Biochemical systems theory

<h2 id="representation">Representation</h2>
The dynamics of a species is represented by a differential equation with the structure:

d
              
                X
                
                  i
                
              
            
            
              d
              t
            
          
        
        =
        
          ∑
          
            j
          
        
        
          μ
          
            i
            j
          
        
        ⋅
        
          γ
          
            j
          
        
        
          ∏
          
            k
          
        
        
          X
          
            k
          
          
            
              f
              
                j
                k
              
            
          
        
        
      
    
    {\displaystyle {\frac {dX_{i}}{dt}}=\sum _{j}\mu _{ij}\cdot \gamma _{j}\prod _{k}X_{k}^{f_{jk}}\,}

where Xi represents one of the nd variables of the model (metabolite concentrations, protein concentrations or levels of gene expression). j represents the nf biochemical processes affecting the dynamics of the species. On the other hand, 
 
 
 
 μ
 
 
 {\displaystyle \mu }
 
ij (stoichiometric coefficient), 
 
 
 
 γ
 
 
 {\displaystyle \gamma }
 
j (rate constants) and fjk (kinetic orders) are two different kinds of parameters defining the dynamics of the system.
The principal difference of <a href="/facts/Power-law/DhAjYwwz">power-law</a> <a href="/facts/Mathematical_model/CGhyuxgz">models</a> 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 modeled. In this way, power-law models have a higher flexibility to reproduce the non-linearity of biochemical systems.
Models using power-law expansions have been used during the last 35 years to model and analyze several kinds of biochemical systems including metabolic networks, genetic networks and recently in cell signalling.

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Dynamical_systems/782gREl5">Dynamical systems</a></li>
<li><a href="/facts/Ludwig_von_Bertalanffy/3R2540Vt">Ludwig von Bertalanffy</a></li>
<li><a href="/facts/Systems_theory/C56Ck7DQ">Systems theory</a></li></ul>

<h2 id="literature">Literature</h2>
Books:

<ul><li>M.A. Savageau, Biochemical systems analysis: a study of function and design in molecular biology, Reading, MA, Addison–Wesley, 1976.</li>
<li>E.O. Voit (ed), Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity, Van Nostrand Reinhold, NY, 1991.</li>
<li>E.O. Voit, Computational Analysis of Biochemical Systems. A Practical Guide for Biochemists and Molecular Biologists, Cambridge University Press, Cambridge, U.K., 2000.</li>
<li>N.V. Torres and E.O. Voit, Pathway Analysis and Optimization in Metabolic Engineering, Cambridge University Press, Cambridge, U.K., 2002.</li></ul>
Scientific articles:

<ul><li>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.</li>
<li>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.</li>
<li>M.R. Atkinson et al., Design of gene circuits using power-law models, in: Cell 113, pp. 597–607, 2003.</li>
<li>F. Alvarez-Vasquez et al., Simulation and validation of modelled sphingolipid metabolism in Saccharomyces cerevisiae, Nature 27, pp. 433(7024), pp. 425–30, 2005.</li>
<li>J. Vera et al., Power-Law models of signal transduction pathways in: Cellular Signalling <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2Fj.cellsig.2007.01.029">10.1016/j.cellsig.2007.01.029</a>), 2007.</li>
<li>Eberhart O. Voit, <a href="http://ase.tufts.edu/chemical/documents/newsWorkshopVoit-saturday.pdf">Applications of Biochemical Systems Theory</a>, 2006.</li></ul>
<h2 id="external-links">External links</h2>
<ul><li><a href="https://savageaulab.bme.ucdavis.edu/">[1]</a> Savageau Lab at UC Davis</li>
<li><a href="http://www.bst.bme.gatech.edu/">[2]</a> Voit Lab at GA Tech</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Biochemical Systems Theory, an introduction. <a href="https://www.hindawi.com/journals/isrn/2013/897658/" target="_blank">https://www.hindawi.com/journals/isrn/2013/897658/</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Athel Cornish-Bowden, Metabolic control analysis FAQ, website 18 April 2007. <a href="/wiki/Athel_Cornish-Bowden" target="_blank">/wiki/Athel_Cornish-Bowden</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
</ol>

Biochemical systems theory open-in-new

Biochemical systems theory