts depend crucially on this assumption and adaptation is the key element for evolution to take place. The immune repertoire is a remarkable example of an adaptable, evolving system whose main role is the defense of living organisms against pathogens (antigens),
where the distinction between self and non-self is made by means of molecular interactions between proteins and antigens, triggering affinity-dependent systemic actions. Specificity of this binding and the infinitude of potential antigenic patterns call for novel mechanisms to generate antibody diversity. Inspired by this problem, we develop a genetic algorithm where agents with antibody information encoded as bit strings evolve their repertoire in the presence of random antigens (encoded as random strings) and reproduce with affinity-dependent rates. We develop a population dynamics with stationary populations constrained by size-dependent, Verhulst-like death rates. We ask what is the best strategy to generate diversity if agents can rearrange their strings a finite number of times. We find that endowing each agent with an inheritable cellular automaton rule for performing rearrangements makes the system more efficient in pattern-matching than if transformations are totally random. In the former implementation, the population evolves to a stationary state where agents with different automata rules coexist.