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

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             <p>The major equations used in locomotion model was:</p>
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             <p>The major equations used in locomotion model were:</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 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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             <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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<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. Illustration of bacteria loaded hydrogel.</p>
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     <p class="fig_illustration">Fig 2. Coupling reaction of microbe and liquid .</p>
 
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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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                    <td>2.3</td> <td>TNTC</td> <td>151</td> <td>18</td> <td>1.21E+08</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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             <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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             <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)<strong>, we ajust the Young's module based on those parameters.  </p>
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<p> $$E_{g}=\frac{\sigma _{g}}{\epsilon _{g}}\left ( 1-v_{pg}v_{g\rho } \right ) (7) $$ <br>
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<p> $$E_{p}=\frac{\sigma _{p}}{\epsilon _{p}}\left ( 1-v_{pg}v_{g\rho } \right ) (8) $$ <br> <p>
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<p>The Young’s moduli of glycan strands Eg and peptide cross-links Ep were calculated (7-8)
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Where dimensionless Poisson's ratios,  and , relate the spontaneous strain arising in one direction given an applied strain in the other.
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Revision as of 00:47, 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.

Initial 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 were:

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

Results

The velocity field of particles was in Gaussian distribution，of which the inner particles move quiker than outer ones (Fig.1).

Fig 1.The locomotion of particle in laminar flow.

Fig 2. Coupling reaction of microbe and liquid .

Adjusted model

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 (1), we ajust the Young's module based on those parameters.

$$E_{g}=\frac{\sigma _{g}}{\epsilon _{g}}\left ( 1-v_{pg}v_{g\rho } \right ) (7) $$

$$E_{p}=\frac{\sigma _{p}}{\epsilon _{p}}\left ( 1-v_{pg}v_{g\rho } \right ) (8) $$

The Young’s moduli of glycan strands Eg and peptide cross-links Ep were calculated (7-8) Where dimensionless Poisson's ratios, and , relate the spontaneous strain arising in one direction given an applied strain in the other.