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| | I would like to introduce myself to you, I am Jayson Simcox but I don't like when people use my complete name. To climb is something she would by no means give up. My wife and I reside in Mississippi but now I'm contemplating other choices. Distributing production is how he makes a residing.<br><br>my web blog - online psychics ([http://1.234.36.240/fxac/m001_2/7330 1.234.36.240]) |
| '''Biochemical systems theory''' is a [[mathematical model]]ling framework for [[biochemical system]]s, based on ordinary [[differential equation]]s (ODE), in which [[biochemistry|biochemical processes]] are represented using '''power-law''' expansions in the variables of the [[system]].
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| This framework, which became known as Biochemical Systems Theory, has been developed since the 1960s by Michael Savageau and others for the [[systems analysis]] of [[biochemical]] processes.<ref>[http://www.biolchem.qui.uc.pt/curso/BST.htm ''Biochemical Systems Theory''], an introduction.</ref> According to Cornish-Bowden (2007) they "regarded this as a general theory of [[metabolic]] control, which includes both metabolic control analysis and flux-oriented theory as special cases".<ref>Athel Cornish-Bowden, [http://bip.cnrs-mrs.fr/bip10/mcafaq4.htm#sava Metabolic control analysis FAQ], website 18 April 2007.</ref>
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| ==Representation==
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| The dynamics of a species is represented by a differential equation with the structure:
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| <center><math>\frac{dX_i}{dt}=\sum_j \mu_{ij} \cdot \gamma_j \prod_k X_k^{f_{jk}}\,</math></center>
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| where X<sub>i</sub> represents one of the n<sub>d</sub> variables of the model (metabolite concentrations, protein concentrations or levels of gene expression). j represents the n<sub>f</sub> biochemical processes affecting the dynamics of the species. On the other hand, <math>\mu</math><sub>ij</sub> (stoichiometric coefficient), <math>\gamma</math><sub>j</sub> (rate constants) and f<sub>jk</sub> (kinetic orders) are two different kinds of parameters defining the dynamics of the system.
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| The principal difference of [[power-law]] [[Mathematical model|models]] with respect to other ODE models used in biochemical systems is that the kinetic orders can be non-integer numbers. A kinetic order can have even negative value when inhibition is modelled. In this way, power-law models have a higher flexibility to reproduce the non-linearity of biochemical systems.
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| Models using power-law expansions have been used during the last 35 years to model and analyse several kinds of biochemical systems including metabolic networks, genetic networks and recently in cell signalling.
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| ==See also==
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| * [[Dynamical systems]]
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| * [[Ludwig von Bertalanffy]]
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| * [[Systems theory]]
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| ==References==
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| {{Reflist}}
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| ==Literature==
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| '''Books:'''
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| * M.A. Savageau, ''Biochemical systems analysis: a study of function and design in molecular biology'', Reading, MA, Addison–Wesley, 1976.
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| * E.O. Voit (ed), ''Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity'', Van Nostrand Reinhold, NY, 1991.
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| * E.O. Voit, ''Computational Analysis of Biochemical Systems. A Practical Guide for Biochemists and Molecular Biologists'', Cambridge University Press, Cambridge, U.K., 2000.
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| * N.V. Torres and E.O. Voit, ''Pathway Analysis and Optimization in Metabolic Engineering'', Cambridge University Press, Cambridge, U.K., 2002.
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| '''Scientific articles:'''
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| * M.A. Savageau, ''Biochemical systems analysis: I. Some mathematical properties of the rate law for the component enzymatic reactions'' in: J. Theor. Biol. 25, pp. 365–369, 1969.
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| * M.A. Savageau, ''Development of fractal kinetic theory for enzyme-catalysed reactions and implications for the design of biochemical pathways'' in: Biosystems 47(1-2), pp. 9–36, 1998.
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| * M.R. Atkinson et al., ''Design of gene circuits using power-law models'', in: Cell 113, pp. 597–607, 2003.
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| * F. Alvarez-Vasquez et al., ''Simulation and validation of modelled sphingolipid metabolism in Saccharomyces cerevisiae'', ''Nature'' 27, pp. 433(7024), pp. 425–30, 2005.
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| *J. Vera et al., ''Power-Law models of signal transduction pathways'' in: Cellular Signalling {{doi|10.1016/j.cellsig.2007.01.029}}), 2007.
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| * Eberhart O. Voit, [http://ase.tufts.edu/chemical/documents/newsWorkshopVoit-saturday.pdf ''Applications of Biochemical Systems Theory''], 2006.
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| ==External links==
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| * [http://www.biolchem.qui.uc.pt/curso/BST.htm Biochemical Systems Theory] an introduction,
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| * http://web.udl.es/Biomath/PowerLaw/
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| * [http://www.powerlawmodels.org/ A Web on Power-law Models for Biochemical Systems]
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| {{DEFAULTSORT:Biochemical Systems Theory}}
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| [[Category:Systems biology]]
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