Models Of Reaction Networks Research Articles

A query-response causal analysis of reaction events in biochemical reaction networks

The stochastic kinetics of biochemical reaction networks is described by a chemical master equation (CME) and the underlying laws of mass action. Assuming network-free simulations of the rule-based models of biochemical reaction networks (BRNs), this paper departs from the usual analysis of network dynamics as the time-dependent distributions of chemical species counts, and instead considers statistically evaluating the sequences of reaction events generated from the stochastic simulations. The reaction event-time series can be used for reaction clustering, identifying rare events, and recognizing the periods of increased or steady-state activity. However, the main aim of this paper is to device an effective method for identifying causally and anti-causally related sub-sequences of reaction events using their empirical probabilities. This allows discovering some of the causal dynamics of BRNs as well as uncovering their short-term deterministic behaviors. In particular, it is proposed that the reaction sub-sequences that are conditionally nearly certain or nearly uncertain can be considered as being causally related. Moreover, since the time-ordering of reaction events is locally irrelevant, the reaction sub-sequences can be transformed into the reaction sets or multi-sets. The distance metrics can be then used to define the equivalences among the reaction events. The proposed method for identifying the causally related reaction sub-sequences has been implemented as a computationally efficient query-response mechanism. The method was evaluated for five models of genetic networks in seven defined numerical experiments. The models were simulated in BioNetGen using the open-source network-free simulator NFsim. This simulator had to be modified first to allow recording the traces of reaction events, and it is available in the Github repository, ploskot/nfsim_1.20. The generated event time-series were analyzed with Python and Matlab scripts. The whole process of data generation, analysis and visualization has been nearly fully automated using shell scripts. This demonstrates the opportunities for substantially increasing the research productivity by creating automated data generation and processing pipelines.

Kinetic modeling on oxidation of arabinose to arabinonic acid in base-free medium over synergistic PtCu/TiO2 catalyst

Arabinonic acid (AA) is an essential building block for the food and pharmaceutical industries. However, green and atomically efficient synthesis of AA remains a grand challenge, as most previous reports have been focused on the alkaline-promoted oxidation of arabinose. In this work, we firstly reported lumped kinetic modeling of the oxidation of arabinose to AA in base-free medium, with detailed reaction networks involved in the C-H and C-C cleavage reactions. It is found that the bimetallic PtCu/TiO2 catalyst displays strong synergism due to electronic coupling at metal-support interface, leading to an almost two-fold enhancement in catalytic activity in comparison with monometallic Pt/TiO2 catalyst. According to detailed analysis on reaction network and kinetic modeling, the presence of Cu mainly contributes to formulating additional active sites for the oxidation and C-C cleavage reactions. The quantitative assessment for conversion of arabinose could provide useful information for modeling and process development for various other important sugars.

Research on the Numerical Method of Pollutant Emission during Gas Turbine Start-up

It was of great research value and significance to predict the pollutant emission from the gas turbine start-up process by numerical method, which could improve the operation and regulation of gas turbines. In the paper, the computational fluid dynamics(CFD)-chemical reaction network (CRN) method was used to study the pollutant emission of gas turbines. According to the control process of the start-up control module, the start-up process had been divided into 12 states, and the CFD numerical analysis was carried out. Based on the data of Damkohler number (Da), temperature and velocity obtained by CFD, the chemical reaction network model of each state point was established. The research showed that the design parameter value of the state point was the basis of compiling the calculation process and source code; The basic data and partition basis for the chemical reaction network could been provided by the results of CFD analysis, which was an important guarantee for accurate prediction of NOx; The method of CFD-CRN could accurately predict NOx emission of gas engine during start-up, and provided reasonable and reliable research means and mathematical methods.

Prediction of NOx emission from two-stage combustion of NH3–H2 mixtures under various conditions using artificial neural networks

This study aims to predict NOx emission from the combustion of ammonia (NH3) and hydrogen (H2) mixtures using Artificial Neural Network (ANN) models. Chemical Reactor Network (CRN) models were utilized to calculate the NOx emission during the Rich-Quench-Lean (RQL) two-stage combustion of NH3–H2 mixtures under various conditions, such as fuel pressures, inlet temperatures, primary air humidification fractions, total equivalent ratios and primary equivalent ratios. The simulation results served as a data set for training and validation of three different ANN models: Backpropagation (BP), Radial Basis Function (RBF), and Generalized Regression Neural Network (GRNN). The results show that all three ANN models can effectively replace the CRN model in accurately predicting NOx concentrations. In particular, the BP model, optimized with 37 hidden neurons, showcased superior performance, achieving a correlation coefficient (R) value of 0.99826 with the simulated results. It had the lowest Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) values of 61.3 and 96.1, respectively. In addition, it achieved the highest coefficient of determination (R2) and Model Efficiency (ME) values of 0.9950 and 0.9908 respectively, surpassing the RBF and GRNN models. These results suggest that the BP model has significant potential as an alternative to the CRN model for predicting NOx emissions from two-stage combustion of NH3–H2 mixtures, demonstrating both accuracy and efficiency.

Catalyst: Fast and flexible modeling of reaction networks.

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst's broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.

Microbial community ecosystem network model for chemical energy transport

Microorganisms thriving in low-energy ecosystems have evolved diverse strategies to sustain life, including individual-level energy conservation, optimizing energy utilization through interspecies competition, and mutually beneficial interspecies syntrophy. This study introduces a novel community-level strategy to enhance energy efficiency. We employed an oxidation-reduction (redox) reaction network model to capture the intricate metabolic interactions within microbial communities. Our findings highlight the importance of microbial functional diversity in facilitating metabolic handoffs, leading to an improved energy utilization efficiency. Moreover, the mutualistic division of labor and the resulting complexity of redox pathways actively facilitate material cycling, thereby enhancing energy exploitation. These findings provide new insights into the potential of self-organized ecological interactions to develop efficient energy utilization strategies, with significant implications for the functioning and evolution of microbial ecosystems.

A simplified mechanism of hydrogen addition to methane combustion for the pollutant emission characteristics of a gas-fired boiler

The reaction mechanism of hydrogen-enriched methane (HEM) combustion is significant in the combustion process. In this study, four widely used reaction mechanisms for methane combustion are simplified to investigate the pollutant emission characteristics of a gas-fired boiler used for HEM combustion. The laminar burn velocity (LBV) and ignition delay time (IDT) of the four detailed and four simplified mechanisms are compared, and the simplified San Diego mechanism is identified as the optimal mechanism using relative error and population standard deviation analysis. The temperatures and key components of the simplified San Diego mechanism are also compared with those of the detailed San Diego mechanism under various XH2. Based on the simplified San Diego mechanism, a chemical reactor network model for gas-fired boilers is further established to investigate the pollutant emissions of HEM combustion, in which the hydrogen doping ratio XH2 ranged from 0 to 80% and the inlet air and fuel temperature Tin ranged from 300 K to 600 K. Results showed that at Tin = 300 K with XH2 ranging from 0 to 80%, the mole fraction of NO increase by 1.94 times because of the increase in peak flame temperature; moreover, the mole fractions of N2O, CO, and CO2 decrease by approximately 25%, 50%, and 52%, respectively. With XH2 ranging from 0 to 40% and Tin ≥ 500 K, the mole fraction of NO decreases because the reduction reaction of NO + H = N + OH is promoted, whereas when XH2 is further increased to 80%, the increased H promotes the increase in NO again. CO emissions decreased as XH2 increased from 0 to 80%, whereas they increased by approximately 1.3 times as Tin increased from 300 K to 600 K because of the CO2 decomposition. N2O emissions decreased by more than 25% as XH2 increased from 0 to 80%. Additionally, CO2 emissions decrease by 52% with an increase in XH2 and by only 5% with an increase in Tin, indicating that XH2 has a larger impact on CO2 emissions. The proposed optimal HEM combustion mechanism is conducive to improving the efficiency of numerical calculations.

Comment on "Validity of path thermodynamic description of reactive systems: Microscopic simulations".

The assertions made in a recent paper [Phys. Rev. E 107, 014106 (2023)10.1103/PhysRevE.107.014106] regarding the validity of path thermodynamics are ill founded and contradict well-known results. Following up on a previous Comment, I show that, for both models of chemical reaction networks considered in the aforementioned paper, path thermodynamics yields values of the entropy production rates fully consistent with those expected from standard chemical thermodynamics in the large-system limit.

Model-to-model Bayesian calibration of a Chemical Reactor Network for pollutant emission predictions of an ammonia-fuelled multistage combustor

Low-fidelity, cost-effective, physics-based models are useful for assessing the environmental performance of novel combustion systems, especially those utilizing alternative fuels, like hydrogen and ammonia. However, these models require calibration and quantification of their limitations to be reliable predictive tools. This paper presents a framework for calibrating a simplified Chemical Reactor Network model using higher-fidelity Computational Fluid Dynamics data from a micro-gas-turbine-like combustor fuelled with pure ammonia. A Bayesian inference strategy that explicitly accounts for model error is used to calibrate the most relevant CRN parameters based on NO emissions data from CFD simulations and to estimate the model's structural uncertainty. The calibrated CRN model accurately predicts NO emissions within the design space and can extrapolate reasonably well to conditions outside the calibration range. By utilizing this framework, low-fidelity models can be employed to explore various operating conditions during the preliminary design of innovative combustion systems.

Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species' Concentrations.

The current manuscript addresses the problem of parameter estimation for kinetic models of chemical reaction networks from observed time series partial experimental data of species concentrations. It is demonstrated how the Kron reduction method of kinetic models, in conjunction with the (weighted) least squares optimization technique, can be used as a tool to solve the above-mentioned ill-posed parameter estimation problem. First, a new trajectory-independent measure is introduced to quantify the dynamical difference between the original mathematical model and the corresponding Kron-reduced model. This measure is then crucially used to estimate the parameters contained in the kinetic model so that the corresponding values of the species' concentrations predicted by the model fit the available experimental data. The new parameter estimation method is tested on two real-life examples of chemical reaction networks: nicotinic acetylcholine receptors and Trypanosoma brucei trypanothione synthetase. Both weighted and unweighted least squares techniques, combined with Kron reduction, are used to find the best-fitting parameter values. The method of leave-one-out cross-validation is utilized to determine the preferred technique. For nicotinic receptors, the training errors due to the application of unweighted and weighted least squares are 3.22 and 3.61 respectively, while for Trypanosoma synthetase, the application of unweighted and weighted least squares result in training errors of 0.82 and 0.70 respectively. Furthermore, the problem of identifiability of dynamical systems, i.e., the possibility of uniquely determining the parameters from certain types of output, has also been addressed.

(Invited) How to Identify, Parameterise and Use Complex Electrode Kinetic Models

Electrochemical engineering transfers knowledge from surface/material level to higher levels to build well performing porous electrodes, cells and systems. Modeling accompanies this process at all levels, as it allows for deeper insights into limitations and for subsequent knowledge-driven design and optimization. Modeling tools at higher levels are already well established and predictive, when it comes to heat and mass transfer, as these phenomena are widespread in engineering. They struggle, however, to reproduce or predict the electrochemical behavior of electrodes.The situation at the electrode level becomes tricky, as there frequently are complex reaction networks at the surface. These lead to a relationship of current, voltage and reactants, which cannot be accurately described by a Tafel- or Butler-Volmer-type rate equation. Identifying suitable reaction network models including reaction kinetic equations and parameterizing them is a challenge; this talk will present promising solutions and their application to selected examples from the electrolysis and battery field.Besides the electrode surface itself, changes in electrolyte composition close to the electrode surface may occur, which alter electrode performance dramatically. Models may need to account not only for diffusion and migration of the main reactants, but also for transport of intermediates and chemical reactions in the electrolyte as well as phase changes. How can one be sure to have implemented proper processes and parameters? Also here, the talk will give an insight into promising solutions and the application to selected examples including oxygen reduction and CO2 reduction.The thus identified and parameterized models reveal process limitations and sensitivities which allow for better design and operation of the electrodes. They are further suitable for integration into porous electrode or cell models for design and diagnosis purposes on higher levels.

Design and Simulation of a Multilayer Chemical Neural Network That Learns via Backpropagation.

The design and implementation of adaptive chemical reaction networks, capable of adjusting their behavior over time in response to experience, is a key goal for the fields of molecular computing and DNA nanotechnology. Mainstream machine learning research offers powerful tools for implementing learning behavior that could one day be realized in a wet chemistry system. Here we develop an abstract chemical reaction network model that implements the backpropagation learning algorithm for a feedforward neural network whose nodes employ the nonlinear "leaky rectified linear unit" transfer function. Our network directly implements the mathematics behind this well-studied learning algorithm, and we demonstrate its capabilities by training the system to learn a linearly inseparable decision surface, specifically, the XOR logic function. We show that this simulation quantitatively follows the definition of the underlying algorithm. To implement this system, we also report ProBioSim, a simulator that enables arbitrary training protocols for simulated chemical reaction networks to be straightforwardly defined using constructs from the host programming language. This work thus provides new insight into the capabilities of learning chemical reaction networks and also develops new computational tools to simulate their behavior, which could be applied in the design and implementations of adaptive artificial life.

Descriptors for binding energies at clusters: The case of nanosilicates as models of interstellar dust grains.

Binding energies of radicals and molecules at dust grain surfaces are important parameters for understanding and modeling the chemical inventory of interstellar gas clouds. While first-principles methods can reliably be used to compute such binding energies, the complex structure and varying sizes and stoichiometries of realistic dust grains make a complete characterization of all adsorption sites exposed by their surfaces challenging. Here, we focus on nanoclusters composed of Mg-rich silicates as models of interstellar dust grains and two adsorbates of particular astrochemical relevance; H and CO. We employ a compressed sensing method to identify descriptors for the binding energies, which are expressed as analytical functions of intrinsic properties of the clusters, obtainable through a single first-principles calculation of the cluster. The descriptors are identified based on a diverse training dataset of binding energies at low-energy structures of nanosilicate clusters, where the latter structures were obtained using a first-principles-based global optimization method. The composition of the descriptors reveals how electronic, electrostatic, and geometric properties of the nanosilicates control the binding energies and demonstrates distinct physical origins of the bond formation for H and CO. The predictive performance of the descriptors is found to be limited by cluster reconstruction, e.g., breaking of internal metal-oxygen bonds, upon the adsorption event, and strategies to account for this phenomenon are discussed. The identified descriptors and the computed datasets of stable nanosilicate clusters along with their binding energies are expected to find use in astrochemical models of reaction networks occurring at silicate grain surfaces.

A Complex Reaction Network Model for Spontaneous Mirror Symmetry Breaking in Viedma Deracemizations.

Attrition-enhanced chiral symmetry breaking in crystals, known as Viedma deracemization, is a promising method for converting racemic solid phases into enantiomerically pure ones under non equilibrium conditions. However, many aspects of this process remain unclear. In this study, we present a new investigation into Viedma deracemization using a comprehensive kinetic rate equation continuous model based on classical primary nucleation theory, crystal growth, and Ostwald ripening. Our approach employs a fully micro-reversible kinetic scheme with a size-dependent solubility following the Gibbs-Thomson rule. To validate our model, we use data from a real NaClO3deracemization experiment. After parametrization, the model shows spontaneous mirror symmetry breaking (SMSB) under grinding. Additionally, we identify a bifurcation scenario with a lower and upper limit of the grinding intensity that leads to deracemization, including a minimum deracemization time within this window. Furthermore, this model uncovers that SMSB is caused by multiple instances of concealed high-order autocatalysis. Our findings provide new insights into attrition-enhanced deracemization and its potential applications in chiral molecule synthesis and understanding biological homochirality.

Predictive control of reactor network model using machine learning for hydrogen-rich gas and biochar poly-generation by biomass waste gasification in supercritical water

Supercritical water gasification (SCWG) technology can convert biomass into hydrogen rich gas and biochar. Fluidized bed reactor is promising for the industrialization of this technology, and the reactor dynamic performance study is of great significance for its scaling up. However, current simulation studies mainly focus on steady-state analysis using Computational Fluid Dynamics (CFD) software, it is difficult to conduct dynamic study due to its high computational costs. To this end, a reactor network model (RNM) that accounts for the flow, heat transfer, and kinetic dynamics for fluidized bed reactor is firstly developed based on the partitioning theory, which can reduce the computation time of dynamic simulation from several days to seconds. Additionally, extensive open-loop simulations of the RNM are carried out to generate the dataset for the development of a recurrent neural network (RNN) model. Additionally, current studies mainly focus on open-loop simulation, closed loop optimization is absent. To this end, a framework for building a machine learning (ML) model and a ML-based nonlinear predictive control scheme is developed. Model predictive control (MPC) schemes based on the RNN model is used to optimize the SCWG process to achieve multiple objectives, such as maximizing hydrogen yield and carbon yield. The open loop simulation results demonstrate that H2 yield decreases from 0.00022 to 0.0002 kg s−1 with temperature reducing from 700 to 600 °C. To increase H2 yield to the setpoint, MPC increases temperature and mass flowrate to 708 °C and 417.57 kg h−1. Additionally, MPC increases carbon yield and minimizing CO2 yield by decreasing temperature to 475 °C and increasing mass flowrate to 407.38 kg h−1.

Statistics and Bias-Free Sampling of Reaction Mechanisms from Reaction Network Models.

Selection bias is inevitable in manually curated computational reaction databases but can have a significant impact on generalizability of quantum chemical methods and machine learning models derived from these data sets. Here, we propose quasireaction subgraphs as a discrete, graph-based representation of reaction mechanisms that has a well-defined associated probability space and admits a similarity function using graph kernels. Quasireaction subgraphs are thus well suited for constructing representative or diverse data sets of reactions. Quasireaction subgraphs are defined as subgraphs of a network of formal bond breaks and bond formations (transition network) composed of all shortest paths between reactant and product nodes. However, due to their purely geometric construction, they do not guarantee that the corresponding reaction mechanisms are thermodynamically and kinetically feasible. As a result, a binary classification of feasible (reaction subgraphs) and infeasible (nonreactive subgraphs) must be applied after sampling. In this paper, we describe the construction and properties of quasireaction subgraphs and characterize the statistics of quasireaction subgraphs from CHO transition networks with up to six non-hydrogen atoms. We explore their clustering using Weisfeiler-Lehman graph kernels.

Semigroup models for biochemical reaction networks

The catalytic reaction system (CRS) formalism by Hordijk and Steel is a versatile method to model autocatalytic biochemical reaction networks. It is particularly suited, and has been widely used, to study self-sustainment and self-generation properties. Its distinguishing feature is the explicit assignment of a catalytic function to chemicals that are part of the system. In this work, it is shown that the subsequent and simultaneous catalytic functions give rise to an algebraic structure of a semigroup with the additional compatible operation of idempotent addition and a partial order. The aim of this article is to demonstrate that such semigroup models are a natural setup to describe and analyze self-sustaining CRS. The basic algebraic properties of the models are established and the notion of the function of any set of chemicals on the whole CRS is made precise. This leads to a natural discrete dynamical system on the power set of chemicals, which is obtained by iteratively considering the self-action on a set of chemicals by its own function. The fixed points of this dynamical system are proven to correspond to self-sustaining sets of chemicals, which are functionally closed. Finally, as the main application, a theorem on the maximal self-sustaining set and a structure theorem on the set of functionally closed self-sustaining sets of chemicals are proven.

Comparison Theorems for Stochastic Chemical Reaction Networks

Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications.

Investigation and optimization of polyolefin elastomers polymerization processes using multi-objective genetic algorithm

The aim of this research is to develop continuous reactor network models to determine the reactor configuration and corresponding optimal operating conditions of a polyolefin elastomers polymerization process. To achieve this objective, a modified vapor-liquid equilibrium model is integrated with both the continuous stirred tank reactor (CSTR) model and the plug flow reactor (PFR) model to accurately predict the vaporization rates of liquid. The multi-objective problem is formulated to maximize the monomer conversion and minimize the total annualized cost simultaneously. To solve the multi-objective problem, the genetic algorithm is utilized to identify the optimal operating conditions. Furthermore, the impact of the reactor combination mode is analyzed by varying the number and sequence of CSTR or PFR. The research findings reveal that a multi-phase CSTR without circulating stream followed by a PFR is the optimal reactor configuration. The proposed configuration can enhance reactor productivity and reduce the total annualized cost simultaneously while meeting the desired polymer properties.

Characterization of Integrase and Excisionase Activity in a Cell-Free Protein Expression System Using a Modeling and Analysis Pipeline.

We present a full-stack modeling, analysis, and parameter identification pipeline to guide the modeling and design of biological systems starting from specifications to circuit implementations and parametrizations. We demonstrate this pipeline by characterizing the integrase and excisionase activity in a cell-free protein expression system. We build on existing Python tools─BioCRNpyler, AutoReduce, and Bioscrape─to create this pipeline. For enzyme-mediated DNA recombination in a cell-free system, we create detailed chemical reaction network models from simple high-level descriptions of the biological circuits and their context using BioCRNpyler. We use Bioscrape to show that the output of the detailed model is sensitive to many parameters. However, parameter identification is infeasible for this high-dimensional model; hence, we use AutoReduce to automatically obtain reduced models that have fewer parameters. This results in a hierarchy of reduced models under different assumptions to finally arrive at a minimal ODE model for each circuit. Then, we run sensitivity analysis-guided Bayesian inference using Bioscrape for each circuit to identify the model parameters. This process allows us to quantify integrase and excisionase activity in cell extracts enabling complex-circuit designs that depend on accurate control over protein expression levels through DNA recombination. The automated pipeline presented in this paper opens up a new approach to complex circuit design, modeling, reduction, and parametrization.