Error-Prone Cellular Automata as Metaphors of Immunity as Computation

Abstract

Modeling the immune system so that its essential functionalities stand out without the need for every molecular or cellular interaction to be taken into account has been challenging for many decades. Two competing approaches have been the clonal selection theory and the idiotypic-network theory, each stemming from a relatively separate set of principles. One recent perspective holding the promise of unification is that of immunity as computation, that is, of immunity as the process of computing the state of the body so that protection can be effected, as well as boosted through learning. Here we investigate the use of cellular automata (CA) as the core abstraction supporting this new perspective. Our choice of CA for this role is based on the potential variety of basins in a CA attractor field. Associating each basin with a consistent set of body states, and moreover providing for the noisy evolution of the CA in time so that jumping between basins is possible, have provided the necessary backdrop. Given a CA rule to be followed by all cells synchronously, our model is based on a probability with which each cell, at each time step, independently updates its own state differently than the rule mandates. Setting up and solving the corresponding Markov chain for its stationary probabilities have revealed that already in the context of elementary CA there exist rules that, while allowing transitions between basins, display remarkable resiliency in terms of basin occupation. For these rules, the long-run probability that the CA is found in a given basin is practically the same as in the deterministic case when the initial CA state is chosen uniformly at random. We argue that, consequently, our single-parameter CA model may be a suitable abstraction of immunity as computation.