Two New Types of Evolution in Quantitative Reaction Systems

A quantitative reaction system is a quadruple of sets inspired by and abstracted from the chemicals existing in a cell, namely the set of reactants, which are consumed in the reaction, the set of inhibitors, which inactivate the reaction, the set of relationships reactant-inhibitor, and the set of new chemicals produced by the reaction. Three new principles are present in a quantitative reaction system. First, the permanency principle, which requires that the reactants are non degradable. Second, the threshold principle, which states that an element is present in a finite quantity in any substrate (environment), Third, the selective inhibitors principle, which means that the inhibitors may block or not a reaction due to their type. Consequently, the environment of each state in this model is a multisets of reactants, the role of inhibitors may be different, depending on the substrate, the substances that do not participate in a reaction are not degraded but they remain unchanged in the substrate. We consider two new types of evolution, namely the arbitrary and maximal activation of the reactions and prove that these modes may be simulated by sequential activation.