Analysis Of Reaction Networks Research Articles

Short relaxation times but long transient times in both simple and complex reaction networks.

When relaxation towards an equilibrium or steady state is exponential at large times, one usually considers that the associated relaxation time τ, i.e. the inverse of the decay rate, is the longest characteristic time in the system. However, that need not be true, other times such as the lifetime of an infinitesimal perturbation can be much longer. In the present work, we demonstrate that this paradoxical property can arise even in quite simple systems such as a linear chain of reactions obeying mass action (MA) kinetics. By mathematical analysis of simple reaction networks, we pin-point the reason why the standard relaxation time does not provide relevant information on the potentially long transient times of typical infinitesimal perturbations. Overall, we consider four characteristic times and study their behaviour in both simple linear chains and in more complex reaction networks taken from the publicly available database ‘Biomodels’. In all these systems, whether involving MA rates, Michaelis–Menten reversible kinetics, or phenomenological laws for reaction rates, we find that the characteristic times corresponding to lifetimes of tracers and of concentration perturbations can be significantly longer than τ.

A moment-convergence method for stochastic analysis of biochemical reaction networks.

Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome this drawback of the moment-closure methods. As such, we develop a new analysis method for stochastic chemical kinetics. This method provides an accurate approximation for the master probability equation (MPE). In particular, the connection between low-order convergent moments and rate constants can be more easily derived in terms of explicit and analytical forms, allowing insights that would be difficult to obtain through direct simulation or manipulation of the MPE. In addition, it provides an accurate and efficient way to compute steady-state or transient probability distribution, avoiding the algorithmic difficulty associated with stiffness of the MPE due to large differences in sizes of rate constants. Applications of the method to several systems reveal nontrivial stochastic mechanisms of gene expression dynamics, e.g., intrinsic fluctuations can induce transient bimodality and amplify transient signals, and slow switching between promoter states can increase fluctuations in spatially heterogeneous signals. The overall approach has broad applications in modeling, analysis, and computation of complex biochemical networks with intrinsic noise.

Improvement of ethylene cracking reaction network with network flow analysis algorithm

Abstract Reaction network model is central to ethylene cracking process simulation. Studying an ethylene cracking reaction (ECR) network, which involves hundreds of components and thousands of reactions, becomes a difficult task. To facilitate a rapid and comprehensive reaction network analysis and improve ECR network, this paper introduced a ranking algorithm called network flow analysis algorithm (NFAA) to a reaction network analysis procedure. NFAA analyses the reaction network with comprehensive information such as network topological structure, reaction mechanism, and process model data. Following NFAA, reactions and species are ranked based on their significances. According to the ranking of reactions, unimportant reactions (lower ranking) in ECR network are removed to reduce ECR network complexity and decrease computational scale without loss of prediction accuracy. On the other hand, rankings provide guidance on adjusting parameters of ECR network. The application of NFAA makes a progress in improvement of ECR reaction network in an industrial case.

A multi-time-scale analysis of chemical reaction networks: II. Stochastic systems.

We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the full chemical master equation for arbitrary systems, and show how to obtain a reduced equation that governs the evolution on the slow time scale. This is done by applying a state space decomposition to the full equation that leads to the reduced dynamics in terms of certain projections and the invariant distributions of the fast system. The rates or propensities of the reduced system are shown to be the rates of the slow reactions conditioned on the expectations of fast steps. We also show that the generator of the reduced system is a Markov generator, and we present an efficient stochastic simulation algorithm for the slow time scale dynamics. We illustrate the numerical accuracy of the approximation by simulating several examples. Graph-theoretic techniques are used throughout to describe the structure of the reaction network and the state-space transitions accessible under the dynamics.

Uncertainty quantification for quantum chemical models of complex reaction networks.

For the quantitative understanding of complex chemical reaction mechanisms, it is, in general, necessary to accurately determine the corresponding free energy surface and to solve the resulting continuous-time reaction rate equations for a continuous state space. For a general (complex) reaction network, it is computationally hard to fulfill these two requirements. However, it is possible to approximately address these challenges in a physically consistent way. On the one hand, it may be sufficient to consider approximate free energies if a reliable uncertainty measure can be provided. On the other hand, a highly resolved time evolution may not be necessary to still determine quantitative fluxes in a reaction network if one is interested in specific time scales. In this paper, we present discrete-time kinetic simulations in discrete state space taking free energy uncertainties into account. The method builds upon thermo-chemical data obtained from electronic structure calculations in a condensed-phase model. Our kinetic approach supports the analysis of general reaction networks spanning multiple time scales, which is here demonstrated for the example of the formose reaction. An important application of our approach is the detection of regions in a reaction network which require further investigation, given the uncertainties introduced by both approximate electronic structure methods and kinetic models. Such cases can then be studied in greater detail with more sophisticated first-principles calculations and kinetic simulations.

Efficiency of the Girsanov Transformation Approach for Parametric Sensitivity Analysis of Stochastic Chemical Kinetics

The most common Monte Carlo methods for sensitivity analysis of stochastic reaction networks are the finite difference (FD), Girsanov transformation (GT), and regularized pathwise derivative (RPD) methods. It has been numerically observed in the literature that the biased FD and RPD methods tend to have lower variance than the unbiased GT method and that centering the GT method (CGT) reduces its variance. We provide a theoretical justification for these observations in terms of system size asymptotic analysis under what is known as the classical scaling. Our analysis applies to GT, CGT, and FD and shows that the standard deviations of their estimators when normalized by the actual sensitivity scale as $\mathcal{O}(N^{1/2}), \mathcal{O}(1)$, and $\mathcal{O}(N^{-1/2})$, respectively, as system size $N \to \infty$. In the case of the FD methods, the $N \to \infty$ asymptotics are obtained keeping the finite difference perturbation $h$ fixed. Our numerical examples verify that our order estimates are sharp and that the variance of the RPD method scales similarly to the FD methods. We combine our large $N$ asymptotics with previously known small $h$ asymptotics to obtain the best choice of $h$ in terms of $N$ and estimate the number $N_s$ of simulations required to achieve a prescribed relative $\mathcal{L}_2$ error $\delta$. This shows that $N_s$ depends on $\delta$ and $N$ as $\delta^{-2 - \frac{\gamma_2}{\gamma_1}} N^{-1}, \delta^{-2}$, and $N \delta^{-2}$ for FD, CGT, and GT, respectively. Here $\gamma_1 >0, \gamma_2>0$ depend on the type of FD method used.

Reaction network analysis for thin film deposition processes

Reaction network analysis for thin film deposition processes

A network dynamics approach to chemical reaction networks

ABSTRACTA treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption, the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory, and which directly relates to the thermodynamics and port-Hamiltonian formulation of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This immediately leads to the characterisation of the set of equilibria and their stability. Furthermore, the assumption of complex balancedness is revisited from the point of view of Kirchhoff's matrix tree theorem. Both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics, and provide additional perspectives to the latter. Finally, using the classical idea of extending the graph of chemical complexes by a ‘zero’ complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action kinetics outflows is given, and a unified framework is provided for structure-preserving model reduction of this important class of open reaction networks.

On the rejection-based algorithm for simulation and analysis of large-scale reaction networks.

Stochastic simulation for in silico studies of large biochemical networks requires a great amount of computational time. We recently proposed a new exact simulation algorithm, called the rejection-based stochastic simulation algorithm (RSSA) [Thanh et al., J. Chem. Phys. 141(13), 134116 (2014)], to improve simulation performance by postponing and collapsing as much as possible the propensity updates. In this paper, we analyze the performance of this algorithm in detail, and improve it for simulating large-scale biochemical reaction networks. We also present a new algorithm, called simultaneous RSSA (SRSSA), which generates many independent trajectories simultaneously for the analysis of the biochemical behavior. SRSSA improves simulation performance by utilizing a single data structure across simulations to select reaction firings and forming trajectories. The memory requirement for building and storing the data structure is thus independent of the number of trajectories. The updating of the data structure when needed is performed collectively in a single operation across the simulations. The trajectories generated by SRSSA are exact and independent of each other by exploiting the rejection-based mechanism. We test our new improvement on real biological systems with a wide range of reaction networks to demonstrate its applicability and efficiency.

Evaluated Kinetics of the Reactions of H and CH3 with n-Alkanes: Experiments with n-Butane and a Combustion Model Reaction Network Analysis.

Presented is a combined experimental and modeling study of the kinetics of the reactions of H and CH3 with n-butane, a representative aliphatic fuel. Abstraction of H from n-alkane fuels creates alkyl radicals that rapidly decompose at high temperatures to alkenes and daughter radicals. In combustion and pyrolysis, the branching ratio for attack on primary and secondary hydrogens is a key determinant of the initial olefin and radical pool, and results propagate through the chemistry of ignition, combustion, and byproduct formation. Experiments to determine relative and absolute rate constants for attack of H and CH3 have been carried out in a shock tube between 859 and 1136 K for methyl radicals and 890 to 1146 K for H atoms. Pressures ranged from 140 to 410 kPa. Appropriate precursors are used to thermally generate H and CH3 in separate experiments under dilute and well-defined conditions. A mathematical design algorithm has been applied to select the optimum experimental conditions. In conjunction with postshock product analyses, a network analysis based on the detailed chemical kinetic combustion model JetSurf 2 has been applied. Polynomial chaos expansion techniques and Monte Carlo methods are used to analyze the data and assess uncertainties. The present results provide the first experimental measurements of the branching ratios for attack of H and CH3 on primary and secondary hydrogens at temperatures near 1000 K. Results from the literature are reviewed and combined with the present data to generate evaluated rate expressions for attack on n-butane covering 300 to 2000 K for H atoms and 400 to 2000 K for methyl radicals. Values for generic n-alkanes and related hydrocarbons are also recommended. The present experiments and network analysis further demonstrate that the C-H bond scission channels in butyl radicals are an order of magnitude less important than currently indicated by JetSurf 2. Updated rate expressions for butyl radical fragmentation reactions are provided.

A Metabolic Phenotype Based on Mitochondrial Ribosomal Protein Expression as a Predictor of Lymph Node Metastasis in Papillary Thyroid Carcinoma

Metabolic reprogramming has been regarded as an essential component of malignant transformation. However, the clinical significance of metabolic heterogeneity remains poorly characterized. The aim of this study was to characterize metabolic heterogeneity in thyroid cancers via the analysis of the expression of mitochondrial ribosomal proteins (MRPs) and genes involved in oxidative phosphorylation (OxPhos), and investigate potential prognostic correlations. Gene set enrichment analysis (GSEA) verified by reverse transcription polymerase chain reaction and gene network analysis was performed using public repository data. Cross-sectional observational study was conducted to classify papillary thyroid cancer (PTC) by the expression of MRP L44 (MRPL44) messenger RNA (mRNA), and to investigate the clinicopathological features. GSEA clearly showed that the expression of OxPhos and MRP gene sets was significantly lower in primary thyroid cancer than in matched normal thyroid tissue. However, 8 of 49 primary thyroid tumors (16.3%) in the public repository did not show a reduction in OxPhos mRNA expression. Remarkably, strong positive correlations between MRPL44 expression and those of OxPhos and MRPs such as reduced nicotinamide adenine dinucleotide dehydrogenase (ubiquinone) 1 α subcomplex, 5; succinate dehydrogenase complex, subunit D; cytochrome c, somatic; adenosine triphosphate synthase, H+ transporting, mitochondrial Fo complex, subunit C1 (subunit 9); and MRP S5 (MRPS5) (P < 0.0001) were clearly denoted, suggesting that MRPL44 is a representative marker of OxPhos and MRP expressions. In laboratory experiments, metabolic heterogeneity in oxygen consumption, extracellular acidification rates (ECARs), and amounts of OxPhos complexes were consistently observed in BCPAP, TPC1, HTH-7, and XTC.UC1 cell lines. In PTCs, metabolic phenotype according to OxPhos amount defined by expression of MRPL44 mRNA was significantly related to lymph node metastasis (LNM) (P < 0.001). Furthermore, multivariate analysis clearly indicated that expression of MRPL44 is associated with an increased risk of lateral neck LNM (odds ratio 9.267, 95% confidence interval 1.852-46.371, P = 0.007). MRPL44 expression may be a representative marker of metabolic phenotype according to OxPhos amount and a useful predictor of LNM.

ChemInform Abstract: Experimental and Theoretical Methods in Kinetic Studies of Heterogeneously Catalyzed Reactions

AbstractReview: 127 refs.

A metabolic phenotype based on mitochondrial ribosomal protein expression as a predictor of lymph node metastasis in papillary thyroid carcinoma.

Metabolic reprogramming has been regarded as an essential component of malignant transformation. However, the clinical significance of metabolic heterogeneity remains poorly characterized. The aim of this study was to characterize metabolic heterogeneity in thyroid cancers via the analysis of the expression of mitochondrial ribosomal proteins (MRPs) and genes involved in oxidative phosphorylation (OxPhos), and investigate potential prognostic correlations. Gene set enrichment analysis (GSEA) verified by reverse transcription polymerase chain reaction and gene network analysis was performed using public repository data. Cross-sectional observational study was conducted to classify papillary thyroid cancer (PTC) by the expression of MRP L44 (MRPL44) messenger RNA (mRNA), and to investigate the clinicopathological features. GSEA clearly showed that the expression of OxPhos and MRP gene sets was significantly lower in primary thyroid cancer than in matched normal thyroid tissue. However, 8 of 49 primary thyroid tumors (16.3%) in the public repository did not show a reduction in OxPhos mRNA expression. Remarkably, strong positive correlations between MRPL44 expression and those of OxPhos and MRPs such as reduced nicotinamide adenine dinucleotide dehydrogenase (ubiquinone) 1 α subcomplex, 5; succinate dehydrogenase complex, subunit D; cytochrome c, somatic; adenosine triphosphate synthase, H+ transporting, mitochondrial Fo complex, subunit C1 (subunit 9); and MRP S5 (MRPS5) (P < 0.0001) were clearly denoted, suggesting that MRPL44 is a representative marker of OxPhos and MRP expressions. In laboratory experiments, metabolic heterogeneity in oxygen consumption, extracellular acidification rates (ECARs), and amounts of OxPhos complexes were consistently observed in BCPAP, TPC1, HTH-7, and XTC.UC1 cell lines. In PTCs, metabolic phenotype according to OxPhos amount defined by expression of MRPL44 mRNA was significantly related to lymph node metastasis (LNM) (P < 0.001). Furthermore, multivariate analysis clearly indicated that expression of MRPL44 is associated with an increased risk of lateral neck LNM (odds ratio 9.267, 95% confidence interval 1.852-46.371, P = 0.007). MRPL44 expression may be a representative marker of metabolic phenotype according to OxPhos amount and a useful predictor of LNM.

An efficient and unbiased method for sensitivity analysis of stochastic reaction networks.

We consider the problem of estimating parameter sensitivity for Markovian models of reaction networks. Sensitivity values measure the responsiveness of an output with respect to the model parameters. They help in analysing the network, understanding its robustness properties and identifying the important reactions for a specific output. Sensitivity values are commonly estimated using methods that perform finite-difference computations along with Monte Carlo simulations of the reaction dynamics. These methods are computationally efficient and easy to implement, but they produce a biased estimate which can be unreliable for certain applications. Moreover, the size of the bias is generally unknown and hence the accuracy of these methods cannot be easily determined. There also exist unbiased schemes for sensitivity estimation but these schemes can be computationally infeasible, even for very simple networks. Our goal in this paper is to present a new method for sensitivity estimation, which combines the computational efficiency of finite-difference methods with the accuracy of unbiased schemes. Our method is easy to implement and it relies on an exact representation of parameter sensitivity that we recently proved elsewhere. Through examples, we demonstrate that the proposed method can outperform the existing methods, both biased and unbiased, in many situations.

Uncoupled analysis of stochastic reaction networks in fluctuating environments.

The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as, for instance, the fluctuations in ribosome copy numbers for a gene regulatory network. While several recent studies demonstrate the importance of accounting for such extrinsic components, the resulting models are typically hard to analyze. In this work we develop a general mathematical framework that allows to uncouple the network from its dynamic environment by incorporating only the environment's effect onto the network into a new model. More technically, we show how such fluctuating extrinsic components (e.g., chemical species) can be marginalized in order to obtain this decoupled model. We derive its corresponding process- and master equations and show how stochastic simulations can be performed. Using several case studies, we demonstrate the significance of the approach.

Experimental and theoretical methods in kinetic studies of heterogeneously catalyzed reactions.

This review aims to illustrate the potential of kinetic analysis in general and microkinetic modeling in particular for rational catalyst design. Both ab initio calculations and experiments providing intrinsic kinetic data allow us to assess the effects of catalytic properties and reaction conditions on the activity and selectivity of the targeted reactions. Three complementary approaches for kinetic analysis of complex reaction networks are illustrated, using select examples of acid zeolite-catalyzed reactions from the authors' recent work. Challenges for future research aimed at defining targets for synthesis strategies that enable us to tune zeolite properties are identified.

Stochastic analysis of biochemical reaction networks with absolute concentration robustness

It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' (ACR) on a wide class of biologically relevant, deterministically modelled mass-action systems. We show here that fundamentally different conclusions about the long-term behaviour of such systems are reached if the systems are instead modelled with stochastic dynamics and a discrete state space. Specifically, we characterize a large class of models that exhibit convergence to a positive robust equilibrium in the deterministic setting, whereas trajectories of the corresponding stochastic models are necessarily absorbed by a set of states that reside on the boundary of the state space, i.e. the system undergoes an extinction event. If the time to extinction is large relative to the relevant timescales of the system, the process will appear to settle down to a stationary distribution long before the inevitable extinction will occur. This quasi-stationary distribution is considered for two systems taken from the literature, and results consistent with ACR are recovered by showing that the quasi-stationary distribution of the robust species approaches a Poisson distribution.

Reaction network analysis and continuous production of isosorbide tert-butyl ethers

Isosorbide is considered a versatile biogenic platform compound for the production of chemicals. The functionalization of its two hydroxyl groups is challenging since they exhibit a different configuration and thus, different reactivity as well as sterical accessibility. We investigated the formation of the respective tert-butyl ethers by an addition reaction of isosorbide to isobutene heterogeneously catalyzed by acidic ion exchange resins. An efficient liquid phase process under ambient conditions in a batch reactor has been developed. The reaction network was unravelled by detailed investigation of the reaction kinetics. Additionally, the feasibility of continuous processing was successfully demonstrated on the lab-scale applying a continuously stirred-tank reactor.

Language-oriented rule-based reaction network generation and analysis: Algorithms of RING

The underlying algorithms of the language interface and post-generation analysis modules in RING, a network generation and analysis tool, are discussed. The front-end is a domain-specific reaction language developed with Silver, a meta-language based on attribute grammars. The language compiler translates user inputs written as a program into internal instructions, catches syntactic and semantic errors, and performs domain-specific optimization to speed up execution. In addition to generating reaction networks, RING allows post-processing analysis options to: (a) obtain reaction pathways and overall mechanisms from initial reactants to desired products using graph traversal algorithms, (b) group together isomers to reduce the size of the network through a novel molecule hashing technique, (c) calculate thermochemical quantities through semi-empirical methods such as group additivity, and (d) formulate and solve kinetic models of the entire or lumped complex network based on a rule-based kinetics specification scheme.

CoNtRol: an open source framework for the analysis of chemical reaction networks

We introduce CoNtRol, a web-based framework for analysis of chemical reaction networks (CRNs). It is designed to be both extensible and simple to use, complementing existing CRN-related tools. CoNtRol currently implements a number of necessary and/or sufficient structural tests for multiple equilibria, stable periodic orbits, convergence to equilibria and persistence, with the potential for incorporation of further tests. Reference implementation: reaction-networks.net/control/. Source code and binaries, released under the GPLv3: reaction-networks.net/control/download/. Documentation: reaction-networks.net/wiki/CoNtRol.