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Summation Theorems (biochemistry)
In metabolic control analysis, a variety of theorems have been discovered and discussed in the literature. The most well known of these are flux and concentration control coefficient summation relationships. These theorems are the result of the stoichiometric structure and mass conservation properties of biochemical networks. Equivalent theorems have not been found, for example, in electrical or economic systems. The summation of the flux and concentration control coefficients were discovered independently by the Kacser/Burns group and the Heinrich/Rapoport group in the early 1970s and late 1960s. If we define the control coefficients using enzyme concentration, then the summation theorems are written as: : \sum_i C^J_ = 1 : \sum_i C^s_ = 0 However these theorems depend on the assumption that reaction rates are proportional to enzyme concentration. An alternative way to write the theorems is to use control coefficients that are defined with respect to the local rates which is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metabolic Control Analysis
In biochemistry, metabolic control analysis (MCA) is a mathematical framework for describing Metabolic pathway, metabolic, Cell signaling#Signaling pathways, signaling, and genetic pathways. MCA quantifies how variables, such as fluxes and Chemical species, species concentrations, depend on Network (mathematics), network parameters. In particular, it is able to describe how network-dependent properties, called control coefficients, depend on Local property, local properties called Elasticity of a function, elasticities or elasticity coefficients. MCA was originally developed to describe the control in metabolic pathways but was subsequently extended to describe signaling and Gene regulatory network, genetic networks. MCA has sometimes also been referred to as ''Metabolic Control Theory,'' but this terminology was rather strongly opposed by Henrik Kacser, one of the founders. More recent work has shown that MCA can be Isomorphism, mapped directly on to classical control theory an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Coefficient (biochemistry)
In biochemistry, control coefficients are used to describe how much influence a given reaction step has on the flux or concentration of the species at steady state. This can be accomplished experimentally by changing the expression level of a given enzyme and measuring the resulting changes in flux and metabolite levels. In theory, any observables, such as growth rate, or even combinations of observables, can be defined using a control coefficient; but flux and concentration control coefficients are by far the most commonly used. The simplest way to look at control coefficients is as the scaled derivatives of the steady-state change in an observable with respect to a change in enzyme activity ( for each species ). For example, the flux control coefficients (, where is the reaction rate) can be written as: C_^J = \frac \frac = \frac \approx \frac while the concentration control coefficients (, where is the concentration of species ) can be written as: C_^ = \frac \frac = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steady State (biochemistry)
In biochemistry, steady state refers to the maintenance of constant internal concentrations of Biomolecule, molecules and ions in the Cell (biology), cells and Organ (biology), organs of living systems. Living organisms remain at a dynamic steady state where their internal composition at both cellular and gross levels are relatively constant, but different from Equilibrium chemistry, equilibrium concentrations. A continuous flux of mass and energy results in the constant Anabolism, synthesis and Catabolism, breakdown of molecules via chemical reactions of biochemical pathways. Essentially, steady state can be thought of as homeostasis at a cellular level. Maintenance of steady state Metabolic regulation achieves a balance between the rate of input of a substrate and the rate that it is degraded or converted, and thus maintains steady state. The rate of metabolic flow, or flux, is variable and subject to metabolic demands. However, in a metabolic pathway, steady state is main ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elasticity Coefficient
In chemistry, the Reaction rate, rate of a chemical reaction is influenced by many different factors, such as temperature, pH, reactant, the concentration of Product (chemistry), products, and other effectors. The degree to which these factors change the reaction rate is described by the elasticity coefficient. This coefficient is defined as follows: \varepsilon_^v = \left(\frac \frac\right)_ = \frac \approx \frac where v denotes the reaction rate and s denotes the Substrate (chemistry), substrate concentration. Be aware that the notation will use lowercase roman letters, such as s, to indicate concentrations. The partial derivative in the definition indicates that the elasticity is measured with respect to changes in a factor S while keeping all other factors constant. The most common factors include substrates, products, enzyme, and effectors. The scaling of the coefficient ensures that it is dimensionless and independent of the units used to measure the reaction rate and m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rate-limiting Step (biochemistry)
In biochemistry, a rate-limiting step is a reaction step that controls the rate of a series of biochemical reactions. The statement is, however, a misunderstanding of how a sequence of enzyme- catalyzed reaction steps operate. Rather than a single step controlling the rate, it has been discovered that multiple steps control the rate. Moreover, each controlling step controls the rate to varying degrees. Blackman (1905) stated as an axiom: "when a process is conditioned as to its rapidity by a number of separate factors, the rate of the process is limited by the pace of the slowest factor." This implies that it should be possible, by studying the behavior of a complicated system such as a metabolic pathway, to characterize a single factor or reaction (namely the slowest), which plays the role of a master or rate-limiting step. In other words, the study of flux control can be simplified to the study of a single enzyme since, by definition, there can only be one 'rate-limiting' step. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
