Actin Automata: Phenomenology and Localizations

Abstract

Actin is a globular protein which forms long filaments in the eukaryotic cytoskeleton, whose roles in cell function include structural support, contractile activity to intracellular signaling. We model actin filaments as two chains of one-dimensional binary-state semi-totalistic automaton arrays to describe hypothetical signaling events therein. Each node of the actin automaton takes state "0" (resting) or "1" (excited) and updates its state in discrete time depending on its neighbor's states. We analyze the complete rule space of actin automata using integral characteristics of space-time configurations generated by these rules and compute state transition rules that support traveling and mobile localizations. Approaches towards selection of the localization supporting rules using the global characteristics are outlined. We find that some properties of actin automata rules may be predicted using Shannon entropy, activity and incoherence of excitation between the polymer chains. We also show that it is possible to infer whether a given rule supports traveling or stationary localizations by looking at ratios of excited neighbors that are essential for generations of the localizations. We conclude by applying biomolecular hypotheses to this model and discuss the significance of our findings in context with cell signaling and emergent behavior in cellular computation.