Abstract: Reactiondiffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear parabolic partial differential equations, whose general form is ÔêétX(x, t) = DΔX(x, t), where X(x, t) is the state vector, D is the matrix of the diffusion coefficients and Δ is the Laplace operator. If the solute move in an homogeneous system in thermal equilibrium, the diffusion coefficients are constants that do not depend on the local concentration of solvent and of solutes and on local temperature of the medium. In this paper a new stochastic reaction-diffusion model in which the diffusion coefficients are function of the local concentration, viscosity and frictional forces of solvent and solute is presented. Such a model provides a more realistic description of the molecular kinetics in non-homogenoeus and highly structured media as the intra- and inter-cellular spaces. The movement of a molecule A from a region i to a region j of the space is described as a first order reaction Ai k- → Aj , where the rate constant k depends on the diffusion coefficient. Representing the diffusional motion as a chemical reaction allows to assimilate a reaction-diffusion system to a pure reaction system and to simulate it with Gillespie-inspired stochastic simulation algorithms. The stochastic time evolution of the system is given by the occurrence of diffusion events and chemical reaction events. At each time step an event (reaction or diffusion) is selected from a probability distribution of waiting times determined by the specific speed of reaction and diffusion events. Redi is the software tool, developed to implement the model of reaction-diffusion kinetics and dynamics. It is a free software, that can be downloaded from http://www.cosbi.eu. To demonstrate the validity of the new reaction-diffusion model, the simulation results of the chaperone-assisted protein folding in cytoplasm obtained with Redi are reported. This case study is redrawing the attention of the scientific community due to current interests on protein aggregation as a potential cause for neurodegenerative diseases.
Abstract: A phorbol-12-myristate-13-acetate (TPA) is a synthetic analogue of phorbol ester (PE), a natural toxic compound of Euphorbiaceae plant. The oil extracted from plants of this family is useful source for primarily biofuel. However this oil might also be used as a foodstuff due to its significant nutrition content. The limitations for utilizing the oil as a foodstuff are mainly due to a toxicity of PE. Currently, a majority of PE detoxification processes are expensive as include multi steps alcohol extraction sequence.
Ozone is considered as a strong oxidative agent. It reacts with PE by attacking the carbon-carbon double bond of PE. This modification of PE molecular structure yields a non toxic ester with high lipid content.
This report presents data on development of simple and cheap PE detoxification process with water application as a buffer and ozone as reactive component. The core of this new technique is an application for a new microscale plasma unit to ozone production and the technology permits ozone injection to the water-TPA mixture in form of microbubbles.
The efficacy of a heterogeneous process depends on the diffusion coefficient which can be controlled by contact time and interfacial area. The low velocity of rising microbubbles and high surface to volume ratio allow efficient mass transfer to be achieved during the process. Direct injection of ozone is the most efficient way to process with such highly reactive and short lived chemical.
Data on the plasma unit behavior are presented and the influence of gas oscillation technology on the microbubble production mechanism has been discussed. Data on overall process efficacy for TPA degradation is shown.
Abstract: The present models and simulation algorithms of intracellular stochastic kinetics are usually based on the premise that diffusion is so fast that the concentrations of all the involved species are homogeneous in space. However, recents experimental measurements of intracellular diffusion constants indicate that the assumption of a homogeneous well-stirred cytosol is not necessarily valid even for small prokaryotic cells. In this work a mathematical treatment of diffusion that can be incorporated in a stochastic algorithm simulating the dynamics of a reaction-diffusion system is presented. The movement of a molecule A from a region i to a region j of the space is represented as a first order reaction Ai k- ! Aj , where the rate constant k depends on the diffusion coefficient. The diffusion coefficients are modeled as function of the local concentration of the solutes, their intrinsic viscosities, their frictional coefficients and the temperature of the system. The stochastic time evolution of the system is given by the occurrence of diffusion events and chemical reaction events. At each time step an event (reaction or diffusion) is selected from a probability distribution of waiting times determined by the intrinsic reaction kinetics and diffusion dynamics. To demonstrate the method the simulation results of the reaction-diffusion system of chaperoneassisted protein folding in cytoplasm are shown.