# Team:Toulouse/Modelling

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 Revision as of 15:58, 14 October 2014 (view source)Kanitzer (Talk | contribs)← Older edit Revision as of 16:02, 14 October 2014 (view source)Kanitzer (Talk | contribs) Newer edit → Line 132: Line 132:

- Bacillus subtilis is a tree endophyte strain. A study [1] showed that Bacillus subtilis 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 B. subtilis is optimum in a tree and if the weather can stop its development during winter. So we decided to work on the Bacillus subtilis 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 [2], 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. + Bacillus subtilis is a tree endophyte strain. A study showed that Bacillus subtilis 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 B. subtilis is optimum in a tree and if the weather can stop its development during winter. So we decided to work on the Bacillus subtilis 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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1. - According to the publication of Xianling Ji[1], after 6 months of Bacillus subtilis 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. + According to the publication of Xianling Ji, after 6 months of Bacillus subtilis 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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- An assessment of the Bacillus subtilis growth in a similar sap, the birch sap [3] was performed in laboratory conditions with optimum growth medium for Bacillus subtilis. Thus, a growth rate μ opt. From this value we can extrapolate a growth curve as a function of temperature. + An assessment of the Bacillus subtilis growth in a similar sap, the birch sap was performed in laboratory conditions with optimum growth medium for Bacillus subtilis. Thus, a growth rate μ opt. From this value we can extrapolate a growth curve as a function of temperature. - For this we used to cardinal temperature model [4]:

+ For this we used to cardinal temperature model:

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Fig 1: bacterial growth (µ) as a function of temperature

Fig 1: bacterial growth (µ) as a function of temperature

-

A logistic model developed by Hiroshi Fujikawa [5] is used to study bacterial growth.

+

A logistic model developed by Hiroshi Fujikawa is used to study bacterial growth.

General logistics formulas

General logistics formulas

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• - [1] Xianling Ji, Guobing Lu, Yingping Gai, Chengchao Zheng & Zhimei Mu (2008) Biological control against bacterial wilt and colonization of mulberry by an endophytic Bacillus subtilis strain. FEMS Microbiol Ecol 65: 565–573 + Xianling Ji, Guobing Lu, Yingping Gai, Chengchao Zheng & Zhimei Mu (2008) Biological control against bacterial wilt and colonization of mulberry by an endophytic Bacillus subtilis strain. FEMS Microbiol Ecol 65: 565–573
• - [2] A. Garnier(1977) Transfert de sève brute dans le tronc des arbres aspects méthodologiques et physiologiques. Ann. Sci. Foresi. 34 (1): 17-45 + A. Garnier(1977) Transfert de sève brute dans le tronc des arbres aspects méthodologiques et physiologiques. Ann. Sci. Foresi. 34 (1): 17-45
• - [3] Heikki Kallio , Tuija Teerinen , Seija Ahtonen , Meri Suihko , Reino R. Linko (1989) Composition and properties of birch syrup (Betula pubescens). J. Agric. Food Chem 37 (1): 51–54 + Heikki Kallio , Tuija Teerinen , Seija Ahtonen , Meri Suihko , Reino R. Linko (1989) Composition and properties of birch syrup (Betula pubescens). J. Agric. Food Chem 37 (1): 51–54
• - [4] L. Rosso, J. R. Lobry & J. P. Flandrois (1992) AN Unexpected Correlation between Cardinal Temperatures of Microbial Growth Highlighted by a New Model. J. theor. Biol. 162 : 447-463 + L. Rosso, J. R. Lobry & J. P. Flandrois (1992) AN Unexpected Correlation between Cardinal Temperatures of Microbial Growth Highlighted by a New Model. J. theor. Biol. 162 : 447-463
• - [5] Hiroshi Fujikawa (2010), Development of a New Logistic Model for Microbial Growth in Foods. Biocontrol of Science Vol 15: 75-80 + Hiroshi Fujikawa (2010), Development of a New Logistic Model for Microbial Growth in Foods. Biocontrol of Science Vol 15: 75-80