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            <h2 class="text-center">Thermosensitive Regulator </h2>
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                <p>This year, we firstly used RNA thermometer as the Thermosensitive Regulator. As this was a part constructed by other team, our wet lab members could perform the experiments based on the former teams’ experiences. Consequently, we didn’t construct the model of RNA thermometer.</p>
                <p>
                    Except for RNA thermometer, we designed the T7 platform as an alternative for Thermosensitive Regulator. It contains arabinose induced promoter, T7 polymerase inserted by thermosensitive intein, T7 promoter and GFP. Combined with Magnetic Receiver, T7 platform should take charge of controlling reporter proteins’ expression level under the temperature changing.
                </p>
                <p>
                    (If you want to learn more details about the thermosensitive regulator, you can <a href="https://2015.igem.org/Team:OUC-China/Project/Thermosensitive_Regulator">click here</a>) 
                </p>
                
                <p>
                   1.To analyze platform’s sensitivity on the temperature change according to the intein’s splicing efficiency;
                </p>
                <p>
                    2.Determine the stability of GFP’s expression level to ensure the regulating effect.
                </p>
                <h2>Deterministic Model</h2>
                <p>
                    Schematic Diagram:
                </p>
                <div style="width: 60%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/4/4e/OUC-China_Modeling_Thermosensitive-Regulator_1.png" alt="" class="img-responsive"></center>
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                <p>
                    Simplified Schematic Diagram:
                </p>
                <div style="width: 60%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/2/2c/OUC-China_Modeling_Thermosensitive-Regulator_2.png" alt="" class="img-responsive"></center>
                </div>
                <div style="width: 60%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/9/97/OUC-China_Modeling_Thermosensitive-Regulator_3.png" alt="" class="img-responsive"></center>
                </div>
                <div style="width: 60%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/b/b6/OUC-China_Modeling_Thermosensitive-Regulator_4.png" alt="" class="img-responsive"></center>
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                <div style="width: 60%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/0/08/OUC-China_Modeling_Thermosensitive-Regulator_5.png" alt="" class="img-responsive"></center>
                </div>
                <div style="width: 60%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/1/1b/OUC-China_Modeling_Thermosensitive-Regulator_6.png" alt="" class="img-responsive"></center>
                </div>
                <div style="width: 60%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/7/74/OUC-China_Modeling_Thermosensitive-Regulator_7.png" alt="" class="img-responsive"></center>
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                <p>We translated the schematic diagram into the following ordinary differential equations:</p>
                <div style="width: 60%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/7/7b/OUC-China_Modeling_Thermosensitive-Regulator_8.png" alt="" class="img-responsive"></center>
                </div>

                <p>The first equation describes the expression level of T7 polymerase controlled by arabinose. Because the complex bio-process was a induction process, we used Hill function to describe the production rate.</p>
                <p>The second equation describes the amount of mRNA of GFP transcribed by T7 polymerase. In this equation we used Michaelis-Menten function to explain its enzyme kinetics.</p>
                <P>The third equation describes the translation rate from mRNA to GFP. </P>

                <h2>Parameter Choice</h2>
                <div style="width: 80%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/7/7b/OUC-China_Modeling_Thermosensitive-Regulator_9.png" alt="" class="img-responsive"></center>
                </div>

                <h3>Degradation Rate of T7 Polymerase β1 </h3>
                <P>Because there be a degradation label “LVA tag” on the T7 polymerase, the degradation rate of it was larger than the common condition. After searched many articles we got the approximate degradation of it.</P>

                <h3>Intein Splicing constant α </h3>
                <P>The most important parameter that we considered was α.GFP’s expression quantity would fluctuate with the change of α. And it influenced the platform’s sensitivity on the temperature change.</P>

                <P>We started from the condition when the initial α equaled to a number between 0.01% and 20% when the temperature didn’t meet the threshold. Then the α changed into a number between 70% and 95% while the temperature got over the threshold. And the comparing results were shown as follow:</P>
<div class="row">
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                            <img src="https://static.igem.org/mediawiki/2015/8/86/OUC-China_Modeling_Thermosensitive-Regulator_10.png" alt="" class="img-responsive">
                            <span><center>(A)</center></span>
                        </div>
                        <div class="col-md-3">
                            <img src="https://static.igem.org/mediawiki/2015/c/c4/OUC-China_Modeling_Thermosensitive-Regulator_11.png" alt="" class="img-responsive">
                            <span><center>(B)</center></span>
                        </div>
                        <div class="col-md-3">
                            <img src="https://static.igem.org/mediawiki/2015/f/fb/OUC-China_Modeling_Thermosensitive-Regulator_12.png" alt="" class="img-responsive">
                            <span><center>(C)</center></span>
                        </div>
                        <div class="col-md-3">
                            <img src="https://static.igem.org/mediawiki/2015/7/7b/OUC-China_Modeling_Thermosensitive-Regulator_13.png" alt="" class="img-responsive">
                            <span><center>(D)</center></span>
                        </div>
</div>






                   <P></p>

                <h2>Initial Results</h2>
                <P>With the parameters chosen above and α equals to 100%, we simulated the expression level of the T7 platform when the temperature got over threshold, which was shown as blow:</P>
 <div class="row">               
<div class="col-md-4">
                            <img src="https://static.igem.org/mediawiki/2015/1/11/OUC-China_Modeling_Thermosensitive-Regulator_14.png" alt="" class="img-responsive">
                            <span><center>(A)</center></span>
                        </div>

                <div class="col-md-4">
                            <img src="https://static.igem.org/mediawiki/2015/b/b1/OUC-China_Modeling_Thermosensitive-Regulator_15.png" alt="" class="img-responsive">
                            <span><center>(B)</center></span>
                        </div>

                <div class="col-md-4">
                            <img src="https://static.igem.org/mediawiki/2015/e/e1/OUC-China_Modeling_Thermosensitive-Regulator_16.png" alt="" class="img-responsive">
                            <span><center>(C)</center></span>
                        </div>
</div>
<span><center>(A) T7 polymerase expression level; (B) mRNA of GFP expression level; (C) GFP expression level.</center></span>

                <h2>Sensitive analysis </h2>
                <p>
                    We performed sensitivity analysis to discover ways to control the expression quantity of the final interest proteins and find ways to adjust the accuracy of the platform.
                </p>

                <P>Local sensitivity analysis involves computing the relative change of the steady state with respect to a change in the parameter. We used MATLAB and sensitivities were calculated for 5% changes in the parameters. The sensitivity coefficient was defined as the ratio of the value with changed parameters and the value with unchanged parameters:</P>
                <div style="width: 20%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/1/15/OUC-China_Modeling_Thermosensitive-Regulator_17.png" alt="" class="img-responsive"></center>
                </div>
                <P>And the </P>
                <div style="width: 80%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/b/b0/OUC-China_Modeling_Thermosensitive-Regulator_18.png" alt="" class="img-responsive"></center>
                </div>

                <h2>Stochastic Model And Noise Analysis </h2>
                <p>It is important to analyze the noise of the platform </p>

<div class="col-md-6">
                            <img src="https://static.igem.org/mediawiki/2015/a/a3/OUC-China_Modeling_Thermosensitive-Regulator_21.png" alt="" class="img-responsive">
                            <span><center>(A)</center></span>
                        </div>
                <div class="col-md-6">
                            <img src="https://static.igem.org/mediawiki/2015/6/6c/OUC-China_Modeling_Thermosensitive-Regulator_22.png" alt="" class="img-responsive">
                            <span><center>(B)</center></span>
                        </div>
                
<div class="col-md-6">
                            <img src="https://static.igem.org/mediawiki/2015/8/85/OUC-China_Modeling_Thermosensitive-Regulator_20.png" alt="" class="img-responsive">
                            <span><center>(D)</center></span>
                        </div>
<div class="col-md-6">
                            <img src="https://static.igem.org/mediawiki/2015/6/68/OUC-China_Modeling_Thermosensitive-Regulator_19.png" alt="" class="img-responsive">
                            <span><center>(C)</center></span>
                        </div>

                

                



















                <p>According to the stochastic model, we calculated the noise value. And the value of the noise, 0.0023 and 0.0224 was very small. Thus we considered our results was receivable.</p>










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                <p>And Néel relaxation is due to the rotation of the magnetization, and its relaxation time is given by:</p>
                <div style="width: 20%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/e/eb/OUC-China_Modeling_Heating_3.png" alt="" class="img-responsive"></center>
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                <p>
                    The anisotropy energy of Fe<sup>2</sup>O<sup>3</sup> core would be calculated with expression given blow:
                </p>
                <div style="width: 20%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/8/8b/OUC-China_Modeling_Heating_4.png" alt="" class="img-responsive"></center>
                </div>
                <p>The two mechanisms operate in parallel, giving the expression for the overall relaxation time :</p>
                <div style="width: 20%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/a/a0/OUC-China_Modeling_Heating_5.png" alt="" class="img-responsive"></center>
                </div>
                <p>Except for the theoretical calculation, we analyzed the χ0 which srands for the equilibrium susceptibility with the result frommagneticanalysis,and conbined with the formula shown blow.We estimated χ0 to be 1.8^(-4).</p>
                <div style="width: 40%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/0/0e/OUC-China_Modeling_Heating_6.png" alt="" class="img-responsive"></center>
                </div>
                <p>
                    With SLP clear in mind, we moved on to the parameter choice and calculation as follow.
                </p>
                <h3>Parameters and Calculation</h3>
                <div style="width: 80%;margin: 0 auto;">
                    <center><img src="https://static.igem.org/mediawiki/2015/4/4c/OUC-China_Modeling_Heating_7.png" alt="" class="img-responsive"></center>
                </div>
                <p>
                    After setting all the parameters, we could initially get the result of SLP. When we set the diameter of ferritin to be 7nm, SLP would reach 8.9*10^(-3) W/g
                </p>
                <p>
                    Then we observed the SLP’s fluctuation with variety of Frequency, MF Strength and Temperature respectively.
                </p>
                <div style="border:solid 1px #FFFFFF;background-color:#FFFFFF;padding:0px 7px">
                    <div class="row">
                        <div class="col-md-4">
                            <img src="https://static.igem.org/mediawiki/2015/7/7b/OUC-China_Modeling_Heating_8.png" alt="" class="img-responsive">
                            <span><center>(A)</center></span>
                        </div>
                        <div class="col-md-4">
                            <img src="https://static.igem.org/mediawiki/2015/5/57/OUC-China_Modeling_Heating_9.png" alt="" class="img-responsive">
                            <span><center>(B)</center></span>
                        </div>
                        <div class="col-md-4">
                            <img src="https://static.igem.org/mediawiki/2015/6/63/OUC-China_Modeling_Heating_10.png" alt="" class="img-responsive">
                            <span><center>(C)</center></span>
                        </div>
                        <span><center>Fig.1. (A) (B) (C) show SLP’s changing caused by frequency, strength of the magnitic felid and temperature, respectively.</center></span>
                    </div>
                </div>
            -->



              
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