Difference between revisions of "Team:ZJU-China/Model"

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             <li>
 
             <li>
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                 <a href="#Cloning" style="background-color: #f6b37f;" class="nav-active rounded"><span>Overview</span></a>
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                 <a href="#technical_feasibility" style="background-color: #f6b37f;" class="nav-active rounded"><span>Technical Feasibility</span></a>
 
             </li>
 
             </li>
 
             <li>
 
             <li>
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                 <a href="#about" style="background-color: #7ecef4;" class="rounded"><span>PART Ⅰ</span></a>
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                 <a href="#commercial_feasibility" style="background-color: #7ecef4;" class="rounded"><span>Commercial Feasibility</span></a>
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            </li>
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                <a href="#services" style="background-color: #f19ec2;" class="rounded"><span>PART Ⅱ</span></a>
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                <a href="#showcase" style="background-color:#eb6877;" class="rounded"><span>PART Ⅲ</span></a>
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            <li>
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                <a href="#appd" style="background-color:#d197f7;" class="rounded"><span>Appendix</span></a>
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                <a href="#our-team" style="background-color: #cce198" class="rounded"><span>References</span></a>
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                                 <li><a href="background.html">Background</a></li>
 
                                 <li><a href="background.html">Background</a></li>
 
                                 <li><a href="domain.html">Design</a></li>
 
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                                 <li><a href="hosting.html">Result</a></li>
 
                                 <li><a href="hosting.html">Result</a></li>
 
                                 <li><a href="hosting.html">Demonstrate</a></li>
 
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                         <li><a href="background.html">Background</a></li>
 
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                         <li><a href="domain.html">Demonstrate</a></li>
 
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     <div class="pagename">
 
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         <h1>Model</h1>
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         <h1>Proof Of Concept</h1>
 
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                    <h2>Overview</h2>
 
  
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                    <br>
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                    <br>
 
                     <p>
 
                     <p>
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                         To understand the production of target antibody and modified magnetosomes and the combination and disaggregation of them, we have established some <i>in-vivo</i> and <i>in-vitro</i> models.
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                         Taking <b>breast cancer</b> which has the highest incidence rate in the world as an opponent, we need to be very careful in dealing with every step of implementing our project into reality.
 +
                        In the real world, we believe that thousands of researchers and drug companies are also worried about the plight of breast cancer treatment and come up with countless ideas.
 +
                        However, if we want to really <b>improve the survival status</b> of breast cancer patients, we need to prove our project is valuable enough to <b>contribute to society</b>.
 +
                        <br>
 +
                        In this page, we extend the content about <b>Proof of Concept</b> on the basis of the project implementation plan, and explain that each part of our project is running in a relevant
 +
                        context.
 
                     </p>
 
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                     <br>
 
                     <br>
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                     <p>
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                     <br>
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                        Our modeling work is comprised of three parts.
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                    </p>
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                    <p>
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                        1) We used two models to describe <b>the reactions in <i>E.coli</i> and magnetotactic bacteria</b> separately.
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                    <p>
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                        2) We used a deterministic model to determine <b>the combination and disaggregation of scFv-Fc and modified magnetosomes <i>in vitro</i>.</b>
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                    </p>
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                    <p>
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                        3) We used two models to describe<b> the movements of modified magnetosomes and its combination with HER2 <i>in vivo</i>.</b>
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             <div class="section about" id="about">
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             <div class="section Cloning" id="technical_feasibility">
 
                 <div class="container1">
 
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                     <h2 style="line-height:1.5;">PART Ⅰ Deterministic Model to Compute the Production of scFv and Modified Magnetosomes</h2>
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                     <h2>Technical Feasibility</h2>
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                     <p>
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                     <h3>Interaction of Two Recombinant Proteins</h3>
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                        To produce scFv and modified magnetosomes, we introduced the plasmid containing target gene into <i>E.coli</i> and magnetotactic bacteria respectively, and finally understood the
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                        final yield of the target product by simulating their metabolic processes respectively.
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                    </p>
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                    <h3><i>E.coli</i></h3>
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                     <p>
 
                     <p>
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                         In <i>E.coli</i>, T7 RNA polymerase is placed under a <i>lac</i> Operon, which can be induced by IPTG. The production of the target protein, scFv-Fc, is controlled by T7 promoter (Figure 1A)<a href="#our-team"><sup>[1]</sup></a>. The combination between T7 RNA polymerase and T7 promoter is determined by Hill function. The ordinary differential equations (ODEs)
+
                         Using the interaction system of Fc-ZZ as our linker, we linked the mamC expressed in <i>E.coli</i> BL21 and scFv expressed in <i>E.coli</i> SHuffle® as a compound BioBrick, indicated that we
−
                        describing these processes are shown as follows, and parameter names and chemical equations can be found in the appendix.
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                        can immobilized scFv on the surface of magnetosomes produced by <i>Magnetospirillum gryphiswaldense</i>.
 
                     </p>
 
                     </p>
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                    <p style="font-size: medium;">
 
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                        \begin{align}
 
−
                        \frac{d}{d t}MR_{E} &= \alpha_MR \cdot O_{total} - \lambda_{MR} \cdot MR_{E}\\
 
−
                        \frac{d}{dt}R_{E}&=\beta_{R} \cdot MR_{E} -2 \cdot k_{2R} \cdot R_{E}^2 +2 \cdot k_{-2R} \cdot R_{2E} -\lambda_{R} \cdot R_{E}\\
 
−
                        \frac{d}{dt}R_{2E}&= 2 \cdot k_{2R} \cdot R_{E}^{2}-2 \cdot k_{-2R} \cdot R_{2E}-k_{r} \cdot R_{2 E} \cdot O_{E} +k_{-r} \cdot \left(O_{total}-O_{E}\right)-k_{dr1} \cdot R_{2E}
 
−
                        \cdot I_{E}^{2} \\& + k_{-dr1} \cdot I_{2}R_{2E}-\lambda_{R2} \cdot R_{2E}\\
 
−
                        \frac{d}{dt}O_{E}&=-k_{r} \cdot R_{2E} \cdot O_{E}+k_{-r} \cdot \left(O_{total}-O_{E}\right)+k_{dr2} \cdot \left(O_{total}-O_{E}\right) \cdot I_{E}^{2}-k_{-dr2} \cdot O_{E}
 
−
                        \cdot I_{2}R_{2E}\\
 
−
                        \frac{d}{dt}I_{E}&= -2 \cdot k_{dr1} \cdot R_{2E} \cdot I_{E}^{2} +2 \cdot k_{-dr1} \cdot I_{2}R_{2E}-2 \cdot k_{dr2} \cdot \left(O_{total}-O_{E}\right) \cdot I_{E}^{2} \\&+2
 
−
                        \cdot k_{-dr2} \cdot O_{E} \cdot I_{2}R_{2 E}+k_{ft} \cdot YI_{exE}+k_{t} \cdot \left(I_{ex}-I_{E}\right)+2 \cdot \lambda_{I2R2} \cdot I_{2}R_{2E}\\
 
−
                        \frac{d}{dt}I_{2}R_{2E}&=k_{dr1} \cdot R_{2E} \cdot I_{E}^{2} -k_{-dr1} \cdot I_{2}R_{2E} +k_{dr2} \cdot \left(O_{total}-O_{E}\right) \cdot I_{E}^{2} -k_{-dr2} \cdot O_{E}
 
−
                        \cdot I_{2}R_{2E} \\&-\lambda_{I2R2} \cdot I_{2}R_{2E}\\
 
−
                        \frac{d}{dt}MY_{E}&=\alpha_{0} \cdot \left(O_{total}-O_{E}\right) +\alpha_{1} \cdot O_{E} -\lambda_{MY} \cdot MY_{E}\\
 
−
                        \frac{d}{dt}Y_{E}&=\beta_{Y} \cdot MY_{E}+\left(k_{ft}+k_{-p}\right) \cdot YI_{exE} -k_{p} \cdot Y_{E} \cdot I_{exE}-\lambda_{Y} \cdot Y_{E}\\
 
−
                        \frac{d}{dt}YI_{exE}&=-\left(k_{ft}+k_{-p}\right) \cdot YI_{exE}+k_{p} \cdot Y_{E} \cdot I_{exE} -\lambda_{YIex} \cdot YI_{exE}\\
 
−
                        \frac{d}{dt}MT7_{E}&=\alpha_{0} \cdot \left(O_{total}-O_{E}\right)+\alpha_{1} \cdot O_{E} -\lambda_{MT7} \cdot MT7_{E}\\
 
−
                        \frac{d}{dt}pT7_{E}&=\beta_{T7} \cdot MT7_{E}-\lambda_{pT7} \cdot pT7_{E}\\
 
−
                        \frac{d}{dt}MF_{E}&=\left(\frac{pT7^{n}}{pT7^{n}+K_{d}^{n}} \cdot \alpha_{MT}+\alpha_{leak}\right) \cdot O_{total}-\lambda_{MF} \cdot MF_{E}\\
 
−
                        \frac{d}{dt}F_{E}&=\beta_{F} \cdot MF_{E}-\lambda_{F} \cdot F_{E}
 
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                        \end{align}
 
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                    </p>
 
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                     <br>
 
                     <br>
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                    <p>
 
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                        According our modeling result, although there's a peak before adding IPTG, the production cannot be maintained during a long period of time. Only after adding IPTG, the
 
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                        concentration of the target protein in the bacteria is maintained at <b>1.3069×10<sup>4</sup> nM.</b>
 
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                    </p>
 
 
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                         <img src="https://static.igem.org/mediawiki/2020/thumb/f/fc/T--ZJU-China--Proof_Of_Concept_fig1.jpg/800px-T--ZJU-China--Proof_Of_Concept_fig1.jpg"></img>
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                         <h6>A</h6>
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                         <h6>Fig1. Western-blot results of immunoprecipitation between mamC-ZZ and scFv-Fc.</h6>
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                        <img src="https://static.igem.org/mediawiki/2020/thumb/1/19/T--ZJU-China--Model_fig1b_arrow.jpg/800px-T--ZJU-China--Model_fig1b_arrow.jpg"></img>
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                    <p>All the protein concentrations from each block were determined by UV spectrophotometry. Total protein obtained mamC-ZZ was <b>24.8mg/mL</b>, purified mamC was <b>0.3mg/mL</b>, purified scFv was
−
                         <h6>B</h6>
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                         <b>0.2mg/mL</b>. In industry, it is not difficult to achieve that level of protein concentration, which proves that our products are easy to be manufactured.</p>
  
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                     </div>
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                     <h3>Effectiveness of scFv</h3>
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                     <br>
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                     <p>In order to prove that scFv-Fc fusion protein can specifically target HER2 positive breast cancer cells, we have demonstrated the specificity and effectiveness of this targeting by flow cytometry.</p>
 +
                    <br><br>
 
                     <div class="imgbox">
 
                     <div class="imgbox">
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                         <h6><b>Figure 1. Induced expression of scFv-Fc.</b> (A) Schematic diagram of the model. (B) Dynamics of target protein. Horizontal axis shows the length of time. Vertical axis demonstrates the amount of protein (scFv-Fc) within
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                         <img src="https://static.igem.org/mediawiki/2020/c/ce/T--ZJU-China--Results_fig10_newone.jpg" alt="">
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                            the system.</h6>
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                        <h6>Fig2. Flow cytometry results of MDA-MB-453 and MDA-MB-231 after incubated with scFv-Fc.</h6>
−
 
+
 
                     </div>
 
                     </div>
 +
                    <p>Obviously, the high HER2 expression cell line (MDA-MB-453) showed a higher fluorescence (about 10 times) than that of the low HER2 expression cell line (MDA-MB-231), indicating that scFv-Fc is more targeted to HER2, and can distinguish breast cancer cells with high and low expression of HER2 (Fig2).</p>
  
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                    <h3>Magnetotactic Bacteria</h3>
 
  
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                    <p>
 
−
                        In magnetotactic bacteria, target protein (mamC-ZZ) is placed under a <i>lac</i> Opera, and the repressor protein LacI is stably expressed in the cell, two molecules of LacI will form a
 
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                        dimer which binds to <i>LacO</i> DNA fragment and represses the expression of target protein (Figure 2A). When IPTG is added and transported into the cell, IPTG molecules will bind with
 
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                        LacI and inhibit its binding to LacO. In this way, target protein can be rescued from suppression<a href="#our-team"><sup>[1]</sup></a>. We assume that all target proteins
 
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                        will be localized to the magnetosome membrane by intracellular transport. The ordinary differential equations (ODEs) describing these processes are shown as follows, parameter
 
−
                        names and chemical equations can be found in the appendix.
 
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                    </p>
 
 
                     <br>
 
                     <br>
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                     <div class="imgbox">
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                     <h3>Modeling Results</h3>
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                        <p style="font-size: medium;">
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                            \begin{align}
+
−
                            \frac{d}{d t}MR_{M} &= \alpha_MR \cdot O_{total} - \lambda_{MR} \cdot MR_{M}\\
+
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                            \frac{d}{dt}R_{M}&=\beta_{R} \cdot MR_{M} -2 \cdot k_{2R} \cdot R_{M}^2 +2 \cdot k_{-2R} \cdot R_{2M} -\lambda_{R} \cdot R_{M}\\
+
−
                            \frac{d}{dt}R_{2M}&=2 \cdot k_{2R} \cdot R_{M}^{2}-2 \cdot k_{-2R} \cdot R_{2M}-k_{r} \cdot R_{2M} \cdot O_{M} +k_{-r} \cdot \left(O_{total}-O_{M}\right)-k_{dr1} \cdot
+
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                            R_{2M} \cdot I_{M}^{2} \\&+k_{-dr1} \cdot I_{2}R_{2M}-\lambda_{R2} \cdot R_{2M}\\
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                            \frac{d}{dt}O_{M}&=-k_{r} \cdot R_{2M} \cdot O_{M}+k_{-r} \cdot \left(O_{total}-O_{M}\right)+k_{dr2} \cdot \left(O_{total}-O_{M}\right) \cdot I_{M}^{2}-k_{-dr2} \cdot O_{M}
+
−
                            \cdot I_{2}R_{2M}\\
+
−
                            \frac{d}{dt}I_{M}&=-2 \cdot k_{dr1} \cdot R_{2M} \cdot I_{M}^{2} +2 \cdot k_{-dr1} \cdot I_{2}R_{2M}-2 \cdot k_{dr2} \cdot \left(O_{total}-O_{M}\right) \cdot I_{M}^{2}
+
−
                            \\&+2 \cdot k_{-dr2} \cdot O_{M} \cdot I_{2}R_{2M}+k_{ft} \cdot YI_{exM}+k_{t} \cdot \left(I_{ex}-I_{M}\right)+2 \cdot \lambda_{I2R2} \cdot I_{2}R_{2M}\\
+
−
                            \frac{d}{dt}I_{2}R_{2M}&=k_{dr1} \cdot R_{2M} \cdot I_{M}^{2} -k_{-dr1} \cdot I_{2}R_{2M} +k_{dr2} \cdot \left(O_{total}-O_{M}\right) \cdot I_{M}^{2} -k_{-dr2} \cdot O_{M}
+
−
                            \cdot I_{2}R_{2M} \\&-\lambda_{I2R2} \cdot I_{2}R_{2M}\\
+
−
                            \frac{d}{dt}MY_{M}&=\alpha_{0} \cdot \left(O_{total}-O_{M}\right) +\alpha_{1} \cdot O_{M} -\lambda_{MY} \cdot MY_{M}\\
+
−
                            \frac{d}{dt}Y_{M}&=\beta_{Y} \cdot MY_{M}+\left(k_{ft}+k_{-p}\right) \cdot YI_{exM} -k_{p} \cdot Y_{M} \cdot I_{exM}-\lambda_{Y} \cdot Y_{M}\\
+
−
                            \frac{d}{dt}YI_{exM}&=-\left(k_{ft}+k_{-p}\right) \cdot YI_{exM}+k_{p} \cdot Y_{M} \cdot I_{exM} -\lambda_{YIex} \cdot YI_{exM}\\
+
−
                            \frac{d}{dt}MZ_{M}&=\alpha_{0} \cdot \left(O_{total}-O_{M}\right)+\alpha_{1} \cdot O_{M} -\lambda_{MZ} \cdot MZ_{M}\\
+
−
                            \frac{d}{dt}Z_{M}&=\beta_{Z} \cdot MZ_{M}-\lambda_{Z} \cdot Z_{M}
+
−
                            \end{align}
+
−
 
+
−
                        </p>
+
−
                    </div>
+
−
 
+
−
                    <br>
+
−
 
+
−
 
+
 
                     <p>
 
                     <p>
−
                         According to our modeling result, the final concentration of target protein mamC-ZZ is <b>2.3625×10<sup>3</sup> nM.</b> Since the concentration of magnetosomes extracted from the
+
                         We simulated the process of the two recombinant proteins from the internal expression of bacteria to the interaction and binding in vitro, and simulated the whole process of
−
                        culture medium whose OD600 reaches <b>1</b> is <b>172 ug per milliliter</b><a href="#our-team"><sup>[2]</sup></a>, the average concentration of magnetosomes is <b>46.83 per cell</b>, and there are
+
                         our final product diffusion in tumors and binding with HER2 as well.
−
                         an average of <b>24.31</b> target protein mamC-ZZ on each magnetosome when assuming that all target proteins are localized to the magnetosome membrane.
+
                        <br>
−
                    </p>
+
                         Through all those modelling results delivered in <a href="https://2020.igem.org/Team:ZJU-China/Model" class="outerlink">Model</a>, we have a general understanding of the
−
                    <br>
+
                         production of two recombinant in <i>E.coli</i> and <i>Magnetospirillum</i>, and the speed and
−
                    <div class="imgbox">
+
                        proportion of the Fc-ZZ interaction system in vitro, and the dispersion and binding of scFv modified magnetosomes in tumor. These data provide us a possible range of contrast
−
                         <img src="https://static.igem.org/mediawiki/2020/3/36/T--ZJU-China--wiki_modelnew_fig3.png"></img>
+
                        agent injection dose in future clinical trials.
−
                         <h6>A</h6>
+
  
−
                    </div>
 
−
                    <br>
 
−
                    <div class="imgbox">
 
−
                        <img src="https://static.igem.org/mediawiki/2020/thumb/d/d4/T--ZJU-China--Model_fig2b_arrow.jpg/800px-T--ZJU-China--Model_fig2b_arrow.jpg"></img>
 
−
                        <h6>B</h6>
 
−
 
−
                    </div>
 
−
                    <br>
 
−
                    <div class="imgbox">
 
−
                        <h6>
 
−
                            <b>Figure 2. Induced expression of mamC-ZZ.</b> (A) Schematic diagram of the model. (B) Dynamics of target protein. Horizontal axis shows the length of time. Vertical axis demonstrates
 
−
                            the amount of protein (mamC-ZZ) within the system.
 
−
                        </h6>
 
−
 
−
                    </div>
 
−
 
−
 
−
 
−
 
−
                </div>
 
−
            </div>
 
−
            <div class="section services" id="services">
 
−
                <div class="container1">
 
−
                    <h2 style="line-height:1.5;">PART Ⅱ Deterministic Model to Determine the Combination and Disaggregation of scFv-Fc and Modified Magnetosomes <i>in Vitro</i></h2>
 
−
                    <br>
 
−
                    <br>
 
−
                    <p>
 
−
                        After scFv-Fc and modified magnetosomes being produced in <i>E.coli</i> and magnetotactic bacteria, they are extracted from cells and purified Fc domain can combine with mamC-ZZ domain
 
−
                        so that these two parts will combine and work together. Assuming that there's no factor causing target protein degradation <i>in vitro</i>, the ordinary differential equations (ODEs)
 
−
                        describing these processes are shown as follows.
 
 
                     </p>
 
                     </p>
−
                    <br>
 
−
                    <p>
 
  
−
                        $$\frac{d}{dt}F=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ$$
+
                     <h3>Further Approach of Technical Feasibility</h3>
−
                        $$\frac{d}{dt}Z=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ$$
+
−
                        $$\frac{d}{dt}FZ=k_{1} \cdot F \cdot Z-k_{-1} \cdot FZ$$
+
−
 
+
−
 
+
−
                     </p>
+
−
                    <br>
+
 
                     <p>
 
                     <p>
−
                         From the modeling result, we can see the reaction between 10 mg/ml modified magnetosomes and 100 ug/ml scFv-Fc is very fast and the production rate is relatively high (Figure 3).
+
                         After we obtain the engineered magnetosomes and equip them with scFv, we will carry out in vitro experiments on cytotoxicity and contrast effect of MagHER2some. When all
 +
                        indexes show a good trend, we will carry out in vivo experiments on mice and follow-up clinical trials through legal application according to the requirements of China's laws.
 +
                        You can learn more from <b>the Clinical Trial</b> section in <a href="https://2020.igem.org/Team:ZJU-China/Implementation" class="outerlink">Implementation</a>.
 
                     </p>
 
                     </p>
−
 
−
                    <br>
 
−
                    <div class="imgbox">
 
−
                        <img src="https://static.igem.org/mediawiki/2020/e/ef/T--ZJU-China--wiki_model_fig3b_new.png"></img>
 
−
                        <h6><b>Figure 3. combination of scFv-Fc and modified magnetosomes </b>(the blue line refers to the combination product of scFv-Fc and modified magnetosomes, and the orange line refers
 
−
                            to pure magnetosomes).</h6>
 
−
 
−
                    </div>
 
−
 
−
 
−
 
−
 
 
                 </div>
 
                 </div>
 
             </div>
 
             </div>
  
−
             <div class="section showcase" id="showcase">
+
 
 +
             <div class="section about" id="commercial_feasibility">
 
                 <div class="container1">
 
                 <div class="container1">
−
                    <h2 style="line-height:1.5;">PART Ⅲ Kinetic Model to Simulate the Diffusion and Binding of Modified Magnetosomes Inside the Tumors</h2>
 
−
                    <br>
 
−
                    <br>
 
−
                    <h3>Magnetosome Diffusion in Internal Environment</h3>
 
−
                    <br>
 
−
                    <br>
 
−
                    <p>
 
−
                        It could be assumed that the magnetosome injected collect around the tumor if exists, since our magnetosome has been proved to stick to HER2 produced by breast cancer cells
 
−
                        specifically. As magnetosome enters into tissue fluid from blood, its concentration changes with time and the distance to the source. This way, we want to depict the alteration
 
−
                        of magnetosome's concentration field to explain the process intuitively by image.
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        First of all, we'd like to focus on the factors which drive magnetosome move or diffuse in tissue fluid. Four respects were considered, involving motions with the flow of
 
−
                        tissue fluid, eddy diffusion caused by natural convection, mass transfer due to the difference of concentration, pure molecular diffusion as magnetosome was regarded as similar
 
−
                        to a molecular in size.
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        To simplify the question, polar coordinates were adopted to substitute a two-dimension or three-dimension gradient. That is to say, small particles were assumed to diffuse
 
−
                        evenly to different directions and scalars were calculated instead of vectors.
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        $$\nabla \boldsymbol{c} \rightarrow \frac{\partial c}{\partial r}$$
 
−
                    </p>
 
  
−
                     <br>
+
                     <h2>Commercial Feasibility</h2>
−
 
+
       
−
 
+
                     <h3>Market Investigation</h3>
−
                    <p>
+
−
                        Macroscopic methods could be useful to solve the problem. Use J to represent the diffusion flux. It is easy to infer motions with the flow of tissue fluid as \(J_{1}=ub \times
+
−
                        \frac{\partial c}{\partial r}\\\).
+
−
                    </p>
+
−
                    <br>
+
−
                     <p>
+
−
                        $$u_{b}=\frac{\pi d^{2}\left(p+\frac{1}{2} \rho g d\right)}{32 \mu_{b} D}$$
+
−
                    </p>
+
−
                    <br>
+
 
                     <p>
 
                     <p>
−
                         According to Fick's First Law, eddy diffusion caused by natural convection is calculated by \(J_{2}=D_{n} \times \frac{\partial c}{\partial r}\\\).
+
                         As a team targeted to develop a novel contrast agent with a innovative design, we conducted a comprehensive investigation with patients, medical specialists in breast cancer,
 +
                        radiologist, researchers in pharmocochemistry, company researchers, etc. You can learn more from the <a href="https://2020.igem.org/Team:ZJU-China/Human_Practices" class="outerlink">Human Practice</a> section.
 +
                        <br>
 +
                        We also developed industry analysis from various aspects, you can learn more from the <a href="https://2020.igem.org/Team:ZJU-China/Implementation" class="outerlink">Implementation</a> section.
 +
                        <br>
 +
                        We gradually figured out that there was a lack of targeted contrast agents in the market. Targeted contrast agents such as MagHER2some have dual economic and social value,
 +
                        because they can reduce the proportion of empirical judgement in the analysis of MRI results, so as to achieve a more accurate prognosis treatment of breast cancer. As a
 +
                        result, the treatment of breast cancer patients will be improved, and much more people will free from the torture of the disease.
  
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        On top of that, natural convection is very weak in both capillaries and tissue fluid flows. We chose to ignore the value of J2 finally, which means \(J_{2} \approx 0\\\).
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        In order to obtain the diffusion flux due to mass transfer, an important constant called mass transfer coefficient was in need, for the expression, \(J_{3}=k_{c} \times
 
−
                        \frac{\partial c}{\partial r}\\\).
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        We used Chaoqun Yao (2020)'s experiment kc data of 1:1 silicone oil-water mixture, to whose viscosity blood and tissue fluid similar<a href="#our-team"><sup>[3]</sup></a>. A
 
−
                        model was built for the relationship between the rate of flow and kc. Microsoft Office Excel was employed to finish the task.
 
−
                    </p>
 
−
                    <br>
 
−
                    <div class="imgbox">
 
−
                        <img src="https://static.igem.org/mediawiki/2020/7/77/T--ZJU-China--wiki_mode_fig6.png"></img>
 
−
                        <h6><b>Figure 4. The influence of rate of flow on mass transfer coefficient.</h6>
 
−
 
−
                    </div>
 
−
                    <br>
 
−
                    <p>
 
−
                        Now we could get the value of Q in our situation. This way, the value of kc could be assumed roughly.
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        $$Q=u_{a} \times \frac{1}{4} \pi d^{2}=4.01 \times 10^{-4} ml/min$$
 
−
                        $$k_{c}=-0.0622 Q^{3}+0.0127 Q^{2}-0.0005 Q+2 \times 10^{-5}=2.00 \times 10^{-2} mm/s$$
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        Dispersion effect also led to the diffusion of magnetosome in tumor tissue. It could be estimated the same way as eddy diffusion caused by natural convection:
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        $$J_{4}=D_{m} \times \frac{\partial c}{\partial r}$$
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        Stokes-Einstein equation was able to be used to calculate the diffusion coefficient as below.
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        $$D_{m}=\frac{k_{b} T}{6 \pi \mu_{b} R}$$
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        Overall diffusion flux could be calculated by superimposing the following diffusion flux.
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        $$J=J_{1}-J_{2}-J_{3}-J_{4}$$
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        It is assumed that the motion of fluid flow obeys the law discovered by Navier and Stokes.
 
−
                    </p>
 
−
                    <br>
 
−
                    <div class="imgbox">
 
−
                        <p style="padding-left:20%">
 
−
                            <i>instantaneous term = - diffusion term + convection term + sourse</i>
 
−
                        </p>
 
−
                    </div>
 
−
                    <p>
 
−
                        That is to say,
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        $$\frac{\partial c}{\partial t}=\frac{\partial J}{\partial r}+u_{a} \nabla \boldsymbol{c}_{\boldsymbol{o}}$$
 
 
                     </p>
 
                     </p>
  
 
                     <br>
 
                     <br>
 +
                    <h3>Advantage Demonstration</h3>
  
 
                     <p>
 
                     <p>
−
                         To solve the following PDE with the help of MatlabR2020a, both initial condition and boundary condition were supposed to be provided.
+
                         Compared with gadolinium based contrast agent (GBCA), MagHER2some goes beyond it from the following three aspects:
 
                     </p>
 
                     </p>
−
                    <br>
 
−
                    <p>
 
−
                        We should provide the relationship between r and c under the circumstance that t–0, when diffusion hadn't happened in our model. At the very beginning, magnetosome collect in
 
−
                        the capillary and it is presumed that there was seldom magnetosome in tissue fluid.
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        $$
 
−
                        \left.c(t, r)\right|_{t=0}=\left\{\begin{array}{ll}
 
−
                        0 & r \neq 0 \\
 
−
                        c_{o} & r=0
 
−
                        \end{array}\right.
 
−
                        $$
 
−
                    </p>
 
−
 
−
 
−
                    <br>
 
−
                    <p>
 
−
                        In comparison to the initial condition, this time we're required to explain how t influences c at the time of rmin=0 and rmax=10, embodying the probable size of the tumor. Soon
 
−
                        we found the condition invalid. At last we expand rmax=100 to produce the image.
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        One of the difficulties was that we failed to describe the alteration of the concentration taking place at the original location where diffusion started precisely and in
 
−
                        detail. A highly rough calculation was attached to it to show the characteristics that the rate of diffusion weakened as the concentration descended and time went by.
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        $$\left.c(t, r)\right|_{r=0}=\frac{c_{o}}{1+0.05 \sqrt{t}}$$
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        Simultaneously, we assumed that when diffusion flux caught the brim space, co would be small enough to be ignored.
 
−
                    </p>
 
−
                    <br>
 
−
                    <p>
 
−
                        $$\left.c(t, r)\right|_{r=100}=0$$
 
−
                    </p>
 
−
                    <br>
 
−
 
 
                     <div class="imgbox">
 
                     <div class="imgbox">
−
                         <img src="https://static.igem.org/mediawiki/2020/8/8f/T--ZJU-China--wiki_mode_fig7.png"></img>
+
                         <img src="https://static.igem.org/mediawiki/2020/thumb/6/6a/T--ZJU-China--Proof_Of_Concept_table1.jpg/800px-T--ZJU-China--Proof_Of_Concept_table1.jpg" alt="">
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                        <h6>Figure 5. (A) Concentration field of magnetosome in tissue fluid. (B) Magnetosome diffused in the tumor issue capillaries around it.</h6>
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                     </div>
 
                     </div>
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                    <br>
 
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                    <h3>Detection and Combination with HER2</h3>
 
  
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                     <p>
+
                     <p>As the table showed above, MagHER2some is an innovative and superior contrast agent compared with traditional products. Based on what we have done during iGEM, we can foresee that MagHER2some will be a highly specific, non-toxic and environmentally friendly product to enhance the MRI contrast.</p>
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                        To describe the combination and degradation with HER2, we have a model about modified magnetosomes <i>in vivo</i>. Assuming that there is no other way to clear magnetosomes and
+
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                        scFv-Fc in the tissue fluid except for phagocytosis by macrophages and the phagocytosis is at a constant rate, the ordinary differential equations (ODEs) describing these
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                        processes are as follows. Parameter names and chemical equations can be found in the appendix.
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                    </p>
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                    <br>
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                    <p>
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                        $$\frac{d}{dt}F=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ -k_{2} \cdot H \cdot F +k_{-2} \cdot FH$$
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                        $$\frac{d}{dt}Z=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ -k_{1} \cdot FH \cdot Z+k_{-1} \cdot ZFH-P$$
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                        $$\frac{d}{dt}FZ=k_{1} \cdot F \cdot Z-k_{-1} \cdot FZ -k_{2} \cdot H \cdot FZ+k_{-2} \cdot ZFH-P$$
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                        $$\frac{d}{dt}H=-k_{2} \cdot H \cdot F+k_{-2} \cdot FH -k_{2} \cdot H \cdot FZ+k_{-2} \cdot ZFH$$
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                        $$\frac{d}{dt}FH=k_{2} \cdot H \cdot F-k_{-2} \cdot FH -k_{1} \cdot FH \cdot Z+k_{-1} \cdot ZFH$$
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                        $$\frac{d}{dt}ZFH=k_{1} \cdot FH \cdot Z-k_{-1} \cdot ZFH+k_{2} \cdot H \cdot FZ-k_{-2} \cdot ZFH$$
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                     </p>
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                     <h3>Commercial Strategy</h3>
 +
                    <p>We have developed a business plan based on our experiments and investigation results. The contents of business plan are a prototype that demonstrate the method that we implement Proof of Concept activities at the early stage of commercialization. You can learn more from the <a href="https://2020.igem.org/Team:ZJU-China/Implementation" class="outerlink">Implementation</a> section.</p>
 
                     <br>
 
                     <br>
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                    <p>
 
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                        We can see in the result that the process of combination finished very quickly (Figure 6A), while the total number of the magnetosomes decreases gradually because of the
 
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                        phagocytosis process (Figure 6B), and the concentration of magnetosomes is one tenth of what it was before after around 120 minutes. We also have results with different
 
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                        concentration of magnetosomes injected (Figure 6C), which shows the combination in a short of time with different injection concentration of modified magnetosomes.
 
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                    </p>
 
 
                     <br>
 
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                    <div class="imgbox">
 
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                        <img src="https://static.igem.org/mediawiki/2020/c/cb/T--ZJU-China--wiki_model_fig6a_new.png"></img>
 
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                        <h6>A</h6>
 
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                    </div>
 
 
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                    <div class="imgbox">
 
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                        <img src="https://static.igem.org/mediawiki/2020/4/44/T--ZJU-China--wiki_model_fig6b_new.png"></img>
 
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                        <h6>B</h6>
 
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                        <img src="https://static.igem.org/mediawiki/2020/a/ae/T--ZJU-China--wiki_model_fig6c_new.png"></img>
 
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                        <h6>C</h6>
 
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                        <h6>Figure 6. (A) Magnetosome binding in a short time. (B) Metabolism of magnetosomes in the body for a long time. (C) The combination of different concentrations of magnetosomes in a
 
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                            short time after injection.</h6>
 
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                <div class="container1">
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                    <h2>Appendix</h2>
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                    <p>
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                        Please consult the following file for a clearer understanding of the formulation of the model.
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                    <br>
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                    <div class="imgbox">
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                        <embed src="https://static.igem.org/mediawiki/2020/6/67/T--ZJU-China--wiki_model_app.pdf" width="750" height="600">
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            <div class="section our-team" id="our-team">
 
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                    <h2>References</h2>
 
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                    <p>
 
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                        [1]. Stamatakis, M., & Mantzaris, N. V. (2009). Comparison of deterministic and stochastic models of the lac operon genetic network. <i>Biophysical journal, 96</i>(3), 887–906.
 
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                        https://doi.org/10.1016/j.bpj.2008.10.028
 
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                        [2]. Xiang, L., Wei, J., Jianbo, S., Guili, W., Feng, G., & Ying, L. (2007). Purified and sterilized magnetosomes from Magnetospirillum gryphiswaldense MSR-1 were not toxic to
 
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                        mouse fibroblasts in vitro. <i>Letters in applied microbiology, 45</i>(1), 75–81. https://doi.org/10.1111/j.1472-765X.2007.02143.x
 
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                        [3]. Yao, C., Ma, H., Zhao, Q., Liu, Y., Zhao, Y., & Chen, G. (2020). Mass transfer in liquid-liquid Taylor flow in a microchannel: Local concentration distribution, mass
 
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                        transfer regime and the effect of fluid viscosity. <i>Chemical Engineering Science</i>, 223, 115734. https://doi.org/10.1016/j.ces.2020.115734
 
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Revision as of 14:44, 27 October 2020

Proof Of Concept

Proof Of Concept



Taking breast cancer which has the highest incidence rate in the world as an opponent, we need to be very careful in dealing with every step of implementing our project into reality. In the real world, we believe that thousands of researchers and drug companies are also worried about the plight of breast cancer treatment and come up with countless ideas. However, if we want to really improve the survival status of breast cancer patients, we need to prove our project is valuable enough to contribute to society.
In this page, we extend the content about Proof of Concept on the basis of the project implementation plan, and explain that each part of our project is running in a relevant context.



Technical Feasibility

Interaction of Two Recombinant Proteins

Using the interaction system of Fc-ZZ as our linker, we linked the mamC expressed in E.coli BL21 and scFv expressed in E.coli SHuffle® as a compound BioBrick, indicated that we can immobilized scFv on the surface of magnetosomes produced by Magnetospirillum gryphiswaldense.



Fig1. Western-blot results of immunoprecipitation between mamC-ZZ and scFv-Fc.


All the protein concentrations from each block were determined by UV spectrophotometry. Total protein obtained mamC-ZZ was 24.8mg/mL, purified mamC was 0.3mg/mL, purified scFv was 0.2mg/mL. In industry, it is not difficult to achieve that level of protein concentration, which proves that our products are easy to be manufactured.

Effectiveness of scFv

In order to prove that scFv-Fc fusion protein can specifically target HER2 positive breast cancer cells, we have demonstrated the specificity and effectiveness of this targeting by flow cytometry.



Fig2. Flow cytometry results of MDA-MB-453 and MDA-MB-231 after incubated with scFv-Fc.

Obviously, the high HER2 expression cell line (MDA-MB-453) showed a higher fluorescence (about 10 times) than that of the low HER2 expression cell line (MDA-MB-231), indicating that scFv-Fc is more targeted to HER2, and can distinguish breast cancer cells with high and low expression of HER2 (Fig2).


Modeling Results

We simulated the process of the two recombinant proteins from the internal expression of bacteria to the interaction and binding in vitro, and simulated the whole process of our final product diffusion in tumors and binding with HER2 as well.
Through all those modelling results delivered in Model, we have a general understanding of the production of two recombinant in E.coli and Magnetospirillum, and the speed and proportion of the Fc-ZZ interaction system in vitro, and the dispersion and binding of scFv modified magnetosomes in tumor. These data provide us a possible range of contrast agent injection dose in future clinical trials.

Further Approach of Technical Feasibility

After we obtain the engineered magnetosomes and equip them with scFv, we will carry out in vitro experiments on cytotoxicity and contrast effect of MagHER2some. When all indexes show a good trend, we will carry out in vivo experiments on mice and follow-up clinical trials through legal application according to the requirements of China's laws. You can learn more from the Clinical Trial section in Implementation.

Commercial Feasibility

Market Investigation

As a team targeted to develop a novel contrast agent with a innovative design, we conducted a comprehensive investigation with patients, medical specialists in breast cancer, radiologist, researchers in pharmocochemistry, company researchers, etc. You can learn more from the Human Practice section.
We also developed industry analysis from various aspects, you can learn more from the Implementation section.
We gradually figured out that there was a lack of targeted contrast agents in the market. Targeted contrast agents such as MagHER2some have dual economic and social value, because they can reduce the proportion of empirical judgement in the analysis of MRI results, so as to achieve a more accurate prognosis treatment of breast cancer. As a result, the treatment of breast cancer patients will be improved, and much more people will free from the torture of the disease.


Advantage Demonstration

Compared with gadolinium based contrast agent (GBCA), MagHER2some goes beyond it from the following three aspects:

As the table showed above, MagHER2some is an innovative and superior contrast agent compared with traditional products. Based on what we have done during iGEM, we can foresee that MagHER2some will be a highly specific, non-toxic and environmentally friendly product to enhance the MRI contrast.

Commercial Strategy

We have developed a business plan based on our experiments and investigation results. The contents of business plan are a prototype that demonstrate the method that we implement Proof of Concept activities at the early stage of commercialization. You can learn more from the Implementation section.