Difference between revisions of "Stoichiometric Matrix (analysis)"

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(Automatic synchronization with BioUML)
(Automatic synchronization with BioUML)
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If a reaction network has ''n'' reactions and ''m'' participating molecular species then the dynamic mass balance equation can be written as
 
If a reaction network has ''n'' reactions and ''m'' participating molecular species then the dynamic mass balance equation can be written as
  
:: [[File:Stoichiometric-Matrix-analysis-stoich1.png]]
+
:: [[File:DAE-models-Stoichiometric-Matrix-stoich1.png]]
  
 
where ''v'' is the flux vector and ''S'' is the concentration vector:
 
where ''v'' is the flux vector and ''S'' is the concentration vector:
  
:: [[File:Stoichiometric-Matrix-analysis-stoich2.png]]
+
:: [[File:DAE-models-Stoichiometric-Matrix-stoich2.png]]
  
 
==== Example ====
 
==== Example ====
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Consider the following system of reactions:
 
Consider the following system of reactions:
  
:: [[File:Stoichiometric-Matrix-analysis-stoich3.png]]
+
:: [[File:DAE-models-Stoichiometric-Matrix-stoich3.png]]
  
 
This systems comprises four reactions and five different molecular species. The stoichiometry matrix for this system can be written as:
 
This systems comprises four reactions and five different molecular species. The stoichiometry matrix for this system can be written as:
  
:: [[File:Stoichiometric-Matrix-analysis-stoich4.png]]
+
:: [[File:DAE-models-Stoichiometric-Matrix-stoich4.png]]
  
 
where the rows correspond to ''S''<sub>1</sub>, ''S''<sub>2</sub>, ''S''<sub>3</sub>, ''S''<sub>4</sub> and ''S''<sub>5</sub>, respectively. Note that the process of converting a reaction scheme into a stoichiometry matrix can be a lossy transformation, for example, the stoichiometries in the second reaction simplify when included in the matrix.
 
where the rows correspond to ''S''<sub>1</sub>, ''S''<sub>2</sub>, ''S''<sub>3</sub>, ''S''<sub>4</sub> and ''S''<sub>5</sub>, respectively. Note that the process of converting a reaction scheme into a stoichiometry matrix can be a lossy transformation, for example, the stoichiometries in the second reaction simplify when included in the matrix.

Revision as of 12:36, 16 May 2013

Analysis title
File:Stoichiometric-Matrix-analysis-icon.png Stoichiometric Matrix
Provider
Institute of Systems Biology
Plugin
biouml.plugins.modelreduction (Model reduction plug-in)

Description

The stoichiometric matrix N provides the linear relationship of the model between the flux rates of the (enzymatic) reactions and the derivatives of the reactant (enzyme) concentrations.

If a reaction network has n reactions and m participating molecular species then the dynamic mass balance equation can be written as

DAE-models-Stoichiometric-Matrix-stoich1.png

where v is the flux vector and S is the concentration vector:

DAE-models-Stoichiometric-Matrix-stoich2.png

Example

Consider the following system of reactions:

DAE-models-Stoichiometric-Matrix-stoich3.png

This systems comprises four reactions and five different molecular species. The stoichiometry matrix for this system can be written as:

DAE-models-Stoichiometric-Matrix-stoich4.png

where the rows correspond to S1, S2, S3, S4 and S5, respectively. Note that the process of converting a reaction scheme into a stoichiometry matrix can be a lossy transformation, for example, the stoichiometries in the second reaction simplify when included in the matrix.

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