scholarly journals Common complexes of decompositions and complex balanced equilibria of chemical reaction networks

2021 ◽  
Vol 87 (2) ◽  
pp. 329-366
Author(s):  
Lauro Fontanil ◽  
◽  
Eduardo Mendoza
Keyword(s):  
Chemical Reaction ◽  
Power Law ◽  
Reaction Network ◽  
Reaction Networks ◽  
Sufficient Condition ◽  
Direct Sum ◽  
Chemical Models ◽  
Complex Balancing ◽  
Independence Properties ◽  
The Given

A decomposition of a chemical reaction network (CRN) is produced by partitioning its set of reactions. The partition induces networks, called subnetworks, that are "smaller" than the given CRN which, at this point, can be called parent network. A complex is called a common complex if it occurs in at least two subnetworks in a decomposition. A decomposition is said to be incidence independent if the image of the incidence map of the parent network is the direct sum of the images of the subnetworks' incidence maps. It has been recently discovered that the complex balanced equilibria of the parent network and its subnetworks are fundamentally connected in an incidence independent decomposition. In this paper, we utilized the set of common complexes and a developed criterion to investigate decomposition’s incidence independence properties. A framework was also developed to analyze decomposition classes with similar structure and incidence independence properties. We identified decomposition classes that can be characterized by their sets of common complexes and studied their incidence independence. Some of these decomposition classes occur in some biological and chemical models. Finally, a sufficient condition was obtained for the complex balancing of some power law kinetic (PLK) systems with incidence independent and complex balanced decompositions. This condition led to a generalization of the Deficiency Zero Theorem for some PLK systems.

Inference of Chemical Reaction Networks Using Hybrid S-system Models

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Dominic P Searson ◽  
Mark J Willis ◽  
Simon J Horne ◽  
Allen R Wright
Keyword(s):  
Chemical Reaction ◽  
Power Law ◽  
Network Inference ◽  
Batch Reactor ◽  
Reaction Network ◽  
Chemical Reaction Networks ◽  
Chemical Reaction Network ◽  
Reaction Networks ◽  
Fed Batch ◽  
System Equations

This article demonstrates, using simulations, the potential of the S-system formalism for the inference of unknown chemical reaction networks from simple experimental data, such as that typically obtained from laboratory scale reaction vessels. Virtually no prior knowledge of the products and reactants is assumed. S-systems are a power law formalism for the canonical approximate representation of dynamic non-linear systems. This formalism has the useful property that the structure of a network is dictated only by the values of the power law parameters. This means that network inference problems (e.g. inference of the topology of a chemical reaction network) can be recast as parameter estimation problems. The use of S-systems for network inference from data has been reported in a number of biological fields, including metabolic pathway analysis and the inference of gene regulatory networks. Here, the methodology is adapted for use as a hybrid modelling tool to facilitate the reverse engineering of chemical reaction networks using time series concentration data from fed-batch reactor experiments. The principle of the approach is demonstrated with noisy simulated data from fed-batch reactor experiments using a hypothetical reaction network comprising 5 chemical species involved in 4 parallel reactions. A co-evolutionary algorithm is employed to evolve the structure and the parameter values of the S-system equations concurrently. The S-system equations are then interpreted in order to construct a network diagram that accurately reflects the underlying chemical reaction network.

Minimal Conditions for Protocell Stationary Growth

2015 ◽  
Vol 21 (2) ◽  
pp. 166-192 ◽  
Author(s):  
Erwan Bigan ◽  
Jean-Marc Steyaert ◽  
Stéphane Douady
Keyword(s):  
Chemical Reaction ◽  
Reaction Network ◽  
Chemical Reaction Networks ◽  
Chemical System ◽  
Reaction Networks ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Stationary Growth ◽  
Underlying Mechanisms ◽  
Self Replication

We show that self-replication of a chemical system encapsulated within a membrane growing from within is possible without any explicit feature such as autocatalysis or metabolic closure, and without the need for their emergence through complexity. We use a protocell model relying upon random conservative chemical reaction networks with arbitrary stoichiometry, and we investigate the protocell's capability for self-replication, for various numbers of reactions in the network. We elucidate the underlying mechanisms in terms of simple minimal conditions pertaining only to the topology of the embedded chemical reaction network. A necessary condition is that each moiety must be fed, and a sufficient condition is that each siphon is fed. Although these minimal conditions are purely topological, by further endowing conservative chemical reaction networks with thermodynamically consistent kinetics, we show that the growth rate tends to increase on increasing the Gibbs energy per unit molecular weight of the nutrient and on decreasing that of the membrane precursor.

scholarly journals A general technique for the detection of switch-like bistability in chemical reaction networks governed by mass action kinetics with conservation laws

2020 ◽  
Author(s):  
Brandon C Reyes ◽  
Irene Otero-Muras ◽  
Vladislav A Petyuk
Keyword(s):  
Conservation Laws ◽  
Signaling Pathways ◽  
Chemical Reaction ◽  
Reaction Network ◽  
Mass Action ◽  
Numerical Continuation ◽  
Reaction Networks ◽  
General Technique ◽  
Bistable Switch ◽  
Mass Action Kinetics

AbstractBackgroundTheoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws.ResultsIn this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves 1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, 2) minimization of the objective function to search for conditions resulting in a zero eigenvalue 3) computation of a confidence level that describes if the global minimum has been found and 4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability.ConclusionsWe have developed a variation of an optimization-based method for discovery of bistability, which is not limited to the structure of the chemical reaction network. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

scholarly journals Early warning signals in chemical reaction networks

2020 ◽  
Vol 56 (26) ◽  
pp. 3725-3728
Author(s):  
Oliver R. Maguire ◽  
Albert S. Y. Wong ◽  
Jan Harm Westerdiep ◽  
Wilhelm T. S. Huck
Keyword(s):  
Complex Systems ◽  
Chemical Reaction ◽  
Early Warning ◽  
Reaction Network ◽  
Chemical Reaction Networks ◽  
Chemical Reaction Network ◽  
Reaction Networks ◽  
Warning Signals ◽  
Early Warning Signals ◽  
Complex Chemical

Many natural and man-made complex systems display early warning signals when close to an abrupt shift in behaviour. Here we show that such early warning signals appear in a complex chemical reaction network.

scholarly journals An algorithm for building and integrating dynamic systems based on reaction networks

2021 ◽  
Vol 8 (1) ◽  
pp. 49
Author(s):  
Petar Chernev
Keyword(s):  
Chemical Reaction ◽  
Dynamic Systems ◽  
Network Theory ◽  
Dynamic Models ◽  
Reaction Network ◽  
Chemical Reaction Network ◽  
Reaction Networks ◽  
Complex Interactions ◽  
Model Complex ◽  
Chemical Reaction Network Theory

In the present work we give an overview and implementation of an algorithm for building and integrating dynamic systems from reaction networks. Reaction networks have their roots in chemical reaction network theory, but their nature is general enough that they can be applied in many fields to model complex interactions. Our aim is to provide a simple to use program that allows for quick prototyping of dynamic models based on a system of reactions. After introducing the concept of a reaction and a reaction network in a general way, not necessarily connected to chemistry, we outlay the algorithm for building its associated system of ODEs. Finally, we give a few example usages where we examine a range of growth-decay models in the context of reaction networks.

scholarly journals A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws

2022 ◽  
Vol 23 (1) ◽  
Author(s):  
Brandon C Reyes ◽  
Irene Otero-Muras ◽  
Vladislav A Petyuk
Keyword(s):  
Conservation Laws ◽  
Signaling Pathways ◽  
Chemical Reaction ◽  
Reaction Network ◽  
Chemical Reaction Networks ◽  
Mass Action ◽  
Numerical Continuation ◽  
Rate Equations ◽  
Reaction Networks ◽  
Bistable Switch

Abstract Background Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws. Results In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of the objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability. Conclusions We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

A Synthon Approach to Artificial Chemistry

2009 ◽  
Vol 15 (1) ◽  
pp. 89-103 ◽  
Author(s):  
Tom Lenaerts ◽  
Hugues Bersini
Keyword(s):  
Chemical Reaction ◽  
Reaction Network ◽  
Logical Structure ◽  
Chemical Reaction Networks ◽  
The Other ◽  
Reaction Networks ◽  
Complex Chemical ◽  
Topological Evolution ◽  
The One ◽  
Insight Into

A coevolutionary model is discussed that incorporates the logical structure of constitutional chemistry and its kinetics on the one hand and the topological evolution of the chemical reaction network on the other hand. The motivation for designing this model is twofold. First, experiments that are to provide insight into chemical problems should be expressed in a syntax that remains as close as possible to real chemistry. Second, the study of physical properties of the complex chemical reaction networks requires growing models that incorporate features realistic from a biochemical perspective. In this article the theory and algorithms underlying the coevolutionary model are explained, and two illustrative examples are provided. These examples show that one needs to be careful in making general claims concerning the structure of chemical reaction networks.

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