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| - | <DIV id="animat">
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| - | <span><p>ipsc</p>
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| - | <img src="https://static.igem.org/mediawiki/2013/4/44/WIKI-MASCOT-STAND.png" /></span></DIV>
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| - | <DIV class="content_body" align="center">
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| - | <DIV class="navigater">
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| - | </DIV>
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| - | <DIV id="cont_column">
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| - | <!--正 文 部 分 开 始-->
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| - | <DIV class="chapter">
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| - | <span>Project/Modeling</span>
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| - |
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| - |
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| - | <h1> 1.Overview </h1>
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| - | <p>
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| - | Modeling is a powerful tool in synthetic biology and engineering. In the iPSCs Safeguard
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| - | project, modeling has provided us with an important engineering approach to characterize our
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| - | pathways and predict their performance, thus helped us with modifying and testing our
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| - | designing.
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| - | </p>
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| - | <p>
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| - | Basically, the models built by us can be divided into two levels.On gene level, we hope to gain insight of the gene expression dynamics of our
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| - |
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| - | whole circuit. And also we tried to better characterize our parts, analyze our experimental data, for all of the sensor, switch, and the killer.
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| - |
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| - | Several tools including ODEs and interpolation are employed.
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| - | </p>
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| - | <p>
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| - | On cell level, we proposed
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| - | the multi-compartment model to trace the change of the iPS cells in different time nodes,
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| - | thus we are able to describe the growth and decay of iPSCs. The number of cells at the
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| - | initial stage, growth rate and death rate of cells caused by suicide gene in our Safe-guard
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| - | pathway were all taken into account.
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| - | </p>
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| - |
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| - |
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| - | <h1>2.Gene expression dynamics of iPSC Safeguard</h1>
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| - | <h2>2.1 analysis of the problem</h2>
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| - | <p>
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| - | Firstly we built a model to help ourselves better understand the gene expression dynamics of the whole circuit. In our device, tTA protein is
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| - |
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| - | firstly expressed by a EF1-α promoter and will then bind to TRE element, activating transcription of gene of interest, in our case suicide gene or
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| - |
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| - | GFP. This process is affected by the Dox suppression effect. And the TRE element alone without tTA protein has a leaky expression. After production
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| - |
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| - | and functioning, the protein of interest will undergo degradation. And to simplify the model, we consider the miRNA degradation effect as part of
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| - |
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| - | this process.
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| - | </p>
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| - | <p>
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| - | Then we wrote down the four chemical reactions in represent of each process.
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| - | </p>
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| - | <br/><img src="https://static.igem.org/mediawiki/2013/0/0a/New_model_1.png" width="200" /><br />
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| - | <p>
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| - | The symbol declaration is:
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| - | </p>
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| - | <p>
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| - | X1:tTA protein
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| - | </p>
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| - | <p>
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| - | D: the TRE promoter
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| - | </p>
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| - | <p>
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| - | X1D:the tTA-TRE complex
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| - | </p>
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| - | <p>
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| - | X2: the protein of interest
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| - | </p>
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| - | <p>
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| - | And we assigned each process with a reaction rate constant.
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| - | </p>
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| - | <p>
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| - | The first process is about binding and dissociation of molecules and is a fast reaction. Time unit for that is second. Since EF1-αis a
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| - |
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| - | constitutive promoter, and we define the initial state as when we remove the Dox from medium, we can regard the concentration of X1, or tTA
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| - |
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| - | protein, as a given value, determined by intensity of EF1-α. Reaction rate constant k1,k-1 are affected by Dox. In the tolerable range descried in
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| - |
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| - | part3, the more Dox we apply to D, the smaller value of k1 for the positive direction and the greater value of k-1 for the negative direction.
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| - | </p>
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| - | <p>
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| - | In the second and third process, k2 and k3 are affected by what kind of TRE promoter we use. There are several available TRE promoters, with which
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| - |
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| - | we can assemble different version of Tet-off system. These promoters differ in leaky expression and switching performance.
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| - | </p>
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| - | <p>
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| - | MiRNA-mediated mRNA degradation lead to a decrease in X2 production, which can be thought as identical with natural degradation of X2, the protein
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| - |
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| - | of interest. So K4 will be affected by the knockdown efficiency of miRNA binding site. We have constructed several binding sites to fine tune this
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| - |
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| - | process.
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| - | </p>
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| - |
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| - | <h2>2.2 solutions and implication</h2>
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| - | <p>
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| - | According the analysis, we then wrote down the ODEs:
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| - | </p>
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| - | <br/><img src="https://static.igem.org/mediawiki/2013/1/10/New_model_2.png" width="400" /><br />
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| - | <p>
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| - | Here [D0] is the initial concentration of promoter Pcmv，c1 is the given concentration of X1 at the beginning. Next we will do some algebra to
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| - |
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| - | simplify the equations and solve the differential equations.
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| - | </p>
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| - | <br/><img src="https://static.igem.org/mediawiki/2013/6/60/New_model_3.png" width="400" /><br />
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| - | <br/><img src="https://static.igem.org/mediawiki/2013/4/4c/New_model_4.png" width="400" /><br />
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| - | <p>
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| - | We use Mathematica’s Dynamic Interactive Function Manipulation to control the variation of the parameters α,β, and thus get curves with
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| - |
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| - | different dynamics and steady state.
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| - | </p>
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| - |
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| - | <div class="figure">
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| - | <img class="fig_img" height="245px" src="https://static.igem.org/mediawiki/2013/9/95/%E5%9B%BE%E7%89%875.png" />
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| - | <img class="fig_img" height="245px" src="https://static.igem.org/mediawiki/2013/5/56/%E5%9B%BE%E7%89%876.png" />
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| - | <img class="fig_img" height="245px" src="https://static.igem.org/mediawiki/2013/1/1e/%E5%9B%BE%E7%89%877.png" />
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| - | <img class="fig_img" height="245px" src="https://static.igem.org/mediawiki/2013/9/91/%E5%9B%BE%E7%89%878.png" />
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| - | <img class="fig_img" height="245px" src="https://static.igem.org/mediawiki/2013/4/4d/%E5%9B%BE%E7%89%879.png" />
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| - | <img class="fig_img" height="245px" src="https://static.igem.org/mediawiki/2013/1/12/%E5%9B%BE%E7%89%8710.png" />
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| - | <img class="fig_img" height="245px" src="https://static.igem.org/mediawiki/2013/7/72/%E5%9B%BE%E7%89%8711.png" />
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| - | <p class="des" style="margin-top:0px;width:700px"><strong>Figure 1. Different values of α,βgenerate curves with different dynamics and steady
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| - |
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| - | state. </strong></p>
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| - | <div class="clear"></div></div>
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| - |
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| - | <p>
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| - | As analyzed in 2.1, choosing different candidates with variant characteristic will affect the parameters in the chemical reactions, and change
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| - |
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| - | values of α and β. We’ve got 4 tet-off systems, a series of miR122 binding sites and experimental characterize them. And also we have two EF1-α
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| - |
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| - | promoters with different enhancers(not mentioned in Result section). This implicate that we can assemble different circuits and fine-tune the
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| - |
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| - | dynamics and steady state. We believe that this is important to practical engineering, just as basic logic is to conceptual designing.
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| - | </p>
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| - |
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| - | <h1>3. Dosage effect of DOX in turning off the Tet-off system</h1>
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| - | <p>
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| - | DOX ,as is discussed above, hinders the binding of tTA to pTRE in Tet-Off system and
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| - | knockdown expression of suicide gene. In our experiment, we employ fluorescence technique to
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| - | manifest the amount of protein product by detecting the strength of the fluorescence.
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| - | </p>
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| - | <br/><img src=" https://static.igem.org/mediawiki/2013/a/aa/Modeling_6.png " width="580" /><br />
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| - | <br>
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| - | Table 1. Stimulating data of GFP-Dox
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| - | </br>
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| - | <br/><img src=" https://static.igem.org/mediawiki/2013/1/19/Modeling_7.png " width="500" /><br />
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| - | <br>
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| - | Figure 4. GFP-Dox line chart
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| - | </br>
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| - | <p>
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| - | Our task is to find the proper curve to fit the sample data. First of all we plot the
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| - | scatter diagram, and according to its tendency, we use type curve to fit the relation of
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| - | GFP-DOX. We use MATLAB to aid our fitting, i.e. to determine the parameter a, b and k.
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| - | </p>
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| - | <br/><img src=" https://static.igem.org/mediawiki/2013/2/2f/Modeling_8.png " width="150" /><br />
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| - | <strong>
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| - | <p>
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| - | %expun.m
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| - | </p>
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| - | <p>
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| - | function y=expun(s,t) %coefficient and variable
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| - | </p>
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| - | <p>
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| - | y=s(1)+s(2)*exp(-s(3)*t)
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| - | </p>
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| - | <p>
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| - | %curvefit.m
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| - | </p>
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| - | <p>
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| - | treal=[0 0.125 0.25 0.5 1 2]; %experimental data
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| - | </p>
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| - | <p>
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| - | yreal=[25 13 10 8 6 5.7];
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| - | </p>
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| - | <p>
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| - | s0=[0.2 0.05 0.05]; %iteration initial value
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| - | </p>
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| - | <p>
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| - | sfit=lsqcurvefit('expun',s0,treal,yreal); %least square curve fit
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| - | </p>
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| - | <p>
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| - | f=expun(sfit,treal);
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| - | </p>
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| - | <p>
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| - | disp(sfit);
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| - | </p>
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| - | </strong>
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| - | <p>
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| - | The result :
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| - | </p>
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| - | <br/><img src=" https://static.igem.org/mediawiki/2013/a/a6/Modeling_9.png " width="500" /><br />
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| - | <br>
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| - | Figure 5. Running result
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| - | </br>
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| - | <p>
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| - | So a=6.4147,b=18.3999,k=7.3173.
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| - | </p>
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| - | <p>
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| - | Then we program the diagram file GFP-DOX.m
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| - | </p>
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| - | <strong>
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| - | <p>
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| - | %GFP-DOX curve
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| - | </p>
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| - | <p>
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| - | treal=[0 0.125 0.25 0.5 1 2]; %experimental data
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| - | </p>
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| - | <p>
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| - | yreal=[25 13 10 8 6 5.7];
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| - | </p>
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| - | <p>
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| - | t=0:0.1:2.5;
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| - | </p>
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| - | <p>
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| - | a=6.4147;b=18.3999;k=7.3173;
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| - | </p>
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| - | <p>
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| - | y=a+b*exp(-k*t);
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| - | </p>
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| - | <p>
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| - | plot(treal,yreal,'rx',t,y,'g');</p>
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| - | <p>
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| - | xlabel('Dosage of DOX');
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| - | </p>
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| - | <p>
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| - | ylabel('GFP');
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| - | </p>
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| - | </strong>
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| - | <br/><img src=" https://static.igem.org/mediawiki/2013/d/dc/Modeling_10.png " width="500" /><br />
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| - | <br>
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| - | Figure 6. GFP-Dox curve
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| - | </br>
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| - | <p>
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| - | As is shown in the figure above, we can conclude that the amount of GFP tend to be steadily
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| - | over 1.5 ug, the higher concentration of DOX we set, the lower GFP we expect. However, under
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| - | the real experimental conditions, over 2.2 ug DOX will lead to the undesired necrosis of the
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| - | cells. This is a trial-experiment which proved that such a balance point for good turning-
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| - | off effect and cell tolerance does exist in a certain interval concentration. More accurate
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| - | experiment should be conducted on stable-transfected iPSCs to find the best cultivating
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| - | condition.
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| - | </p>
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| - |
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| - | <h1>4. Knockdown efficiency interpolation</h1>
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| - |
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| - | <p>
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| - | According to the experimental data, here we use interpolation technique to find the
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| - | relationship between miRNA-122 concentration, the number of miR122 target sites and cell
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| - | knockdown efficiency, which leads to a function with two variables. The knockdown efficiency
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| - | is represented by GFP expression level which is actually the ratio of the amount of GFP and
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| - | that of the parameter GAPDH. The knockdown efficiency then is
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| - | </p>
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| - | <br/><img src=" https://static.igem.org/mediawiki/2013/6/60/Modeling_11.png " width="500" /><br />
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| - | <br/><img src=" https://static.igem.org/mediawiki/2013/2/22/Modeling_12.png " width="400" /><br />
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| - | <br>
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| - | Figure 7. Two target sites, gradient miRNA concentration
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| - | </br>
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| - | <br/><img src=" https://static.igem.org/mediawiki/2013/1/19/Modeling_13.png " width="500" /><br />
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| - | <br>
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| - | Table 2. Experimental data of 2 target sites, gradient miRNA concentration
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| - | </br>
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| - | <br/><img src=" https://static.igem.org/mediawiki/2013/e/ec/Modeling_14.png " width="400" /><br />
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| - | <br>
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| - | Table 3. Experimental data of 0.75ug miRNA plasmid with gradient target sites
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| - | </br>
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| - | <p>
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| - | We use the data above to do the interpolation. We use the griddata function to implement the
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| - | interpolation.
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| - | </p>
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| - | <p>
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| - | MATLAB codes:
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| - | <strong>
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| - | <p>
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| - | clear
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| - | </p>
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| - | <p>
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| - | miRNA=[0 0.025 0.05 0.1 0.25 0.75 0.75 0.75];
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| - | </p>
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| - | <p>
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| - | site=[2 2 2 2 2 1 2 4];
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| - | </p>
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| - | <p>
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| - | KD=[0 29 43 55 64 55 39 32];
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| - | </p>
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| - | <p>
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| - | cx=0:0.01:0.75;
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| - | </p>
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| - | <p>
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| - | cy=0:0.05:4;
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| - | </p>
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| - | <p>
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| - | cz=griddata(miRNA,site,KD,cx,cy','cubic');
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| - | </p>
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| - | <p>
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| - | meshz(cx,cy,cz),rotate3d
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| - | </p>
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| - | <p>
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| - | %shading flat
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| - | </p>
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| - | <p>
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| - | xlabel('miRNA(plasmid ug)'),ylabel('Target Site'),zlabel('knockdown efficiency(%)');
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| - | </p>
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| - |
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| - | </strong>
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| - |
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| - | <br /><img src=" https://static.igem.org/mediawiki/2013/6/6c/Modeling_15.png " width="400" /><br />
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| - |
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| - | <br>
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| - | Figure 8. Knockdown efficiency-mRNA-target site surface chart
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| - | </br>
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| - |
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| - | <h1> 5. The excursion of little mathematician--Data analysis of the FACS data
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| - | </h1>
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| - | <p>
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| - | When our project was proceeding, we found out an interesting problem, that is, how to calculate the killing efficiency of each suicide gene? And
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| - |
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| - | this quantity is also an important part of our modeling. Trying to solve this problem,one of our mathematician, young Yang ZiYi, excursed a little
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| - |
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| - | bit from modeling to data analysis. And he analyzed our data of FACS of our transient transfection experiment of Hep G2.
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| - | </p>
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| - | <p>
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| - | One important point in mathematical analysis about the complicated biological system is, not to draw arbitrary assumption, arbitrary assumption
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| - |
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| - | just lead to disaster. Another important point is not to draw complicated assumption, which is hard to calculate. Base on these rules, Young ZiYi
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| - |
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| - | draw some simple and reasonable assumptions:
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| - | </p>
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| - | <p>
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| - | 1. The initial condition of each parallel well is the same, that means, every well before transient transfection should have the same cell
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| - |
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| - | density, and the cells' state should be approximately the same.
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| - | </p>
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| - | <p>
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| - | 2. In the GFP control group, the cells should be regarded as the same, whether they are transfected with GFP or not, since GFP do not harm the
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| - |
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| - | cells. But lipo-2000 will harm the cells, and may have some long term effect. So the GFP control group would be relatively weaker compare to
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| - |
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| - | negative control, which without any transfection manipulation;
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| - | </p>
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| - | <p>
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| - | 3. The cells transfected with GFP should have an innate death rate r1 after 3 days cultivation. Besides, the ratio of “the initial number of
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| - |
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| - | cells” to “the number of cells harvested via FACS after 3 days” Should be the same, since if you sample any part of the wells you will observe
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| - |
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| - | the same distribution of cells, this means the cell experiment is scalable. Hence, we can define a special “state” to represent GFP cells in
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| - |
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| - | certain well, (r1,n1), n1 is the number of the cells we harvest in 30s, depends on r1 and the initial cell number.
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| - | </p>
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| - | <p>
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| - | 4. In the well we transfect suicide genes, the cells which are transfected with suicide gene will be different from the cells which are not,
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| - |
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| - | due to the killing effect of suicide gene, and the cells without transfection will be at the same condition as GFP control and have the same r1.
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| - |
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| - | Cells transfected with suicide gene will have a different r2, we denote this part of cells by (r2,n2). If the transfection efficiency is a, then
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| - |
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| - | for any initial cell number N0, there will be N0×a cells transfected with suicide gene, the remaining N0×（1-a）are not. Here "a" in an unknown
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| - |
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| - | factor.
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| - | </p>
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| - | <p>
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| - | Then Young ZiYi built a model:
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| - | </p>
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| - | <p>
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| - | In the wells that had been tranfected with suicide genes, the final observed “state” (X, C) of the cells is an combination of two kinds of cells,
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| - |
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| - | one kind with state (r1,n1), the other kind with state (r2,n2). The effect of these two kinds will be summed up together. Then we can write down a
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| - |
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| - | equation:
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| - | </p>
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| - | <br/><img src="https://static.igem.org/mediawiki/2013/6/6b/%E5%85%AC%E5%BC%8F.png" width="400" /><br />
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| - | <p>
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| - | Because we can not easily get the transfection efficiency, we select a reasonable range from experience:[30%,60%], and solve the equation with the
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| - |
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| - | data from FACS, and get the following results:
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| - | </p>
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| - |
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| - | <br/><img src="https://static.igem.org/mediawiki/2013/c/c8/Inate_death_rate_for_3_days.png" width="400" /><br />
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| - | <p>
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| - | It turns out that, the death rate of cells transfected with suicide gene will be greater than 60%, significantly higher than normal cells and GFP
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| - |
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| - | control cells(29.07%, according to our data).
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| - | </p>
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| - | <p>
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| - | Then, We pick up one suicide gene, VP3, and take an “a” value 35% which we believe is fairly closed to the real tranfection efficiency, solve the
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| - |
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| - | equation and get the result r2 and n2. And then, we substitute the calculated r2 and n2 to the left side of the equation, and raise the value of “
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| - |
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| - | a” to predict what the death rate and the “number per 30 seconds” would be when the transfection efficiency is raised. The result is shown in a
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| - |
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| - | chart below
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| - | </p>
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| - | <br/><img src="https://static.igem.org/mediawiki/2013/f/f2/Predicted_death_rate.png" width="400" /><br />
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| - | <br/><img src=" https://static.igem.org/mediawiki/2013/b/b9/Predicted_harvest_cell.png" width="400" /><br />
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| - | <p>
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| - | That makes our model become a real theory, because it predicts something that can be disproved. In the following day, we will try to raise our
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| - |
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| - | transfection efficiency, and try to comparing the result with the prediction.
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| - | </p>
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| - | <p>
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| - | And, let’s wait for the result.
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| - | </p>
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| - |
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| - |
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| - | <h1> 6. Multi-compartment model
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| - | </h1>
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| - | <h2> 6.1 Analysis of the problem
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| - | </h2>
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| - | <p>
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| - | We firstly focus on factors that regulate the performance of the whole pathway. Protein tTA
| |
| - | expressed by a EF1α promoter binds to the promoter pTRE to drive the transcription of
| |
| - | target gene( in this case, eGFP or suicide gene) while Dox acts as a co-repressor
| |
| - | prohibiting the transcription. MiR122 isa downstream part in the pathway after transcription
| |
| - | of target mRNA, and mediated degradation of the mRNA, thus rescue the cell or knockdown its
| |
| - | GFP expression. However, the miR122 level in iPSC was low and insufficient to exert obvious
| |
| - | effect on the expression.
| |
| - | </p>
| |
| - | <p>
| |
| - | Apart from Dox concentration,we also monitored other parameters, including cell number after
| |
| - | the stable infection and number of cell that survived the Suicide Gene. Moreover, we also
| |
| - | kept track of fluoresence intensity of the control group who has been transfected with GFP,
| |
| - | which can be employed to indicate the GOI expression level driven by Tet-Off system.
| |
| - | </p>
| |
| - | <p>
| |
| - | In pratical, we planned to monitor the cell group scale every 5 hours and technically, we
| |
| - | counted the total clone area instead of cell number.
| |
| - | </p>
| |
| - |
| |
| - | <h2> 6.2 Symbols declaration and assumption
| |
| - | </h2>
| |
| - | <p>
| |
| - | X1: initial number of iPS cells with Suicide Gene
| |
| - | </p>
| |
| - | <p>
| |
| - | X2: number of the iPS cells whose TRE have been combined with tTA
| |
| - | </p>
| |
| - | <p>
| |
| - | X3: number of iPS cells which have died from expressing Suicide Gene
| |
| - | </p>
| |
| - | <p>
| |
| - | k1: converting rate of the number of cells from phase X1 to phase X2
| |
| - | </p>
| |
| - | <p>
| |
| - | k2: converting rate of the number of cells from phase X2 to phase X3
| |
| - | </p>
| |
| - | <p>
| |
| - | The unit of ki(i=1,2) is hour-1.We measured it by dividing the absolute value of the cell
| |
| - | number difference between former phase and latter phase, with the time period length.
| |
| - | </p>
| |
| - | <p>
| |
| - | Two cases are taken into account. In case (a), self-renewal and replication of cels are
| |
| - | ingored while in case (b), we take that into consideration. To further simplify the model,
| |
| - | we also assumed that every single cell in phase X1 turns into n1 state before phase X2, and
| |
| - | every single cell in phase X2 turns into n2 state before phase X3. We simulated the kinetic
| |
| - | process of gene expression and assumed an even distribution of cell content in the
| |
| - | medium,after which the phase can be regarded as a compartment.
| |
| - | </p>
| |
| - |
| |
| - |
| |
| - | <h2> 6.3 Solution
| |
| - | </h2>
| |
| - | <p>
| |
| - | For each compartment, we construct unsteady state equilibrium equation, hence we obtain the
| |
| - | ordinary equations
| |
| - | </p>
| |
| - |
| |
| - | <img src=" https://static.igem.org/mediawiki/2013/e/e3/Modeding_1.png " width="150" />
| |
| - |
| |
| - | <p>
| |
| - | For case (b), we just need to modify the scalar coefficients of the equations above, and we
| |
| - |
| |
| - | obtain
| |
| - | </p>
| |
| - |
| |
| - | <br /><img src=" https://static.igem.org/mediawiki/2013/5/53/Modeling_2.png " width="150" /><br />
| |
| - | <br /><img src=" https://static.igem.org/mediawiki/2013/f/f8/Modeling_3.png " width="500" /><br />
| |
| - | <br>
| |
| - | Figure 1. dynamic process
| |
| - | <br />
| |
| - | <p>
| |
| - | We are going to solve X1(t), X2(t),X3(t), then we will plot the time course curve.
| |
| - | </p>
| |
| - | <p>
| |
| - | The initial conditions of the differential equations are as follows:
| |
| - | </p>
| |
| - | <p>
| |
| - | X1(0)= 5000 cells, X2(0)=0 cell, X3(0)=0 cell
| |
| - | </p>
| |
| - | <p>
| |
| - | k1=1day<sup>-1</sup>,k2=1 day<sup>-1</sup>
| |
| - | </p>
| |
| - | <p>
| |
| - | As for case b, the cell replicates every 26 hours, to simplify we consider one cell turns into 2 cells before next phase. Therefore, n1=n2=2.
| |
| - | </p>
| |
| - | <p>
| |
| - | Source code
| |
| - | </p>
| |
| - | <p>
| |
| - | <strong>
| |
| - | %igem_test1.m-Solution of the IPS cell differentiation model
| |
| - | </p>
| |
| - | <p>
| |
| - | %using MATLAB function ode45.m to integrate the differential equations
| |
| - | </p>
| |
| - | <p>
| |
| - | %that are contained in the file cell_diff_eq.m
| |
| - | </p>
| |
| - | <p>
| |
| - | clc; clear all;
| |
| - | </p>
| |
| - | <p>
| |
| - | %set the initial conditions, constants and time span
| |
| - | </p>
| |
| - | <p>
| |
| - | xzero=[5000,0,0];tmax=4;
| |
| - | </p>
| |
| - | <p>
| |
| - | k1=1; k2=1;
| |
| - | </p>
| |
| - | <p>
| |
| - | tspan=0:0.1: tmax;
| |
| - | </p>
| |
| - | <p>
| |
| - | N=3;
| |
| - | </p>
| |
| - | <p>
| |
| - | %Integrate the equations
| |
| - | </p>
| |
| - | <p>
| |
| - | [t X]=ode45(@cell_diff_eq,tspan,xzero,[ ],k1,k2);
| |
| - | </p>
| |
| - | <p>
| |
| - | last=X(length(X),N);
| |
| - | </p>
| |
| - | <p>
| |
| - | %Plot time curve
| |
| - | </p>
| |
| - | <p>
| |
| - | plot(t,X(:,1),'-',t, X(:,2),'-',t, X(:,3),'-.');
| |
| - | </p>
| |
| - | <p>
| |
| - | legend('X1','X2','X3');
| |
| - | </p>
| |
| - | <p>
| |
| - | xlabel('time,days');
| |
| - | </p>
| |
| - | <p>
| |
| - | ylabel('number of cells');
| |
| - | </p>
| |
| - | <p>
| |
| - | function dx= cell_diff_eq(t,x,k1,k2)
| |
| - | </p>
| |
| - | <p>
| |
| - | %cell expression kinetic procedure
| |
| - | </p>
| |
| - | <p>
| |
| - | dx=[-k1*x(1);
| |
| - | k1*x(1)-k2*x(2);
| |
| - |
| |
| - | k2*x(2); ];
| |
| - | </strong>
| |
| - | </p>
| |
| - |
| |
| - | <br/><img src=" https://static.igem.org/mediawiki/2013/9/95/Modeling_4.png " width="500" /><br />
| |
| - | <br> Figure 2. The result of case (a)
| |
| - |
| |
| - | <br/><img src=" https://static.igem.org/mediawiki/2013/a/a8/Modeling_5.png " width="500" /><br />
| |
| - | <br> Figure 3. The result of case (b)
| |
| - | </p>
| |
| - |
| |
| - |
| |
| - | 7.reference
| |
| - | </h1>
| |
| - | <p>
| |
| - | [1] Systems biology in practice concepts, implementation and application / (德) E. Klipp等著
| |
| - |
| |
| - | ; 主译:贺福初, 杨
| |
| - |
| |
| - | 芃原, 朱云平 ,上海 : 复旦大学出版社, 2007
| |
| - | </p>
| |
| - | <p>
| |
| - | [2]Numerical methods in biomedical engineering / (美) Stanley M. Dunn, Alkis Constantinides,
| |
| - |
| |
| - | Prabhas V. Moghe著
| |
| - |
| |
| - | ; 封洲燕译,北京 : 机械工业出版社, 2009
| |
| - | </p>
| |
| - | <p>
| |
| - | [3]miRNA regulatory circuits in ES cells differentiation: chemical kinetics modeling
| |
| - |
| |
| - | approach , Luo Z, Xu X, Gu
| |
| | | | |
| - | P, Lonard D, Gunaratne PH, et al. (2011)
| + | <head> |
| - | </p> | + | |
| - | <p>
| + | |
| - | [4]kinetic signatures of microRNA modes of action, N Morozova, A Zinovyev, N Nonne, LL
| + | |
| | | | |
| - | Pritchard - RNA, 2012
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