Team:Toulouse/Modelling

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   <p style="margin:0 auto; color:#696969; width:960px; padding-top:20px; font-size:16px;"> Project&nbsp;&nbsp;&nbsp;>&nbsp;&nbsp;&nbsp;Modeling</p>
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   <p style="margin:0 auto; color:#696969; width:960px; padding-top:20px; font-size:16px;">Results&nbsp;&nbsp;&nbsp;>&nbsp;&nbsp;&nbsp;Modeling
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<p class="texte">
<p class="texte">
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Modeling is a tool used to simplify and study systems. We can try to predict behavior with bibliographic informations or informations obtained from experiment.</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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Our project focuses on the development of our engineered bacterium in tree. The bacterial growth in trees seems to be unknown, so 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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<p class="texte">
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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. So we decided to work on the <i>Bacillus subtilis</i> growth in function of the temperature during the year. 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 which can vary with temperatures 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 branch do not contain same amount of sap and wood. The average speed of the plane tree sap is 2.4m/h, which 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 tree endophyte strain. A study showed that <i>B. 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>B. subtilis'</i> in function of the temperature during the year.  
 +
<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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<ol class="list1">
<ol class="list1">
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<li>
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According to the publication of <b>Xianling Ji</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. 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>B. 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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Only temperature impact on bacterial growth.
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Only temperature impacts on bacterial growth.
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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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<p class="texte">
<p class="texte">
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An assessment of the <i>Bacillus subtilis</i> growth in a similar sap, the birch sap 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>B. subtilis</i> growth in a similar sap was performed in laboratory conditions with optimum growth medium for <i>B. subtilis</i>. The composition sap used was the one from birch sap.<br>
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For this we used to <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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<p class="texte">
<p class="texte">
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T: Temperature.</br>
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T: Temperature</br>
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µ_opt: optimal growth rate.</br>
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µ<sub>opt</sub>: Optimal growth rate</br>
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µ: growth rate at T.</br>
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µ: growth rate at temperature T</br>
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T_max = max temperature supported by bacteria.</br>
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T<sub>max</sub>: Maximum temperature supported by bacteria</br>
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T_min = min temperature supported by bacteria.</br>
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T<sub>min</sub>: Minimum temperature supported by bacteria</br>
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T_opt = optimum temperature for the growth.</br></br>
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T<sub>opt</sub>: Optimum temperature for the growth</br></br>
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     Necessary parameters for this function are minimun temperature T_min and maximum temperature T_max, optimal temperature for the growth T_opt and optimal growth rate µ_opt.</br>
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     Necessary parameters for this function are minimun temperature T<sub>min</sub> and maximum temperature T<sub>max</sub>, optimal temperature for the growth T<sub>opt</sub> and optimal growth rate µ<sub>opt</sub>.</br>
</br>
</br>
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     T_min: 10°C</br>
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     T<sub>min</sub>: 10°C</br>
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     T_max: 52°C</br>
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     T<sub>max</sub>: 52°C</br>
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     T_opt: 37°C</br>
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     T<sub>opt</sub>: 37°C</br>
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     µ_opt: 8.5968 cfu/d</br></br>
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     µ<sub>opt</sub>: 8.5968 cfu/d</br></br>
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The optimal growth rate (µ_opt) is obtained experimentally with a similar birch sap environment.</br>
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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 (growth test performed at 10°C and 4°C under similar conditions for the measurement of μ_opt), survival rate after 24h was 0.3 % at 10°C and null at 4°C.
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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>
<p class="texte">  
<p class="texte">  
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<center style="margin-top: -52px;"><img style="" src="http://2014.igem.org/wiki/images/b/b1/Plot_growth_rate.png" alt="Figure1"></center>
<center style="margin-top: -52px;"><img style="" src="http://2014.igem.org/wiki/images/b/b1/Plot_growth_rate.png" alt="Figure1"></center>
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<p class="legend">Fig 1: bacterial growth (µ) as a function of temperature</p>
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<p class="legend">Figure 1: Bacterial growth (µ) as a function of temperature</p>
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<p class="texte"> A logistic model developed by <b>Hiroshi Fujikawa</b> is used to study bacterial growth.</p>
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<p class="texte"> A logistic model developed by <b>Hiroshi Fujikawa</b> (See References) is used to study bacterial growth.</p>
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<p class="legend">General logistics formulas</p>
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<p class="legend">General logistics formulas:</p>
<center style="margin:-44px 0 65px;"><img style="" src="http://2014.igem.org/wiki/images/c/c3/Form_general_fonction.png" alt="General logistics formulas"></center>
<center style="margin:-44px 0 65px;"><img style="" src="http://2014.igem.org/wiki/images/c/c3/Form_general_fonction.png" alt="General logistics formulas"></center>
<p class="texte">
<p class="texte">
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In our cases, µ depends on the temperature. N corresponds to the bacterial population, Nmin and Nmax are two asymptotes. Parameter "m" is a curvature parameter; larger is m, smaller is the curvature of the deceleration phase with the model. Parameter n is a parameter related to the period lag; larger is n, shorter is the period of lag. 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 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 case, the growth rate µ depends on the temperature.  
 +
<br>N corresponds to the bacterial population, N<sub>min</sub> and N<sub>max</sub> are two asymptotes.  
 +
<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>
 +
<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 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.
 +
<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 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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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 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.
</br>
</br>
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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 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.
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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>).
</br>
</br>
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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 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).
</p>
</p>
<center><img style="" src="http://2014.igem.org/wiki/images/5/53/Bacterial_growth.png" alt="Figure2"></center>
<center><img style="" src="http://2014.igem.org/wiki/images/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>
<p class="texte">
<p class="texte">
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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 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.  
</p>
</p>
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<p class="texte">
<p class="texte">
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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 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>B. 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.
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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 Annexe).
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<ul>
<ul>
<li class="tree"><p class="texte">
<li class="tree"><p class="texte">
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Xianling Ji, Guobing Lu, Yingping Gai, Chengchao Zheng & Zhimei Mu (2008) <b>Biological control against bacterial wilt and colonization of mulberry by an endophytic Bacillus subtilis strain.</b> FEMS Microbiol Ecol 65: 565–573
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Xianling Ji, Guobing Lu, Yingping Gai, Chengchao Zheng,and Zhimei Mu. (2008) <b>Biological control against bacterial wilt and colonization of mulberry by an endophytic <i>Bacillus subtilis</i> strain.</b> FEMS Microbiol Ecol 65: 565–573.
</li></p>
</li></p>
<li class="tree"><p class="texte">
<li class="tree"><p class="texte">
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A. Garnier(1977) <b>Transfert de sève brute dans le tronc des arbres aspects méthodologiques et physiologiques.</b> Ann. Sci. Foresi. 34 (1): 17-45
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A. Garnier. (1977) <b>Transfert de sève brute dans le tronc des arbres aspects méthodologiques et physiologiques.</b> Ann. Sci. Foresi. 34 (1): 17-45.
</li></p>
</li></p>
<li class="tree"><p class="texte">
<li class="tree"><p class="texte">
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Heikki Kallio , Tuija Teerinen , Seija Ahtonen , Meri Suihko , Reino R. Linko (1989) <b>Composition and properties of birch syrup (Betula pubescens).</b> J. Agric. Food Chem 37 (1): 51–54
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Heikki Kallio, Tuija Teerinen, Seija Ahtonen, Meri Suihko, and Reino R. Linko. (1989) <b>Composition and properties of birch syrup (<i>Betula pubescens</i>).</b> J. Agric. Food Chem 37 (1): 51–54.
</li></p>
</li></p>
<li class="tree"><p class="texte">
<li class="tree"><p class="texte">
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L. Rosso, J. R. Lobry & J. P. Flandrois (1992) AN <b>Unexpected Correlation between Cardinal Temperatures of Microbial Growth Highlighted by a New Model.</b> J. theor. Biol. 162 : 447-463
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L. Rosso, J. R. Lobry, and J. P. Flandrois. (1992) AN <b>Unexpected Correlation between Cardinal Temperatures of Microbial Growth Highlighted by a New Model.</b> J. theor. Biol. 162 : 447-463.
</li></p>
</li></p>
<li class="tree"><p class="texte">
<li class="tree"><p class="texte">
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Hiroshi Fujikawa (2010), <b>Development of a New Logistic Model for Microbial Growth in Foods.</b> Biocontrol of Science Vol 15: 75-80
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Hiroshi Fujikawa. (2010) <b>Development of a New Logistic Model for Microbial Growth in Foods.</b> Biocontrol of Science Vol 15: 75-80.
</li></p>
</li></p>
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<p class="texte"> To upload the script and the table <a href="http://2014.igem.org/wiki/images/0/01/Annexes.zip">Click Here</a></p>
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<p class="texte"> To download the script and the table <a href="http://2014.igem.org/wiki/images/0/01/Annexes.zip">Click Here</a></p>
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     <a href="http://2014.igem.org/Team:Toulouse/Project/Spreading" class="page-nav-right" style="width:447px; float:left; display:block;text-decoration:none; color:#666; font-size:18px;">Spreading
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     <a href="http://2014.igem.org/Team:Toulouse/Result/experimental-results" class="page-nav-right" style="width:447px; float:left; display:block;text-decoration:none; color:#666; font-size:18px;">Experimental results
       <img src="http://2014.igem.org/wiki/images/2/26/Template-igem2014-img-arrowleft.png" style="display:block; padding-top:10px;"/>
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color:#666; font-size:18px;">Parts</br>
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      <img src="http://2014.igem.org/wiki/images/e/ea/Template-igem2014-img-arrowright.png" style="display:block; float:right; padding-top:10px; " />
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Latest revision as of 03:17, 18 October 2014