Models Of Reaction Networks Research Articles

A reactor network model for predicting NOx emissions in an industrial natural gas burner

A chemical reactor network (CRN) is developed and applied to the modeling of a natural gas burner. The CRN development is based on experimental and CFD simulation results of the BERL 300 kW test. The CRN element arrangement, reactor volumes, and flow splits are adjusted based on the best agreement with characteristic temperatures of the reactive flow, aiming to reproduce the experimental NOx emissions data. A sensitivity analysis and a parametric study of the CRN are carried out to evaluate its sensitivity to the flow splits adjustments and its ability to predict emission with air preheat and turndown operation, as well as the influence of the reaction mechanism employed. The best agreement was obtained in the air preheat simulations using Konnov 0.4 mechanism, while the GRI-Mech 3.0 is accurate only within 110 K preheating. The turndown operation results are relatively accurate for turndown ratio between 1.0 and 1.3.

Model‐based identifiable parameter determination applied to a simultaneous saccharification and fermentation process model for bio‐ethanol production

In this work, a methodology for the model-based identifiable parameter determination (MBIPD) is presented. This systematic approach is proposed to be used for structure and parameter identification of nonlinear models of biological reaction networks. Usually, this kind of problems are over-parameterized with large correlations between parameters. Hence, the related inverse problems for parameter determination and analysis are mathematically ill-posed and numerically difficult to solve. The proposed MBIPD methodology comprises several tasks: (i) model selection, (ii) tracking of an adequate initial guess, and (iii) an iterative parameter estimation step which includes an identifiable parameter subset selection (SsS) algorithm and accuracy analysis of the estimated parameters. The SsS algorithm is based on the analysis of the sensitivity matrix by rank revealing factorization methods. Using this, a reduction of the parameter search space to a reasonable subset, which can be reliably and efficiently estimated from available measurements, is achieved. The simultaneous saccharification and fermentation (SSF) process for bio-ethanol production from cellulosic material is used as case study for testing the methodology. The successful application of MBIPD to the SSF process demonstrates a relatively large reduction in the identified parameter space. It is shown by a cross-validation that using the identified parameters (even though the reduction of the search space), the model is still able to predict the experimental data properly. Moreover, it is shown that the model is easily and efficiently adapted to new process conditions by solving reduced and well conditioned problems.

Dynamical properties of Discrete Reaction Networks

Reaction networks are commonly used to model the dynamics of populations subject to transformations that follow an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete Reaction Networks (DRNs). DRNs can be seen as modeling the underlying discrete nondeterministic transitions of stochastic models of reaction networks. In that sense, a proof of non-reachability in a given DRN has immediate implications for any concrete stochastic model based on that DRN, independent of the choice of kinetic laws and constants. Moreover, if we assume that stochastic kinetic rates are given by the mass-action law (or any other kinetic law that gives non-vanishing probability to each reaction if the required number of interacting substrates is present), then reachability properties are equivalent in the two settings. The analysis of two types of global dynamical properties of DRNs is addressed: irreducibility, i.e., the ability to reach any discrete state from any other state; and recurrence, i.e., the ability to return to any initial state. Our results consider both the verification of such properties when species are present in a large copy number, and in the general case. The necessary and sufficient conditions obtained involve algebraic conditions on the network reactions which in most cases can be verified using linear programming. Finally, the relationship of DRN irreducibility and recurrence with dynamical properties of stochastic and continuous models of reaction networks is discussed.

Identification of alterations in the Jacobian of biochemical reaction networks from steady state covariance data at two conditions

Model building of biochemical reaction networks typically involves experiments in which changes in the behavior due to natural or experimental perturbations are observed. Computational models of reaction networks are also used in a systems biology approach to study how transitions from a healthy to a diseased state result from changes in genetic or environmental conditions. In this paper we consider the nonlinear inverse problem of inferring information about the Jacobian of a Langevin type network model from covariance data of steady state concentrations associated to two different experimental conditions. Under idealized assumptions on the Langevin fluctuation matrices we prove that relative alterations in the network Jacobian can be uniquely identified when comparing the two data sets. Based on this result and the premise that alteration is locally confined to separable parts due to network modularity we suggest a computational approach using hybrid stochastic-deterministic optimization for the detection of perturbations in the network Jacobian using the sparsity promoting effect of [Formula: see text]-penalization. Our approach is illustrated by means of published metabolomic and signaling reaction networks.

CRN Application to Predict the NOx Emissions for Industrial Combustion Chamber

The development of chemical reactor network (CRN) models to predict the NOx emissions is very important for the modern combustion system design. In this study, the new chemical reactor network models are constructed based on the computational fluid dynamics (CFD) to simulate the burning process of the industrial combustor. The boundary and the operating conditions used for these CRN models reflect the typical operating conditions of the industrial combustor. The global mechanism has been developed by GRI 3.0 in the UW chemical reactor code. For the reliability of the predictive models, the models were analyzed and compared to the experimental industrial combustor research. Finally, the CRN models have shown to be efficient estimating accurately NOx emissions with a very short response time.

Modeling of an Opposed Multiburner Gasifier with a Reduced-Order Model

A reduced-order model (ROM) is considered a promising solution for engineering simulation of a gasifier. In this study, a ROM of a commercial-scale opposed multiburner gasifier is developed based on a reactor network model (RNM). The RNM blocking for this gasifier is established and validated based on analysis of the gasifier flow field. The particle flow in the gasifier is characterized by the particle residence time in each reactor of the RNM. The random pore model and the “effective factor” method are employed to model the char gasification rate under high pressure and temperature. The interphase heat transfer and heat loss through the refractory wall are calculated. In model validation, the simulation results show well agreement with the industrial data. The model provides distributions of the gas temperature and compositions in the gasifier. Effects of the particle size on the particle temperature and carbon conversion are discussed quantitatively. It is observed that fine particles can be completely...

Differential algebra for control systems design: Constructive computation of canonical forms

Many systems can be represented using polynomial differential equations, particularly in process control, biotechnology, and systems biology [1], [2]. For example, models of chemical and biochemical reaction networks derived using the law of mass action have the form ẋ = Sv(k,x), (1) where x is a vector of concentrations, S is the stoichiometric matrix, and v is a vector of rate expressions formed by multivariate polynomials with real coefficients k . Furthermore, a model containing nonpolynomial nonlinearities can be approximated by such polynomial models as explained in "Model Approximation". The primary aims of differential algebra (DALG) are to study, compute, and structurally describe the solution of a system of polynomial differential equations,f (x,ẋ, ...,x <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(k)</sup> ) =0, (2) where f is a polynomial [3]-[6]. Although, in many instances, it may be impossible to symbolically compute the solutions, or these solutions may be difficult to handle due to their size, it is still useful to be able to study and structurally describe the solutions. Often, understanding properties of the solution space and consequently of the equations is all that is required for analysis and control design.

Synthesis of N,N,N′,N′-Tetraoctyl-3-oxapentane-1,5-diamide (TODGA) and Its Steam Thermolysis-Nitrolysis as a Nuclear Waste Solvent Minimization Method

The amide based nuclear extractant, N,N,N′,N′-tetraoctyl-3-oxapentane-1,5-diamide (TODGA), was synthesized by an alternate route. A noncatalytic steam thermolysis and nitrolysis of TODGA was investigated in a SS 316 flow reactor as a nuclear waste solvent minimization method. All the reaction products of steam thermolysis and nitrolysis of TODGA were identified by using gas chromatography-thermal conductivity-flame ionization-mass spectroscopic detection techniques to get the complete mass balance. In the pyrolysis products, C1–C4 hydrocarbon gases, NOx, alkyl amines, and unconverted TODGA were characterized and quantified. The experimental data for the steam pyrolysis of TODGA was obtained in a temperature range of 550–1100 °C at overall atmospheric pressure. A continuous steam pyrolysis of TODGA in a SS 316 flow reactor over a temperature range of 850 to 1000 °C was found to be an irreversible, pseudo-first-order reaction with approximate activation energy of 123 kJ/mol. A comprehensive reaction network model was proposed to include the reaction mechanism of steam thermolysis of TODGA. The present experimental data and product’s statistics of the steam nitrolysis of TODGA estimates that the possibility of the explosive runaway reactions during the nitration of TODGA at elevated temperatures is rare.

Recent Progress in Visualizing Constraint-Based Flux-Balance Models in Cytoscape

The last several years have seen an explosion in the quality and quantity of genome-scale data. From metabolism to transcription and translation, the “-omics” revolution has given systems biologists the ability to develop increasingly comprehensive models of biochemical reaction networks. But as the size and scope of systems-level models has increased, it has become more difficult to understand and communicate their behavior in an intuitive manner. We believe that a robust set of tools designed to aid in the visualization of systems-level models can offer a way forward in this regard. We will report on recent advances in the development of several plugins for the popular Cytoscape network visualization software platform. These plugins are designed to represent large constraint-based models in an immediately understandable way. Several plugins are under development, including functionalities for importing and updating hand-curated maps from the BiGG database, and mapping flux distributions throughout reaction networks, but the centerpiece will be a unique algorithmic approach to network lay-out that will create highly-readable maps with little or no hand-curation necessary.

Analyzing the Evolution of Biochemical Reaction System with a Complex Network Based Approach

Complex network theory has recently been used in System biology, but so far the resulting networks have only been analyzed statically. In this work, the biochemical reaction network (BRN) model is proposed based on the complex network theory and the dynamics of the network is analyzed on the molecular-scale. Given the initial ate and the evolution rules of the biochemical network, we demonstrated how the biochemical reaction network achieving homeostasis. The evolution of the biochemical reaction network is studied in perspective of average degree and edges. Comparing with the network features of random graphs, the network features from the proposed BRN model can reveal more biological sense.

Hydrocracking of n-hexadecane on noble metal/silica–alumina catalysts

Bifunctional catalysts consisting of platinum or palladium on amorphous silica–alumina were prepared and tested in the hydrocracking of n-hexadecane (n-C16H34). Product selectivities toward mono-branched and multi-branched feed isomers and cracking products have been determined in a wide range of conversions, varying liquid hourly space velocity at constant operating parameters (pressure=30bar; temperature=310°C; H2/n-C16H34 feed molar ratio=10).A simple kinetic study is presented, in which the reactions are approximated by a network of pseudo first order irreversible reaction steps. The reaction network model was fitted to the experimental data, and kinetic constants for the different reaction steps were obtained. It could be concluded that mono-branched feed isomers are primary products in the hydrocracking/hydroisomerization reaction network; multi-branched isomers are formed mainly from mono-branched as a secondary product. On the platinum catalyst cracking products were formed as primary products, and it proved to be slightly more active than the palladium based one, at the same metallic molar loading. It could be shown that the platinum catalyst yields cracking products both via a bifunctional metal/acid mechanism and by monofunctional (metal only) hydrogenolysis. This second mechanism accounted for the higher activity of the platinum catalyst.

Stochastic model reduction using a modified Hill-type kinetic rate law

In the present work, we address a major challenge facing the modeling of biochemical reaction networks: when using stochastic simulations, the computational load and number of unknown parameters may dramatically increase with system size and complexity. A proposed solution to this challenge is the reduction of models by utilizing nonlinear reaction rate laws in place of a complex multi-reaction mechanism. This type of model reduction in stochastic systems often fails when applied outside of the context in which it was initially conceived. We hypothesize that the use of nonlinear rate laws fails because a single reaction is inherently Poisson distributed and cannot match higher order statistics. In this study we explore the use of Hill-type rate laws as an approximation for gene regulation, specifically transcription repression. We matched output data for several simple gene networks to determine Hill-type parameters. We show that the models exhibit inaccuracies when placed into a simple feedback repression model. By adding an additional abstract reaction to the models we account for second-order statistics. This split Hill rate law matches higher order statistics and demonstrates that the new model is able to more accurately describe the mean protein output. Finally, the modified Hill model is shown to be modular and models retain accuracy when placed into a larger multi-gene network. The work as presented may be used in gene regulatory or cell-signaling networks, where multiple binding events can be captured by Hill kinetics. The added benefit of the proposed split-Hill kinetics is the improved accuracy in modeling stochastic effects. We demonstrate these benefits with a few specific reaction network examples.

Model-based design of synthetic, biological systems

Synthetic biology brings engineering tools and perspectives to the design of living systems. In contrast to classical cell engineering approaches, synthetic biology enables cellular networks to be understood as a combination of modular elements in much the same way as unit operations combine to describe a chemical plant. Consequently, models for the behavior of these designed systems are inspired by frameworks developed for traditional chemical engineering design. There are direct analogies between cellular metabolism and reaction networks in a chemical process. As examples, thermodynamic and kinetic models of chemical reaction networks have been used to simulate fluxes within living systems and predict the performance of synthetic parts. Concepts from process control have been brought to bear on the design of transcriptional and translational regulatory networks. Such engineering frameworks have greatly aided the design and understanding of living systems and have enabled the design of cells exhibiting complex dynamic behavior and high productivity of desirable compounds. This review summarizes efforts to quantitatively model cellular behavior (both endogenous and synthetic), especially as related to the design of living systems.

Estimation and Discrimination of Stochastic Biochemical Circuits from Time-Lapse Microscopy Data

The ability of systems and synthetic biologists to observe the dynamics of cellular behavior is hampered by the limitations of the sensors, such as fluorescent proteins, available for use in time-lapse microscopy. In this paper, we propose a generalized solution to the problem of estimating the state of a stochastic chemical reaction network from limited sensor information generated by microscopy. We mathematically derive an observer structure for cells growing under time-lapse microscopy and incorporates the effects of cell division in order to estimate the dynamically-changing state of each cell in the colony. Furthermore, the observer can be used to discrimate between models by treating model indices as states whose values do not change with time. We derive necessary and sufficient conditions that specify when stochastic chemical reaction network models, interpreted as continuous-time Markov chains, can be distinguished from each other under both continual and periodic observation. We validate the performance of the observer on the Thattai-van Oudenaarden model of transcription and translation. The observer structure is most effective when the system model is well-parameterized, suggesting potential applications in synthetic biology where standardized biological parts are available. However, further research is necessary to develop computationally tractable approximations to the exact generalized solution presented here.

SPSens: a software package for stochastic parameter sensitivity analysis of biochemical reaction networks

SPSens is a software package for the efficient computation of stochastic parameter sensitivities of biochemical reaction networks. Parameter sensitivity analysis is a valuable tool that can be used to study robustness properties, for drug targeting, and many other purposes. However its application to stochastic models has been limited when Monte Carlo methods are required due to extremely high computational costs. SPSens provides efficient, state of the art sensitivity analysis algorithms in a single software package so that sensitivity analysis can be easily performed on stochastic models of biochemical reaction networks. SPSens implements the algorithms in C and estimates sensitivities with respect to both infinitesimal and finite perturbations to system parameters, in many cases reducing variance by orders of magnitude compared to basic methods. Included among the features of SPSens are serial and parallel command line versions, an interface with Matlab, and several example problems. SPSens is distributed freely under GPL version 3 and can be downloaded from http://sourceforge.net/projects/spsens/. The software can be run on Linux, Mac OS X and Windows platforms.

Easy parameter identifiability analysis with COPASI

Background and scopeDifferential equation systems modeling biochemical reaction networks can only give quantitative predictions, when they are in accordance with experimental data. However, even if a model can well recapitulate given data, it is often the case that some of its kinetic parameters can be arbitrarily chosen without significantly affecting the simulation results. This indicates a lack of appropriate data to determine those parameters. In this case, the parameter is called to be practically non-identifiable. Well-identified parameters are paramount for reliable quantitative predictions and, therefore, identifiability analysis is an important topic in modeling of biochemical reaction networks. Here, we describe a hidden feature of the free modeling software COPASI, which can be exploited to easily and quickly conduct a parameter identifiability analysis of differential equation systems by calculating likelihood profiles. The proposed combination of an established method for parameter identifiability analysis with the user-friendly features of COPASI offers an easy and rapid access to parameter identifiability analysis even for non-experts. AvailabilityCOPASI is freely available for academic use at http://www.copasi.org.

A numerical characteristic method for probability generating functions on stochastic first-order reaction networks

We propose an efficient and accurate numerical scheme for solving probability generating functions arising in stochastic models of general first-order reaction networks by using the characteristic curves. A partial differential equation derived by a probability generating function is the transport equation with variable coefficients. We apply the idea of characteristics for the estimation of statistical measures, consisting of the mean, variance, and marginal probability. Estimation accuracy is obtained by the Newton formulas for the finite difference and time accuracy is obtained by applying the fourth order Runge–Kutta scheme for the characteristic curve and the Simpson method for the integration on the curve. We apply our proposed method to motivating biological examples and show the accuracy by comparing simulation results from the characteristic method with those from the stochastic simulation algorithm.

Reaction Kinetics of the Lignin Conversion in Supercritical Water

The effect of temperature (390–450 °C) and residence time (0.5–10 s) at a pressure of 25 MPa was investigated for lignin conversion in supercritical water (SCW) using a continuous flow apparatus designed to rapidly heat the system to the desired reaction temperature. Conversion of lignin in SCW occurs rapidly, and complete depolymerization can be achieved within a 5 s residence time. A high degree of depolymerization is achieved from rapid heating to supercritical temperatures. In addition, supercritical conditions result in a high yield of solid that does not significantly change with an increase in temperature or residence time. To test the suggested hypothesis that the formation of low molecular weight fragments and cross-linking of these fragments forms higher molecular weight fragments, the yield of char, gaseous products, phenolic compounds (phenol, guaiacol, catechol, o-cresol, m-cresol, and catechol) and aromatic hydrocarbons (benzene, toluene, and naphthalene) were determined. The formation of phenolic compounds at short residence time indicates that ether bonds in lignin are easily degraded under supercritical conditions. A reaction network model was proposed, and the subsequent kinetic parameters for the conversion pathways were determined by assuming a first-order reaction. It is observed that the rate constant of overall lignin conversion obeys Arrhenius behavior. The individual rate constants of each reaction in the network are evaluated to determine conformity to Arrhenius behavior.

Structural and practical identifiability of approximate metabolic network models

Parameter estimation from experimental data is a crucial problem in quantitative modeling of biochemical reaction networks. An especially important issue, raised by the complexity of the models and the challenging nature of the experimental data, is parameter identifiability. Despite several approaches proposed in the systems biology literature, no agreement exists on the analysis of structural and practical identifiability, and the relations among the two. In this paper we propose a mathematical framework for the analysis of identifiability of metabolic network models, establish basic results and methods for the structural and practical identifiability analysis of the class of so-called linlog models, and discuss the results on the basis of an artificial example.

Robustness-based Model Validation of an Apoptosis Signalling Network Model

Models of intracellular biochemical reaction networks are difficult to parameterise due to the low number of quantitative time series experimental values. Therefore, model validation or invalidation plays an important role, as it allows to check qualitatively whether a model structure is suited or not to reproduce qualitatively the experimental findings.This paper analyses the robustness of an experimentally validated polynomial differential equation model of TNF-induced pro-and anti-apoptotic signalling. The bistability of the median model is shown robust to large single parameter variations. Only two parameters (XIAP and Procaspase-3 production rates) are shown to be fragile, in particular when changed simultaneously. Therefore, the model seems valid from the point of view of robustness analysis of the bistability.Many biological experiments quantify average concentrations or the percentage of viable cells, while other methods such as microscopy-based experiments observe single cells. The integration of single cell and cell population behaviour of TNF-induced pro- and anti-apoptotic signalling has been achieved via a cell ensemble model, whose robustness is also analysed here. We show that within the cell population there are cells with not only quantitative differences, but also qualitative ones. In particular, all cells are not bistable. The degree of robustness applicable for the median cell is expanded to combine mono- and bistable models. This measure, applied solely to the two-dimensional subspace of fragile parameters, is shown to correlate well with the time of death. While robustness of bistability can serve for model validation of the median cell model, it cannot for the model of the cell population.