Team:Toulouse/Modelling

From 2014.igem.org

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<br>The parameter m is a curvature parameter. Larger m is, smaller is the curvature of the deceleration phase with the model.  
<br>The parameter m is a curvature parameter. Larger m is, smaller is the curvature of the deceleration phase with the model.  
<br>The parameter n is a parameter related to the period lag. Larger n is, shorter is the period of lag.  
<br>The parameter n is a parameter related to the period lag. Larger n is, shorter is the period of lag.  
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<br>N<sub>min</sub> is slightly lower than N<sub>0</sub>. When N is small at the initial state (N = N<sub>0</sub>) <i>i.e.</i> N is close to N<sub>min</sub>(, N<sub>min</sub>/N is almost equal to 1. Therefore the term (1-(N<sub>min</sub>/N)) is less than 1 and the growth is very slow.  
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<br>N<sub>min</sub> is slightly lower than N<sub>0</sub>. When N is small at the initial state (N = N<sub>0</sub>) <i>i.e.</i> N is close to N<sub>min</sub>, N<sub>min</sub>/N is almost equal to 1. Therefore the term (1-(N<sub>min</sub>/N)) is nearly 0 and the growth is very slow.  
<br>If N decrease until reach N<sub>min</sub>, the term (1-(N<sub>min</sub>/N)) is equal to 0. Therefore the growth is null.
<br>If N decrease until reach N<sub>min</sub>, the term (1-(N<sub>min</sub>/N)) is equal to 0. Therefore the growth is null.
<br> Similarly when N is equal to N<sub>max</sub> the term (1-(N/N<sub>max</sub>)) is equal to 0 and the growth is blocked.</br>
<br> Similarly when N is equal to N<sub>max</sub> the term (1-(N/N<sub>max</sub>)) is equal to 0 and the growth is blocked.</br>
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To overcome this we labor under two conditions , positive growth and negative growth, so two equations.This led to the writing of this model:</p>
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To overcome this we worked under two conditions: positive and negative growth. Theses conditions can be translated in two equations. This lead to the writing of this model:</p>
<center style="margin: 65px 0;"><img style="" src="https://static.igem.org/mediawiki/2014/f/f8/Form_part.png" alt="model"></center>
<center style="margin: 65px 0;"><img style="" src="https://static.igem.org/mediawiki/2014/f/f8/Form_part.png" alt="model"></center>
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with n = 1 and m = 0.5</br></br>
with n = 1 and m = 0.5</br></br>
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Term (1-(Nmin/N)) is not taken into account when there is growth and (1-(N/Nmax)) is not taken into account when there is bacterial decay.</br>
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The term (1-(Nmin/N)) is not taken into account when there is growth. <br>The term (1-(N/Nmax)) is not taken into account when there is bacterial decay.</br>
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Meteorological records of the Toulouse region of 2011-2013 are used to do averages daily temperatures. Thus we can determine <i>B.subtilis</i> growth during a year on Toulouse. This values are obtained for each day by the average on the hightest and the lowest temperature.
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Meteorological records of the Toulouse region during the years 2011-2013 are used to do average daily temperatures. Thus we can determine <i>B.subtilis</i> growth in a tree located in Toulouse during a year. This values are obtained for each day by the average on the highest and the lowest temperature.
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The density of green wood plane is about 650kg/m³. The average diameter of the trunks of the trees in question is about 0.80m and 15m high. This represents a volume of 30 m³ . The weight of the trunk is therefore 19,604kg .
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The density of green wood plane is about 650kg/m³. The average diameter of the trunks of the concerned trees is about 0.80m and 15m high. This represents a volume of 30m³. Therefore the weight of the trunk is 19,604kg.
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Added to this weight the weight of branches, twigs, leaves about 25% and about 15% of roots (<a href="http://www.guichetdusavoir.org/viewtopic.php?t=25895">source-FR</a>).
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We need to add to this weight the weight of branches, twigs, about 25% of leaves and about 15% of roots (<a href="http://www.guichetdusavoir.org/viewtopic.php?t=25895">source-FR</a>).
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The average weight of a plane tree is 27,446kg where in inoculated 10mL of bacterial culture at 10⁹cfu/mL, ie 10^10 bacterial cells. This represents 3.64x10² cfu/g of fresh plant (N0).
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<!--pas compris ces deux dernières phrases-->
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The average weight of a plane tree is 27,446kg where in inoculated 10mL of bacterial culture at 10⁹cfu/mL, <i>i.e.</i> 10^10 bacterial cells. This represents 3.64x10² cfu/g of fresh plant (N0).
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<center><img style="" src="https://static.igem.org/mediawiki/2014/5/53/Bacterial_growth.png" alt="Figure2"></center>
<center><img style="" src="https://static.igem.org/mediawiki/2014/5/53/Bacterial_growth.png" alt="Figure2"></center>
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<p class="legend">Fig 2: (<span style="color:#000000; font-family:'Open Sans'; font-size:14px;">black</span>) Bacillus Subtilis growth curve during one year (N is cells quantity by g of fresh plant). (<span style="color:#FF0040; font-family:'Open Sans'; font-size:14px;">red</span>) average temperature. (<span style="color:#0101DF; font-family:'Open Sans'; font-size:14px;">blue</span>) threshold at 10 °C.</p>
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<p class="legend">Figure 2: (<span style="color:#000000; font-family:'Open Sans'; font-size:14px;">black</span>) <i>Bacillus subtilis</i> growth curve during one year (N is cell quantity by g of fresh plant). (<span style="color:#FF0040; font-family:'Open Sans'; font-size:14px;">red</span>) average temperature. (<span style="color:#0101DF; font-family:'Open Sans'; font-size:14px;">blue</span>) threshold at 10°C.</p>
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In practice, temperature variations are certainly lower in tree than outside, especially if roots extend very deep. Composition of the tree sap must also intervene in the growth rate, nutrient content of sap is also temperature dependent. The effects of the decrease of the temperature in winter also involves a fall of the sap and this must also be involved in the disappearance of our strain in the tree. The period of <i>Bacillus subtilis</i> growth is certainly affected by the change in temperature, the rise of sap, its composition variations can consequently slow the growth rate.
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In practice, temperature variations are certainly lower in tree than outside, especially if roots extend very deep. Composition of the tree sap must also intervene in the growth rate and nutrient content of sap is also temperature dependent. The effects of the decrease of the temperature in winter also induces a fall of the sap and this must also be involved in the disappearance of our strain in the tree. The period of <i>Bacillus subtilis</i> growth is certainly affected by the change in temperature, the rise of sap ans sap composition variations. All these parameters can consequently slow or fast the growth rate.
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The modeling work is done with the programming language 'R' script attached.
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The modeling work is done with the programming language 'R' script attached (See Annexes).
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Revision as of 15:22, 16 October 2014