Nonlinear Biochemical Systems Research Articles

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.

RESEARCHING THE CONNATURAL MONOTERPENIC HYDROCARBONS BIOSYNTHESIS DYNAMICS APPLYING THE KINETIC MODEL AND THE STATE SPACE MODEL

To investigate in succession the dynamics of monoterpenic hydrocarbons biosynthesis in plants of genus Artemisia the algorithm, which connects the intermediates analysis of results after each stage processes and the comparison of theoretical conclusions with new experimental data is developed in this article. It is proved that the uniform kinetic model of chemical essential compounds transformations in a stream from the glucose, mevalonate and isoprene to monoterpenes developed by authors is universal kinetics model in order to explain the connatural biosynthesis of monoterpenes in any ethereous carrier plants. There are founded some kinetic (by specific velocities of biochemical stages of metamorphosis) and a balance sheet (by rations between ring closure degrees) relations during the monoterpenes connatural biosynthesis corresponding to the vegetative phases. The state space model (SSM) for open nonlinear biochemical system is compounded. In this model macroscopic metamorphosis of essential substances is introduced as the sequence of vector's micro-alterations (or a velocity of the modification of a system's biochemical composition) in a orthogonal system of co-ordinates. At the application of the model to substantiate with the theory of a kinetic chemo-systematics, which becomes clear correlations between plants-producers is offered. The biochemical substantiation of individual distinctive indications between plants of genus Artemisia for seven types is introduced, such as: A.abrotanum, A.annua, A.dracunculus, A.glauca, A.scoparia (two c hemostrains) and A.taurica. The mathematical model of molecular-and-phylogenetic exposition of the relationship in a flora based on the example of genus Artemisia is compounded. The influence of environmental factors on kinetic parameters of monoterpenes biosynthesis in plants of the genus A.scoparia from different regions of their growth by means of comparative graph-analytic and matrix analyses of their accumulation dynamics in plants by own results of the experiment and the literary data with the made by authors modeling calculations is proved. The possibility to combine the systematization of plants based on morph-anatomic principles and chemo-regular principles based on the kinetic particularities of monoterpenes biosynthesis during the chemo-phases in vegetative taxons is shown.

Elucidating the genotype-phenotype map by automatic enumeration and analysis of the phenotypic repertoire.

Background:The gap between genotype and phenotype is filled by complex biochemical systems most of which are poorly understood. Because these systems are complex, it is widely appreciated that quantitative understanding can only be achieved with the aid of mathematical models. However, formulating models and measuring or estimating their numerous rate constants and binding constants is daunting. Here we present a strategy for automating difficult aspects of the process.Methods:The strategy, based on a system design space methodology, is applied to a class of 16 designs for a synthetic gene oscillator that includes seven designs previously formulated on the basis of experimentally measured and estimated parameters.Results:Our strategy provides four important innovations by automating: (1) enumeration of the repertoire of qualitatively distinct phenotypes for a system; (2) generation of parameter values for any particular phenotype; (3) simultaneous realization of parameter values for several phenotypes to aid visualization of transitions from one phenotype to another, in critical cases from functional to dysfunctional; and (4) identification of ensembles of phenotypes whose expression can be phased to achieve a specific sequence of functions for rationally engineering synthetic constructs. Our strategy, applied to the 16 designs, reproduced previous results and identified two additional designs capable of sustained oscillations that were previously missed.Conclusions:Starting with a system’s relatively fixed aspects, its architectural features, our method enables automated analysis of nonlinear biochemical systems from a global perspective, without first specifying parameter values. The examples presented demonstrate the efficiency and power of this automated strategy.

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.

Correction: A Linear Framework for Time-Scale Separation in Nonlinear Biochemical Systems

This article has been republished to address equation and symbol formatting errors and errors in figure citations. This republication addresses the errors referenced in the previous formal correction. The publisher apologizes for the errors.

OPTIMAL STATE ESTIMATION AND ON-LINE OPTIMISATION OF A BIOCHEMICAL REACTOR

Abstract An on-line optimising control strategy involving a two level extended Kalman filter (EKF) for dynamic model identification and a functional conjugate gradient method for determining optimal operating condition is proposed and applied to a biochemical reactor. The optimiser incorporates the identified model and determines the optimal operating condition while maximising the process performance. This strategy is computationally advantageous as it involves separate estimation of states and process parameters in reduced dimensions. In addition to assisting on-line dynamic optimisation, the estimated time varying uncertain process parameter information can also be useful for continuous monitoring of the process. This strategy ensures that the biochemical reactor is operated at the optimal operation while taking care of the disturbances that are encountered during operation. The simulation results demonstrate the usefulness of the two level EKF assisted dynamic optimizer for on-line optimising control of uncertain nonlinear biochemical systems.

Correction: A Linear Framework for Time-Scale Separation in Nonlinear Biochemical Systems

Correction: A Linear Framework for Time-Scale Separation in Nonlinear Biochemical Systems

A linear framework for time-scale separation in nonlinear biochemical systems.

Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights in areas such as enzyme kinetics, allosteric enzymes, G-protein coupled receptors, ion channels, gene regulation and post-translational modification. In each case, internal molecular complexity has been eliminated, leading to rational algebraic expressions among the remaining components. This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation. Here we show that these calculations are all instances of a single graph-theoretic framework. Despite the biochemical nonlinearity to which it is applied, this framework is entirely linear, yet requires no approximation. We show that elimination of internal complexity is feasible when the relevant graph is strongly connected. The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level.

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.

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.

Joint State and Parameter Estimation For Biochemical Dynamic Pathways With Iterative Extended Kalman Filter: Comparison With Dual State and Parameter Estimation

A biochemical dynamic pathway is usually modeled as a nonlinear system described by a set of nonlinear ODEs. In most cases, only partial states can be measured. Moreover, the system parameters, reaction rates, may be unknown or poorly known. Therefore, it is of significance to estimate the states and parameters, for analyzing the biochemical dynamic pathway. Due to the limitation of some traditional parameter estimation approaches, it is natural to choose sequential methods such as extended Kalman filter to do the parameter estimation for biochemical dynamic pathways. In this paper, dual/joint state and parameter estimation with iterative extended Kalman filter (EKF) are investigated to obtain state and parameter estimates for a biochemical pathway simultaneously. The simulated results between two methods are compared to show the validity of parameter estimation for a biochemical dynamic pathway. It has shown that, for the nonlinear biochemical system, the joint state and parameter estimation with EKF, can give desirable convergence and estimation performance.

EXPERIENCE AND CHALLENGES IN IDENTIFICATION OF NON-LINEAR SYSTEMS: BIOCHEMICAL AND ENVIRONMENTAL APPLICATIONS

In this short paper for the panel discussion on „Experience and challenges in identification of non-linear systems„ some major issues with respect to identification of non-linear biochemical and environmental systems are presented.

Controllability of non-linear biochemical systems

Mathematical methods of biochemical pathway analysis are rapidly maturing to a point where it is possible to provide objective rationale for the natural design of metabolic systems and where it is becoming feasible to manipulate these systems based on model predictions, for instance, with the goal of optimizing the yield of a desired microbial product. So far, theory-based metabolic optimization techniques have mostly been applied to steady-state conditions or the minimization of transition time, using either linear stoichiometric models or fully kinetic models within biochemical systems theory (BST). This article addresses the related problem of controllability, where the task is to steer a non-linear biochemical system, within a given time period, from an initial state to some target state, which may or may not be a steady state. For this purpose, BST models in S-system form are transformed into affine non-linear control systems, which are subjected to an exact feedback linearization that permits controllability through independent variables. The method is exemplified with a small glycolytic–glycogenolytic pathway that had been analyzed previously by several other authors in different contexts.

Controllability of non-linear biochemical systems

Controllability of non-linear biochemical systems

Sufficient Conditions for Coordination of Coupled Nonlinear Biochemical Systems: Analysis of a Simple, Representative Example

Under conditions of stress and environmental fluctuations, how do coupled biochemical systems maintain the balance of metabolic fluxes? Using a model derived from a representative glycolysis example, this work derives sufficient coordination conditions for guaranteeing the balance of metabolic fluxes in the coupled systems subjected to any fluctuations. For diffusion-like coupling, it is explicitly shown that the sufficient conditions are the linear summation of individual uncoupled systems. For this case, coupling strength is not a key factor affecting the balance of metabolic fluxes, although it may affect the emergence of certain dynamic patterns. When the sufficient coordination conditions are satisfied, coupled systems always settle onto stable finite states, independently of the nature (type, period or amplitude) of external signals. When they are not, external signals may force the stable states of coupled systems to lose their coordination, resulting in the coupled systems having no stable finite states which is inconsistent with most normal biological functions. Numerical simulations support the analytical results. The generalization of this result for other coupled nonlinear biochemical systems is discussed. Finally, the maintenance of such biological coordination is discussed in the context of genetic engineering and environmental fluctuations.

Concentration fluctuations in a mesoscopic oscillating chemical reaction system.

Under sustained pumping, kinetics of macroscopic nonlinear biochemical reaction systems far from equilibrium either can be in a stationary steady state or can execute sustained oscillations about a fixed mean. For a system of two dynamic species X and Y, the concentrations n(x) and n(y) will be constant or will repetitively trace a closed loop in the (n(x), n(y)) phase plane, respectively. We study a mesoscopic system with n(x) and n(y) very small; hence the occurrence of random fluctuations modifies the deterministic behavior and the law of mass action is replaced by a stochastic model. We show that n(x) and n(y) execute cyclic random walks in the (n(x), n(y)) plane whether or not the deterministic kinetics for the corresponding macroscopic system represents a steady or an oscillating state. Probability distributions and correlation functions for n(x)(t) and n(y)(t) show quantitative but not qualitative differences between states that would appear as either oscillating or steady in the corresponding macroscopic systems. A diffusion-like equation for probability P(n(x), n(y), t) is obtained for the two-dimensional Brownian motion in the (n(x), n(y)) phase plane. In the limit of large n(x), n(y), the deterministic nonlinear kinetics derived from mass action is recovered. The nature of large fluctuations in an oscillating nonequilibrium system and the conceptual difference between "thermal stochasticity" and "temporal complexity" are clarified by this analysis. This result is relevant to fluorescence correlation spectroscopy and metabolic reaction networks.

Time Resolved Multi-Spectroscopic Reaction Image Analyzer -A Novel Image Analyzer for Biochemical and Reaction Diffusion System-

A time-resolved multi-spectroscopic image analyzer (TRMSIA) for nonlinear biochemical and reaction diffusion system was developed. The reaction diffusion behavior of Belousov-Zhabaotinsky(BZ) reaction as a probe reaction was studied using this system. The TRMSIA consisted of a light source, multi-spectroscopic part, binocular microscope with a high resolution CCD detector, and computer part. The change in the concentration can be quantitatively measured by absorbance at 10 different wavelengths. It can measure wave velocity by line-profile process using the high-speed time-resolved spectroscopy. As a result, we can analyze quantitatively the dynamics of chemical waves under various conditions with a simple procedure. The TRMSIA-fluorescencce system also proved to be versatile analysis for the biochemical systems, such as the luminous becteria.

Sufficient Conditions for Coordination of a Nonlinear Biochemical System under External Forcing

Sufficient Conditions for Coordination of a Nonlinear Biochemical System under External Forcing

Effects of Noise on Coordination of Nonlinear Biochemical Systems

Effects of noisy fluctuations in environment on coordination of nonlinear biochemical systems have been analyzed both theoretically and numerically. Once noise induces dynamical changes in a nonlinear biochemical system, response of flux to noisy fluctuations depends on both the dynamics of the system, the nature of the superimposed noise and the values of kinetical parameters, while a steady-state flux in the absence of noise may only depend on the values of kinetical parameters. For a branched biochemical system, noise may induce significant redistribution of flux among the branched reactions. Furthermore, noise may destroy coordination of a nonlinear biochemical system, when it cannot accommodate noise-induced changes. An empirical method has been suggested to determine whether coordination of a biochemical system is destroyed by environmental noise, and a general approach for studying coordination of biochemical systems under noisy fluctuations has also been presented. The theoretical results suggest that studies on coordination and homoeostasis of nonlinear biochemical systems must take their nonlinearities into account. The implications of the theoretical results for understanding flux control, homoeostasis and coordination of nonlinear biochemical systems in the presence of noise have been discussed.

Dynamics of non-linear biochemical systems and the evolutionary significance of time hierarchy

Several non-linear reaction networks are analyzed in order to study the influence of time hierarchy on the dynamics of biochemical systems. The analysis is based on the assumption that the separation of the time constants within metabolic systems is a direct consequence of strong differences of enzyme concentrations. Therefore, as variable system parameters, only the enzyme concentrations are considered. By investigation of the stationary states of various three-component models with feedback-activation bifurcation diagrams within a two-dimensional parameter space, the enzyme simplex, are constructed. The diagrams contain the information about the number of stationary states, their stability properties as well as the type of motion expected at different parameter combinations. The results support the hypothesis that systems with separated time constants generally show a simple dynamic behaviour. Complex motions can be expected mainly for systems without time hierarchy, which are characterized by parameters located within the centre of the enzyme simplex. Quantitative measures for the time hierarchy and the complexity of the dynamics are derived. It is supposed that the separation of time constants is a main feature of the evolution of biochemical systems. The hypothesis is further supported by the consideration of the time hierarchy of the glycolytic pathway.