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Register a new userEnumeration and Online Library of Mass-Action Reaction Networks
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The aim of this work is to make available to the community a large collection of mass-action reaction networks of a given size for further research. The set is limited to what can be computed on a modern multi-core desktop in reasonable time (< 20 days). We have currently generated over 47 million unique reaction networks. All currently generated sets of networks are available and as new sets are completed they will also be made available. Also provided are programs for translating them into different formats, along with documentation and examples. Source code and binaries for all the programs are included. These can be downloaded from (http://www.sys-bio.org/networkenumeration). This library of networks will allow for thorough studies of the reaction network space. Additionally, these methods serve as an example for future work on enumerating other types of biological networks, such as genetic regulatory networks and mass-action networks that include regulation.
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In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the abilities to form bonds between different types of atoms and molecules create much of the properties we experience in our everyday life, especially in all biological activity. There are essentially two types of processes related to biochemical reaction networks, the interactions among molecules and interactions involving their conformational changes, so in a sense, their internal state. The first type of processes can be conveniently approximated by the so-called mass-action kinetics, but this is not necessarily so for the second kind where molecular states do not define any kind of density or concentration. In this paper we demonstrate the necessity to study reaction networks in a stochastic formulation for which we can construct a coherent approximation in terms of specific space-time scales and the number of particles. The continuum limit procedure naturally creates equations of Fokker-Planck type where the evolution of the concentration occurs on a slower time scale when compared to the evolution of the conformational changes, for example triggered by binding or unbinding events with other (typically smaller) molecules. We apply the asymptotic theory to derive the effective, i.e. macroscopic dynamics of the biochemical reaction system. The theory can also be applied to other processes where entities can be described by finitely many internal states, with changes of states occuring by arrival of other entities described by a birth-death process.
Understanding the system level adaptive changes taking place in an organism in response to variations in the environment is a key issue of contemporary biology. Current modeling approaches such as the constraint-based flux balance analyses (FBA) have proved highly successful in analyzing the capabilities of cellular metabolism, including its capacity to predict deletion phenotypes, the ability to calculate the relative flux values of metabolic reactions and the properties of alternate optimal growth states. Here, we use FBA to thoroughly assess the activity of the Escherichia coli, Helicobacter pylori, and Saccharomyces cerevisiae metabolism in 30,000 diverse simulated environments. We identify a set of metabolic reactions forming a connected metabolic core that carry non-zero fluxes under all growth conditions, and whose flux variations are highly correlated. Furthermore, we find that the enzymes catalyzing the core reactions display a considerably higher fraction of phenotypic essentiality and evolutionary conservation than those catalyzing non-core reactions. Cellular metabolism is characterized by a large number of species-specific conditionally-active reactions organized around an evolutionary conserved always active metabolic core. Finally, we find that most current antibiotics interfering with the bacterial metabolism target the core enzymes, indicating that our findings may have important implications for antimicrobial drug target discovery.
The Bond Graph approach and the Chemical Reaction Network approach to modelling biomolecular systems developed independently. This paper brings together the two approaches by providing a bond graph interpretation of the chemical reaction network concept of complexes. Both closed and open systems are discussed. The method is illustrated using a simple enzyme-catalysed reaction and a trans-membrane transporter.
Autocatalysis underlies the ability of chemical and biochemical systems to replicate. Recently, Blokhuis et al. gave a stoechiometric definition of autocatalysis for reaction networks, stating the existence of a combination of reactions such that the balance for all autocatalytic species is strictly positive, and investigated minimal autocatalytic networks, called {em autocatalytic cores}. By contrast, spontaneous autocatalysis -- namely, exponential amplification of all species internal to a reaction network, starting from a diluted regime, i.e. low concentrations -- is a dynamical property. We introduce here a topological condition (Top) for autocatalysis, namely: restricting the reaction network description to highly diluted species, we assume existence of a strongly connected component possessing at least one reaction with multiple products (including multiple copies of a single species). We find this condition to be necessary and sufficient for stoechiometric autocatalysis. When degradation reactions have small enough rates, the topological condition further ensures dynamical autocatalysis, characterized by a strictly positive Lyapunov exponent giving the instantaneous exponential growth rate of the system. The proof is generally based on the study of auxiliary Markov chains. We provide as examples general autocatalytic cores of Type I and Type III in the typology of Blokhuis et al. In a companion article, Lyapunov exponents and the behavior in the growth regime are studied quantitatively beyond the present diluted regime .
Deterministic reaction networks (RNs) are tools to model diverse biological phenomena characterized by particle systems, when there are abundant number of particles. Examples include but are not limited to biochemistry, molecular biology, genetics, epidemiology, and social sciences. In this chapter we propose a new type of decomposition of RNs, called fiber decomposition. Using this decomposition, we establish lifting of mass-action RNs preserving stationary properties, including multistationarity and absolute concentration robustness. Such lifting scheme is simple and explicit which imposes little restriction on the reaction networks. We provide examples to illustrate how this lifting can be used to construct RNs preserving certain dynamical properties.
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