Monotonicity in chemical reaction systems

Plug-in context providers for reaction systems

A distributed reaction system consists of a finite set of reaction systems that either interact with a common environment or interact with each other by communicating products or reactions. A reaction system is a well-known qualitative formal model of interactions between biochemical reactions. A reaction is a triplet of nonempty sets representing chemicals, called the set of reactants, the set of inhibitors, and the set of products. A reaction corresponds to a chemical reaction performed on a set of chemicals, and a reaction system is a finite nonempty set of reactions. In this paper, we examine two variants of distributed reaction systems. We introduce the notion of a distributed reaction system with communication by request (a qDRS for short), where sets of products are communicated between the component reaction systems by queries. First, we show that every qDRS can be represented by a reaction system. After that we compare distributed reaction systems with communication by request to extended distributed reaction systems (EDRSs), models that were introduced in a previous paper. We prove that extended distributed reaction systems, where a context automaton provides input for the component reaction systems, simulate distributed reaction systems with communication by request and distributed reaction systems with communication by request simulate special variants of extended distributed reaction systems. Furthermore, we assign languages to these two variants of distributed reaction systems. We prove that the class of agreement languages of extended distributed reaction systems is equal to the class of languages of nondeterministic multihead finite automata and the agreement language of every distributed reaction system with communication by request is an element of a certain subregular language class.

A new approach to the unmeasurable state reconstruction problem for nonlinear chemical reaction systems in the presence of model uncertainty is proposed. In particular, a new robust nonlinear state estimation method is developed that explicitly uses all the available useful information associated with: (i) a dynamic model inevitably characterized by uncertainty, and (ii) a set of sensor measurements in order to accurately reconstruct other key quantities/variables that cannot be measured on-line due to physical and/or technical limitations. The problem of interest is conveniently formulated and addressed within the context of singular partial differential equations (PDE) theory, leading to a nonlinear state estimator that possesses a state-dependent gain computed through the solution of a system of first-order singular PDEs. A set of necessary and sufficient conditions is presented that ensure the existence and uniqueness of a locally analytic solution to the aforementioned system of singular PDEs, and a series solution method that can be easily implemented via a MAPLE code is developed. Under these conditions, the convergence of the estimation error or the mismatch between the actual unmeasurable states and their estimates is analyzed and characterized in the presence of model uncertainty. Finally, the performance of the proposed nonlinear etimator and its convergence properties are evaluated in an illustrative biochemical reaction system that exhibits nonlinear behavior coupled with parametric uncertainty, and the estimation objective is to accurately reconstruct the unmeasurable substrate concentration using the available cell mass concentration measurements and the model of the system under consideration.

Reaction systems, introduced by Ehrenfeucht and Rozenberg, are computational models inspired by biochemical reactions transpiring within the living cells. Numerous studies focus on rs functions specified by minimal reaction systems, due to their simplicity and rich generative power. Manzoni et al [1] showed that every reaction system can be simulated by a minimal reaction system over an expanded background set. Motivated by their work, we introduce hybrid reaction systems as generalizations of reaction systems. Every rs function is then canonically expressible as a composition of two functions specified by minimal hybrid reaction systems. Using our new approach, the result of Manzoni et al [1] is revisited and strengthened.

Reaction systems are a formal model for computational processing in which reactions operate on sets of entities (molecules) providing a framework for dealing with qualitative aspects of biochemical systems. This paper is concerned with reaction systems in which entities can have discrete concentrations, and so reactions operate on multisets rather than sets of entities. The resulting framework allows one to deal with quantitative aspects of reaction systems, and a bespoke linear-time temporal logic allows one to express and verify a wide range of key behavioural system properties. In practical applications, a reaction system with discrete concentrations may only be partially specified, and the possibility of an effective automated calculation of the missing details provides an attractive design approach. With this idea in mind, the current paper discusses parametric reaction systems with parameters representing unknown parts of hypothetical reactions. The main result is a method aimed at replacing the parameters in such a way that the resulting reaction system operating in a specified external environment satisfies a given temporal logic formula.This paper provides an encoding of parametric reaction systems in smt, and outlines a synthesis procedure based on bounded model checking for solving the synthesis problem. It also reports on the initial experimental results demonstrating the feasibility of the novel synthesis method.

Cellular functions are realized through the dynamics of chemical reaction networks formed by thousands of chemical reactions. Numerical studies have empirically demonstrated that small differences in network structures among species or tissues can cause substantial changes in dynamics. However, a general principle for behavior changes in response to network structure modifications is not known. The chemical reaction system possesses substructures called buffering structures, which are characterized by a certain topological index being zero. It was proven that the steady-state response to modulation of reaction parameters inside a buffering structure is localized in the buffering structure. In this study, we developed a method to systematically identify the loss or creation of buffering structures induced by the addition of a single degradation reaction from network structure alone. This makes it possible to predict the qualitative and macroscopic changes in regulation that will be caused by the network modification. This method was applied to two reaction systems: the central metabolic system and the mitogen-activated protein kinases signal transduction system. Our method enables identification of reactions that are important for biological functions in living systems.

We propose a novel molecular computing scheme for statistical inference. We focus on the much-studied statistical inference problem of computing maximum likelihood estimators for log-linear models. Our scheme takes log-linear models to reaction systems, and the observed data to initial conditions, so that the corresponding equilibrium of each reaction system encodes the corresponding maximum likelihood estimator. The main idea is to exploit the coincidence between thermodynamic entropy and statistical entropy. We map a Maximum Entropy characterization of the maximum likelihood estimator onto a Maximum Entropy characterization of the equilibrium concentrations for the reaction system. This allows for an efficient encoding of the problem, and reveals that reaction networks are superbly suited to statistical inference tasks. Such a scheme may also provide a template to understanding how in vivo biochemical signaling pathways integrate extensive information about their environment and history.

Spatially homogeneous chemical reaction systems with one or two intermediate reaction pro-ducts and with autocatalytic reactionsteps are considered. Because of their non-linearities, such open systems show already primitive forms of self-organization. In order to express the "information" contained in the structures occuring, a theory is developped for measuring that quantity by help of a fictive detector: In treating the stochastic reaction kinetics in the Fokker-Planck-equation approximation, expressions are derived for the averaged amount of information one gets by doing a measurement with the detector and for the temporal conservation of the message being detected. This concept is applied to a one-component reaction scheme that exhibits a non-equilibrium phase transition of second order resulting in bistability of the steady state. When pushing this reaction system from the near equilibrium side through its critical region to bi-stability, a certain amount of information becomes quasi conserved, thus giving rise to a definition of the degree of order of a self-organizating system. The problem of how the reaction system can be integrated into a greater chemical network as a "bit"-generator, is discussed. To explain what is necessary for the onset of a hard mode instability giving birth to limit-cycle behaviour, a two-component reaction scheme is constructed by superposing onto reaction steps causing conservative concentration oscillations those reactions of the former model system which are responsible for the instability occuring there. By applying the information formalism, again, a quasi-conservation of information is indicated, but with respect to a much smaller time scale. The consequences for using oscillating reaction models as an information pump within a network, and the necessity of a feed-back mechanism in order to get real information storage, are shortly mentioned. Finally, a one-component reaction scheme is outlined that shows successive phase transitions, each of these instabilities bringing out a higher degree of organization.

Reaction systems are a formal framework for modeling processes driven by biochemical reactions. They are based on the mechanisms of facilitation and inhibition. A main assumption is that if a resource is available, then it is present in sufficient amounts and as such, several reactions using the same resource will not compete concurrently against each other; this makes reaction systems very different as a modeling framework than traditional frameworks such as ODEs or continuous time Markov chains. We demonstrate in this paper that reaction systems are rich enough to capture the essential characteristics of ODE-based models. We construct a reaction system model for the heat shock response in such a way that its qualitative behavior correlates well with the quantitative behavior of the corresponding ODE model. We construct our reaction system model based on a novel concept of dominance graph that captures the competition on resources in the ODE model. We conclude with a discussion on the expressivity of reaction systems as compared to that of ODE-based models.

The evolution of a reaction system is usually driven by a fixed set of unconstrained rules. In this paper, we present a different approach by imposing some constraints over the rules. Thus, we define restricted reaction systems which are working with mutually exclusive rules, namely rules that are not allowed to be applied together in the same computational step. We investigate the relationship between the reaction systems and the new restricted reaction systems. Additionally, we analyze the notion of reversibility in both reaction systems and restricted reaction systems.

Cytochrome P450 model and liver microsomal oxidations of drugs were compared using phencyclidine. In general, the chemical reaction systems produced many oxidation products. Besides the formation of the cyclohexane-4-hydroxyl compound (2), hydroxylation of the aromatic ring was favored in the Fenton reaction system (Fe2+ + H2O2). Formation of an m-hydroxylated product (m-5) was the main aromatic oxidation pathway in the Udenfriend reaction (Fe2+-ascorbic acid-O2), and 2, the piperidine-3-hydroxyl compound (3), and the piperidine-4-hydroxyl compound (4) were also formed. In the system using meso-tetraphenylporphinatoiron chloride (Fe(III)TPPC1) with an oxidant, the main product was the piperidine-3-oxo compound (8). In the liver microsomes system, 2, 4, 8, and m-5, which were all generated by the chemical oxidation reactions, were detected as metabolites of phencyclidine. They were formed by cytochrome P450-dependent reactions. Chemical oxidation systems can be used to study drug metabolism; they can reveal some tendencies of the real metabolic reactions, are easy to operate, and yield sufficient amounts of product.

The stochastic dynamical behaviors of an elementary reaction system can be investigated by the chemical Langevin equation (CLE). However, most of the reactions in engineering belong to complex reactions. It is not appropriate to describe the random evolution process of a complex chemical reaction system by directly using CLE because the foundation of the deviation of CLE is the equilibrium equation of the number of molecules in elementary reaction systems. In the study, the chemical Langevin equation for complex reactions (CLE-CR) is proposed based on the random process theory by introducing the extent of reactions to express the reaction rates of complex reactions. The reaction rates of complex reactions are regarded as some random variables following Poisson distribution. To illustrate the essential consistency of CLE-CR and CLE, the physical meaning of the propensity function in CLE is comprehensively discussed. A numerical example from chemical engineering is employed to demonstrate the effectiveness of CLE-CR and the solving procedure. The results show that CLE-CR can be conveniently applied into engineering to investigate the stochastic dynamical behaviors of complex reaction systems, giving the probabilistic information of the concentration evolution of chemical constituents.

Modelling of complex liquid–solid reaction systems in semibatch reactors: Claisen condensation in industrial scale

Piezoelectric performance can be improved by using crystal-axis oriented materials because piezoelectric properties of the ferroelectric materials are dependent on the crystal-axis direction. In this study, we tried to fabricate Ba1−xCaxTiO3 (BCT) oriented ceramics by reactive template grain growth (RTGG) method using H1.07Ti1.73O4 layered titanate (HTO) plate-like particles as the reactive template. BCT ceramics with [110]-orientation were prepared using HTO-BaCO3-Ca(OH)2 (HBC) and HTO-BaCO3-Ca(OH)2-TiO2 (HBCT) reaction systems. The degree of orientation and the relative density of the BCT ceramics are dependent on the green sheet preparation conditions, such as dispersion condition and added binder amount, calcination temperature and starting material composition. In these reaction systems, firstly oriented BCT particles are formed by a topotactic reaction of HTO template particles with Ba and Ca matrix components, and then, BCT oriented ceramic is formed by the growth of the oriented BCT particles. BCT ceramics with higher density and higher orientation can be fabricated using HBCT reaction system than HBC reaction system, where the orientation degree is dependent strongly on the ratio of HTO template particle to TiO2 matrix particle.

Compositional semantics and behavioural equivalences for reaction systems with restriction