Quantitative Reaction Systems

We propose a new variant of reaction system that intends to take into account a few aspects of a biological reaction that have been considered at most partially in former works. These aspects are: (i) in the former variants, all the substances of the substrate completely vanish after identifying the set of reactants such that the result does not contain any former component of the substrate unless it is produced by the reaction, (ii) in any substrate, each element is either present in an arbitrary large number of copies, or it is not present at al, (iii) the effect of any inhibitor is the same but in biology the effect of inhibitors may be different due to their type. Our model considers multisets of reactants such that it is a more quantitative model than a qualitative one, inhibitors may be of different types such that their role may vary depending on the substrate, the substances that are not involved in the reaction remain in the substrate. We consider a parallel mode of enabling the reactions and prove that this mode may be simulated by sequential enabling. Later on, we define a computational model based on quantitative reaction systems and prove that their computation power equals that of multiset Turing machines.