非稳态酶活化动力学的布尔函数图论分析

以非稳态酶动力学的布尔函数图形方法研究非稳态酶活化动力学问题,推导出此类反应的非稳态酶动力学方程,并对此动力学方程进行了讨论,分析了酶活化反应体系的非稳态酶动力学过程．     

高效液相色谱法在脱氧核糖核酸酶解动力学

为了更好地对脱氧核糖核酸酶解动力学过程进行研究,建立脱氧核糖核酸(DNA)酶解液中4种脱氧核苷酸(腺嘌呤脱氧核苷酸(dAMP)、鸟嘌呤脱氧核苷酸(dGMP)、胞嘧啶脱氧核苷酸(dCMP)、胸腺嘧啶脱氧核苷酸(dTMP))的高效液相测定方法,能将酶解液中4种脱氧核苷酸完全分离并准确定量.在此基础上,对DNA酶解的动力学进行初步研究,其反应机理为不存在底物和产物抑制的双底物顺序反应,动力学方程为x=1/bln(1+abt)(其中a=0.372 3ρ0-0.974;b=-0.049 3ρ20+1.115 3ρ0 - 1.110 3),该方程可以很好地描述DNA酶解过程,误差仅为3.31%.     

竞争性抑制的非稳态酶动力学布尔函数图论研究

以非稳戊酶动力学的布尔函数图形方法,来研究一类竞争性抑制的非稳态酶动力学问题,推导出此类反应的百稳态酶动力学方程,并对此动力学方程进行了讨论,分析了此类竞争性抑制酶反应体系的非稳态酶动力学问题。     

反竞争性抑制的非稳态酶动力学布尔函数图解研究

以非稳态酶动力学的布尔函数图形方法,来研究一类反竞争性抑制的非稳态酶动力学问题,推导出此类反应的非稳态酶动力学方程,并对此动力学方程进行了讨论,分析了此类反竞争性制酶反应体系的非稳态酶动力学问题。     

Ping Pong Bi Bi机制的非稳态酶动力学分布函数图论研究

以非稳态酶动力学的布尔函数图形方法,来研究一类PingPongBiBi机制的非记酶动力学问题,推导出此类反应的非稳态酶动力学方程,并对此动力学方程进行了讨论,分析了此类PingPongBiBi机制酶反应体系的非稳态酶动力学方程。     

高效液相色谱法在脱氧核糖核酸酶解动力学研究中的应用

为了更好地对脱氧核糖核酸酶解动力学过程进行研究,建立脱氧核糖核酸（DNA）酶解液中4种脱氧核苷酸（腺嘌呤脱氧核苷酸（dAMP）、鸟嘌呤脱氧核苷酸（dGMP）、胞嘧啶脱氧核苷酸（dCMP）、胸腺嘧啶脱氧核苷酸（dTMP））的高效液相测定方法,能将酶解液中4种脱氧核苷酸完全分离并准确定量。在此基础上,对DNA酶解的动力学进行初步研究,其反应机理为不存在底物和产物抑制的双底物顺序反应,动力学方程为x=1／bin（1＋abt）（其中a=0．3723p0—0．974;b=-0．0493p0^2＋1．1150p0-1．1103）,该方程可以很好地描述DNA酶解过程,误差仅为3．31％.     

Random Bi Bi机制的非稳态酶动力学布尔函数图论研究

本文以非稳态酶动力学的布尔函数图形方法^[1],来研究一类Random Bi Bi机制的非稳态酶动力学问题,推导同此类反应的非稳态酶动力学方程,并对此动力学方程进行了讨论,分析了此类Random Bi Bi机制酶反应体系的非稳态酶动力学方程。     

一类非竞争性抑制的非稳态酶动力学布尔函数图解研究

本文以非稳态酶动力学的布尔函数图形方法^[1],来研究一类非竞争性抑制的非稳态酶动力学问题,推导出此类反应的非稳态酶动力学方程,并对此动力学方程进行了讨论,分析了此类非竞争性抑制的非稳态酶动力学的动力学过程。     

α-氯丙酸脱卤酶发酵动力学模型

对α-氯丙酸脱卤酶发酵动力学进行了研究。基于Logistic方程和Luedeking-Piret方程,得到了描述Pseudomonas W20菌发酵过程菌体生长、α-氯丙酸脱卤酶生成及基质消耗的动力学数学模型和模型参数,对试验数据与模型进行了验证比较,模型计算值与试验结果拟合良好,平均相对误差大部分小于10%;对脱卤酶反应动力学进行了研究,结果表明脱卤酶的脱卤反应基本符合米氏方程,并求得最大反应速率V_(max)=1.11×10~(-5)mol/(g·min),表观米氏常数K_m=3.72×10~(-3)mol/L。     

元宝枫叶蛋白酶的动力学特征

酶促动力学是研究酶促反应的速度及各种因素如底物浓度、酶浓度、抑制剂、激活剂、温度、pH等对酶促反应速度影响的科学,是酶学研究中重要的内容。在一定条件下,酶促反应都有其特定的动力学参数,如Km值（米氏常数）和Vmax值（最大反应速率）等。Km是反映酶动力学性质的重要特征性常数,对某一酶促反应而言,在一定条件下都有特定的Km值,可以用来鉴别酶。Km值还可以判断酶的专一性和天然底物,     

Equations of substrate-limited growth: the case for blackman kinetics

A simplified model of cell metabolism, consisting of a series of linked reversible enzymatic reactions dependent on the concentration of a single external substrate has been developed. The general mathematical solution for this system of reactions is presented. This general solution confirms the concept of a rate-limiting step, or “master reaction”, in biological systems as first proposed by Blackman. The maximum rate of such a process is determined by, and equal to, the maximum rate of the slowest forward reaction in the series. Of practical interest in modeling the growth rate of cells are three cases developed from the general model. The simplest special case results in the Monod equation when the maximum forward rate of one enzymatic reaction in the cell is much less than the maximum forward rate of any other enzymatic reactions. More realistic is the case where the maximum forward rates of more than one enzymatic reaction are slow. When two slow enzymatic reactions are separated from each other by any number of fast reactions that overall can be described by a large equilibrium constant, the Blackman form results: and A third case is that in which two slow enzymatic steps are separated by an equilibrium constant that is not large. Unlike the Monod and Blackman forms, which contain only two arbitrary constants, this model contains three arbitrary constants: The Monod and Blackman forms are special cases of this three constant form. In comparing equations with two arbitrary constants the Monod equation gave poorer fit of the data in most cases than the Blackman form. It is concluded that workers modeling the growth of microorganisms should give a t least as much consideration to the Blackman form as is given to the Monod equation.     

Towards Kinetic Modeling of Global Metabolic Networks: Methylobacterium extorquens AM1 Growth as Validation

Here we report a systematic method for constructing a large scale kinetic metabolic model and its initial application to the modeling of central metabolism of Methylobacterium extorquens AM1, a methylotrophic and environmental important bacterium. Its central metabolic network includes formaldehyde metabolism, serine cycle, citric acid cycle, pentose phosphate pathway, gluconeogensis, PHB synthesis and acetyl-CoA conversion pathway, respiration and energy metabolism. Through a systematic and consistent procedure of finding a set of parameters in the physiological range we overcome an outstanding difficulty in large scale kinetic modeling: the requirement for a massive number of enzymatic reaction parameters. We are able to construct the kinetic model based on general biological considerations and incomplete experimental kinetic parameters. Our method consists of the following major steps: 1) using a generic enzymatic rate equation to reduce the number of enzymatic parameters to a minimum set while still preserving their characteristics; 2) using a set of steady state fluxes and metabolite concentrations in the physiological range as the expected output steady state fluxes and metabolite concentrations for the kinetic model to restrict the parametric space of enzymatic reactions; 3) choosing enzyme constants K’s and K’eqs optimized for reactions under physiological concentrations, if their experimental values are unknown; 4) for models which do not cover the entire metabolic network of the organisms, designing a dynamical exchange for the coupling between the metabolism represented in the model and the rest not included.     

The enzyme activity allosteric regulation model based on the composite nature of catalytic and regulatory sites concept

A new kinetic model of enzymatic catalysis is proposed, which postulates that enzyme solutions are equilibrium systems of oligomers differing in the number of subunits and in the mode of their assembly. It is suggested that the catalytic and regulatory sites of allosteric enzymes are of composite nature and appear as a result of subunits joining. Two possible joining modes are postulated at each oligomerization step. Catalytic site may arise on oligomer formed only by one of these modes. Effector acts by fastening together components of certain oligomeric form and increases the life time of this form. It leads to a shift of oligomer equilibrium and increases a proportion of effector-binding oligomers. Effectors-activators bind the oligomers carrying composite catalytic sites and effectors-inhibitors bind the oligomers, which do not carry active catalytic sites. Thus, catalytic activity control in such system is explained by effector-induced changes of a catalytic sites number, but not of a catalytic site activity caused by changes of subunit's tertiary structure. The postulates of the model do not contradict available experimental data and lead to a new type of general rate equation, which allows to describe and understand the specific kinetic behavior of allosteric enzymes as well as Michaelis type enzymes. All known rate equations of allosteric The equation was tested by modeling the kinetics of human erythrocyte phosphofructokinase. It enabled to reproduce quantitatively the 66 kinetic curves experimentally obtained for this enzyme under different reaction conditions.     

The Enzyme Activity Allosteric Regulation Model Based on the Composite Nature of Catalytic and Regulatory Sites Concept

Abstract

A new kinetic model of enzymatic catalysis is proposed, which postulates that enzyme solutions are equilibrium systems of oligomers differing in the number of subunits and in the mode of their assembly. It is suggested that the catalytic and regulatory sites of allosteric enzymes are of composite nature and appear as a result of subunits joining. Two possible joining modes are postulated at each oligomerization step. Catalytic site may arise on oligomer formed only by one of these modes. Effector acts by fastening together components of certain oligomeric form and increases the life time of this form. It leads to a shift of oligomer equilibrium and increases a proportion of effector-binding oligomers. Effectors-activators bind the oligomers carrying composite catalytic sites and effectors-inhibitors bind the oligomers, which do not carry active catalytic sites. Thus, catalytic activity control in such system is explained by effector-induced changes of a catalytic sites number, but not of a catalytic site activity caused by changes of subunit's tertiary structure.

The postulates of the model do not contradict available experimental data and lead to a new type of general rate equation, which allows to describe and understand the specific kinetic behavior of allosteric enzymes as well as Michaelis type enzymes. All known rate equations of allosteric

The equation was tested by modeling the kinetics of human erythrocyte phosphofructokinase. It enabled to reproduce quantitatively the 66 kinetic curves experimentally obtained for this enzyme under different reaction conditions.     

A generic rate law for surface-active enzymes

Many biochemical reactions are confined to interfaces, such as membranes or cell walls. Despite their importance, no canonical rate laws describing the kinetics of surface-active enzymes exist. Combining the approach chosen by Michaelis and Menten 100 years ago with concepts from surface chemical physics, we here present an approach to derive generic rate laws of enzymatic processes at surfaces. We illustrate this by a simple reversible conversion on a surface to stress key differences to the classical case in solution. The available area function, a concept from surface physics which enters the rate law, covers different models of adsorption and presents a unifying perspective on saturation effects and competition between enzymes. A remarkable implication is the direct dependence of the rate of a given enzyme on all other enzymatic species able to bind at the surface. The generic approach highlights general principles of the kinetics of surface-active enzymes and allows to build consistent mathematical models of more complex pathways involving reactions at interfaces.     

Evaluation of a simplified generic bi-substrate rate equation for computational systems biology

The evaluation of a generic simplified bi-substrate enzyme kinetic equation, whose derivation is based on the assumption of equilibrium binding of substrates and products in random order, is described. This equation is much simpler than the mechanistic (ordered and ping-pong) models, in that it contains fewer parameters (that is, no K(i) values for the substrates and products). The generic equation fits data from both the ordered and the ping-pong models well over a wide range of substrate and product concentrations. In the cases where the fit is not perfect, an improved fit can be obtained by considering the rate equation for only a single set of product concentrations. Due to its relative simplicity in comparison to the mechanistic models, this equation will be useful for modelling bi-substrate reactions in computational systems biology.     

Maintenance Integration in Manufacturing Systems: From the Modeling Tool to Evaluation

In manufacturing systems, wear-out and eventual failure are unavoidable. However, to reduce the rate of their occurrence and to prolong the life of equipment or the capacity for extended productive use of the equipment under the necessary technological functioning and servicing, maintenance can be performed. For large manufacturing systems, maintenance integration involves a particular development concerned with both complexity models and computing time. This paper presents an effective way of modeling complex manufacturing systems through hierarchical and modular analysis by using stochastic Petri nets and Markov chains. In the proposed approach, the integration of maintenance policies in a manufacturing system is facilitated by the development of a generic model. With this generic modeling, the user doesn't need to code the strategies but only to instantiate the generic model with the structure of the manufacturing system. This method allows various maintenance strategies to be coded in the generic model with the aim of studying their influence on system dependability and performance.     

Cellulose hydrolysis in evolving substrate morphologies I: A general modeling formalism

We develop a general framework for a realistic rate equation modeling of cellulose hydrolysis using non‐complexed cellulase. Our proposed formalism, for the first time, takes into account explicitly the time evolution of the random substrate morphology resulting from the hydrolytic cellulose chain fragmentation and solubilization. This is achieved by integrating novel geometrical concepts to quantitatively capture the time‐dependent random morphology, together with the enzymatic chain fragmentation, into a coupled morphology‐plus‐kinetics rate equation approach. In addition, an innovative site number representation, based on tracking available numbers of β(1,4) glucosidic bonds, of different “site” types, exposed to attacks by different enzyme types, is presented. This site number representation results in an ordinary differential equation (ODE) system, with a substantially reduced ODE system size, compared to earlier chain fragmentation kinetics approaches. This formalism enables us to quantitatively simulate both the hydrolytically evolving random substrate morphology and the profound, and heretofore neglected, morphology effects on the hydrolysis kinetics. By incorporating the evolving morphology on an equal footing with the hydrolytic chain fragmentation, our formalism provides a framework for the realistic modeling of the entire solubilization process, beyond the short‐time limit and through near‐complete hydrolytic conversion. As part I of two companion papers, the present paper focuses on the development of the general modelling formalism. Results and testable experimental predictions from detailed numerical simulations are presented in part II. Biotechnol. Bioeng. 2009; 104: 261–274 © 2009 Wiley Periodicals, Inc.     

New chemical adaptor unit designed to release a drug from a tumor targeting device by enzymatic triggering

A new controlled drug delivery system for selective chemotherapy was developed. It is based on a chemical adaptor unit, that releases a drug by a spontaneous cyclization mechanism after cleavage of an enzymatic substrate. It also provides a generic linkage of a drug with a targeting device in a manner set to be triggered by defined enzymatic activity. The system is generic and allows using a variety of drugs, targeting devices, and enzymes by introducing the corresponding substrate as a trigger for drug release in the chemical adaptor.     

Relations between biochemical thermodynamics and biochemical kinetics

The parameters in steady-state or rapid-equilibrium rate equations for enzyme-catalyzed reactions depend on the temperature, pH, and ionic strength, and may depend on the concentrations of specific species in the buffer. When the complete rate equation (i.e. the equation with parameters for the reverse reaction as well as the forward reaction) is determined, there are one or more Haldane relations between some of the kinetic parameters and the apparent equilibrium constant for the reaction that is catalyzed. When the apparent equilibrium constant can be calculated from the kinetic parameters, the equilibrium composition can be calculated. This is remarkable because the kinetic parameters all depend on the properties of the enzymatic site, but the apparent equilibrium constant and the equilibrium composition do not. The effects of ionic strength and pH on the unoccupied enzymatic site and the occupied enzymatic site have to cancel in the Haldane relation or in the calculation of the apparent equilibrium constant using the rate constants for the steps in the mechanism. Several simple enzymatic mechanisms and their complete rate equations are discussed.