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| − | <h3 class="uppercase color-primary mb40 " style="margin-bottom: 40px;font-size:50px"><center>MODEL</center> </h3>
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| − | <center><p class="font1" style="font-weight: 500; text-align: center; font-size: 25px; color: rgb(75, 151, 165); ">Introduction</p></center><br /><br />
| + | |
| − | <p style="font-size:16px">This year, our team creates a mathematical representation of our concrete self-healing system. This representation, or model, constructs a judging scale with which we can utilize to regulate the four main environmental factors affecting our final concrete healing efficiency (reflected by mineralization activity). </p><br /><br />
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| − | <p style="font-size:16px">
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| − | The four factors are: <br /><img src="https://static.igem.org/mediawiki/2017/c/c6/T--SZU-China--equation.jpg " width="25%" /></br>
| + | |
| − | </p>
| + | |
| − | <p style="font-size:16px">Based on this model, we can also design the best ‘package'– the microcapsule shells with adequate nutrition combination.</p>
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| − | <br />
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| − | <p style="font-size:16px">This modelling process, presented below, can be seen as a feedback from the wet lab (experiment result) and the dry lab(modelling analysis).</p><br /><br />
| + | |
| − | | + | |
| − | <p style="font-size:16px">The following page shows how we conducted modelling approaches to achieve our goals. To begin with, we make some definition.</p><br /><br />
| + | |
| − | <br /><br />
| + | |
| − | <center><span class="font1" style="font-weight: 500; text-align: center; font-size: 25px; color: rgb(75, 151, 165); ">Definition</span></center><br /><br />
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| − |
| + | |
| − | <br/><br/>
| + | |
| − | <ul style="font-size:16px;" class="def">Variables and nomenclature:<li> concentration of spores - c[Spore]</li> <li> concentration of carbon source(C3H5O3Na) - c[C3H5O3Na]</li><li> concentration of nitrogen source(NaNO3) - c[NaNO3]</li><li> pH of the media - pH</li></ul><br />
| + | |
| − | <ul style="font-size: 16px;" class="def">Goal of model:<li> Use preliminary data to guide future experiments.</li></ul>
| + | |
| − | <br /><br />
| + | |
| − | <center><span class="font1" style="font-weight: 500; text-align: center; font-size: 25px; color: rgb(75, 151, 165); ">Procedure</span></center><br /><br />
| + | |
| − | <p style="font-size:16px">
| + | |
| − | 1. Standardizing variables: transforming variables into the same scale. Here we utilize the z-score standardizing method, such that
| + | |
| − | </p>
| + | |
| − | <div style="text-align:center"><img src="https://static.igem.org/mediawiki/2017/0/07/T--SZU-China--standardization.jpg" width="30%" ><br /></div><br />
| + | |
| − | <p style="font-size:16px">
| + | |
| − | where the symbols in the formula are variable, standardized variable, sample mean, andstandard deviation respectively.
| + | |
| − | </p>
| + | |
| − | <p style="font-size:16px">2. Fitting functions of each variable with polynomial function.</p>
| + | |
| − | <p style="font-size:16px">3. Getting the overall relationship using linear least square method.</p><br /><br /><br />
| + | |
| − | <center> <span class="font1" style="font-weight: 500; text-align: center; font-size: 25px; color:rgb(75, 151, 165); ">Results</span></center><br /><br />
| + | |
| − | | + | |
| − | | + | |
| − | <div style="text-align: center;margin: 24px 0;z-index:-1;">
| + | |
| − | <img src="https://static.igem.org/mediawiki/2017/2/24/T--SZU-China--model1.png " width="90%" style="box-shadow: 0px 0px 2px #1E1E1E;">
| + | |
| − | </div>
| + | |
| − | | + | |
| − | <p style="font-size:16px">The graph above depicts the polynomial regression of 4 factors. In general, for each of those four factors, the mineralization activity shows the similar tendency of going up first and down later with the increase of each factor.</p><br /><br />
| + | |
| − | | + | |
| − | <p style="font-size:16px">The fitted functions are showed as follows:</p>
| + | |
| − | <div style="text-align:center"><img src="https://static.igem.org/mediawiki/2017/1/1d/T--SZU-China--fitting.jpg" width="60%" ><br /></div>
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| − |
| + | |
| − | <p style="font-size:16px">We then fitted x with y linearly to get the overall regression equation which can describe the weight of four variables respectively.</p><br /><br />
| + | |
| | | | |
| − | <center><span class="font1" style="font-weight:bold;font-size:16px">Overall regression equation:</span></center><br /><br />
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| | + | </div> |
| | + | </div> |
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| − | <p style="font-size: 16px"> with</p>< br />< br /> | + | <div class="container-fluid"> |
| | + | <div class="col-10 offset-1 shadow"> |
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| | + | <h1 class="h1" style="color: #469789; text-align: center;">Model</h1> |
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| | + | <div class="col-8 offset-2"> |
| | + | |
| | + | <p style="font-size: 18px; font-weight: bold;"> |
| | + | On this page, two mathematical models were constructed to analysis the efficiency of our producet based on simulation and experiment. <br />Click the frame to see the details. |
| | + | </p> |
| | + | |
| | + | |
| | + | </div> |
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| | + | </div> |
| | + | <div class="card-body text-center"> |
| | + | <a style="color: #469789;" href="https://2018.igem.org/Team:SZU-China/Epidemic_Model"><h3 >Epidemic Model </h3></a> |
| | + | <p class="card-text" >We developed a epidemic model with ordinary differential equation to predict the population dynamics of cockroaches infected by Metarhizium anisopliae. We then performed numerical simulations on the model and sensitivity analysis on some key parameters to find they impacts. |
| | + | </p> |
| | + | </div> |
| | + | </div> |
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| − | <div style="text- align:center"><img src="https://static.igem.org/mediawiki/ 2017/ b/ be/T--SZU-China-- regressiontransform. jpg" width=" 30%" >< br /></ div> | + | </div> |
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| | + | <div class="col-4 offset-2 "> |
| | + | <div id="card2" class="card border-3 h-100"> |
| | + | <div class="view text-center"> |
| | + | <img id="icon" class="card-img-top" style="width: 96px;" src="https://static.igem.org/mediawiki/ 2018/ 4/ 4b/T--SZU-China-- Model_home2. png" /> |
| | + | </div> |
| | + | <div class="card-body text-center"> |
| | + | <a style="color: #469789;" href="https://2018.igem.org/Team:SZU-China/Statistic_Model"><h3 >Statistic Model</h3></a> |
| | + | <p class="card-text">We constructed a statistical model for our experimental data from simulating room. It can give us a clear and scientific understanding that whether there had significant difference in migration rate, mortality and gnawing rate between each products.</p> |
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| − | <p style="font-size:16px">where a<sub>i1</sub>represents the coefficient of the highest power term of curve-fitting equation, such that the coefficient of the highest power term are of the same scale.</p><br /><br />
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| − | <br/>
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| − | <p style="font-size:16px">From the equation above, we can see that nitrogen source has the maximum weight, while pH has the minimum weight, which means nitrogen source is the most essential nutrition for B.subtilis spore. Additionally, the low weight of pH shows that spores are not sensitive to the change of pH in a relatively apt range, although there is a sharp decline in activity when pH reaches 11.</p><br />
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| − | <br /><p style="font-size:16px">In summary, as long as we keep the environment below the boundary high-pH point, it makes no much difference how much we have improved the alkaline resistance of <i>B.subtilis</i> spore. In this way, this model instructs us on how to modify our formulation, such that the ingredients can be made full use of.</p><br />
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