Biochemical Reaction Systems Research Articles

Spatial patterns of the Brusselator model with asymmetric Lévy diffusion

Abstract The formation of spatial patterns is an important issue in reaction–diffusion systems. Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion (such as normal or fractional Laplace diffusion), namely, assuming that spatial environments of the systems are homogeneous. However, the complexity and heterogeneity of spatial environments of biochemical reactions in vivo can lead to asymmetric diffusion of reactants. Naturally, there arises an open question of how the asymmetric diffusion affects dynamical behaviors of biochemical reaction systems. To answer this, we build a general asymmetric Lévy diffusion model based on the theory of a continuous time random walk. In addition, we investigate the two-species Brusselator model with asymmetric Lévy diffusion, and obtain a general condition for the formation of Turing and wave patterns. More interestingly, we find that even though the Brusselator model with symmetric diffusion cannot produce steady spatial patterns for some parameters, the asymmetry of Lévy diffusion for this model can produce wave patterns. This is different from the previous result that wave instability requires at least a three-species model. In addition, the asymmetry of Lévy diffusion can significantly affect the amplitude and frequency of the spatial patterns. Our results enrich our knowledge of the mechanisms of pattern formation.

Macroscopic limit for stochastic chemical reactions involving diffusion and spatial heterogeneity

To model bio-chemical reaction systems with diffusion one can either use stochastic, microscopic reaction–diffusion master equations or deterministic, macroscopic reaction–diffusion system. The connection between these two models is not only theoretically important but also plays an essential role in applications. This paper considers the macroscopic limits of the chemical reaction–diffusion master equation for first-order chemical reaction systems in highly heterogeneous environments. More precisely, the diffusion coefficients as well as the reaction rates are spatially inhomogeneous and the reaction rates may also be discontinuous. By carefully discretizing these heterogeneities within a reaction–diffusion master equation model, we show that in the limit we recover the macroscopic reaction–diffusion system with inhomogeneous diffusion and reaction rates.

A study of nonlinear fractional-order biochemical reaction model and numerical simulations

This article depicts an approximate solution of systems of nonlinear fractional biochemical reactions for the Michaelis–Menten enzyme kinetic model arising from the enzymatic reaction process. This present work is concerned with fundamental enzyme kinetics, utilised to assess the efficacy of powerful mathematical approaches such as the homotopy perturbation method (HPM), homotopy analysis method (HAM), and homotopy analysis transform method (HATM) to get the approximate solutions of the biochemical reaction model with time-fractional derivatives. The Caputo-type fractional derivatives are explored. The proposed method is implemented to formulate a fractional differential biochemical reaction model to obtain approximate results subject to various settings of the fractional parameters with statistical validation at different stages. The comparison results reveal the complexity of the enzyme process and obtain approximate solutions to the nonlinear fractional differential biochemical reaction model.

DNA Reaction System That Acquires Classical Conditioning.

Biochemical reaction networks can exhibit plastic adaptation to alter their functions in response to environmental changes. This capability is derived from the structure and dynamics of the reaction networks and the functionality of the biomolecule. This plastic adaptation in biochemical reaction systems is essentially related to memory and learning capabilities, which have been studied in DNA computing applications for the past decade. However, designing DNA reaction systems with memory and learning capabilities using the dynamic properties of biochemical reactions remains challenging. In this study, we propose a basic DNA reaction system design that acquires classical conditioning, a phenomenon underlying memory and learning, as a typical learning task. Our design is based on a simple mechanism of five DNA strand displacement reactions and two degradative reactions. The proposed DNA circuit can acquire or lose a new function under specific conditions, depending on the input history formed by repetitive stimuli, by exploiting the dynamic properties of biochemical reactions induced by different input timings.

Application of a novel numerical simulation to biochemical reaction systems.

Recent advancements in omics and single-cell analysis highlight the necessity of numerical methods for managing the complexity of biological data. This paper introduces a simulation program for biochemical reaction systems based on the natural number simulation (NNS) method. This novel approach ensures the equitable treatment of all molecular entities, such as DNA, proteins, H2O, and hydrogen ions (H+), in biological systems. Central to NNS is its use of stoichiometric formulas, simplifying the modeling process and facilitating efficient and accurate simulations of diverse biochemical reactions. The advantage of this method is its ability to manage all molecules uniformly, ensuring a balanced representation in simulations. Detailed in Python, NNS is adept at simulating various reactions, ranging from water ionization to Michaelis-Menten kinetics and complex gene-based systems, making it an effective tool for scientific and engineering research.

Multimolecular Competition Effect as a Modulator of Protein Localization and Biochemical Networks in Cell-Size Space.

Cells are small, closed spaces filled with various types of macromolecules. Although it is shown that the characteristics of biochemical reactions in vitro are quite different from those in living cells, the role of the co-existence of various macromolecules in cell-size space remains still elusive. Here, using a constructive approach, it is demonstrated that the co-existence of various macromolecules themselves has the ability to tune protein localization for spatiotemporal regulation and a biochemical reaction system in a cell-size space. Both experimental and theoretical analyses reveal that enhancement of interfacial effects by a large surface-area-to-volume ratio facilitates membrane localization of molecules in the cell-size space, and the interfacial effects are alleviated by competitive binding to lipid membranes among multiple proteins even if their membrane affinities are weak. These results indicate that competition for membrane binding among various macromolecules in the cell-size space plays a role in regulating the spatiotemporal molecular organization and biochemical reaction networks. These findings shed light on the importance of surrounding molecules for biochemical reactions using purified elements in small spaces.

Identifying Conditions for Protein Synthesis Inside Giant Vesicles Using Microfluidics toward Standardized Artificial Cell Production.

To expand the range of practical applications of artificial cells, it is important to standardize the production process of giant (cell-sized) vesicles that encapsulate reconstituted biochemical reaction systems. For this purpose, a rapidly developing microfluidics-based giant vesicle generation system is a promising approach, similar to the droplet assay systems that are already widespread in the market. In this study, we examined the composition of the solutions used to generate vesicles encapsulating the in vitro transcription-translation (IVTT) system. We show that tuning of the lipid composition and adding poly(vinyl alcohol) to the outer solution improved the stability of the transition process into the lipid membrane so that protein synthesis proceeded in vesicles. The direct integration of α-hemolysin nanopores synthesized in situ was also demonstrated. These protein-synthesizing monodisperse giant vesicles can be prepared by using a simple microfluidic fabrication/operation with a commercial IVTT system.

Design and Fabrication of a Fully-Integrated, Miniaturised Fluidic System for the Analysis of Enzyme Kinetics

The lab-on-a-chip concept, enabled by microfluidic technology, promises the integration of multiple discrete laboratory techniques into a miniaturised system. Research into microfluidics has generally focused on the development of individual elements of the total system (often with relatively limited functionality), without full consideration for integration into a complete fully optimised and miniaturised system. Typically, the operation of many of the reported lab-on-a-chip devices is dependent on the support of a laboratory framework. In this paper, a demonstrator platform for routine laboratory analysis is designed and built, which fully integrates a number of technologies into a single device with multiple domains such as fluidics, electronics, pneumatics, hydraulics, and photonics. This facilitates the delivery of breakthroughs in research, by incorporating all physical requirements into a single device. To highlight this proposed approach, this demonstrator microsystem acts as a fully integrated biochemical assay reaction system. The resulting design determines enzyme kinetics in an automated process and combines reservoirs, three-dimensional fluidic channels, optical sensing, and electronics in a low-cost, low-power and portable package.

Correlation analysis between amino acids and bacterial communities of Wuliangye-flavour liquor fermentation in aged fermentation pit

Fermented grain (Zaopei) is the main microbial habitat and biochemical reaction system of health factors for Wuliangye-flavour liquor fermentation. In the present work, the bacterial communities in four depths of Zaopei, from the same fermentation pit, aged over 60 years, and amino acids as major health factors in four liquors from directly corresponding Zaopei were investigated by Illumina MiSeq sequencing and liquid chromatography mass spectrometry (LC-MS), respectively. Results showed that a total of 18 amino acids were detected in the four liquors, and eight dominant bacterial genera were observed in four Zaopei corresponding to the four liquors. Meanwhile, total amino acids, 12 amino acids (Glu, Asp, Val, Ile, Cys, Met, Lys, Arg, Gly, Ala, Tyr, and Thr), bacterial richness, and the percentages of Lactobacillus and Pseudomonas increased with the increase in Zaopei’s depth; five amino acids (Cit, Phe, Leu, Pro, and Ser), and the percentages of Pediococcus and Bacteroides, first increased and then decreased, with the increase in Zaopei’s depth. Moreover, the 12 amino acids were significantly (p < 0.01) and strongly (|ρ| > 0.8) positively correlated with Lactobacillus and Pseudomonas. Therefore, these results can provide relevant data support for increasing amino acid content in Wuliangye-flavour liquor.

Revised model of the tissue factor pathway of thrombin generation: Role of the feedback activation of FXI

BackgroundBiochemical reaction networks are self‐regulated in part due to feedback activation mechanisms. The tissue factor (TF) pathway of blood coagulation is a complex reaction network controlled by multiple feedback loops that coalesce around the serine protease thrombin. ObjectivesOur goal was to evaluate the relative contribution of the feedback activation of coagulation factor XI (FXI) in TF‐mediated thrombin generation using a comprehensive systems‐based analysis. Materials and MethodsWe developed a systems biology model that improves the existing Hockin‐Mann (HM) model through an integrative approach of mathematical modeling and in vitro experiments. Thrombin generation measured using in vitro assays revealed that the feedback activation of FXI contributes to the propagation of thrombin generation based on the initial concentrations of TF or activated coagulation factor X (FXa). We utilized experimental data to improve the robustness of the HM model to capture thrombin generation kinetics without a role for FXI before including the feedback activation of FXI by thrombin to construct the extended (ext.) HM model. Results and ConclusionsUsing the ext.HM model, we predicted that the contribution of positive feedback of FXI activation by thrombin can be abolished by selectively eliminating the inhibitory function of tissue factor pathway inhibitor (TFPI), a serine protease inhibitor of FXa and TF‐activated factor VII (FVIIa) complex. This prediction from the ext.HM model was experimentally validated using thrombin generation assays with function blocking antibodies against TFPI and plasmas depleted of FXI. Together, our results demonstrate the applications of combining experimental and modeling techniques in predicting complex biochemical reaction systems.

Stationary and Time-Dependent Molecular Distributions in Slow-Fast Feedback Circuits

Biochemical reaction systems, in particular those that govern the expression of genes in single cells, involve discrete numbers of molecules and are inherently stochastic. This study concerns reaction systems with two molecular species and an arbitrary number of reactions, the rates of which conform to a scaling of the classical type in the first species (but not the second). For limiting values of the scaling parameter, the first species is highly abundant, evolves slowly, and buffers the relatively fast fluctuation of the second, scarce, species. The scale separation facilitates the construction of asymptotic approximations to the molecular distributions: the large-time behavior is described by a WKB approximation, which is further resolved into a tractable mixture of metastable modes; the earlier-time dynamics are described by quasi-stationary and linear noise approximations. The paper presents the theory and the algebraic recipes that are required to implement it. The framework is applied on two reaction systems with positive feedback: a delayed feedback circuit and a gene autoregulation model with cooperative binding of the protein to the promoter. For the former, the approximation scheme results into a mixture of Gaussian/Poisson modes for the inactive/active protein distribution. For the latter, the analysis elucidates the effects of bursty gene expression, promoter responsivity, and protein sequestration on bimodality of protein distributions.

Identification of dynamic mass-action biochemical reaction networks using sparse Bayesian methods.

Identifying the reactions that govern a dynamical biological system is a crucial but challenging task in systems biology. In this work, we present a data-driven method to infer the underlying biochemical reaction system governing a set of observed species concentrations over time. We formulate the problem as a regression over a large, but limited, mass-action constrained reaction space and utilize sparse Bayesian inference via the regularized horseshoe prior to produce robust, interpretable biochemical reaction networks, along with uncertainty estimates of parameters. The resulting systems of chemical reactions and posteriors inform the biologist of potentially several reaction systems that can be further investigated. We demonstrate the method on two examples of recovering the dynamics of an unknown reaction system, to illustrate the benefits of improved accuracy and information obtained.

The partition representation of enzymatic reaction networks and its application for searching bi-stable reaction systems.

The signal transduction system, which is known as a regulatory mechanism for biochemical reaction systems in the cell, has been the subject of intensive research in recent years, and its design methods have become necessary from the viewpoint of synthetic biology. We proposed the partition representation of enzymatic reaction networks consisting of post-translational modification reactions such as phosphorylation, which is an important basic component of signal transduction systems, and attempted to find enzymatic reaction networks with bistability to demonstrate the effectiveness of the proposed representation method. The partition modifiers can be naturally introduced into the partition representation of enzymatic reaction networks when applied to search. By randomly applying the partition modifiers as appropriate, we searched for bistable and resettable enzymatic reaction networks consisting of four post-translational modification reactions. The proposed search algorithm worked well and we were able to find various bistable enzymatic reaction networks, including a typical bistable enzymatic reaction network with positive auto-feedbacks and mutually negative regulations. Since the search algorithm is divided into an evaluation function specific to the characteristics of the enzymatic reaction network to be searched and an independent algorithm part, it may be applied to search for dynamic properties such as biochemical adaptation, the ability to reset the biochemical state after responding to a stimulus, by replacing the evaluation function with one for other characteristics.

Using entropy-driven amplifier circuit response to build nonlinear model under the influence of L\xe9vy jump

BackgroundBioinformatics is a subject produced by the combination of life science and computer science. It mainly uses computer technology to study the laws of biological systems. The design and realization of DNA circuit reaction is one of the important contents of bioinformatics.ResultsIn this paper, nonlinear dynamic system model with Lévy jump based on entropy-driven amplifier (EDA) circuit response is studied. Firstly, nonlinear biochemical reaction system model is established based on EDA circuit response. Considering the influence of disturbance factors on the system, nonlinear biochemical reaction system with Lévy jump is built. Secondly, in order to prove that the constructed system conforms to the actual meaning, the existence and uniqueness of the system solution is analyzed. Next, the sufficient conditions for the end and continuation of EDA circuit reaction are certified. Finally, the correctness of the theoretical results is proved by numerical simulation, and the reactivity of THTSignal in EDA circuit under different noise intensity is verified.ConclusionsIn EDA circuit reaction, the intensity of external noise has a significant impact on the system. The end of EDA circuit reaction is closely related to the intensity of Lévy noise, and Lévy jump has a significant impact on the nature of biochemical reaction system.

The prokaryotic community, physicochemical properties and flavors dynamics and their correlations in fermented grains for Chinese strong-flavor Baijiu production

Fermented grain (FG), a complex and unique ecosystem, is the main microbial habitats, biochemical reaction system and direct source of flavor compounds for the Chinese strong-flavor Baijiu (CSFB) production. However, the dynamics of physicochemical properties, prokaryotic community and flavor compounds of FGs during the long-term fermentation process are still not completely clear. Here, the above topics on FGs in the actual production process were comprehensively studied by using a combination of physicochemical analysis, GC–MS detection and Illumina HiSeq sequencing methods. The whole fermentation process could be divided into two stages including early (0–25d) and the later stage (25–60d) based on the dynamics of FG physicochemical properties and the changes of prokaryotic community diversity. A total of 41phyla and 364 genera were detected, and 9 of them were dominant genera in FG complex ecosystem, including Lactobacillus, Pediococcus, Ochrobactrum, Bacillus etc. Among them, the dynamics of 29 top10 genera in FGs were mainly influenced by the starch and total acid, followed by NH4+ and ethanol, and 7 genera (hubs, e.g., Clostridium, Methanosaeta, Bacillus, etc.) of them may play important roles in FG ecosystem stability. A total of 71 volatiles including 33 esters, 14 alcohols, 9 fatty acids, 5 phenols, and 10 other compounds were detected in the FGs, and most of them formed in the early stage. Some important flavor substances (e.g., ethyl octanoate, 3-methylbutanol, hexanoate, etc.) increased in the later stage. Moreover, the formation of some flavor compound might require multiple microbes involved. For instance, ten of the top10 genera, including Lactobacillus, Clostridium, Methanosarcina, Sedimentibacter, Bacillus, etc., were significantly and positively correlated with four important esters. This study may help to clarify the complex correlations among prokaryotic community, physicochemical properties and flavors, allow the improvement of CSFB quality by using bioaugmentation and/or controlling environmental factors, and shed more light on the ecological rules guiding community assembly in FGs.

Geometry and symmetry in biochemical reaction systems

Complex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the language and tools of graph theory. However, graph representations only describe pairwise interactions between molecular species and so are not well suited to modelling complex sets of reactions that may involve numerous reactants and/or products. Here, we make use of a recently developed hypergraph theory of chemical reactions that naturally allows for higher-order interactions to explore the geometry and quantify functional redundancy in biochemical reactions systems. Our results constitute a general theory of automorphisms for oriented hypergraphs and describe the effect of automorphism group structure on hypergraph Laplacian spectra.

Exploring dissipative sources of non-Markovian biochemical reaction systems.

Many biological processes including important intracellular processes are governed by biochemical reaction networks. Usually, these reaction systems operate far from thermodynamic equilibrium, implying free-energy dissipation. On the other hand, single reaction events happen often in a memory manner, leading to non-Markovian kinetics. A question then arises: how do we calculate free-energy dissipation (defined as the entropy production rate) in this physically real case? We derive an analytical formula for calculating the energy consumption of a general reaction system with molecular memory characterized by nonexponential waiting-time distributions. It shows that this dissipation is composed of two parts: one from broken detailed balance of an equivalent Markovian system with the same topology and substrates, and the other from the direction-time dependence of waiting-time distributions. But, if the system is in a detailed balance and the waiting-time distribution is direction-time independent, there is no energy dissipation even in the non-Markovian case. These general results provide insights into the physical mechanisms underlying nonequilibrium processes. A continuous-time random-walk model and a generalized model of stochastic gene expression are chosen to clearly show dissipative sources and the relationship between energy dissipation and molecular memory.

Tropical Abstraction of Biochemical Reaction Networks with Guarantees

Biochemical molecules interact through modification and binding reactions, giving raise to a combinatorial number of possible biochemical species. The time-dependent evolution of concentrations of the species is commonly described by a system of coupled ordinary differential equations (ODEs). However, the analysis of such high-dimensional, non-linear system of equations is often computationally expensive and even prohibitive in practice. The major challenge towards reducing such models is providing the guarantees as to how the solution of the reduced model relates to that of the original model, while avoiding to solve the original model.In this paper, we have designed and tested an approximation method for ODE models of biochemical reaction systems, in which the guarantees are our major requirement. Borrowing from tropical analysis techniques, we look at the dominance relations among terms of each species' ODE. These dominance relations can be exploited to simplify the original model, by neglecting the dominated terms. As the dominant subsystems can change during the system's dynamics, depending on which species dominate the others, several possible modes exist. Thus, simpler models consisting of only the dominant subsystems can be assembled into hybrid, piecewise smooth models, which approximate the behavior of the initial system. By combining the detection of dominated terms with symbolic bounds propagation, we show how to approximate the original model by an assembly of simpler models, consisting in ordinary differential equations that provide time-dependent lower and upper bounds for the concentrations of the initial model's species.The utility of our method is twofold. On the one hand, it provides a reduction heuristics that performs without any prior knowledge of the initial system's behavior (i.e., no simulation of the initial system is needed in order to reduce it). On the other hand, our method provides sound interval bounds for each species, and hence can serve to evaluate the faithfulness of tropicalization reduction heuristics for ODE models of biochemical reduction systems. The method is tested on several case studies.

Lipid sponge droplets as programmable synthetic organelles.

Living cells segregate molecules and reactions in various subcellular compartments known as organelles. Spatial organization is likely essential for expanding the biochemical functions of synthetic reaction systems, including artificial cells. Many studies have attempted to mimic organelle functions using lamellar membrane-bound vesicles. However, vesicles typically suffer from highly limited transport across the membranes and an inability to mimic the dense membrane networks typically found in organelles such as the endoplasmic reticulum. Here, we describe programmable synthetic organelles based on highly stable nonlamellar sponge phase droplets that spontaneously assemble from a single-chain galactolipid and nonionic detergents. Due to their nanoporous structure, lipid sponge droplets readily exchange materials with the surrounding environment. In addition, the sponge phase contains a dense network of lipid bilayers and nanometric aqueous channels, which allows different classes of molecules to partition based on their size, polarity, and specific binding motifs. The sequestration of biologically relevant macromolecules can be programmed by the addition of suitably functionalized amphiphiles to the droplets. We demonstrate that droplets can harbor functional soluble and transmembrane proteins, allowing for the colocalization and concentration of enzymes and substrates to enhance reaction rates. Droplets protect bound proteins from proteases, and these interactions can be engineered to be reversible and optically controlled. Our results show that lipid sponge droplets permit the facile integration of membrane-rich environments and self-assembling spatial organization with biochemical reaction systems.

Unified dimensionless transformation in enzyme kinetics: Application to mathematical analyses of ten biochemical reaction systems

A novel general principle was proposed to transform enzyme kinetic equations into unified dimensionless forms. The principle consists of six steps. The principle was applied to ten complex biochemical reaction systems and their characteristics were mathematically analyzed. The approach has six merits.: (i) the number of parameters is reduced, (ii) the rate expressions and their progress curves become much simpler, easily understood and are analyzed globally by the newly defined dimensionless time, T, (iii) the relative magnitude of kinetic constants and of the maximum velocity involved in the rate equations are straightforwardly estimated by three type m values, (iv) mass balance and stoichiometric relationship of the dimensionless rate expressions are exactly the same format as of the actual rate expressions, (v) 2D or 3D plots of the unified dimensionless equations can be depicted without inputs of the actual experimental data of the variables and kinetic constants, and (vi) the newly defined dimensionless inactivation constant, Kiact, is useful to estimate the effect of the enzyme inactivation on the batch reactions. The principle is beneficial for the mathematical analyses of complex biochemical reactions involving two or more kinds of enzymes, for those involving two or more substrates or for those involving both.