Team:Toulouse/Modelling

From 2014.igem.org

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Modeling is a tool used to simplify and study systems. It helps us to predict behavior thanks to bibliographic or experimental informations.</br>
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Modeling is a tool used to simplify and study systems. It helps us to predict behavior of biological systems using bibliographic or experimental data.</br>
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The following modelisation focuses on the development of our engineered bacterium (called SubtiTree) in trees. The bacterial growth in trees seems to be unknown, thus we must infer <i>Bacillus subtilis'</i> behavior.</p>
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The following modelisation focuses on the development of a bacterium in trees. The bacterial growth in trees seems to be unknown, thus we must infer <i>Bacillus subtilis'</i> behavior.</p>
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<i>Bacillus subtilis</i> is a tree endophyte strain. A study showed that <i>Bacillus subtilis</i> could develop and fully colonize a tree, reaching a concentration of 10⁵ cells per gram of fresh plant. We need to know in which conditions the growth of <i>B. subtilis</i> is optimum in a tree and if the weather can stop its development during winter. Therefore we decided to work on the <i>Bacillus subtilis'</i> growth in function of the temperature during the year.  
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<i>Bacillus subtilis</i> is a tree endophyte strain. A study showed that <i>Bacillus subtilis</i> could develop and fully colonize a tree, reaching a concentration of 10<sup>5</sup> cells per gram of fresh plant. We need to know in which conditions the growth of <i>B. subtilis</i> is optimum in a tree and if the weather can stop its development during winter. Therefore we decided to work on the growthof <i>Bacillus subtilis'</i> in function of the temperature during the year.  
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<br>Modeling bacterial growth in a tree section generates some difficulties. We need to know the distance between two tree extremities (treetops and root) or the speed sap flow. However the speed sap flow can vary with temperature during the day and seasons cause of the type of sap (phloem, xylem). Furthermore a tree is not an homogeneous system: its roots, trunk and branches do not contain the same amount of sap and wood. <br>The average speed of the plane tree sap is 2.4m/h, which means that in a day the sap of a 30m tree will flow from one extremity to the other. Tree is reduced to a bioreactor.
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<br>Modeling bacterial growth in a tree section generates some difficulties. We need to know the distance between two tree extremities (treetops and root) or the speed sap flow. However the flow of speed sap can vary with temperature during the day. The composition of sap also varies due to seasons and type of container (phloem, xylem). Furthermore a tree is not an homogeneous system: its roots, trunk and branches do not contain the same amount of sap and wood. <br>The average speed of the plane tree sap is 2.4 m/h, which means that in a day the sap of a 30 m tree will flow from one extremity to the other. We thus reduced the tree to a bioreactor.
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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 10<sup>5</sup> cells per gram of fresh plant. We assume that 10<sup>5</sup> cells/g is the maximum concentration.
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An assessment of the <i>Bacillus subtilis</i> growth in a similar sap was performed in laboratory conditions with optimum growth medium for <i>Bacillus subtilis</i>. The composition sap used was the one from birch sap.<br>
An assessment of the <i>Bacillus subtilis</i> growth in a similar sap was performed in laboratory conditions with optimum growth medium for <i>Bacillus subtilis</i>. The composition sap used was the one from birch sap.<br>
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In these conditions, the growth rate μ is optimal. From this value we can extrapolate a growth curve as a function of temperature. We used the <b>cardinal temperature model</b>: </p>
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In these conditions, the growth rate µ is optimal. From this value we can extrapolate a growth curve as a function of temperature. We used the <b>cardinal temperature model</b>: </p>
   
   
<center style="margin-bottom:50px;"><img style="" src="http://2014.igem.org/wiki/images/8/85/Formules_Rosso.png" alt="cardinal temperature model"></center>
<center style="margin-bottom:50px;"><img style="" src="http://2014.igem.org/wiki/images/8/85/Formules_Rosso.png" alt="cardinal temperature model"></center>
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The optimal growth rate (µ<sub>opt</sub>) is obtained experimentally with a similar birch sap environment.</br>
The optimal growth rate (µ<sub>opt</sub>) is obtained experimentally with a similar birch sap environment.</br>
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The growth rate is negative below 10°C (according to growth tests performed at 10°C and 4°C under similar conditions for the measurement of μ<sub>opt</sub>), survival rate after 24h was 0.3 % at 10°C and null at 4°C.<br>
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The growth rate is negative below 10°C (according to growth tests performed at 10°C and 4°C under similar conditions for the measurement of µ<sub>opt</sub>), survival rate after 24h was 0.3 % at 10°C and null at 4°C.<br>
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Conditions apply:</p>
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Conditions applied:</p>
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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>
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 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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Meteorological records of the Toulouse region during the years 2011-2013 are used to calculate 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 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 650 kg/m³. The average diameter of the trunks of the concerned trees is about 0.80 m and they are 15 m high. This represents a volume of 30 m³. Therefore the weight of the trunk is 19.604 kg.
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 3.64x10²cfu/g of fresh plant (N0).
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The average weight of a tree plane is 27,446kg. We inoculated 10 mL of bacterial culture at 10<sup>9</sup>cfu/mL, <i>i.e.</i> 10<sup>10</sup> bacterial cells. This represents 3.64x10<sup>2</sup>cfu/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 decreases below 4°C corresponding to the 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 the most suitable to administer the strain in the tree. Starting in December the temperature decreases below 4°C, corresponding to the threshold below which bacteria starts to die.  
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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.
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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 in the trunk and sap composition variations. All these parameters can consequently slow-down or boost 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 23:36, 17 October 2014