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    <div id="MD-content-all" class="MD-content-container" style="margin-top:calc(25vh - 30px);">
        <div class="MD-title">
            <a style="border-bottom-style: solid;">Nernst Equilibrium Model</a>
        </div>

        <div id="MD1" class="cd-section MD-margin-title1ToUp">
            <div class="MD-title-1" style="border-left-style:solid;padding-left:10px;">
                <a>Purpose</a>
            </div>

            <div class="MD-content MD-margin-toTitle1">
                <p class="MD-content-p">
                    In the previous model, we successfully obtained the relationship between intracellular H2O2
                    concentration and extracellular H2O2 concentration. Therefore, we were going to establish the
                    relationship between intracellular H2O2 concentration and roGFP2-Orp1 in order to evaluate the
                    antioxidant function signal output of our entire system.
                </p>
            </div>
        </div>

        <div id="MD2" class="cd-section">
            <div class="MD-title-1 MD-margin-title1ToUp" style="border-left-style:solid;padding-left:10px;">
                <a>Model Hypothesis</a>
            </div>

            <div class="MD-content MD-margin-toTitle1">
                <p class="MD-content-p">
                    1. The roGFP2-Orp1 is a fusion protein, and Orp1 is a catalase. Therefore, the reaction process of
                    the protein with H2O2 can be considered as a classical enzymatic reaction meaning that this
                    reaction is a Michael equation, and the oxidation state of roGFP2 is one of the reaction products.
                </p>

                <p class="MD-content-p MD-margin-toP">
                    2. The total intracellular concentration of roGFP2 is constant. And roGFP2 has two states,
                    oxidative state and reductive state. And the intercellular protein concentration is depended on the
                    transcription rate of promoter.
                </p>

                <p class="MD-content-p MD-margin-toFormula">
                    3. The two absorption peak values of roGFP2 at 405 nm and 488 nm are linear with the protein
                    concentration in two states.
                </p>
            </div>
        </div>

        <div id="MD3" class="cd-section MD-margin-toP">
            <div class="MD-title-1 MD-margin-title1ToUp" style="border-left-style:solid;padding-left:10px;">
                <a>Model analysis and construction</a>
            </div>

            <div class="MD-content MD-margin-toTitle1">
                <p class="MD-content-p">
                    According to Hypothesis 1, we consider the reaction process of intracellular hydrogen peroxide with
                    roGFP2 as an enzymatic reaction process, which is consistent with the Michael equation.
                </p>

                <p class="MD-formula MD-margin-toP">
                    $$V=\frac{v_{max}[H_{2}O_{2}]}{K_{m}+[H_{2}O_{2}]}$$
                </p>

                <p class="MD-content-p MD-margin-toP">
                    Here we define a new parameter <i>OxD<sub>roGFP2</sub></i> to reflect the degree of oxidation of
                    roGFP2.
                    Meanwhile, facilitate subsequent calculations.
                </p>

                <p class="MD-formula MD-margin-toP">
                    $$OxD_{roGFP2}=\frac{[roGFP2_{ox}]}{[roGFP2_{ox}]+[roGFP2_{red}]}$$
                </p>

                <p class="MD-content-p MD-margin-toP">
                    According to Hypothesis 3, we can correlate the redox state of roGFP2 with the fluorescence value
                    measured by the macroscopic observables easily. To establish this relationship, several molecular
                    quantities followed need to be defined. i405<sub>red</sub>, i405<sub>ox</sub>, i488<sub>red</sub>,
                    and i488<sub>ox</sub> are the fluorescence
                    intensities contributed by a single roGFP2 molecule at the indicated wavelength and redox state.
                    N<sub>total </sub>is the total number of roGFP2 molecules. N<sub>red</sub> is the number of reduced
                    roGFP2 molecules. N<sub>ox</sub>
                    is the number of oxidized roGFP2 molecules. Based on the assumption that the overall fluorescence
                    intensity is equal to the sum of the fluorescence intensities from the individual roGFP2 molecules,
                    the relationships were given in Table 3.
                </p>

                <p class="MD-content-p MD-margin-toP">
                    Table 3. Relationships Between Fluorescence Intensities and Probe Molecules
                </p>
                <div class="table-head">
                    <table>
                        <colgroup>
                            <col style="width: 30%;" />
                            <col style="width: 30%;" />
                            <col style="width: 40%;" />
                        </colgroup>
                        <thead>
                            <tr style="font-size: 20px;">
                                <th>Condition</th>
                                <th>Formula</th>
                                <th></th>
                            </tr>
                        </thead>
                    </table>
                </div>
                <div class="table-body">
                    <table>
                        <colgroup>
                            <col style="width: 30%;" />
                            <col style="width: 30%;" />
                            <col style="width: 40%;" />
                        </colgroup>
                        <tbody style="font-size: 16px;">

                            <tr>
                                <td>Limiting condition 1:</td>
                                <td>N<sub>total</sub> = N<sub>red</sub></td>
                                <td>I405<sub>red</sub> = N<sub>total</sub> · i405<sub>red</sub></td>
                            </tr>

                            <tr>
                                <td>Complete reduction</td>
                                <td>N<sub>ox</sub> = 0</td>
                                <td>I488<sub>red</sub> = Ntotal · i488<sub>red</sub></td>
                            </tr>

                            <tr>
                                <td>Limiting condition 2:</td>
                                <td>N<sub>total</sub> = N<sub>ox</sub></td>
                                <td>I405<sub>ox</sub> = N<sub>total</sub> · i405<sub>ox</sub></td>
                            </tr>

                            <tr>
                                <td>Complete oxidation</td>
                                <td>N<sub>red</sub> = 0</td>
                                <td>I488<sub>ox</sub> = N<sub>total</sub> · i488<sub>ox</sub></td>
                            </tr>

                            <tr>
                                <td rowspan="2">Actual measurement</td>
                                <td rowspan="2">N<sub>total</sub> = N<sub>red</sub> + N<sub>ox</sub></td>
                                <td>I405 = N<sub>ox</sub> · i405<sub>ox</sub> + N<sub>red</sub> · i405<sub>red</sub></td>

                            </tr>

                            <tr>
                                <td>I488 = N<sub>ox</sub> · i488<sub>ox</sub> + N<sub>red</sub> · i488<sub>red</sub></td>
                            </tr>

                        </tbody>
                    </table>
                </div>

                <p class="MD-content-p MD-margin-toP">
                    By substituting the resulting equations (right column of Table 3) into OxD<sub>roGFP2</sub>=N<sub>ox</sub>/N<sub>total</sub>,
                    the
                    relationship between OxD<sub>roGFP2</sub> and the macroscopic observables can be deduced.(一篇参考文献)
                </p>

                <p class="MD-formula MD-margin-toP">
                    $$oxD_{roGFP2}=\frac{I405\cdot I488_{red}-I405_{red}\cdot I488}{I405\cdot I488_{red}-I405\cdot
                    I488_{ox}+I405_{ox}\cdot I488-I405_{red}\cdot I488}$$
                </p>

                <p class="MD-content-p MD-margin-toP">
                    After the above relationship is completed, since the absolute protein concentration determination
                    is difficult, we define the relative reaction rate as
                </p>

                <p class="MD-formula MD-margin-toP">
                    $$V^{'}=\frac{V}{[roGFP2_{ox}]+[roGFP2_{red}]}$$
                </p>

                <p class="MD-formula MD-margin-toP">
                    $$OxD_{roGFP2}=\frac{[roGFP2_{ox}]}{[roGFP2_{ox}]+[roGFP2_{red}]}$$
                </p>

                <p class="MD-formula MD-margin-toP">
                    $$V^{'}=\frac{OxD^{'}-OxD}{t^{'}-t}$$
                </p>

                <p class="MD-content-p MD-margin-toP">
                    At the same time, according to Hypothesis 2, roGFP2<sub>total</sub> is constant, but the protein
                    concentration could not be measured by us. So we thought that under the same promoter conditions,
                    the protein concentration was basically the same and according to the data provided in the previous
                    literature, it is known that in yeast cells, the Eno2 protein concentration is around 0.5
                    mM.(一篇参考文献)
                </p>

                <p class="MD-content-p MD-margin-toP">
                    So we could get:
                </p>

                <p class="MD-formula MD-margin-toP">
                    $$[roGFP2_{total}]=0.5\ mM$$
                </p>

                <p class="MD-content-p MD-margin-toP">
                    In order to obtain the two constants in the Micheal equation, we measured the reaction rate of the
                    reaction in yeast cells by applying different concentrations of H<sub>2</sub>O<sub>2</sub> and
                    using the simulation
                    results of the H<sub>2</sub>O<sub>2</sub> Decomposition Model in combination with the function of
                    roGFP2. The results
                    were as follows:
                </p>

                <figure class="MD-Fig MD-margin-toContentP">
                    <img src="https://static.igem.org/mediawiki/2018/6/6c/T--BIT-China--iGEM2018-Modeling10.PNG">
                    <figcaption>Fig.4 Fluorescence ratio measurement data from wet experiment</figcaption>
                </figure>

                <figure class="MD-Fig MD-margin-toContentP">
                    <img src="https://static.igem.org/mediawiki/2018/e/e0/T--BIT-China--iGEM2018-Modeling11.PNG">
                    <figcaption>Fig.5 Reaction rate measurement data from wet experiment</figcaption>
                </figure>

                <p class="MD-content-p MD-margin-toP">
                    Calculate two constants by double reciprocal mapping.
                </p>

                <figure class="MD-Fig MD-margin-toContentP">
                    <img src="https://static.igem.org/mediawiki/2018/5/5c/T--BIT-China--iGEM2018-Modeling12.PNG">
                    <figcaption>Fig.6 v<sub>max⁡</sub> and K<sub>m⁡</sub> calculation using double reciprocal mapping</figcaption>
                </figure>

                <p class="MD-formula MD-margin-toP">
                    $$v_{max}=0.015207$$
                </p>

                <p class="MD-formula MD-margin-toP">
                    $$K_{m}=0.451642$$
                </p>

                <p class="MD-content-p MD-margin-toP">
                    The relationship between the change in fluorescence intensity of roGFP2 and the concentration of
                    intracellular H<sub>2</sub>O<sub>2</sub> is set up successfully.
                </p>
            </div>
        </div>

        <div id="MD4" class="cd-section MD-margin-toP">
            <div class="MD-title-1" style="border-left-style:solid;padding-left:10px;">
                <a>Summary</a>
            </div>

            <p class="MD-content-p MD-margin-toP">
                Our model has been successfully implemented. Different concentrations of intracellular H<sub>2</sub>O<sub>2</sub>
                can change
                the spectral properties of our system's roGFP2, and successfully convert our selected ROS signal
                (Intercellular H<sub>2</sub>O<sub>2</sub> concentration) into a visualized fluorescent signal that
                means we can evaluate the
                intercellular H<sub>2</sub>O<sub>2</sub> concentration easily through calculate the OxD value.
                However, due to time and experimental limitation, our model is only a preliminary establishment, and
                its subsequent calibration work is limited by experiment and time, there is no enough time to continue
                optimization .We also hoped that there will be follow-up teams to continue to finish our models.

            </p>
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            <p style="font-size:15px;margin: 0;padding: 0;margin-top: 4px;">Institute of
                Biotransformation and synthetic biosystem School of Chemistry and Chemical Engineering.
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                Beijing Institute of Technology
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                100081, Beijing
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                Email:lichun@bit.edu.cn
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