Two-step simulations of reaction systems by minimal ones

Reaction systems were introduced by Ehrenfeucht and Rozenberg with biochemical applications in mind. The model is suitable for the study of subset functions, that is, functions from the set of all subsets of a finite set into itself. In this study the number of resources of a reaction system is essential for questions concerning generative capacity. While all functions (with a couple of trivial exceptions) from the set of subsets of a finite set S into itself can be defined if the number of resources is unrestricted, only a specific subclass of such functions is defined by minimal reaction systems, that is, the number of resources is smallest possible. On the other hand, minimal reaction systems constitute a very elegant model. In this paper we simulate arbitrary reaction systems by minimal ones in two derivation steps. Various techniques for doing this consist of taking names of reactions or names of subsets as elements of the background set. In this way also subset functions not at all definable by reaction systems can be generated. We follow the original definition of reaction systems, where both reactant and inhibitor sets are assumed to be nonempty

Towards an efficient multiscale modeling of low-dimensional reactive systems: study of numerical closure procedures

In this paper, we present a study on how to develop an efficient multiscale simulation strategy for the dynamics of chemically active systems on low-dimensional supports. Such reactions are encountered in a wide variety of situations, ranging from heterogeneous catalysis to electrochemical or (membrane) biological processes, to cite a few. We analyzed in this context different techniques within the framework of an important multiscale approach known as the equation free method (EFM), which "bridges the multiscale gap" by building microscopic configurations using macroscopic-level information only. We hereby considered two simple reactive processes on a one-dimensional lattice, the simplicity of which allowed for an in-depth understanding of the parameters controlling the efficiency of this approach. We demonstrate in particular that it is not enough to base the EFM on the time evolution of the average concentrations of particles on the lattice, but that the time evolution of clusters of particles has to be included as well. We also show how important it is for the accuracy of this method to carefully choose the procedure with which microscopic states are constructed, starting from the measured macroscopic quantities. As we also demonstrate that some errors cannot be corrected by increasing the number of observed macroscopic variables, this work points towards which procedures should be used in order to generate efficient and reliable multiscale simulations of these systems.Comment: 15 pages, 11 figure

Modeling the complex dynamics of enzyme-pathway coevolution.

Peer reviewedPostprin

A stochastic model of catalytic reaction networks in protocells

Protocells are supposed to have played a key role in the self-organizing processes leading to the emergence of life. Existing models either (i) describe protocell architecture and dynamics, given the existence of sets of collectively self-replicating molecules for granted, or (ii) describe the emergence of the aforementioned sets from an ensemble of random molecules in a simple experimental setting (e.g. a closed system or a steady-state flow reactor) that does not properly describe a protocell. In this paper we present a model that goes beyond these limitations by describing the dynamics of sets of replicating molecules within a lipid vesicle. We adopt the simplest possible protocell architecture, by considering a semi-permeable membrane that selects the molecular types that are allowed to enter or exit the protocell and by assuming that the reactions take place in the aqueous phase in the internal compartment. As a first approximation, we ignore the protocell growth and division dynamics. The behavior of catalytic reaction networks is then simulated by means of a stochastic model that accounts for the creation and the extinction of species and reactions. While this is not yet an exhaustive protocell model, it already provides clues regarding some processes that are relevant for understanding the conditions that can enable a population of protocells to undergo evolution and selection.Comment: 20 pages, 5 figure