MP Systems modeling framework
Metabolic P systems, shortly MP systems, are a special class of deterministic P systems (introduced in 1998 by Gheorghe Paun), proposed as models for biological metabolism. Their dynamics are computed by a molar multiset rewriting regulated by functions, where reactions act on object populations, rather than on single objects (as P system rules do).
The dynamics is deterministic at a population level, whereas nothing can be said about the dynamical evolution of single objects. This situation resembles what happens in the macroscopic gas laws, which specify deterministic relationships among pressure, volume and temperature measures, but do not cope with the mechanical behaviour of single molecules.
Two main features of MP systems are relevant for their application in modeling real complex phenomena. Their dynamics is easily computed by suitable recurrent equations, also called metabolic algorithms, and moreover, these equations can be stated by suitable algebraic manipulations of data coming from macroscopic observation of the system under investigation. The essence of the metabolic algorithm is the following: compute reaction units, which give a matter partition, apply reactions to the matter assigned to them, and finally collect their products, after removing the matter they consume.
Given a biological process of interest, all its variables can be split in two different kinds: chemical substances, which have a mass and transform according to the mass conservation principle, and other parameter elements, with no mass (e.g., light, volume), that provide some observed values or evolve according to some specific laws. Substances are measured by (conventional) moles, which correspond to suitable population units. For each substance, the mass of a mole specifies the matter quantity (in terms of some mass unit) associated to a mole of the substance.
The biochemical reactions of the process are seen as rewriting rules. The observation time interval is established on the base of either the kind of process or the kind of study in which one is interested; for example, faster biological processes require shorter time intervals.