Fixed points and attractors of reactantless and inhibitorless reaction systems

Reaction systems are discrete dynamical systems that model biochemical processes in living cells using finite sets of reactants, inhibitors, and products. We investigate the computational complexity of a comprehensive set of problems related to the existence of fixed points and attractors in two constrained classes of reaction systems, in which either reactants or inhibitors are disallowed. These problems have biological relevance and have been extensively studied in the unconstrained case; however, they remain unexplored in the context of reactantless or inhibitorless systems. Interestingly, we demonstrate that although the absence of reactants or inhibitors simplifies the system’s dynamics, it does not always lead to a reduction in the complexity of the considered problems

Efficient simulation of reaction systems on graphics processing units

Reaction systems represent a theoretical framework based on the regulation mechanisms of facilitation and inhibition of biochemical reactions. The dynamic process defined by a reaction system is typically derived by hand, starting from the set of reactions and a given context sequence. However, this procedure may be error-prone and time-consuming, especially when the size of the reaction system increases. Here we present HERESY, a simulator of reaction systems accelerated on Graphics Processing Units (GPUs). HERESY is based on a fine-grained parallelization strategy, whereby all reactions are simultaneously executed on the GPU, therefore reducing the overall running time of the simulation. HERESY is particularly advantageous for the simulation of large-scale reaction systems, consisting of hundreds or thousands of reactions. By considering as test case some reaction systems with an increasing number of reactions and entities, as well as an increasing number of entities per reaction, we show that HERESY allows up to 29 7 speed-up with respect to a CPU-based simulator of reaction systems. Finally, we provide some directions for the optimization of HERESY, considering minimal reaction systems in normal form

Efficient simulation of reaction systems on graphics processing units

Reaction systems represent a theoretical framework based on the regulation mechanisms of facilitation and inhibition of biochemical reactions. The dynamic process defined by a reaction system is typically derived by hand, starting from the set of reactions and a given context sequence. However, this procedure may be error-prone and time-consuming, especially when the size of the reaction system increases. Here we present HERESY, a simulator of reaction systems accelerated on Graphics Processing Units (GPUs). HERESY is based on a fine-grained parallelization strategy, whereby all reactions are simultaneously executed on the GPU, therefore reducing the overall running time of the simulation. HERESY is particularly advantageous for the simulation of large-scale reaction systems, consisting of hundreds or thousands of reactions. By considering as test case some reaction systems with an increasing number of reactions and entities, as well as an increasing number of entities per reaction, we show that HERESY allows up to 29Ã\u97 speed-up with respect to a CPU-based simulator of reaction systems. Finally, we provide some directions for the optimization of HERESY, considering minimal reaction systems in normal form