P systems with control nuclei: The concept

We describe an extension of P systems where each membrane has an associated control nucleus responsible with the generation of the rules to be applied in that membrane. The nucleus exports a set of rules which are applied in the membrane region (only for one step, but in the usual maximal-parallel way), then the rules are removed and a new iteration of this process takes place. This way, powerful control mechanisms may be included in P systems themselves, as opposed to using the level of “strategies” previously exploited for simulating P systems. The nuclei may contain general programs for generating rules, ranging from those using information on the full system, to more restricted programs where only local information in the nuclei themselves and the associated membranes is used. The latter approach, mixed with a particular mechanism for the representation of the control programs, the rules, and the export procedure is powerful enough for modeling complex biological applications, e.g., to develop a detailed model for cell growth and division in normal and abnormal (tumoral) evolution of biological systems.