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| | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Design">Design</a> | | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Design">Design</a> |
| | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Notebook">Notebook</a> | | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Notebook">Notebook</a> |
| − | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Model">Model</a>
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| | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Results">Results</a> | | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Results">Results</a> |
| | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Demonstrate">Demonstrate</a> | | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Demonstrate">Demonstrate</a> |
| | + | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Method">Method</a> |
| | </div> | | </div> |
| | </li> | | </li> |
| − | <li class="nav-item dropdown mx-3"> | + | |
| − | <a class="nav-link dropdown-toggle" href="#" id="navbardrop" data-toggle="dropdown"> | + | |
| − | PARTS
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| − | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Parts">Parts Overview</a>
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| − | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Basic_Part">Basic Parts</a>
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| − | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Improve">Improved Parts</a>
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| − | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Composite_Part">Composite Parts</a>
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| − | </div>
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| | </a> | | </a> |
| | <div class="dropdown-menu"> | | <div class="dropdown-menu"> |
| − | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Model">Model</a> | + | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Model">Overview</a> |
| | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Decision_Model">Decision Model</a> | | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Decision_Model">Decision Model</a> |
| | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Dynamics_Model">Dynamics Model</a> | | <a class="dropdown-item" href="https://2019.igem.org/Team:CAU_China/Dynamics_Model">Dynamics Model</a> |
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| − | <h1 class="text-center">Decision Model</h1> | + | <h1 class="text-center">Overview</h1> |
| − | <h2>Introduction</h2>
| + | |
| | <div class="row"> | | <div class="row"> |
| | <div class="col-12"> | | <div class="col-12"> |
| − | <p> In our project, we develop a mathematical method to decide which pathway we could use because we have several candidates and need to conduct a scientific and rational method to find out the most suitable one. Therefore, an Analytic Hierarchy Process (AHP) is performed. By doing so, we can combine our subjective and objective factors into consideration and finally get the one from candidates.</p> | + | <p> Our models are mainly used to help us design and predict the whole project. Firstly, to find out which pathway is worth to be constructed in our project, we conducted an AHP model, which is a decision model used in pre-project process. By using AHP, we decide to make an Astaxanthin pathway in E.coli. Secondly, in order to help experiment find the suitable experiment condition, we work out an Logistic Regression to predict the E.coli population. By doing this, we successfully find the most suitable experiment bacterial concentration. Finally, our team use System Dynamic Model(SDM) to control our pathway and predict the final product. With such a model, we can give the experiment designing process a huge inspiration. The total modeling project based on the sight that we have to use mathematic methods to help our project and surely we reach the goal! |
| − | <h2>Construct hierarchy model</h2>
| + | </p> |
| − | <p> To use the AHP model, we need to list our candidates first. Combining with our project design and references we have read, we finally select 3 candidate pathways, which are Astaxanthin pathway, Ginsenosides pathway1, and Cannabinoid pathway2 respective- ly. In addition, during our discussion and interviews with different expertise, we select 5 most critical criteria we need to consider. Thanks for our human practice working, we can finally determine the criteria we need to use in our AHP model.</p>
| + | |
| − | <p> By using 3 candidates and 5 criteria, the hierarchy model is established. (Figure 1)</p>
| + | |
| − | | + | |
| − | </div>
| + | |
| − | </div>
| + | |
| − | <div class="row">
| + | |
| − | <div class="col-xs-12" >
| + | |
| − | <img src="https://2019.igem.org/wiki/images/9/9d/T--CAU_China--Mod1.png" style="width:450px;height:300px;margin-left: 32%;margin-top: 0%;" class="figure-img img-fluid rounded text-center" alt="A generic square placeholder image with rounded corners in a figure." >
| + | |
| − | <b style="margin-left: 45%;">Figure 1:</b> Hierarchy Model Structure
| + | |
| − | </div>
| + | |
| − | </div>
| + | |
| − | <h2>Construct Comparison Matrix</h2>
| + | |
| − | <div class="row">
| + | |
| − | <div class="col-12">
| + | |
| − | <p> After having the hierarchy structure, we further construct comparison matrix. When comparing the relative importance of the ith element to the jth element to the factor above, we use the quantified relative weight $a_{ij}$ to describe. Suppose there are a total of n elements to participate in the comparison, then matrix $ A={\{a_{ij}\}}_{n\times n}$ called comparison matrix. The value of $a_{ij}$ in the comparison matrix is assigned according to the following scale.</p>
| + | |
| − | | + | |
| − | | + | |
| − | </div>
| + | |
| − | </div>
| + | |
| − | | + | |
| − | <div class="row" style="background-color: white;">
| + | |
| − | <div class="col-12">
| + | |
| − | <ul style="">
| + | |
| − | <li>$a_{ij}=1$ which implies that element $i$ and element $j$ have the same importance to the previous level factor.</li>
| + | |
| − | <li>$a_{ij}=3$ which implies that element $i$ is slightly more important than element $j$.</li>
| + | |
| − | <li>$a_{ij}=5$ which implies that element $i$ is more important than element $j$.</li>
| + | |
| − | <li>$a_{ij}=7$ which implies that element $i$ is much more important than element $j$.</li>
| + | |
| − | <li>$a_{ij}=9$ which implies that element $i$ is extremely more important than element$j$.</li>
| + | |
| − | <li>$a_{ij}=2n, n=1,2,3,4$ which implies that the importance of the elements $i$ and$j$ is between $a_{ij}=2n-1$ and $a_{ij}=2n+1$.</li>
| + | |
| − | <li>$a_{ij}=\frac{1}{n}, n=1,2,\cdots,9,$ if and only if $a_{ij}=n$.</li>
| + | |
| − | </ul>
| + | |
| − | </div>
| + | |
| − | </div>
| + | |
| − | <div class="row">
| + | |
| − | <div class="col-12">
| + | |
| − | <p> By using the scale above, we construct our comparison matrix as follows.</p>
| + | |
| − | \begin{equation}
| + | |
| − | Goal\:\:Matrix:\quad
| + | |
| − | \left(
| + | |
| − | \begin{array}{ccccc}
| + | |
| − | 1 & 2 & 7 & 5 & 5 \\
| + | |
| − | 1/2 & 1 & 4 & 3 & 3 \\
| + | |
| − | 1/7 & 1/4 & 1 & 1/2 & 1/3 \\
| + | |
| − | 1/5 & 1/3 & 2 & 1 & 1 \\
| + | |
| − | 1/5 & 1/3 & 3 & 1 & 1
| + | |
| − | \end{array}
| + | |
| − | \right)
| + | |
| − | \end{equation}
| + | |
| − | <p> Criteria Matrix</p>
| + | |
| − | \begin{equation}
| + | |
| − | B1:\quad
| + | |
| − | \left(
| + | |
| − | \begin{array}{ccc}
| + | |
| − | 1 & 1/8 & 1/3 \\
| + | |
| − | 3 & 1 & 1/3 \\
| + | |
| − | 8 & 3 & 1
| + | |
| − | \end{array}
| + | |
| − | \right)
| + | |
| − | \end{equation}
| + | |
| − | \begin{equation}
| + | |
| − | B2:\quad
| + | |
| − | \left(
| + | |
| − | \begin{array}{ccc}
| + | |
| − | 1 & 2 & 5 \\
| + | |
| − | 1/2 & 1 & 2 \\
| + | |
| − | 1/5 & 1/2 & 1
| + | |
| − | \end{array}
| + | |
| − | \right)
| + | |
| − | \end{equation}
| + | |
| − | \begin{equation}
| + | |
| − | B3:\quad
| + | |
| − | \left(
| + | |
| − | \begin{array}{ccc}
| + | |
| − | 1 & 1 & 3 \\
| + | |
| − | 1 & 1 & 3 \\
| + | |
| − | 1/3 & 1/3 & 1
| + | |
| − | \end{array}
| + | |
| − | \right)
| + | |
| − | \end{equation}
| + | |
| − | \begin{equation}
| + | |
| − | B4:\quad
| + | |
| − | \left(
| + | |
| − | \begin{array}{ccc}
| + | |
| − | 1 & 3 & 4 \\
| + | |
| − | 1/3 & 1 & 1 \\
| + | |
| − | 1/4 & 1 & 1
| + | |
| − | \end{array}
| + | |
| − | \right)
| + | |
| − | \end{equation}
| + | |
| − | \begin{equation}
| + | |
| − | B5:\quad
| + | |
| − | \left(
| + | |
| − | \begin{array}{ccc}
| + | |
| − | 1 & 4 & 1/4 \\
| + | |
| − | 1 & 1 & 1/4 \\
| + | |
| − | 4 & 1 & 1
| + | |
| − | \end{array}
| + | |
| − | \right)
| + | |
| − | \end{equation}
| + | |
| − | <p> Where, the Goal Matrix represents different degrees of impor- tance of criteria to the final goal(pathway selection), and Criteria Matrix B1 to B5 represent different degrees of capablity of alter- native pathway to each criteria.</p>
| + | |
| − | <h2>Consistency test</h2>
| + | |
| − | <p> Obviously, we can find out the matrix above has a characteristic:</p>
| + | |
| − | $$ a_{ij}>0 $$
| + | |
| − | $$ a_{ji}=\frac{1}{a_{ij}} $$
| + | |
| − | <p> which means our matrix is a Reciprocal matrix: Further analysis finds that if $A$ is a completely consistent reciprocal matrix, we have a relationship $a_{ij}a_{jk}=a_{ik},\;\; \forall i,j,k=1,2,\cdots,n$. In fact, however, it is impossible to satisfy the equations above when constructing a comparison matrix. As a result, we use CR, which called Random Consistency Ratio to measure the degree of inconsistancy of a matrix and evaluate whether we could accept such an inconsistancy. The algorithm is listed as follows. </p>
| + | |
| − | <h4>Step 1</h4>
| + | |
| − | <p> Calculate an indicator CI (Consistency Index) that measures the degree of inconsistency in a comparison matrix A ($n>1$ matrix)</p>
| + | |
| − | \begin{equation}\nonumber
| + | |
| − | CI=\frac{\lambda_{max}-n}{n-1}
| + | |
| − | \end{equation}
| + | |
| − | <p> $\lambda_{max}$ means the maximum eigenvalue, and $n$ is the order of the matrix</p>
| + | |
| − | <h4>Step 2</h4>
| + | |
| − | <p> Calculate an indicator $RI$ (Random consistency Index), a comparison matrix consistency test standards, which only determined by the order of the matrix.</p>
| + | |
| − | <p> Instead of using theRI presented by Saaty (1980) direct- ly,we conduct a new method to calculateRI by ourselves. By doing so, our model can be more precise. The improved algorithm is presented below.</p>
| + | |
| − | </div>
| + | |
| − | </div>
| + | |
| − | <div class="row" style="background-color: white;">
| + | |
| − | <div class="col-12">
| + | |
| − | <ul style="">
| + | |
| − | <li>i For a certain matrix order 5, we randomly extract $10$ values from 1, 2, ..., 9, 1/2, 1/3, ..., 1/9 as the upper triangular element, the main diagonal element takes 1 and the lower triangular element goes to the reciprocal of the triangular element, thereby obtaining the matrix R.</li>
| + | |
| − | <li>ii Calculate CI value of the matrix R.</li>
| + | |
| − | <li>iii Iterate the previous step.</li>
| + | |
| − | <li>iv Calculate the average of all CI values.</li>
| + | |
| − | | + | |
| − | </ul>
| + | |
| − | </div>
| + | |
| − | </div>
| + | |
| − | <div class="row">
| + | |
| − | <div class="col-12">
| + | |
| − | <p> After 10 iterations, we get the value of RI when matrix order is 5. And the value of RI is 1.1108.</p>
| + | |
| − | <h4>Step 3</h4>
| + | |
| − | <p> Calculate the $CR$ (Consistency Ratio) of the comparison matrix $A$ according to the following formula,</p>
| + | |
| − | \begin{equation}
| + | |
| − | CR=\frac{CI}{RI}
| + | |
| − | \end{equation}
| + | |
| − | <h4>Step 4</h4>
| + | |
| − | <p> When $CR < 0.1$, we can determine that the comparison matrix $A$ has satisfactory consistency, or the degree of inconsistency is acceptable; otherwise, the comparison matrix $A$ is adjusted until satisfactory consistency is achieved.</p>
| + | |
| − | <h3>1.5 Calculate weight value and hierarchical total order</h3>
| + | |
| − | <p> After getting the relatively consistant matrix, we use MATLAB to calculate
| + | |
| − | eigenvector of each matrix. And then use Z-score standardization to ensure all values in eigenvector are within the range of 0-1. The vector which is standardized is called weight vector. </p>
| + | |
| − | <p> By calculating matrixes above, we get 6 weight vectors. Where, $\omega_{U}$ represents the weight vector of Goal Matrix (1)</p>
| + | |
| − | $$\omega_{U}=(0.475,0.263,0.051,0.103,0.126)^{T}$$
| + | |
| − | <p>and $\omega_{B_{i}},\;\;i=1,2,3,4$ represents the weight values of Criteria Matrix B1 to B5</p>
| + | |
| − | $$\omega_{B1}=(0.082,0.236,0.682)^{T}$$
| + | |
| − | $$\omega_{B2}=(0.606,0.265,0.129)^{T}$$
| + | |
| − | $$\omega_{B3}=(0.429,0.429,0.143)^{T}$$
| + | |
| − | $$\omega_{B4}=(0.636,0.185,0.179)^{T}$$
| + | |
| − | $$\omega_{B5}=(0.167,0.167,0.667)^{T}$$
| + | |
| − | <p>And also, they could be regarded as Our lab’s Capability score, Degree of Innovation score, Time Consuming score, Market Potential score and Experiment Cost score of each candidate. </p>
| + | |
| − | <p> Finally, according to the weight vectors above, we can get a total score of each candidate.</p>
| + | |
| − | \begin{equation}
| + | |
| − | Total\;\;Score=\sum_{n=1}^{5}\omega_{Ui}\times\omega_{Bnj}\quad\quad (i=1,2,3,4,5;\;j=1,2,3)
| + | |
| − | \end{equation}
| + | |
| − | | + | |
| − | </div>
| + | |
| − | </div>
| + | |
| − | | + | |
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| − | <b style="margin-left: 38%;">Figure 2:</b> Total score of each candidate
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| − | <P> According to the total score of each candidate, we choose the one with highest score, which is Astaxanthin pathway From now on, our project starts!</P>
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| − | <h2>References</h2>
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| − | <li id="ref_1"> <a href=>Dai, Z., Liu, Y., Zhang, X., Zhang, X., Shi, M., Wang, D., . . . Huang, L. (2013). Metabolic engineering of saccharomyces cerevisiae for production of ginsenosides. Metabolic Engineering, 20, 146-156. doi:10.1016/j.ymben.2013.10.004</a></li>
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| − | <li id="ref_2"> <a href=>Luo, X., Reiter, M. A., d'Espaux, L., Wong, J., Denby, C. M., Lechner, A., . . . Keasling, J. D. (2019). Complete biosynthesis of cannabinoids and their unnatural analogues in yeast. Nature, 567(7746), 123-126. doi:10.1038/s41586-019-0978-9</a></li>
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