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Ordinary differential equations (ODEs) are a widespread formalism for the mathematical modeling of natural and engineering systems, whose analysis is generally performed by means of numerical integration methods. However, real-world models are often characterized by stiffness, a circumstance that can lead to prohibitive execution times. In such cases, the practical viability of many computational tools—e.g., sensitivity analysis—is hampered by the necessity to carry out a large number of simulations. In this work, we present ginSODA, a general-purpose black-box numerical integrator that distributes the calculations on graphics processing units, and allows to run massive numbers of numerical integrations of ODE systems characterized by stiffness. By leveraging symbolic differentiation, meta-programming techniques, and source code hashing, ginSODA automatically builds highly optimized binaries for the CUDA architecture, preventing code re-compilation and allowing to speed up the computation with respect to the sequential execution. ginSODA also provides a simplified Python interface, which allows to define a system of ODEs and the test to be performed in a few lines of code. According to our results, ginSODA provides up to a 25× speedup with respect to the sequential execution

In this chapter we present an application of membrane systems to the study of intracellular diffusive processes. In particular, a class of membrane systems, called tau-DPP, is used for the modeling, simulation and analysis of bacterial chemotaxis. Two different models of this signal transduction pathway are presented. The first is a single volume model used to investigate the properties of bacterial chemotaxis and to analyze the effects of different perturbations (deletion of chemotactic proteins, addition of distinct amounts of external ligand, effect of different methylation states of the receptors) on the system dynamics. The second model represents a multivolume extension of the former, and it is exploited for the analysis of the diffusive processes that give rise to the formation of concentration gradients throughout the bacterial cytoplasm. The outcome of stochastic simulations of both models are exploited to analyze the process of synchronization of flagella, in order to evaluate the running and tumbling time intervals of bacterial cells

The computational investigation of a biological system often requires the execution of a large number of simulations to analyze its dynamics, and to derive useful knowledge on its behavior under physiologicaland perturbed conditions. This analysis usually turns out into very high computational costs when simulations are run on central processing units (CPUs), therefore demanding a shift to the use of high performance processors. In this work we present a simulator of biological systems, called cupSODA, which exploits the higher memory bandwidth and computational capability of graphics processing units (GPUs). This software allows to execute parallel simulations of the dynamics of biological systems, by first deriving a set of ordinary differential equations from reaction-based mechanistic models defined according to the massaction kinetics, and then exploiting the numerical integration algorithm LSODA. We show that cupSODA can achieve a 112× speedup on GPUs with respect to equivalent executions of LSODA on CPUs.

Taking inspiration from some laws of Nature—energy transformation and chemical reactions—we consider two different paradigms of computation in the framework of Membrane Computing. We first study the computational power of energy-based P systems, a model of membrane systems where a fixed amount of energy is associated with each object and the rules transform objects by manipulating their energy. We show that if we assign local priorities to the rules, then energy-based P systems are as powerful as Turing machines; otherwise, they can be simulated by vector addition systems, and hence are not universal. Then, we consider stochastic membrane systems where computations are performed through chemical networks. We show how molecular species and chemical reactions can be used to describe and simulate the functioning of Fredkin gates and circuits. We conclude the paper with some research topics related to computing with energy-based P systems and with chemical reactions.

Stochastic simulations based on the tau leaping method are applicable to well stirred chemical systems reacting within a single fixed volume. In this paper we propose a novel method, based on the tau leaping procedure, for the simulation of complex systems composed by several communicating regions. The new method is here applied to dynamical probabilistic P systems, which are characterized by several features suitable to the purpose of performing stochastic simulations distributed in many regions. Conclusive remarks and ideas for future research are finally presented

In [3] P systems with gemmation of mobile membranes were examined. It was shown that (extended) systems with eight membranes are as powerful as the Turing machines. Moreover, it was proved that extended gemmating P systems with only pre-dynamical rules are still computationally complete: In this case nine membranes are needed to obtain this computational power. In this paper we improve the above results concerning the size bound of extended gemmating P systems, namely we prove that these systems with at most five membranes (with meta-priority relations and without communication rules) form a class of universal computing devices, while in the case of extended systems with only pre-dynamical rules six membranes are enough to determine any recursively enumerable language.

We consider rewriting P systems with parallel application of evolution rules, where no conflicts on the communication of objects can arise. Different parallelism methods are used and only rules which have the same target indication can be simultaneously applied to a common string. The computational power is analyzed, with respect to Lindenmayer systems, and some relations among different parallel rewriting P systems are studied. Some open problems are also formulated.