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| | <p>The relative amount of a particular metabolite taken part in a reaction is represented by its stoichiometric coefficient, so for instance metabolite B has a stoichiometric coefficient of 2 in reaction r2. The whole network of reactions that represents the metabolism of can be represented in a stoichiometric matrix S of m rows and r columns, where m are the amount of metabolites and r the amount of reactions in the network. The matrix will then contain on the i,jth entry the stoichiometric coefficient of metabolite i in reaction j. The stoichiometric coefficient will be negative when the metabolite is a substrate (on the left side of the reaction) and positive when a metabolite is a product (on the right side of the reaction). So our example network can thus be represented in a matrix of S of 3 rows and 5 columns as can be seen in figure 3. To illustrate let’s consider position 1,1 in the matrix, since the first column represents reaction r1 and the first row the metabolite A, we put in the stoichiometric coefficient of A in r1 which is 1.</p> | | <p>The relative amount of a particular metabolite taken part in a reaction is represented by its stoichiometric coefficient, so for instance metabolite B has a stoichiometric coefficient of 2 in reaction r2. The whole network of reactions that represents the metabolism of can be represented in a stoichiometric matrix S of m rows and r columns, where m are the amount of metabolites and r the amount of reactions in the network. The matrix will then contain on the i,jth entry the stoichiometric coefficient of metabolite i in reaction j. The stoichiometric coefficient will be negative when the metabolite is a substrate (on the left side of the reaction) and positive when a metabolite is a product (on the right side of the reaction). So our example network can thus be represented in a matrix of S of 3 rows and 5 columns as can be seen in figure 3. To illustrate let’s consider position 1,1 in the matrix, since the first column represents reaction r1 and the first row the metabolite A, we put in the stoichiometric coefficient of A in r1 which is 1.</p> |
| | <p>S=</p> | | <p>S=</p> |
| − | <table class="c7"><tbody><tr class="c1"><td class="c12" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td><td class="c6" colspan="1" rowspan="1"><p class="c2"><span class="c8">r1</span></p></td><td class="c6" colspan="1" rowspan="1"><p class="c2"><span class="c8">r2</span></p></td><td class="c6" colspan="1" rowspan="1"><p class="c2"><span class="c8">r3</span></p></td><td class="c6" colspan="1" rowspan="1"><p class="c2"><span class="c8">r4</span></p></td><td class="c6" colspan="1" rowspan="1"><p class="c2"><span class="c8">r5</span></p></td></tr><tr class="c10"><td class="c9" colspan="1" rowspan="1"><p class="c2"><span class="c8">A</span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2"><span class="c0">1</span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2"><span class="c0">-3</span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td></tr><tr class="c10"><td class="c9" colspan="1" rowspan="1"><p class="c2"><span class="c8">B</span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2"><span class="c0">2</span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2"><span class="c0">-2</span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2"><span class="c0">-1</span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td></tr><tr class="c1"><td class="c9" colspan="1" rowspan="1"><p class="c2"><span class="c8">C</span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2"><span class="c0">1</span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td><td class="c3" colspan="1" rowspan="1"><p class="c2"><span class="c0">-1</span></p></td></tr><tr class="c1"><td class="c9" colspan="1" rowspan="1"><p class="c2"><span class="c8">D</span></p></td><td class="c11" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td><td class="c11" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td><td class="c11" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td><td class="c11" colspan="1" rowspan="1"><p class="c2"><span class="c0">1</span></p></td><td class="c11" colspan="1" rowspan="1"><p class="c2 c4"><span class="c0"></span></p></td></tr></tbody></table> | + | <figure><img src="https://static.igem.org/mediawiki/2018/6/6f/T--Groningen--stochtabel.png"width="50%></figure> |
| − | <table><tr><th></th><th>r1</th><th>r2</th><th>r3</th><th>r4</th><th>r5</th></tr><tr><td>A</td><td>1</td><td>-3</td><td></td><td></td><td></td></tr><tr><td>B</td><td></td><td>2</td><td>-2</td><td>-1</td><td></td></tr><tr><td>C</td><td></td><td></td><td>1</td><td></td><td>-1</td></tr><tr><td>D</td><td></td><td></td><td></td><td>1</td><td></td></tr></table>
| + | |
| | <p>The flux or reaction rate through each reaction can be represented in a vector v of length r, where r are the amount of reactions in the network and every position in the vector represents the flux through a reaction. If the network is at steady state the following holds:</p><figure><img src="https://static.igem.org/mediawiki/2018/4/40/T--Groningen--Flux-based-sxv.png"></figure> | | <p>The flux or reaction rate through each reaction can be represented in a vector v of length r, where r are the amount of reactions in the network and every position in the vector represents the flux through a reaction. If the network is at steady state the following holds:</p><figure><img src="https://static.igem.org/mediawiki/2018/4/40/T--Groningen--Flux-based-sxv.png"></figure> |
| | <p>Where S is the stoichiometric matrix and v is the reaction rate vector. Since what we want to know is the flux through each reaction, given a stoichiometric matrix S that represents the whole metabolic network of our cell we have to solve the above equation for v. There usually is no single v that satisfy the above equation, but rather a whole solution space. In order to narrow down this solution space, we maximize a biologically plausible objective such as biomass growth and select only those flux values that together can optimize this objective. </p> | | <p>Where S is the stoichiometric matrix and v is the reaction rate vector. Since what we want to know is the flux through each reaction, given a stoichiometric matrix S that represents the whole metabolic network of our cell we have to solve the above equation for v. There usually is no single v that satisfy the above equation, but rather a whole solution space. In order to narrow down this solution space, we maximize a biologically plausible objective such as biomass growth and select only those flux values that together can optimize this objective. </p> |
