Team:Toulouse/Modelling

From 2014.igem.org

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<i>Bacillus subtilis</i> is a trees endophyte strain, a study [1] showed that <i>Bacillus subtilis</i> could develop and colonize fully a tree and reach a concentration of 10⁵ cells per g of fresh plant. We need to know in which conditions the growth are optimum in a tree and if the weather can stop its development in winter. We work on the <i>Bacillus subtilis</i> growth in function of the temperature during year. Modeling bacterial growth in a tree section generate some difficulties, we need to know distance between two tree extremities (treetops and root) or the speed sap flow which can vary with temperature during the day and seasons, cause of the type of sap (phloem, xylem). Furthermore tree is not a homogeneous system, its roots, trunk and branch do not contain same amount of sap and wood. The average speed of the plane tree sap is 2.4m/h [2] that means that in a day the sap will flow from one end to the other of a tree 30m. Tree is reduced to a bioreactor.
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<i>Bacillus subtilis</i> is a trees endophyte strain, a study <b>[1]</b> showed that <i>Bacillus subtilis</i> could develop and colonize fully a tree and reach a concentration of 10⁵ cells per g of fresh plant. We need to know in which conditions the growth are optimum in a tree and if the weather can stop its development in winter. We work on the <i>Bacillus subtilis</i> growth in function of the temperature during year. Modeling bacterial growth in a tree section generate some difficulties, we need to know distance between two tree extremities (treetops and root) or the speed sap flow which can vary with temperature during the day and seasons, cause of the type of sap (phloem, xylem). Furthermore tree is not a homogeneous system, its roots, trunk and branch do not contain same amount of sap and wood. The average speed of the plane tree sap is 2.4m/h <b>[2]</b> that means that in a day the sap will flow from one end to the other of a tree 30m. Tree is reduced to a bioreactor.
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According to the publication of Xianling Ji[1], after 6 months of <i>Bacillus subtilis</i> growth in a tree bacteria cells reach a concentration of 10⁵ cells per gram of fresh plant. Assume that 10⁵ cells / g is the maximum concentration.
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According to the publication of <b>Xianling Ji[1]</b>, after 6 months of <i>Bacillus subtilis</i> growth in a tree bacteria cells reach a concentration of 10⁵ cells per gram of fresh plant. Assume that 10⁵ cells / g is the maximum concentration.
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An assessment of the <i>Bacillus subtilis</i> growth in a similar sap, the birch sap [3] was performed in laboratory conditions with optimum growth medium for <i>Bacillus subtilis</i>. Thus, a growth rate μ opt. From this value we can extrapolate a growth curve as a function of temperature.
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An assessment of the <i>Bacillus subtilis</i> growth in a similar sap, the birch sap <b>[3]</b> was performed in laboratory conditions with optimum growth medium for <i>Bacillus subtilis</i>. Thus, a growth rate μ opt. From this value we can extrapolate a growth curve as a function of temperature.
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For this we used to cardinal temperature model [4]: </p>
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For this we used to <b>cardinal temperature model [4]</b>: </p>
   
   
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<img style="" src="https://static.igem.org/mediawiki/2014/8/85/Formules_Rosso.png" alt="cardinal temperature model">
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<center><img style="" src="https://static.igem.org/mediawiki/2014/8/85/Formules_Rosso.png" alt="cardinal temperature model"></center>
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Conditions apply:</p>
Conditions apply:</p>
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If | T<= 4°C            -> µ = -1</br>
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    | 4°C<T<= 10°C      -> µ = -0.97</br>
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If<span style="color:#FFFFFF; font-family:'Open Sans'; font-size:14px;">__</span>| T<= 4°C            -> µ = -1</br>
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    | T > 10°C          -> µ = f(T) with f(T) egal to cardinal temperature model.</br>
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<span style="color:#FFFFFF; font-family:'Open Sans'; font-size:14px;">____</span>| 4°C<T<= 10°C      -> µ = -0.97</br>
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<span style="color:#FFFFFF; font-family:'Open Sans'; font-size:14px;">____</span>| T > 10°C          -> µ = f(T) with f(T) egal to cardinal temperature model.</p>
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<img style="" src="https://static.igem.org/mediawiki/2014/b/b1/Plot_growth_rate.png" alt="Figure1">
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<center><img style="" src="https://static.igem.org/mediawiki/2014/b/b1/Plot_growth_rate.png" alt="Figure1"></center>
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<p class="texte"><center>Fig 1: bacterial growth (µ) as a function of temperature</center></p>
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<p class="legend">Fig 1: bacterial growth (µ) as a function of temperature</p>
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<p class="texte"> A logistic model developed by Hiroshi Fujikawa [5] is used to study bacterial growth.</p>
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<p class="texte"> A logistic model developed by <b>Hiroshi Fujikawa [5]</b> is used to study bacterial growth.</p>
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<p class="texte"><center> General logistics formulas</center></p>
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<p class="legend">General logistics formulas</p>
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<img style="" src="" alt="General logistics formulas">
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<center><img style="" src="https://static.igem.org/mediawiki/2014/c/c3/Form_general_fonction.png" alt="General logistics formulas"></center>
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    In our cases, µ depending of the temperature. N corresponds to the bacterial population, Nmin and Nmax are two asymptotes.Parameter "m" is a curvature parameter; With a larger m, the curvature of the deceleration phase with the model is smaller. Parameter n is a parameter related to the period lag. With a larger n, the period of lag is shorter. Nmin is slightly lower than N0, when N is small, close to Nmin, as the initial state (N is equal to N0), Nmin / N is almost equal to 1 so the term ( 1 - ( Nmin / N) ) is less than 1, growth is very slow. If N decrease until reach Nmin the term (1-(Nmin/N)) is equal to 0 thus there are can not be any growth. Similarly when N is equal to Nmax the term (1- (N / Nmax ) ) is equal to 0 and the growth is blocked.</br>
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In our cases, µ depending of the temperature. N corresponds to the bacterial population, Nmin and Nmax are two asymptotes.Parameter "m" is a curvature parameter; With a larger m, the curvature of the deceleration phase with the model is smaller. Parameter n is a parameter related to the period lag. With a larger n, the period of lag is shorter. Nmin is slightly lower than N0, when N is small, close to Nmin, as the initial state (N is equal to N0), Nmin / N is almost equal to 1 so the term ( 1 - ( Nmin / N) ) is less than 1, growth is very slow. If N decrease until reach Nmin the term (1-(Nmin/N)) is equal to 0 thus there are can not be any growth. Similarly when N is equal to Nmax the term (1- (N / Nmax ) ) is equal to 0 and the growth is blocked.</br>
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>
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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<img style="" src="" alt="model">
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<center><img style="" src="https://static.igem.org/mediawiki/2014/f/f8/Form_part.png" alt="model"></center>
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<img style="" src="" alt="Figure2">
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<center><img style="" src="https://static.igem.org/mediawiki/2014/5/53/Bacterial_growth.png" alt="Figure2"></center>
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Fig 2: (black) Bacillus Subtilis growth curve during one year. (red) average temperature. (blue) threshold at 10 °C.
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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. (<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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[2] A. Garnier(1977) Transfert de sève brute dans le tronc des arbres aspects méthodologiques et physiologiques. Ann. Sci. Foresi. 34 (1): 17-45 .
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[2] A. Garnier(1977) Transfert de sève brute dans le tronc des arbres aspects méthodologiques et physiologiques. Ann. Sci. Foresi. 34 (1): 17-45
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<p class="title2">
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Annexe
Annexe
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script
script
tableau des temperatures.
tableau des temperatures.

Revision as of 10:03, 11 October 2014