Underlying Reaction Network Research Articles

Design patterns of biological cells.

Design patterns are generalized solutions to frequently recurring problems. They were initially developed by architects and computer scientists to create a higher level of abstraction for their designs. Here, we extend these concepts to cell biology to lend a new perspective on the evolved designs of cells' underlying reaction networks. We present a catalog of 21 design patterns divided into three categories: creational patterns describe processes that build the cell, structural patterns describe the layouts of reaction networks, and behavioral patterns describe reaction network function. Applying this pattern language to the E. coli central metabolic reaction network, the yeast pheromone response signaling network, and other examples lends new insights into these systems.

Mechanistic proposal for the conversion of syngas to light alkanes in Zn-ZSM-5 zeolite linking theoretical calculations to experimental characterizations

The direct syngas conversion to olefins, aromatics and other hydrocarbons has attracted increasing attention while unraveling the complex reaction mechanism is of great challenge. It was recently demonstrated that zinc-exchanged zeolites could selectively convert syngas to alkanes, particular ethane, and [Zn–O–Zn] motif is likely the intrinsic active site. The underlying reaction network however remains ambiguous. Herein, we proposed a reaction mechanism for the direct conversion of syngas to light alkanes including methane and ethane using density functional theory calculations in periodic [Zn–O–Zn]-ZSM-5 zeolite model. The evolution of syngas to ethane follows the sequence of CO → CH2O → CH2CO → CH3CHO → C2H6. The activation of CO to formaldehyde initiates the reaction. The [Zn–O–Zn] site can readily be reduced by CO to [Zn–Zn] site, which either inserts aldehydes to form [Zn–O-CnH2n-Zn] motif for chain propagation to higher aldehydes, or converts aldehydes to alkanes for chain termination. Ketene is the first intermediate after the C–C bond coupling between [Zn–O–CH2–Zn] and CO. Both the structures and the evolution sequence of the involved intermediates in the proposal (formyl, methylene, acetyl, ethyl) coincide quite well with experimentally quasi in-situ characterized results. The proposed reaction network consisting of initiation, propagation and termination sub-cycles unifies the formation pathway of methane, ethane, and higher alkanes, and bears some resemblance to the Fischer-Tropsch synthesis for syngas conversion. This theoretical work thus further vindicates the critical role of [Zn–O–Zn] site and may proffer some implications to tailor alkane selectivity in metal-exchanged zeolites for syngas conversion.

Computing all persistent subspaces of a reaction-diffusion system

An algorithm is presented for computing a reaction-diffusion partial differential equation (PDE) system for all possible subspaces that can hold a persistent solution of the equation. For this, all possible sub-networks of the underlying reaction network that are distributed organizations (DOs) are identified. Recently it has been shown that a persistent subspace must be a DO. The algorithm computes the hierarchy of DOs starting from the largest by a linear programming approach using integer cuts. The underlying constraints use elementary reaction closures as minimal building blocks to guarantee local closedness and global self-maintenance, required for a DO. Additionally, the algorithm delivers for each subspace an affiliated set of organizational reactions and minimal compartmentalization that is necessary for this subspace to persist. It is proved that all sets of organizational reactions of a reaction network, as already DOs, form a lattice. This lattice contains all potentially persistent sets of reactions of all constrained solutions of reaction-diffusion PDEs. This provides a hierarchical structure of all persistent subspaces with regard to the species and also to the reactions of the reaction-diffusion PDE system. Here, the algorithm is described and the corresponding Python source code is provided. Furthermore, an analysis of its run time is performed and all models from the BioModels database as well as further examples are examined. Apart from the practical implications of the algorithm the results also give insights into the complexity of solving reaction-diffusion PDEs.

Monte Carlo samplers for efficient network inference.

Accessing information on an underlying network driving a biological process often involves interrupting the process and collecting snapshot data. When snapshot data are stochastic, the data's structure necessitates a probabilistic description to infer underlying reaction networks. As an example, we may imagine wanting to learn gene state networks from the type of data collected in single molecule RNA fluorescence in situ hybridization (RNA-FISH). In the networks we consider, nodes represent network states, and edges represent biochemical reaction rates linking states. Simultaneously estimating the number of nodes and constituent parameters from snapshot data remains a challenging task in part on account of data uncertainty and timescale separations between kinetic parameters mediating the network. While parametric Bayesian methods learn parameters given a network structure (with known node numbers) with rigorously propagated measurement uncertainty, learning the number of nodes and parameters with potentially large timescale separations remain open questions. Here, we propose a Bayesian nonparametric framework and describe a hybrid Bayesian Markov Chain Monte Carlo (MCMC) sampler directly addressing these challenges. In particular, in our hybrid method, Hamiltonian Monte Carlo (HMC) leverages local posterior geometries in inference to explore the parameter space; Adaptive Metropolis Hastings (AMH) learns correlations between plausible parameter sets to efficiently propose probable models; and Parallel Tempering takes into account multiple models simultaneously with tempered information content to augment sampling efficiency. We apply our method to synthetic data mimicking single molecule RNA-FISH, a popular snapshot method in probing transcriptional networks to illustrate the identified challenges inherent to learning dynamical models from these snapshots and how our method addresses them.

Persistent Subspaces of Reaction-Based Dynamical Systems

Various types of dynamical systems, such as ordinary differential equations (ODEs) or partial differential equations (PDEs), are widely applied not only in chemistry but also in many scientific disciplines to model the dynamics arising from interactions described by reactions between molecules, individuals, or species. This study provides an overview of how Chemical Organization Theory (COT) can be used to analyze such systems by identifying all potentially persistent species solely from the underlying reaction network, without the need for simulations or even knowledge of reaction constants or kinetic laws. Two minimalist examples with only three resp. four species are used to introduce all fundamental definitions including a new, naturally arising concept of persistence, and to illustrate the fore-mentioned technique without mathematical details such as proofs. Thereby, COT is shown to provide measures to analyze, compare, and construct very complex systems on an abstract level and thus to complement other powerful techniques for the analysis of complex systems such as deficiency, RAF theory, elementary modes, graph theory, Lyapunov functions, and bifurcation theory.

Dynamics of hydroxide-ion-driven reversible autocatalytic networks.

In living systems adaptive regulation requires the presence of nonlinear responses in the underlying chemical networks. Positive feedbacks, for example, can lead to autocatalytic bursts that provide switches between two stable states or to oscillatory dynamics. The stereostructure stabilized by hydrogen bonds provides an enzyme its selectivity, rendering pH regulation essential for its functioning. For effective control, triggers by small concentration changes play roles where the strength of feedback is important. Here we show that the interaction of acid-base equilibria with simple reactions with pH-dependent rate can lead to the emergence of a positive feedback in hydroxide ion concentration during the hydrolysis of some Schiff bases in the physiological pH range. The underlying reaction network can also support bistability in an open system.

On the diversity of fossil and alternative gasoline combustion chemistry: A comparative flow reactor study

Recent progress in molecular combustion chemistry allows for detailed investigation of the intermediate species pool even for complex chemical fuel compositions, as occur for technical fuels. This study provides detailed investigation of a comprehensive set of complex alternative gasoline fuels obtained from laminar flow reactors equipped with molecular-beam sampling techniques for observation of the combustion intermediate species pool in homogeneous gas phase reactions. The combination of ionization techniques including double-imaging photoelectron photoion coincidence (i2PEPICO) spectroscopy enables deeper mechanistic insights into the underlying reaction network relevant to technical fuels. The selected fuels focus on contemporary automotive engine application as drop-in fuels compliant to European EN 228 specification for gasoline. Therefore, potential alternative gasoline blends containing oxygenated hydrocarbons as octane improvers obtainable from bio-technological production routes, e.g., ethanol, iso-butanol, methyl tert‑butyl ether (MTBE), and ethyl tert‑butyl ether (ETBE), as well as a Fischer-Tropsch surrogate were investigated. The fuel set is completed by two synthetic naphtha fractions obtained from Fischer-Tropsch and methanol-to-gasoline processes alongside with a fossil reference gasoline. In total, speciation data for 11 technical fuels from two atmospheric flow reactor setups are presented. Detailed main and intermediate species profiles are provided for slightly rich (ϕ = 1.2) and lean (ϕ = 0.8) conditions for intermediate to high temperatures. Complementary, the isomer distribution on different mass channels, like m/z = 78 u fulvene/benzene, of four gasolines was investigated. Experimental findings are analyzed in terms of the detailed fuel composition and literature findings for molecular combustion chemistry. Influences of oxygenated fuel components as well as composition of the hydrocarbon fractions are examined with a particular focus on the soot precursor chemistry. This dataset is available for validation of chemical kinetic mechanisms for realistic gasolines containing oxygenated hydrocarbons.

Hydrogenation of Accreting C Atoms and CO Molecules–Simulating Ketene and Acetaldehyde Formation Under Dark and Translucent Cloud Conditions

Abstract Simple and complex organic molecules (COMs) are observed along different phases of star and planet formation and have been successfully identified in prestellar environments such as dark and translucent clouds. Yet the picture of organic molecule formation at those earliest stages of star formation is not complete and an important reason is the lack of specific laboratory experiments that simulate carbon atom addition reactions on icy surfaces of interstellar grains. Here we present experiments in which CO molecules as well as C and H atoms are codeposited with H2O molecules on a 10 K surface mimicking the ongoing formation of an “H2O-rich” ice mantle. To simulate the effect of impacting C atoms and resulting surface reactions with ice components, a specialized C-atom beam source is used, implemented on SURFRESIDE3, an ultra-high vacuum cryogenic setup. Formation of ketene (CH2CO) in the solid state is observed in situ by means of reflection absorption IR spectroscopy. C18O and D isotope labeled experiments are performed to further validate the formation of ketene. Data analysis supports that CH2CO is formed through C-atom addition to a CO molecule, followed by successive hydrogenation transferring the formed :CCO into ketene. Efficient formation of ketene is in line with the absence of an activation barrier in C+CO reaction reported in the literature. We also discuss and provide experimental evidence for the formation of acetaldehyde (CH3CHO) and possible formation of ethanol (CH3CH2OH), two COM derivatives of CH2CO hydrogenation. The underlying reaction network is presented and the astrochemical implications of the derived pathways are discussed.

Reaction Network Analysis of the Ruthenium‐Catalyzed Reduction of Carbon Dioxide to Dimethoxymethane

AbstractDue to the growing interest in dimethoxymethane (DMM) as formaldehyde synthon and fuel additive, new and more efficient routes toward the formaldehyde analog are being investigated. One approach is the reductive transformation of carbon dioxide using a ruthenium phosphine catalyst and a Lewis acid additive in methanol. In the present work, we investigated the underlying reaction network, consisting of several intermediates, equilibria and side products, through in situ IR spectroscopy. We determined rate constants and activation parameters for the hydrogenation steps. Their temperature‐dependent differences can be used to influence the product selectivity in this catalysis. To favor DMM formation, the acetalization equilibrium and especially the amount of water formed were identified as promising optimization opportunities. Simulation of concentration profiles on the basis of the proposed kinetic model enables the prediction of experimental product distributions for various reaction parameters, demonstrating the power of reaction network analysis for process optimization.

Inverse Power Law Scaling of Energy Dissipation Rate in Nonequilibrium Reaction Networks.

The energy dissipation rate in a nonequilibrium reaction system can be determined by the reaction rates in the underlying reaction network. By developing a coarse-graining process in state space and a corresponding renormalization procedure for reaction rates, we find that energy dissipation rate has an inverse power-law dependence on the number of microscopic states in a coarse-grained state. The dissipation scaling law requires self-similarity of the underlying network, and the scaling exponent depends on the network structure and the probability flux correlation. Existence of the inverse dissipation scaling law is shown in realistic biochemical systems such as biochemical oscillators and microtubule-kinesin active flow systems.

Identifiability of stochastically modelled reaction networks

Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous-time Markov processes. In this manuscript, the identifiability of the underlying network structure with a given stochastic system dynamics is studied. It is shown that some data types related to the associated stochastic dynamics can uniquely identify the underlying network structure as well as the system parameters. The accuracy of the presented network inference is investigated when given dynamical data are obtained via stochastic simulations.

Modeling Thrombin Generation in Plasma under Diffusion and Flow

We investigate the capacity of published numerical models of thrombin generation to reproduce experimentally observed threshold behavior under conditions in which diffusion and/or flow are important. Computational fluid dynamics simulations incorporating species diffusion, fluid flow, and biochemical reactions are compared with published data for thrombin generation in vitro in 1) quiescent plasma exposed to patches of tissue factor and 2) plasma perfused through a capillary coated with tissue factor. Clot time is correctly predicted in individual cases, and some models qualitatively replicate thrombin generation thresholds across a series of tissue factor patch sizes or wall shear rates. Numerical results suggest that there is not a genuine patch size threshold in quiescent plasma—clotting always occurs given enough time—whereas the shear rate threshold observed under flow is a genuine physical limit imposed by flow-mediated washout of active coagulation factors. Despite the encouraging qualitative results obtained with some models, no single model robustly reproduces all experiments, demonstrating that greater understanding of the underlying reaction network, and particularly of surface reactions, is required. In this direction, additional simulations provide evidence that 1) a surface-localized enzyme, speculatively identified as meizothrombin, is significantly active toward the fluorescent thrombin substrate used in the experiments or, less likely, 2) thrombin is irreversibly inhibited at a faster-than-expected rate, possibly explained by a stimulatory effect of plasma heparin on antithrombin. These results highlight the power of simulation to provide novel mechanistic insights that augment experimental studies and build our understanding of complex biophysicochemical processes. Further validation work is critical to unleashing the full potential of coagulation models as tools for drug development and personalized medicine.

Weakly Reversible Mass-Action Systems With Infinitely Many Positive Steady States

We show that weakly reversible mass-action systems can have a continuum of positive steady states, coming from the zeroes of a multivariate polynomial. Moreover, the same is true of systems whose underlying reaction network is reversible and has a single connected component. In our construction, we relate operations on the reaction network to the multivariate polynomial occurring as a common factor in the system of differential equations.

An Invitation to Pharmacostatics.

Pharmacology, the study of interactions between biological processes and therapeutic agents, is traditionally presented as consisting of two subdisciplines: pharmacokinetics, which is about the distribution and metabolism of drugs in organisms, and pharmacodynamics, which is about the organisms' response to drugs. In discovery-stage pharmacology however, one primary concern is what we call pharmacostatics, the characterization of equilibrium parameters and states of core interactions of physiologic and therapeutic interest. This usually takes the form of studying dose-response curves, without consideration for the relevant qualitative properties of the underlying reaction networks, e.g., the existence, multiplicity and asymptotic stability of steady states. Furthermore, steady-state calculations customarily employ manually derived closed-form expressions based on approximating assumptions. While these formulas may seem adequate most of the time, the assumptions need not apply, and there are genuine though seemingly uncommon cases where this approach is not feasible and/or fails to explain non-monotone dose-response curves. It is this paper's aim to stimulate interest in mathematical problems arising in pharmacostatics. We specifically pose two problems about a particular relevant class of networks of reversible binding reactions. The first problem is to exploit a certain fixed-point formulation of the equilibrium equation to devise an algorithmic method that would be compellingly preferable to current practice in the pharmacostatics context. The second problem is to explicitly anticipate the possibility of non-monotone dose-response curves from network topology. Addressing these problems would positively impact biopharmaceutical research, and they have inherent mathematical interest.

Using Separable Nonnegative Matrix Factorization Techniques for the Analysis of Time-Resolved Raman Spectra.

The key challenge of time-resolved Raman spectroscopy is the identification of the constituent species and the analysis of the kinetics of the underlying reaction network. In this work we present an integral approach that allows for determining both the component spectra and the rate constants simultaneously from a series of vibrational spectra. It is based on an algorithm for nonnegative matrix factorization that is applied to the experimental data set following a few pre-processing steps. As a prerequisite for physically unambiguous solutions, each component spectrum must include one vibrational band that does not significantly interfere with the vibrational bands of other species. The approach is applied to synthetic "experimental" spectra derived from model systems comprising a set of species with component spectra differing with respect to their degree of spectral interferences and signal-to-noise ratios. In each case, the species involved are connected via monomolecular reaction pathways. The potential and limitations of the approach for recovering the respective rate constants and component spectra are discussed.

Hamiltonian perspective on compartmental reaction–diffusion networks

Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction network, the obtained reaction–diffusion system is a distributed-parameter port-Hamiltonian system on a compact spatial domain. Motivated by the need for computer-based design, we offer a spatially consistent discretization of the PDE system and, in a systematic manner, recover a compartmental ODE model on a simplicial triangulation of the spatial domain. Exploring the properties of a balanced weighted Laplacian matrix of the reaction network and the Laplacian of the simplicial complex, we characterize the space of equilibrium points and provide a simple stability analysis on the state space modulo the space of equilibrium points. The paper rules out the possibility of the persistence of spatial patterns for the compartmental balanced reaction–diffusion networks.

Automatic identification of structured process models based on biological phenomena detected in (fed-)batch experiments

In this paper, we present a set of methods to automatically propose structured process models from an automated analysis of (fed-)batch experiments. Therefore, the measurements are numerically compensated for the influence of feeding and sampling, and the qualitative behavior of the measurements is revealed. As measurements from fermentations are inherently noisy, we introduce a method that divides the compensated curves into several episodes in a probabilistic framework to better handle these shortcomings. The probability of biological phenomena that reveal crucial information about the underlying reaction network is calculated. Since the phenomena detection is measurement-driven, its reliability depends on the measurement situation, e.g., the number of samples taken and experiments considered, measurement noise, etc. We show a possible approach to test the uncertainty of the phenomena detection against these influences. Finally, model structures are proposed automatically based on the detected biological phenomena. An experimental validation of the approach is shown, using real fermentation data from fed-batch cultivations of Streptomyces tendae.

On the origin of bistability in the Stage 2 of the Huang-Ferrell model of the MAPK signaling

Mitogen-activated protein kinases (MAPKs) are important signal transducing enzymes, unique to eukaryotes, that are involved in many pathways of cellular regulation. Successive phosphorylation cascades mediated by MAPKs serve as sensitive switches initiating various cellular processes. Apart from this basic feature, the underlying reaction network is capable of displaying other nonlinear phenomena including bistable steady states and hysteresis as well as periodic oscillations. We show that from the mechanistic point of view, bistability is a consequence of interaction between single and double phosphorylation/dephosphorylation pathways in a Stage 2 subsystem of the Huang-Ferrell model. Within this subsystem we uncover the core subnetwork obtained by systematic reduction relying on the methods of stoichiometric network analysis. For the core model we show that there is either one stable steady state or three steady states of which two are stable and point out the role of interplay between the single and double phosphorylation subnetworks in generating bistability.

A Scalable Algorithm to Explore the Gibbs Energy Landscape of Genome-Scale Metabolic Networks

The integration of various types of genomic data into predictive models of biological networks is one of the main challenges currently faced by computational biology. Constraint-based models in particular play a key role in the attempt to obtain a quantitative understanding of cellular metabolism at genome scale. In essence, their goal is to frame the metabolic capabilities of an organism based on minimal assumptions that describe the steady states of the underlying reaction network via suitable stoichiometric constraints, specifically mass balance and energy balance (i.e. thermodynamic feasibility). The implementation of these requirements to generate viable configurations of reaction fluxes and/or to test given flux profiles for thermodynamic feasibility can however prove to be computationally intensive. We propose here a fast and scalable stoichiometry-based method to explore the Gibbs energy landscape of a biochemical network at steady state. The method is applied to the problem of reconstructing the Gibbs energy landscape underlying metabolic activity in the human red blood cell, and to that of identifying and removing thermodynamically infeasible reaction cycles in the Escherichia coli metabolic network (iAF1260). In the former case, we produce consistent predictions for chemical potentials (or log-concentrations) of intracellular metabolites; in the latter, we identify a restricted set of loops (23 in total) in the periplasmic and cytoplasmic core as the origin of thermodynamic infeasibility in a large sample () of flux configurations generated randomly and compatibly with the prior information available on reaction reversibility.

Methods for Biochemical Model Decomposition and Quantitative Submodel Comparison

AbstractComparing alternative models for a given biochemical system is in general a very difficult problem: the models may focus on different aspects of the same system and may consist of very different species and reactions. The numerical setups of the models also play a crucial role in the quantitative comparison. When the alternative designs are submodels of a reference model, for example, knockdown mutants of a model, the problem of comparing them becomes simpler: they all have very similar, although not identical, underlying reaction networks, and the biological constraints are given by those in the reference model. In the first part of our study, we review several known methods for model decomposition and for quantitative comparison of submodels. We describe knockdown mutants, elementary flux modes, control‐based decomposition, mathematically controlled comparison and its extension, local submodel comparison and a discrete approach for comparing continuous submodels. In the second part of the paper we present a new statistical method for comparing submodels, which complements the methods presented in the review. The main difference between our approach and the known methods is related to the important question of how to chose the numerical setup in which to perform the comparison. In the case of the reviewed methods, the comparison is made in the numerical context of the reference model, i.e., in each of the alternative models both the kinetics of the reactions and the initial values of all variables are chosen to be identical to those from the reference model. We propose in this paper a different approach, better suited for response networks, where each alternative model is assumed to start from its own steady state under basal conditions. We demonstrate our approach with a case study focusing on the heat shock response in eukaryotes.