Biochemical Reaction Model Research Articles

Evidence for rate‐dependent filtering of global extrinsic noise by biochemical reactions in mammalian cells

Recent studies have revealed that global extrinsic noise arising from stochasticity in the intracellular biochemical environment plays a critical role in heterogeneous cell physiologies. However, it remains largely unclear how such extrinsic noise dynamically influences downstream reactions and whether it could be neutralized by cellular reactions. Here, using fluorescent protein (FP) maturation as a model biochemical reaction, we explored how cellular reactions might combat global extrinsic noise in mammalian cells. We developed a novel single‐cell assay to systematically quantify the maturation rate and the associated noise for over a dozen FPs. By exploiting the variation in the maturation rate for different FPs, we inferred that global extrinsic noise could be temporally filtered by maturation reactions, and as a result, the noise levels for slow‐maturing FPs are lower compared to fast‐maturing FPs. This mechanism is validated by directly perturbing the maturation rates of specific FPs and measuring the resulting noise levels. Together, our results revealed a potentially general principle governing extrinsic noise propagation, where timescale separation allows cellular reactions to cope with dynamic global extrinsic noise.

Technological and constructor solutions for the design of silage trenches using CAD

The features of the technological process of silage formation are described. A kinetic model of biochemical reactions in the preparation of silage juice was developed and investigated. The kinetic model was the ratio of the growth rate of the silage mass under the influence of a complex of factors on it: specific growth rate, concentration of microorganisms, the use of various additives. The models of emission processes occurring with the synthesis of methane and carbon dioxide are studied. A system of automated monitoring and control of the technological process of silage has been developed. The accounting and monitoring of greenhouse gases generated during silage decomposition is also an important environmental challenge. The design of silage trenches included calculations of the bearing capacity of the base and the stability of clay slopes. For the computer-aided design system, the AutoLISP software module of the AutoCAD environment was used. The developed computer-aided design system allows speeding up the construction of outline drawings with various geometric parameters of the silage trench.

Application of fractional derivative on non-linear biochemical reaction models

Systems of ordinary differential equations play an important role in analyzing the dynamics for real world situations such as cell signaling pathways, population growth, enzymatic inhibitor reactions, and ecological models. Although, using differential equations have a great advantage to understand the dynamical behavior for such systems but most of the biological models have memory or sometimes called after effects. Such effects in the systems are often neglected. The idea of fractional-order differential equations gives a great role in understanding and identifying these effects on the model dynamics. In this paper, we review the basic ideas of fractional differential equations and their applications on non-linear biochemical reaction models. We apply this idea to a non-linear model of enzyme inhibitor reactions. The suggested method provides a good step forwards to understand the model dynamics in complex enzymatic reactions. We use a numerical approach to calculate some computational simulation of the model for different initial conditions and parameters.

Numerical modelling of the effects of cold atmospheric plasma on mitochondrial redox homeostasis and energy metabolism

A biochemical reaction model clarifies for the first time how cold atmospheric plasmas (CAPs) affect mitochondrial redox homeostasis and energy metabolism. Fundamental mitochondrial functions in pyruvic acid oxidation, the tricarboxylic acid (TCA) cycle and oxidative phosphorylation involving the respiratory chain (RC), adenosine triphosphate/adenosine diphosphate (ATP/ADP) synthesis machinery and reactive oxygen species/reactive nitrogen species (ROS/RNS)-mediated mechanisms are numerically simulated. The effects of CAP irradiation are modelled as 1) the influx of hydrogen peroxide (H{}_{2}O{}_{2}) to an ROS regulation system and 2) the change in mitochondrial transmembrane potential induced by RNS on membrane permeability. The CAP-induced stress modifies the dynamics of intramitochondrial H{}_{2}O{}_{2} and superoxide anions, i.e., the rhythm and shape of ROS oscillation are disturbed by H{}_{2}O{}_{2} infusion. Furthermore, CAPs control the ROS oscillatory behaviour, nicotinamide adenine dinucleotide redox state and ATP/ADP conversion through the reaction mixture over the RC, the TCA cycle and ROS regulation system. CAPs even induce a homeostatic or irreversible state transition in cell metabolism. The present computational model demonstrates that CAPs crucially affect essential mitochondrial functions, which in turn affect redox signalling, metabolic cooporation and cell fate decision of survival or death.

Numerical Different Methods for Solving the Nonlinear Biochemical Reaction Model

In this paper, we are interested in Sumudu Decomposition Method (SDM) and Hermite collocation method. SDM is considered as a mixture of Adomian decomposition method and the Sumudu transform method. Firstly, SDM and Hermite collocation method are applied to obtain the solutions of a nonlinear biochemical reaction model. In addition, our numerical results are compared opposite to those of the traditional numerical method that were obtained for these two methods. Signal flow graph and Simulink of MATLAB of this model are represented. The stability of equilibrium point is studied. Finally, we show that SDM and Hermite collocation method are extremely symmetry and similar.

Theory of Ion and Electron Transport Coupled with Biochemical Conversions in an Electroactive Biofilm

Bioelectrochemical systems are electrochemical cells that rely on conductive biofilms covering an electrode. We consider the example of a microbial fuel cell, and we derive a dynamic model of ion transport, biochemical reactions and electron transport inside such a biofilm. After validating the model against data, we evaluate model output to obtain an understanding of the transport of ions and electrons through a current-producing biofilm. For a system fed with a typical wastewater stream containing organic molecules and producing 5 A/m$^{2}$, our model predicts that transport of the organic molecules is not a limiting factor. However, the pH deep within the biofilm drops significantly, which can inhibit current production of such biofilms. Our results suggest that the electronic conductivity of the biofilm does not limit charge transport significantly, even for a biofilm as thick as 100 $\mu\mathrm{m}$. Our study provides an example of how physics-based modelling helps to understand complex coupled processes in bioelectrochemical systems.

Approximate analytical solution of fractional order biochemical reaction model and its stability analysis

Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to biochemists. In this paper, an effective and powerful mathematical technique, viz. fractional homotopy analysis transform method (FHATM), is employed to get the numerical solutions of biochemical reaction model with time fractional derivatives. The adopted scheme is the beautiful copulation of homotopy analysis technique and Laplace transform algorithm. This paper shows that the adopted scheme is quite easy as well as computationally attractive in the context of a solution procedure. The Caputo-type fractional derivatives are considered in the present paper. Approximate results of the probability density functions of the time fractional biochemical reaction model are computed for miscellaneous fractional Brownian motions as well as for classical motion and are presented graphically. The time fractional biochemical reaction model with respect to stability analysis for various values of fractional order [Formula: see text] is also analyzed. In the context of stability discussion, we have used the fractional Routh–Hurwitz stability criterion to establish the local stability of the biochemical reaction model of fractional order.

Analysis of stochastic multimolecular biochemical reaction model with lévy jumps

In this paper, a stochastic multimolecular biochemical reaction model with lévy jumps is investigated. Firstly, we prove the existence and uniqueness of the global positive solution. Then we derive the conditions when the reaction will end and when the reaction will proceed. Moreover, the existence of positive recurrence to the solutions is studied by constructing suitable Lyapunov functions. Results show that the end and persistence of the reaction are closely related to the intensity of lévy noise. Finally, numerical simulations are carried out to illustrate the theoretical results.

Analysis of multimodal stochastic oscillations in a biochemical reaction model

В работе изучается динамика двумерной биохимической модели Голдбетера под действием случайных возмущений. Модель описывает ферментативную реакцию с нелинейной рециркуляцией продукта в субстрат. Мы исследовали параметрические зоны, где система обнаруживает явление бистабильности - сосуществование двух аттракторов. В системе возможны следующие случаи бистабильности: сосуществование двух периодических режимов, представленных устойчивыми предельными циклами, либо сосуществование устойчивого равновесия и предельного цикла. Зоны притяжения аттракторов разделены неустойчивым предельным циклом, играющим роль сепаратрисы. С помощью прямого численного моделирования поведения системы продемонстрированы индуцированные шумом переходы стохастических траекторий между детерминированными аттракторами, приводящие к появлению мультимодальных осцилляций. Показано, как воздействие случайного шума на систему меняет частотные и амплитудные характеристики колебательных режимов.

Numerical Treatment by Using a Hybrid Efficient Technique for the Biochemical Reaction Model

In this article, we implement a spectral collocation method by using the properties of Legendre and Lagrange polynomials for solving the resulting nonlinear system of ODEs of the biochemical reaction model. This technique reduces the proposed model to a system of algebraic equations. We prove the uniqueness and present the local stability of the given model. A comparison with the numerical solution is obtained by using the RK4 method and the previously published results using the Picard-Pade method. The proposed method introduces a promising tool for solving many nonlinear systems of differential equations. Numerical illustrations are stated to demonstrate utility, validity and the great potential of the introduced method.

State-Space Abstractions for Probabilistic Inference: A Systematic Review


 
 
 
 Tasks such as social network analysis, human behavior recognition, or modeling biochemical reactions, can be solved elegantly by using the probabilistic inference framework. However, standard probabilistic inference algorithms work at a propositional level, and thus cannot capture the symmetries and redundancies that are present in these tasks.
 Algorithms that exploit those symmetries have been devised in different research fields, for example by the lifted inference-, multiple object tracking-, and modeling and simulation-communities. The common idea, that we call state space abstraction, is to perform inference over compact representations of sets of symmetric states. Although they are concerned with a similar topic, the relationship between these approaches has not been investigated systematically.
 This survey provides the following contributions. We perform a systematic literature review to outline the state of the art in probabilistic inference methods exploiting symmetries. From an initial set of more than 4,000 papers, we identify 116 relevant papers. Furthermore, we provide new high-level categories that classify the approaches, based on common properties of the approaches. The research areas underlying each of the categories are introduced concisely. Researchers from different fields that are confronted with a state space explosion problem in a probabilistic system can use this classification to identify possible solutions. Finally, based on this conceptualization, we identify potentials for future research, as some relevant application domains are not addressed by current approaches.
 
 
 

Stochastic Thermodynamic Interpretation of Information Geometry.

In recent years, the unified theory of information and thermodynamics has been intensively discussed in the context of stochastic thermodynamics. The unified theory reveals that information theory would be useful to understand nonstationary dynamics of systems far from equilibrium. In this Letter, we have found a new link between stochastic thermodynamics and information theory well-known as information geometry. By applying this link, an information geometric inequality can be interpreted as a thermodynamic uncertainty relationship between speed and thermodynamic cost. We have numerically applied an information geometric inequality to a thermodynamic model of a biochemical enzyme reaction.

The Impact of Global Sensitivities and Design Measures in Model-Based Optimal Experimental Design

In the field of chemical engineering, mathematical models have been proven to be an indispensable tool for process analysis, process design, and condition monitoring. To gain the most benefit from model-based approaches, the implemented mathematical models have to be based on sound principles, and they need to be calibrated to the process under study with suitable model parameter estimates. Often, the model parameters identified by experimental data, however, pose severe uncertainties leading to incorrect or biased inferences. This applies in particular in the field of pharmaceutical manufacturing, where usually the measurement data are limited in quantity and quality when analyzing novel active pharmaceutical ingredients. Optimally designed experiments, in turn, aim to increase the quality of the gathered data in the most efficient way. Any improvement in data quality results in more precise parameter estimates and more reliable model candidates. The applied methods for parameter sensitivity analyses and design criteria are crucial for the effectiveness of the optimal experimental design. In this work, different design measures based on global parameter sensitivities are critically compared with state-of-the-art concepts that follow simplifying linearization principles. The efficient implementation of the proposed sensitivity measures is explicitly addressed to be applicable to complex chemical engineering problems of practical relevance. As a case study, the homogeneous synthesis of 3,4-dihydro-1H-1-benzazepine-2,5-dione, a scaffold for the preparation of various protein kinase inhibitors, is analyzed followed by a more complex model of biochemical reactions. In both studies, the model-based optimal experimental design benefits from global parameter sensitivities combined with proper design measures.

CFD modeling of formaldehyde biodegradation in an immobilized cell bioreactor with disc-shaped Kissiris support

Packed-bed bioreactors (PBRs) have been recognized as a breakthrough technology in industrial wastewater treatment plants due to high removal efficiency and low investment and operating cost. A coupled computational fluid dynamic (CFD) model, combining the fluid dynamics with biochemical reactions was developed to simulate the dynamic behavior of formaldehyde (FA) biodegradation by Ralstonia eutropha in an immobilized cell bioreactor with disk-shaped Kissiris pieces operating in batch-recycling and continuous mode. The multiphase CFD model was investigated to promote the design, optimization and scale-up of the existent environmental technologies on the decontamination of aqueous streams. The Eulerian CFD model was developed to evaluate the effect of different inlet substrate concentrations (1.67–20mol/m3 of FA) and feed flow rates (6–60.3mL/min) on the treatment efficiency under unsteady-state condition by visualizing concentration profiles for FA depletion. To validate the CFD model effectively, the theoretical calculations were compared against experimental biodegradation data reported in the literature and the time-dependent simulation results illustrated a satisfactory agreement with the experimental data. The results clearly demonstrated that the bioreactor operating in batch-recycling mode was more efficient in means of pollutant elimination while increasing the feed flow rate and inlet FA concentration had reverse effect on FA removal efficiency of the bioreactor. The Eulerian computations have shown promising results on how fluid dynamics can be correlated with biochemical reaction model (Luong inhibition model) and reasonably predict the formaldehyde concentration variations along the bioreactor.

Analysis of inexact Krylov subspace methods for approximating the matrix exponential

Krylov subspace methods have proved quite effective at approximating the action of a large sparse matrix exponential on a vector. Their numerical robustness and matrix-free nature have enabled them to make inroads into a variety of applications. A case in point is solving the chemical master equation (CME) in the context of modeling biochemical reactions in biological cells. This is a challenging problem that gives rise to an extremely large matrix due to the curse of dimensionality. Inexact Krylov subspace methods that build on truncation techniques have helped solve some CME models that were considered computationally out of reach as recently as a few years ago. However, as models grow, truncating them means using an even smaller fraction of their whole extent, thereby introducing more inexactness. But experimental evidence suggests an apparent success and the aim of this study is to give theoretical insights into the reasons why. Essentially, we show that the truncation can be put in the framework of inexact Krylov methods that relax matrix–vector products and compute them expediently by trading accuracy for speed. This allows us to analyze both the residual (or defect) and the error of the resulting approximations to the matrix exponential from the viewpoint of inexact Krylov methods.

A Comparison of Deterministic and Stochastic Modeling Approaches for Biochemical Reaction Systems: On Fixed Points, Means, and Modes.

In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still expected to provide relevant indications on the underlying dynamics.

Integrated Modeling of Transport Processes, Buffer Equilibria, and Biochemical Reactions in Chromatography Columns Using CADET

Integrated Modeling of Transport Processes, Buffer Equilibria, and Biochemical Reactions in Chromatography Columns Using CADET

Integrated modeling of transport processes, buffer equilibria and biochemical reactions in chromatography columns using CADET

Integrated modeling of transport processes, buffer equilibria and biochemical reactions in chromatography columns using CADET

A study of nonlinear biochemical reaction model

The present study deals with the introduction of an alteration in Legendre wavelets method by availing of the Picard iteration method for system of differential equations and named it Legendre wavelet-Picard method (LWPM). Convergence of the proposed method is also discussed. In order to check the competence of the proposed method, basic enzyme kinetics is considered. Systems of nonlinear ordinary differential equations are formed from the considered enzyme-substrate reaction. The results obtained by the proposed LWPM are compared with the numerical results obtained from Runge–Kutta method of order four (RK-4). Numerical results and those obtained by LWPM are in excellent conformance, which would be explained by the help of table and figures. The proposed method is easy and simple to implement as compared to the other existing analytical methods used for solving systems of differential equations arising in biology, physics and engineering.

Process Simulation of Complex Biological Pathways in Physical Reactive Space and Reformulated for Massively Parallel Computing Platforms.

Biological systems encompass complexity that far surpasses many artificial systems. Modeling and simulation of large and complex biochemical pathways is a computationally intensive challenge. Traditional tools, such as ordinary differential equations, partial differential equations, stochastic master equations, and Gillespie type methods, are all limited either by their modeling fidelity or computational efficiency or both. In this work, we present a scalable computational framework based on modeling biochemical reactions in explicit 3D space, that is suitable for studying the behavior of large and complex biological pathways. The framework is designed to exploit parallelism and scalability offered by commodity massively parallel processors such as the graphics processing units (GPUs) and other parallel computing platforms. The reaction modeling in 3D space is aimed at enhancing the realism of the model compared to traditional modeling tools and framework. We introduce the Parallel Select algorithm that is key to breaking the sequential bottleneck limiting the performance of most other tools designed to study biochemical interactions. The algorithm is designed to be computationally tractable, handle hundreds of interacting chemical species and millions of independent agents by considering all-particle interactions within the system. We also present an implementation of the framework on the popular graphics processing units and apply it to the simulation study of JAK-STAT Signal Transduction Pathway. The computational framework will offer a deeper insight into various biological processes within the cell and help us observe key events as they unfold in space and time. This will advance the current state-of-the-art in simulation study of large scale biological systems and also enable the realistic simulation study of macro-biological cultures, where inter-cellular interactions are prevalent.