Team:Toulouse/Modelling

From 2014.igem.org

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According to the publication of <b>Xianling Ji</b> (See References), after six months of <i>Bacillus subtilis'</i> growth in a tree, bacteria cells reach a concentration of 10⁵ cells per gram of fresh plant. We assume that 10⁵ cells/g is the maximum concentration.
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According to the publication of <b>Xianling Ji</b> (See References), after six months of <i>Bacillus subtilis</i> growth in a tree, bacteria cells reach a concentration of 10⁵ cells per gram of fresh plant. We assume that 10⁵ cells/g is the maximum concentration.
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It is believed that there is no leakage of cells.
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It is assumed that there is no leakage of cells.
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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>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.  
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<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.
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<br>If N decreases until it reaches N<sub>min</sub>, the term (1-(N<sub>min</sub>/N)) is equal to 0. Therefore the growth is null.
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<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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<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 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>
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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 leads to the writing of this model:</p>
<center style="margin: 65px 0;"><img style="" src="http://2014.igem.org/wiki/images/f/f8/Form_part.png" alt="model"></center>
<center style="margin: 65px 0;"><img style="" src="http://2014.igem.org/wiki/images/f/f8/Form_part.png" alt="model"></center>
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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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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.
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>).
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 tree plane is 27,446kg. We 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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The average weight of a tree plane is 27,446kg. We inoculated 10mL of bacterial culture at 10⁹cfu/mL, <i>i.e.</i> 10^10 bacterial cells. This represents 3.64x10²cfu/g of fresh plant (N0).
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In our model, growth starts only from 10°C, which happens between March and April. This period seems to be suitable to put the strain in the tree. From December the temperature decreased below 4°C, threshold below which bacteria die.  
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In our model, growth starts only from 10°C, which happens between March and April. This period seems to be suitable to put the strain in the tree. From December the temperature decreases below 4°C corresponding to the threshold below which bacteria die.  
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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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In practice, temperature variations are certainly lower in trees 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 of temperature, the rise of sap ans sap composition variations. All these parameters can consequently slow or fast the growth rate.
The modeling work is done with the programming language 'R' script attached (See Annexe).
The modeling work is done with the programming language 'R' script attached (See Annexe).

Revision as of 21:53, 17 October 2014