Difference between revisions of "Team:SJTU-BioX-Shanghai/Adhesion"

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                     Initial Assumptions
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             <p>The major equations used in locomotion model were:</p>
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             <p>The major equations used in locomotion model was:</p>
  
 
<p>$$\rho \frac{\partial u_{fluid} }{\partial t}+\rho (u_{fluid}\cdot \triangledown )=\triangledown \cdot [-pI+\mu (\triangledown u_{fluid}+(\triangledown u_{fluid})^{T}]+F+\rho g (1) $$  <br/>
 
<p>$$\rho \frac{\partial u_{fluid} }{\partial t}+\rho (u_{fluid}\cdot \triangledown )=\triangledown \cdot [-pI+\mu (\triangledown u_{fluid}+(\triangledown u_{fluid})^{T}]+F+\rho g (1) $$  <br/>
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             <p> The velocity field of particles was in Gaussian distribution，of which the inner particles move quiker than outer ones (Fig.1).  
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             <p> The simulation of microbe's locomotion demonstrated in Fig 1, was in overall Gaussian distribution. The micro-particles in outer field move slower than the inner, which may mainly due to the higher intense of drag force near to the colon epithelium. </p>
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             <!--******************************Fig 1****************************-->
 
             <!--******************************Fig 1****************************-->
 
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<!--******************************illustration of hydrogel introduction****************************-->
 
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<img src="https://static.igem.org/mediawiki/2018/d/d7/T--SJTU-BioX-Shanghai--model_coupling.gif"/>
 
<img src="https://static.igem.org/mediawiki/2018/d/d7/T--SJTU-BioX-Shanghai--model_coupling.gif"/>
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     <p class="fig_illustration">Fig 2. Coupling reaction of microbe and liquid .</p>
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     <p class="fig_illustration">Fig 2. Illustration of bacteria loaded hydrogel.</p>
 
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            <!--*****************************Table 1****************************-->
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                <p class="table_illustration">Table 1. Colony forming units per 0.1 OD<sub>600</sub></p>
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                    <th rowspan="2">samples</th>
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                    <th colspan="3">dilution factor</th>
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                    <th rowspan="2">CFU/mL</th>
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                    <td>8&times;10<sup>4</sup></td>
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                    <td>8&times;10<sup>5</sup></td>
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                    <td>1.1</td> <td>TNTC</td> <td>48</td> <td>11</td> <td>3.84E+07</td>
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                </tr>
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                    <td>1.2</td> <td>248</td> <td>41</td> <td>10</td> <td>3.28E+07</td>
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                    <td>1.3</td> <td>172</td> <td>54</td> <td>5</td> <td>4.32E+07</td>
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                    <td>2.1</td> <td>TNTC</td> <td>143</td> <td>20</td> <td>1.14E+08</td>
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                </tr>
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                    <td>2.2</td> <td>TNTC</td> <td>153</td> <td>25</td> <td>1.22E+08</td>
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                </tr>   
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                    <td>2.3</td> <td>TNTC</td> <td>151</td> <td>18</td> <td>1.21E+08</td>
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                    <td>3.1</td> <td>TNTC</td> <td>119</td> <td>16</td> <td>9.52E+07</td>
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                </tr>
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                    <td>3.2</td> <td>TNTC</td> <td>125</td> <td>19</td> <td>1.00E+08</td>
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                    <td>3.3</td> <td>TNTC</td> <td>89</td> <td>18</td> <td>7.12E+07</td>
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                    <td>4.1</td> <td>TNTC</td> <td>209</td> <td>16</td> <td>1.67E+08</td>
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                    <td>4.2</td> <td>TNTC</td> <td>130</td> <td>17</td> <td>1.04E+08</td>
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                    <td>4.3</td> <td>TNTC</td> <td>164</td> <td>10</td> <td>1.31E+08</td>
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             <p> We then considered some biological fators that may influence the binding of E.coli to epithelium. Considering the concentrations of IgA and mucin in colorectal microenvironment may influence the specific binding property demonstrated in Kirstie McLoughlin's work (<strong>1), we ajust the young's module based on those parameters.  </p>
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             <p>XXX XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX  XXX </p>
 
              
 
              
 
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Revision as of 00:39, 18 October 2018

Adhesion Model

Overview

The locomotion and adhesion of E.coli in real human body were too complex to describe and to detect, whereas the adhesion to detachment ratio was essential for our engineered E.coli’s specific binding performance to lesions. Therefore, we want to simulate the those process through in silico modeling.

The major two questions we want to ask are:

  • 1. How would microbe move in the mucus layer.
  • 2. To which extent engineered E.coli could specifically bind to CRC lesions.

Assumptions

  • 1. The fluid environment of colon was laminar flow with 1 atm Pa. .
  • 2. The elastic properties of E.coli was mainly defined by peptidoglycan layer.
  • 3. The force field in colon was in macro scale.

Theory

The major equations used in locomotion model was:

$$\rho \frac{\partial u_{fluid} }{\partial t}+\rho (u_{fluid}\cdot \triangledown )=\triangledown \cdot [-pI+\mu (\triangledown u_{fluid}+(\triangledown u_{fluid})^{T}]+F+\rho g (1) $$
$$\rho \frac{\partial ^{2}u_{solid}}{\partial t^{2}}= \triangledown \cdot \left ( F S \right )^{t}+F_{v}, F=I+\triangledown u_{solid} (2) $$
$$S=S_{ad}+\jmath _{i}F^{-T}_{ineI}\left ( C:\epsilon _{eI} \right )F^{-1}_{ineI}, \epsilon _{eI}=\frac{1}{2}\left ( F^{T_{eI}}F_{eI}-I \right ), F_{eI}=FF^{-1}_{ineI} (3)$$
$$ S_{ad}=S_{0}+S_{ext}+S_{q} (4) $$
$$ \epsilon =\frac{1}{2}[(\triangledown u_{solid})^{T}+\triangledown u_{solid}+(\triangledown u_{solid})^{T}\triangledown u_{solid}] (5) $$
$$ C=C(E,\vartheta ) (6)$$

Results

The simulation of microbe's locomotion demonstrated in Fig 1, was in overall Gaussian distribution. The micro-particles in outer field move slower than the inner, which may mainly due to the higher intense of drag force near to the colon epithelium.

Fig 1.The locomotion of particle in laminar flow.

Fig 2. Illustration of bacteria loaded hydrogel.

The table template is here.

Table 1. Colony forming units per 0.1 OD600

samples dilution factor CFU/mL
8×104 8×105 8×106
1.1 TNTC 48 11 3.84E+07
1.2 248 41 10 3.28E+07
1.3 172 54 5 4.32E+07
2.1 TNTC 143 20 1.14E+08
2.2 TNTC 153 25 1.22E+08
2.3 TNTC 151 18 1.21E+08
3.1 TNTC 119 16 9.52E+07
3.2 TNTC 125 19 1.00E+08
3.3 TNTC 89 18 7.12E+07
4.1 TNTC 209 16 1.67E+08
4.2 TNTC 130 17 1.04E+08
4.3 TNTC 164 10 1.31E+08

Section5

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