Nonlinear Biochemical Reaction Research Articles

Quantifying Information of Dynamical Biochemical Reaction Networks.

A large number of complex biochemical reaction networks are included in the gene expression, cell development, and cell differentiation of in vivo cells, among other processes. Biochemical reaction-underlying processes are the ones transmitting information from cellular internal or external signaling. However, how this information is measured remains an open question. In this paper, we apply the method of information length, based on the combination of Fisher information and information geometry, to study linear and nonlinear biochemical reaction chains, respectively. Through a lot of random simulations, we find that the amount of information does not always increase with the length of the linear reaction chain; instead, the amount of information varies significantly when this length is not very large. When the length of the linear reaction chain reaches a certain value, the amount of information hardly changes. For nonlinear reaction chains, the amount of information changes not only with the length of this chain, but also with reaction coefficients and rates, and this amount also increases with the length of the nonlinear reaction chain. Our results will help to understand the role of the biochemical reaction networks in cells.

Kashuri Fundo Decomposition Method for Solving Michaelis-Menten Nonlinear Biochemical Reaction Model

In most of the real life problems, we encounter with nonlinear differential equations. Problems are made more understandable by modeling them with these equations. In this way, it becomes easier to interpret the problems and reach the results. In 1913, the basic enzymatic reaction model introduced by Michaelis and Menten to describe enzyme processes is an example of nonlinear differential equation. This model is the one of the simplest and best-known approaches of the mechanisms used to model enzyme-catalyzed reactions and is the most studied. For most nonlinear differential equations, it is very difficult to get an analytical solution. For this reason, various studies have been carried out to find approximate solutions to such equations. Among these studies, those in which two different methods are used by blending attract attention. In this study, a blended form of the Kashuri Fundo transform method and the Adomian decomposition method, so-called the Kashuri Fundo decomposition method, is used to find a solution to the Michaelis-Menten nonlinear biochemical reaction model in this way. This method has been applied to the biochemical reaction model and an approximate solution has been obtained for this model without complex calculations. This shows that the hybrid method is an effective, reliable, simpler and time-saving method in reaching the solutions of nonlinear differential equations.

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.

Approximate Solutions of the Michaelis–Menten Nonlinear Biochemical Reaction Model Using Sigmoid-Weighted Neural Networks

The Michaelis–Menten nonlinear biochemical reaction model is a simple and powerful framework to illustrate enzyme processes. In this research, we are interested in deriving an approximate solutions of this well known model. We perform a simple technique based on sigmoid-weighted neural network with back propagation algorithm. Differences between approximate solutions and the classical numerical methods are compared. The results ensure that the proposed method has high accuracy in comparison with the classical methods. Our results can be considered as a basis for investigating other biochemical reaction models within the future.

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 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.

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.

Extended Parker–Sochacki method for Michaelis–Menten enzymatic reaction model

In this article, a new approach—namely, the extended Parker–Sochacki method (EPSM)—is presented for solving the Michaelis–Menten nonlinear enzymatic reaction model. The Parker–Sochacki method (PSM) is combined with a new resummation method called the Sumudu–Padé resummation method to obtain approximate analytical solutions for the model. The obtained solutions by the proposed approach are compared with the solutions of PSM and the Runge–Kutta numerical method (RKM). The comparison proves the practicality, efficiency, and correctness of the presented approach. It serves as a basis for solving other nonlinear biochemical reaction models in the future.

Numerical solutions of nonlinear biochemical model using a hybrid numerical-analytical technique

In this paper, a hybrid numerical-analytical technique resulting from the combination of the differential transformation method and the Pade approximation technique; hereby referred to as differential transformation-Pade approximation technique (DTPAT) is introduced and applied for numerical solutions to the nonlinear biochemical reaction model. The obtained numerical results via the DTPAT are in excellent agreement with those obtained using ADM, PIM, RK4, HPM, and MPHM. The DTPAT increases the convergent rate of the series solutions obtained via the DTM, is showed to be very effective; it requires less computational work, and hence a promising technique for both linear and nonlinear systems in other areas of medical and biomedical sciences.

Numerical solution to nonlinear biochemical reaction model using hybrid polynomial basis differential evolution technique

In this paper, we present an approximate numerical solution to the well known Michaelis-Menten nonlinear biochemical reaction system using a stochastic technique based on hybrid polynomial basis evolutionary computing. The approximate solution is expanded as a linear combination of polynomial basis with unknown parameters. The system of nonlinear differential equation is transformed into an equivalent global error minimization problem. A trial solution is formulated using a fitness function with unknown parameters. Two popular evolutionary algorithms such as Genetic algorithm (GA) and Differential evolution (DE) are used to solve the minimization problem and to obtain the unknown parameters. The effectiveness of the proposed technique is demonstrated in contrast with fourth-order Runge Kutta method (RK-4) and some well known standard methods including homotopy perturbation method (HPM), variational iteration method (VIM), differential transform method (DTM), and modified Picard iteration method (Picard-Pade). The comparisons of numerical results validate the efficacy and viability of the suggested technique. The results are found to be in sharp agreement with RK-4 compared to some popular standard methods.

An effective method for computing the noise in biochemical networks

We present a simple yet effective method, which is based on power series expansion, for computing exact binomial moments that can be in turn used to compute steady-state probability distributions as well as the noise in linear or nonlinear biochemical reaction networks. When the method is applied to representative reaction networks such as the ON-OFF models of gene expression, gene models of promoter progression, gene auto-regulatory models, and common signaling motifs, the exact formulae for computing the intensities of noise in the species of interest or steady-state distributions are analytically given. Interestingly, we find that positive (negative) feedback does not enlarge (reduce) noise as claimed in previous works but has a counter-intuitive effect and that the multi-OFF (or ON) mechanism always attenuates the noise in contrast to the common ON-OFF mechanism and can modulate the noise to the lowest level independently of the mRNA mean. Except for its power in deriving analytical expressions for distributions and noise, our method is programmable and has apparent advantages in reducing computational cost.

Inner Approximations of Consistent Parameter Sets by Constraint Inversion and Mixed-Integer Programming

Mathematical modeling has become an indispensable tool in the analysis, prediction and control of chemical and biological systems. However, the estimation of consistent model parametrizations and model invalidation are challenging tasks, but crucial for reliable model-based analysis and prediction. Set-based estimation methods are useful to determine guaranteed outer approximations of consistent parameter sets, i. e. consistent parametrizations are never excluded. However, these conservative outer approximating sets often include inconsistent parametrizations which lead to inconsistent models and hence possibly wrong model-based predictions. This paper proposes a set-based framework to determine inner approximations, i.e. the model is guaranteed consistent with measurement data for all parametrizations from this set. Our approach is based on the reformulation and inversion of measurement data constraints and by imposing nonlinear constraints on binary variables. The relaxation of the mixed-integer nonlinear feasibility problem into a mixed-integer linear feasibility problem allows the inner approximations to be determined efficiently. The applicability of this approach is demonstrated considering a nonlinear biochemical reaction network.

NAMBU BRACKET FORMULATION OF NONLINEAR BIOCHEMICAL REACTIONS BEYOND ELEMENTARY MASS ACTION KINETICS

We develop a Nambu bracket formulation for a wide class of nonlinear biochemical reactions by exploiting previous work that focused on elementary biochemical mass action reactions. To this end, we consider general reaction mechanisms including for example enzyme kinetics. Furthermore, we go beyond elementary reactions and account for reactions involving stoichiometric coefficients different from unity. In particular, we show that the stoichiometric matrix of biochemical reactions can be expressed in terms of Nambu brackets. Finally, we solve the sign problem that arises in the context of coupled biochemical reactions.

Lattice Boltzmann simulation of substrate flow past a cylinder with PSB biofilm for bio-hydrogen production

Based on hydrogen production by photosynthetic bacteria (PSB) in biofilm bioreactor, in the present study, a substrate solution with specific inlet concentration flowing past a circular cylinder with biochemical reaction in an attached thin PSB biofilm is numerically simulated by applying the lattice Boltzmann method (LBM). A non-equilibrium extrapolation method is employed to handle the velocity and concentration curved boundary. The model is validated by available theoretical and numerical results in terms of the drag and lift coefficients and concentration profiles. The good agreement demonstrated that LBM is an effective method to simulate nonlinear biochemical reaction systems with curved boundary. The velocity profile and concentration distributions of the substrate and hydrogen are determined, and the effect of Reynolds number on mass transfer characteristics is also discussed by introducing Sherwood number. The simulation results show that for both the substrate and product the concentration extension along X- and Y-directions decrease with increasing Reynolds number. The highest hydrogen concentration is obtained at the back of the cylinder. Furthermore, increasing Reynolds number results in decreasing substrate consumption efficiency, while hydrogen yield almost keeps a steady value.

EMERGENCE OF INTRINSIC REPRESENTATIONS OF IMAGES BY FEEDFORWARD AND FEEDBACK PROCESSES AND BIOLUMINESCENT PHOTONS IN EARLY RETINOTOPIC AREAS

Recently, we put forward a redox molecular hypothesis involving the natural biophysical substrate of visual perception and imagery. Here, we explicitly propose that the feedback and feedforward iterative operation processes can be interpreted in terms of a homunculus looking at the biophysical picture in our brain during visual imagery. We further propose that the brain can use both picture-like and language-like representation processes. In our interpretation, visualization (imagery) is a special kind of representation i.e., visual imagery requires a peculiar inherent biophysical (picture-like) mechanism. We also conjecture that the evolution of higher levels of complexity made the biophysical picture representation of the external visual world possible by controlled redox and bioluminescent nonlinear (iterative) biochemical reactions in the V1 and V2 areas during visual imagery. Our proposal deals only with the primary level of visual representation (i.e. perceived "scene").

Quantitative Analysis of Integrated Energy Metabolism of Muscle Cells: Experimental and Theoretical Studies

Quantitative analysis, in combination with detailed experimental studies, is the basis of Molecular System Bioenergetics (MSB) which takes into account specific interactions between cellular components, formation of metabolic dissipative structures and resulting system level properties such as metabolic compartmentation. There are several experimental and theoretical approaches used: studies in vivo kinetics of mitochondrial respiration regulation; Metabolic Control Analysis of integrated energy metabolism; mathematical modeling. Cardiac cells are characterized by high level of structural organization with very regular arrangement of mitochondria and their interaction with cytoskeleton. Heterodimeric tubulin containing beta II isoform is connected to mitochondrial outer membrane, specifically controls VDAC permeability and is coexpressed with mitochondrial creatine kinase. These proteins form with ATP Synthasome a supercomplex Mitochondrial Interactosome (MI) in which the kinetics of regulation of respiration by MtCK is significantly altered in comparison with mitochondria in vitro affinity for extramitochondrial ATP is strongly decreased due to limited permeability of VDAC but for creatine increased. Metabolic Control Analysis of reactions in MI showed that flux control coefficients are significantly increased for reactions of ADP/ATP recycling coupled with phosphocreatine production by MtCK. These experimental data are the basis of the mathematical model of compartmentalized energy transfer and show that about 90 % of energy is carried out of mitochondria by phosphocreatine due to specific structure of MI. This model explains well the metabolic aspects of Frank -Starling law of the heart. In cancerous HL −1 cells of cardiac phenotype MtCK and beta II tubulin are not expressed. Mathematical models based on the theory of homogenous intracellular medium and CK equilibrium do not explain adequately the experimental observations. In future development, application of single-molecule enzyme kinetics and theory of nonlinear biochemical reaction networks is necessary.

1P311 非線形生化学反応動力学の統一とNMRメタボロミクス(非平衡・生体リズム,第48回日本生物物理学会年会)

1P311 非線形生化学反応動力学の統一とNMRメタボロミクス(非平衡・生体リズム,第48回日本生物物理学会年会)

Stochastic Bistability and Bifurcation in a Mesoscopic Signaling System with Autocatalytic Kinase

Bistability is a nonlinear phenomenon widely observed in nature including in biochemical reaction networks. Deterministic chemical kinetics studied in the past has shown that bistability occurs in systems with strong (cubic) nonlinearity. For certain mesoscopic, weakly nonlinear (quadratic) biochemical reaction systems in a small volume, however, stochasticity can induce bistability and bifurcation that have no macroscopic counterpart. We report the simplest yet known reactions involving driven phosphorylation-dephosphorylation cycle kinetics with autocatalytic kinase. We show that the noise-induced phenomenon is correlated with free energy dissipation and thus conforms with the open-chemical system theory. A previous reported noise-induced bistability in futile cycles is found to have originated from the kinase synchronization in a bistable system with slow transitions, as reported here.

On multistage homotopy-perturbation method applied to nonlinear biochemical reaction model

The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by an adaptation of the standard analytic homotopy-perturbation method (HPM). The standard HPM is converted into a hybrid numeric–analytic method called the multistage HPM (MHPM). The numerical results obtained from the MHPM and the classical fourth-order Runge–Kutta (RK4) method are in complete agreement.

Nonequilibrium Thermodynamics and Nonlinear Kinetics in a Cellular Signaling Switch

We develop a rigorous nonequilibrium thermodynamics for an open system of nonlinear biochemical reactions responsible for cell signal processing. We show that the quality of the biological switch consisting of a phosphorylation-dephosphorylation cycle, such as those in protein kinase cascade, is controlled by the available intracellular free energy from the adenosine triphosphate (ATP) hydrolysis in vivo: DeltaG=k(B)Tln(([ATP]/K(eq)[ADP]), where K(eq) is the equilibrium constant. The model reveals the correlation between the performance of the switch and the level of DeltaG. The result demonstrates the importance of nonequilibrium thermodynamics in analyzing biological information processing, provides its energetic cost, establishes an interplay between signal transduction and energy metabolism in cells, and suggests a biological function for phosphoenergetics in the ubiquitous phosphorylation signaling.