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Branched Pathways
Branched pathways, also known as branch points (not to be confused with the mathematical branch point), are a common pattern found in metabolism. This is where an intermediate Chemical species, species is chemically made or transformed by multiple enzymatic processes. Linear biochemical pathway, linear pathways only have one enzymatic reaction producing a species and one enzymatic reaction consuming the species. Branched pathways are present in numerous metabolic reactions, including glycolysis, the synthesis of lysine, glutamine, and penicillin, and in the production of the aromatic amino acids. In general, a single branch may have b producing branches and d consuming branches. If the intermediate at the branch point is given by s_i, then the rate of change of s_i is given by: : \sum_^b v_i-\sum_^d v_j=\frac At steady-state when ds_i/dt = 0 the consumption and production rates must be equal: : \sum_^b v_i=\sum_^d v_j Biochemical pathways can be investigated by computer si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Branch Point
In the mathematical field of complex analysis, a branch point of a multivalued function is a point such that if the function is n-valued (has n values) at that point, all of its neighborhoods contain a point that has more than n values. Multi-valued functions are rigorously studied using Riemann surfaces, and the formal definition of branch points employs this concept. Branch points fall into three broad categories: algebraic branch points, transcendental branch points, and logarithmic branch points. Algebraic branch points most commonly arise from functions in which there is an ambiguity in the extraction of a root, such as solving the equation w^2=z for w as a function of z. Here the branch point is the origin, because the analytic continuation of any solution around a closed loop containing the origin will result in a different function: there is non-trivial monodromy. Despite the algebraic branch point, the function w is well-defined as a multiple-valued function and, in an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flux Balance Analysis
In biochemistry, flux balance analysis (FBA) is a mathematical method for simulating the metabolism of cells or entire unicellular organisms, such as ''Escherichia coli, E. coli'' or yeast, using genome-scale reconstructions of metabolic networks. Genome-scale reconstructions describe all the biochemical reactions in an organism based on its entire genome. These reconstructions model metabolism by focusing on the interactions between metabolites, identifying which metabolites are involved in the various reactions taking place in a cell or organism, and determining the genes that encode the enzymes which Enzyme catalysis, catalyze these reactions (if any). History Earliest work in FBA dates back to the early 1980s. Papoutsakis demonstrated that it was possible to construct flux balance equations using a metabolic map. It was Watson,Watson MR (1984) Metabolic maps for the Apple II. 12, 1093-1094 however, who first introduced the idea of using linear programming and an objective f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Algebra
Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathematics), matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as line (geometry), lines, plane (geometry), planes and rotation (mathematics), rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to Space of functions, function spaces. Linear algebra is also used in most sciences and fields of engineering because it allows mathematical model, modeling many natural phenomena, and computing efficiently with such models. For nonlinear systems, which cannot be modeled with linear algebra, it is often used for dealing with first-order a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System Of Equations
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a: * System of linear equations, * System of nonlinear equations, * System of bilinear equations, * System of polynomial equations, * System of differential equations, or a * System of difference equations See also * Simultaneous equations model, a statistical model in the form of simultaneous linear equations * Elementary algebra Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra introduces variable (mathematics ..., for elementary methods {{set index article Equations Broad-concept articles de:Gleichung#Gleichungssysteme ... [...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] |
Product Inhibition
Product inhibition is a type of enzyme inhibition where the product of an enzyme reaction inhibits its production. Cells utilize product inhibition to regulate of metabolism as a form of negative feedback controlling metabolic pathways. Product inhibition is also an important topic in biotechnology, as overcoming this effect can increase the yield of a product, such as an antibiotic. Product inhibition can be competitive, non-competitive or uncompetitive. Mitigation of product inhibition Reactor design One method to reduce product inhibition is the use of a membrane reactor. These bioreactors uses a membrane to separate products from the rest of the reactor, limiting their inhibition. If the product differs greatly in size from the cells producing it, and the substrate feeding the cells, then the reactor can utilize a semipermeable membrane allowing to products to exit the reactor while leaving the cells and substrate behind to continue reacting making more product. Other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SBML
The Systems Biology Markup Language (SBML) is a representation format, based on XML, for communicating and storing computational models of biological processes. It is a free and open standard with widespread software support and a community of users and developers. SBML can represent many different classes of biological phenomena, including metabolic networks, cell signaling pathways, regulatory networks, infectious diseases, and many others. It has been proposed as a standard for representing computational models in systems biology today. History Late in the year 1999 through early 2000, with funding from the Japan Science and Technology Corporation (JST), Hiroaki Kitano and John C. Doyle assembled a small team of researchers to work on developing better software infrastructure for computational modeling in systems biology. Hamid Bolouri was the leader of the development team, which consisted of Andrew Finney, Herbert Sauro, and Michael Hucka. Bolouri identified the need ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Branch Ccf
A branch, also called a ramus in botany, is a stem that grows off from another stem, or when structures like veins in leaves are divided into smaller veins. History and etymology In Old English, there are numerous words for branch, including , , , and . There are also numerous descriptive words, such as (that is, something that has bled, or 'bloomed', out), (literally 'little bough'), (literally 'on growth'), and (literally 'offspringing'). Numerous other words for twigs and boughs abound, including , which still survives as the ''-toe'' in ''mistletoe''. Latin words for branch are or . The latter term is an affix found in other modern words such as ''cladodont'' (prehistoric sharks with branched teeth), ''cladode'' (flattened leaf-like branches), or ''cladogram'' (a branched diagram showing relations among organisms). Woody branches Large branches are known as boughs and small branches are known as twigs. The term ''twig'' usually refers to a terminus, while ''bough' ... [...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] |
Enzyme
An enzyme () is a protein that acts as a biological catalyst by accelerating chemical reactions. The molecules upon which enzymes may act are called substrate (chemistry), substrates, and the enzyme converts the substrates into different molecules known as product (chemistry), products. Almost all metabolism, metabolic processes in the cell (biology), cell need enzyme catalysis in order to occur at rates fast enough to sustain life. Metabolic pathways depend upon enzymes to catalyze individual steps. The study of enzymes is called ''enzymology'' and the field of pseudoenzyme, pseudoenzyme analysis recognizes that during evolution, some enzymes have lost the ability to carry out biological catalysis, which is often reflected in their amino acid sequences and unusual 'pseudocatalytic' properties. Enzymes are known to catalyze more than 5,000 biochemical reaction types. Other biocatalysts include Ribozyme, catalytic RNA molecules, also called ribozymes. They are sometimes descr ... [...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] |
