Revision as of 11:38, 27 October 2020

Model

Overview

To understand the production of target antibody and modified magnetosomes and the combination and disaggregation of them, we have established some in vivo and in vitro models.

Our modeling work is comprised of 3 parts.

1) We used 2 models to describe the reactions in E. coli and magnetotactic bacteria separately.

2) We used 1 deterministic model to determine the combination and disaggregation of SCFV-Fc and modified magnetosomes in vitro.

3) We used 2 models to describe the movements and the combination with HER2 of modified magnetosomes in vivo.

PART Ⅰ Deterministic model to compute the production of ScFv and modified magnetosomes

To product ScFv and modified magnetosomes, we introduced the plasmid containing the target gene into E. coli and magnetotactic bacteria respectively, and finally understood the final yield of the target product by simulating their metabolic processes respectively.

E. coli

In E. coli, T7 RNA polymerase is placed under a lac Operon, which can be induced by IPTG. The production of the target protein, ScFv-Fc, is controlled by T7 promoter (Fig.1a) ^[1]. The combination between T7 RNA polymerase and T7 promoter is determined by Hill function. The ordinary differential equations (ODEs) describing these processes are shown as follows, and parameter names and chemical equations can be found in the appendix.

\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} \end{align}

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 concentration of the target protein in the bacteria is maintained at 1.3069×10⁴ nM.

a

b

Fig.1 Induced expression of ScFv-Fc 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 the system.

Magnetotactic bacteria

In magnetotactic bacteria, target protein (mamC-Zz) is placed under a lac Opera, and the repressor protein LacI is stably expressed in the cell, 2 molecules of LacI will form a dimer which binds to LacO DNA fragment and represses the expression of target protein (Fig. 2a). When IPTG is added and transported into the cell, IPTG molecules will bind with LacI and inhibit its binding to LacO. In this way, target protein can be rescued from suppression ^[1].. We assume that all target proteins 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.

\begin{align} \frac{d}{d t}MR_{M} &= \alpha_MR \cdot O_{total} - \lambda_{MR} \cdot MR_{M}\\ \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 R_{2M} \cdot I_{M}^{2} \\&+k_{-dr1} \cdot I_{2}R_{2M}-\lambda_{R2} \cdot R_{2M}\\ \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}

According to our modeling result, the final concentration of target protein mamC-Zz is 2.3625×10³ nM. Since the concentration of magnetosomes extracted from the culture medium whose OD600 reaches 1 is 172ug per milliliter ^[2], the average concentration of magnetosomes is 46.83 per cell, and there are an average of 24.31 target protein mamC-Zz on each magnetosome when assuming that all target proteins are localized to the magnetosome membrane.

a

b

Fig. 2 Induced expression of mamC-Zz 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.

PART Ⅱ Deterministic model to determine the combination and disaggregation of SCFV-Fc and modified magnetosomes in vitro

After ScFv-Fc and modified magnetosomes being produced in E. coli and magnetotactic bacteria, they are extracted from cells and purified. Fc domain can combine with Zz domain so that these two parts will combine and work together. Assuming that there’s no factor causing target protein degradation in vitro, the ordinary differential equations (ODEs) describing these processes are shown as follows.

$$\frac{d}{dt}F=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ$$ $$\frac{d}{dt}Z=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ$$ $$\frac{d}{dt}FZ=k_{1} \cdot F \cdot Z-k_{-1} \cdot FZ$$

From the modeling result, we can see the reaction between 10mg/ml modified magnetosomes and 100ug/ml ScFv-Fc is very fast and the production rate is relatively high (Fig. 3).

Fig. 3 combination of ScFv-Fc and modified magnetosomes ( the blue line refers to the combination product of ScFv-Fc and modified magnetosomes, and the orange line refers to pure magnetosomes)

PART Ⅲ Kinetic model to simulate the diffusion and binding of modified magnetosomes inside the tumor

Magnetosome diffusion in internal environment

It could be assumed that the magnetosome injected collect around the tumor if exists, since our magnetosome has been proved to stick to her-2 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.

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.

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.

$$\nabla \boldsymbol{c} \rightarrow \frac{\partial c}{\partial r}$$

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 $J_{1}=ub \times \frac{\partial c}{\partial r}\\$.

$$u_{b}=\frac{\pi d^{2}\left(p+\frac{1}{2} \rho g d\right)}{32 \mu_{b} D}$$

According to Fick’s First Law, eddy diffusion caused by natural convection is calculated by $J_{2}=D_{n} \times \frac{\partial c}{\partial r}\\$.

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 $J_{2} \approx 0\\$.

In order to obtain the diffusion flux due to mass transfer, an important constant called mass transfer coefficient was in need, for the expression, $J_{3}=k_{c} \times \frac{\partial c}{\partial r}\\$.

We used Chaoqun Yao(2020)’s experiment kc data of 1:1 silicone oil-water mixture, to whose viscosity blood and tissue fluid similar^[3]. A model was built for the relationship between the rate of flow and kc. Microsoft Office Excel was employed to finish the task.

Fig. 4 the influence of rate of flow on mass transfer coefficient

Now we could get the value of Q in our situation. This way, the value of kc could be assumed roughly.

$$Q=u_{a} \times \frac{1}{4} \pi d^{2}=4.01 \times 10^{-4} ml/min$$ $$k_{c}=-0.0622 Q^{3}+0.0127 Q^{2}-0.0005 Q+2 \times 10^{-5}=2.00 \times 10^{-2} mm/s$$

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:

$$J_{4}=D_{m} \times \frac{\partial c}{\partial r}$$

Stokes-Einstein equation was able to be used to calculate the diffusion coefficient as below.

$$D_{m}=\frac{k_{b} T}{6 \pi \mu_{b} R}$$

Overall diffusion flux could be calculated by superimposing the following diffusion flux.

$$J=J_{1}-J_{2}-J_{3}-J_{4}$$

It is assumed that the motion of fluid flow obeys the law discovered by Navier and Stokes.

instantaneous term = - diffusion term + convection term + sourse

That is to say,

$$\frac{\partial c}{\partial t}=\frac{\partial J}{\partial r}+u_{a} \nabla \boldsymbol{c}_{\boldsymbol{o}}$$

To solve the following PDE with the help of MatlabR2020a, both initial condition and boundary condition were supposed to be provided.

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.

$$ \left.c(t, r)\right|_{t=0}=\left\{\begin{array}{ll} 0 & r \neq 0 \\ c_{o} & r=0 \end{array}\right. $$

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.

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.

$$\left.c(t, r)\right|_{r=0}=\frac{c_{o}}{1+0.05 \sqrt{t}}$$

Simultaneously, we assumed that when diffusion flux caught the brim space, co would be small enough to be ignored.

$$\left.c(t, r)\right|_{r=100}=0$$

Fig. 5 a) concentration field of magnetosome in tissue fluid b) Magnetosome diffused in the tumor issue capillaries around it.

Detection and combination with HER2

To describe the combination and degradation with HER2, we have a model about modified magnetosomes in vivo. Assuming that there is no other way to clear magnetosomes and 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 processes are as follows. Parameter names and chemical equations can be found in the appendix.

$$\frac{d}{dt}F=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ -k_{2} \cdot H \cdot F +k_{-2} \cdot FH$$ $$\frac{d}{dt}Z=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ -k_{1} \cdot FH \cdot Z+k_{-1} \cdot ZFH-P$$ $$\frac{d}{dt}FZ=k_{1} \cdot F \cdot Z-k_{-1} \cdot FZ -k_{2} \cdot H \cdot FZ+k_{-2} \cdot ZFH-P$$ $$\frac{d}{dt}H=-k_{2} \cdot H \cdot F+k_{-2} \cdot FH -k_{2} \cdot H \cdot FZ+k_{-2} \cdot ZFH$$ $$\frac{d}{dt}FH=k_{2} \cdot H \cdot F-k_{-2} \cdot FH -k_{1} \cdot FH \cdot Z+k_{-1} \cdot ZFH$$ $$\frac{d}{dt}ZFH=k_{1} \cdot FH \cdot Z-k_{-1} \cdot ZFH+k_{2} \cdot H \cdot FZ-k_{-2} \cdot ZFH-P$$

We can see in the result that the process of combination finished very quickly (Fig.6a), while the total number of the magnetosomes decreases gradually because of the phagocytosis process (Fig.6b), and the concentration of magnetosomes is one tenth of what it was before after around 120 minutes. We also have results with different concentration of magnetosomes injected (Fig.6c), which shows the combination in a short of time with different injection concentration of modified magnetosomes.

a

b

c

Fig. 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 short time after injection

Appendix

Please consult the following file for a clearer understanding of the formulation of the model.

Reference

[1] Stamatakis, M., & Mantzaris, N. V. (2009). Comparison of deterministic and stochastic models of the lac operon genetic network. Biophysical journal, 96(3), 887–906. https://doi.org/10.1016/j.bpj.2008.10.028

[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 mouse fibroblasts in vitro. Letters in applied microbiology, 45(1), 75–81. https://doi.org/10.1111/j.1472-765X.2007.02143.x

[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 transfer regime and the effect of fluid viscosity. Chemical Engineering Science, 223, 115734. https://doi.org/10.1016/j.ces.2020.115734

@@ Line 68: / Line 68: @@
      <title>Model</title>
-     <link rel="stylesheet" type="text/css"
+     <link rel="stylesheet" type="text/css" href="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/CSS&action=raw&ctype=text/css" />
-        href="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/CSS&action=raw&ctype=text/css" />
      <!-- <link href="assets/css/style.css" rel="stylesheet"> -->
-     <link rel="stylesheet" type="text/css"
+     <link rel="stylesheet" type="text/css" href="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/CSS/barcss/site&action=raw&ctype=text/css" />
-        href="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/CSS/barcss/site&action=raw&ctype=text/css" />
-     <link rel="stylesheet" type="text/css"
+     <link rel="stylesheet" type="text/css" href="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/CSS/barcss/jquery&action=raw&ctype=text/css" />
-        href="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/CSS/barcss/jquery&action=raw&ctype=text/css" />
@@ Line 85: / Line 82: @@
      <link rel="stylesheet" href="https://cdn.staticfile.org/font-awesome/4.7.0/css/font-awesome.css">
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/jquery&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/jquery&action=raw&ctype=text/javascript"></script>
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/code&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/scroll.js&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/code&action=raw&ctype=text/javascript"></script>
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/lightbox&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/main&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/scroll.js&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/lightbox&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/main&action=raw&ctype=text/javascript"></script>
      <script src="https://2020.igem.org/common/MathJax-2.5-latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
@@ Line 136: / Line 128: @@
          <ul>
              <li>
-                 <a href="#Cloning" style="background-color: #f6b37f;"
+                 <a href="#Cloning" style="background-color: #f6b37f;" class="nav-active rounded"><span>Overview</span></a>
-                    class="nav-active rounded"><span>Overview</span></a>
              </li>
              <li>
@@ Line 165: / Line 156: @@
              style="background-image: url('https://static.igem.org/mediawiki/2020/b/b9/T--ZJU-China--wiki_navback2.png');">
              <div class="container">
-                 <a class="navbar-brand" href="index.html" style="left:-10%;margin:-20px"><img
+                 <a class="navbar-brand" href="index.html" style="left:-10%;margin:-20px"><img src="https://static.igem.org/mediawiki/2020/7/7f/T--ZJU-China--temt.png" class="img-fluid" width="150px"></a>
-                        src="https://static.igem.org/mediawiki/2020/7/7f/T--ZJU-China--temt.png" class="img-fluid"
-                        width="150px"></a>
                  <div class="collapse navbar-collapse" id="navbarResponsive">
@@ Line 237: / Line 226: @@
          <!-- Mobile Menu Start -->
          <nav class="mobile_menu hidden d-none">
-             <a href="index.html"><img class="mobile-logo"
+             <a href="index.html"><img class="mobile-logo" src="https://static.igem.org/mediawiki/2020/7/7f/T--ZJU-China--temt.png" alt="Logo"></a>
-                    src="https://static.igem.org/mediawiki/2020/7/7f/T--ZJU-China--temt.png" alt="Logo"></a>
              <ul class="nav navbar-nav navbar-right menu">
                  <li class="dropdown active">
@@ Line 304: / Line 292: @@
-         <div class="pagestyle"
+         <div class="pagestyle" style="background-image: url('https://static.igem.org/mediawiki/2020/c/cd/T--ZJU-China--wiki_navback.jpg');top:120px;">
-            style="background-image: url('https://static.igem.org/mediawiki/2020/c/cd/T--ZJU-China--wiki_navback.jpg');top:120px;">
              <div class="section Cloning" id="Cloning">
                  <div class="container1">
@@ Line 312: / Line 299: @@
                      <p>
-                         To understand the production of targeted antibody and modified magnetosomes, as well as the combination
+                         To understand the production of target antibody and modified magnetosomes and the combination and disaggregation of them, we have established some in vivo and in vitro models.
-                        and disaggregation of them, we have established in-vivo and in-vitro models.
                      </p>
                      <br>
                      <p>
-                         Our modeling work is comprised of three parts.
+                         Our modeling work is comprised of 3 parts.
                      </p>
                      <p>
-) We used two models to describe <b>reactions in <i>E. coli</i> and magnetotactic bacteria</b> separately.
+) We used 2 models to describe the reactions in E. coli and magnetotactic bacteria separately.
                      </p>
                      <p>
-) We used a deterministic model to determine <b>the combination and disaggregation of scFv-Fc and
+) We used 1 deterministic model to determine the combination and disaggregation of SCFV-Fc and modified magnetosomes in vitro.
-                            modified magnetosomes in vitro.</b>
                      </p>
                      <p>
-) We used two models to describe <b>the movements of modified magnetosomes and its combination with HER2 in vivo.</b>
+) We used 2 models to describe the movements and the combination with HER2 of modified magnetosomes in vivo.
-                    </p>
-                </div>
-            </div>
-            <div class="section about" id="about">
-                <div class="container1">
-                    <h2 style="line-height:1.5;">PART Ⅰ Deterministic Model to Compute the Production of scFv and
-                        Modified Magnetosomes</h2>
-                    <p>
-                        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 final yield of
-                        the target product by simulating their metabolic processes respectively.
-                    </p>
-                    <h3><i>E.coli</i></h3>
-                    <p>
-                        In <i>E.coli</i>, T7 RNA polymerase is placed under a <a>lac</a> Operon, which can be induced by IPTG. The
-                        production of the target protein, scFv-Fc, is controlled by <a>T7</a> promoter (Fig.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) describing
-                        these processes are shown as follows, and parameter names and chemical equations can be found in
-                        the appendix.
-                    </p>
-                    <p style="font-size: medium;">
-                        \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}
-                        \end{align}
-                    </p>
-                    <br>
-                    <p>
-                        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 concentration of the
-                        target protein in the bacteria is maintained at <b>1.3069×10<sup>4</sup> nM</b>.
-                    </p>
-                    <br>
-                    <div class="imgbox">
-                        <img src="https://static.igem.org/mediawiki/2020/a/ab/T--ZJU-China--wiki_model_fig1.png"></img>
-                        <h6>a</h6>
-                    </div>
-                    <br>
-                    <div class="imgbox">
-                        <img src="https://static.igem.org/mediawiki/2020/1/1e/T--ZJU-China--wiki_model_fig1b_new.png"></img>
-                        <h6>b</h6>
-                    </div>
-                    <br>
-                    <div class="imgbox">
-                        <h6>Fig.1 Induced expression of scFv-Fc
-                            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 the
-                            system.</h6>
-                    </div>
-                    <h3>Magnetotactic Bacteria</h3>
-                    <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 dimer
-                        which binds to <i>LacO</i> DNA fragment and represses the expression of target protein (Fig. 2a). When
-                        IPTG is added and transported into the cell, IPTG molecules will bind with 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 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.
-                    </p>
-                    <br>
-                    <div class="imgbox">
-                        <p style="font-size: medium;">
-                            \begin{align}
-                            \frac{d}{d t}MR_{M} &= \alpha_MR \cdot O_{total} - \lambda_{MR} \cdot MR_{M}\\
-                            \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 R_{2M} \cdot
-                            I_{M}^{2} \\&+k_{-dr1} \cdot I_{2}R_{2M}-\lambda_{R2} \cdot R_{2M}\\
-                            \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>
-                        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 culture
-                        medium whose OD600 reaches <b>1</b> is <b>172ug per milliliter</b> <a href="#our-team"><sup>[2]</sup></a>, the
-                        average concentration of magnetosomes is 46.83 per cell, and there are an average of 24.31
-                        target protein mamC-ZZ on each magnetosome when assuming that all target proteins are localized
-                        to the magnetosome membrane.
-                    </p>
-                    <br>
-                    <div class="imgbox">
-                        <img src="https://static.igem.org/mediawiki/2020/3/36/T--ZJU-China--wiki_modelnew_fig3.png"></img>
-                        <h6>a</h6>
-                    </div>
-                    <br>
-                    <div class="imgbox">
-                        <img src="https://static.igem.org/mediawiki/2020/5/5d/T--ZJU-China--wiki_model_fig2b_new.png"></img>
-                        <h6>b</h6>
-                    </div>
-                    <br>
-                    <div class="imgbox">
-                        <h6>
-                            Fig. 2 Induced expression of mamC-ZZ 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 in Vitro</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 ZZ domain so that these
-                        two parts will combine and work together. Assuming that there’s no factor causing target protein
-                        degradation in vitro, the ordinary differential equations (ODEs) describing these processes are
-                        shown as follows.
-                    </p>
-                    <br>
-                    <p>
-                        $$\frac{d}{dt}F=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ$$
-                        $$\frac{d}{dt}Z=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ$$
-                        $$\frac{d}{dt}FZ=k_{1} \cdot F \cdot Z-k_{-1} \cdot FZ$$
-                    </p>
-                    <br>
-                    <p>
-                        From the modeling result, we can see the reaction between 10mg/ml modified magnetosomes and
-ug/ml scFv-Fc is very fast and the production rate is relatively high (Fig. 3).
-                    </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>Fig. 3 Combination of scFv-Fc and modified magnetosomes ( 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 class="section showcase" id="showcase">
-                <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 magnetosomes injected collect around the tumor if exists, since our
-                        magnetosome has been proved to stick to her-2 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>
-                    <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>
-                        According to Fick’s First Law, eddy diffusion caused by natural convection is calculated by
-                        \(J_{2}=D_{n} \times \frac{\partial c}{\partial r}\\\).
-                    </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>Fig. 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>
-                    <br>
-                    <p>
-                        To solve the following PDE with the help of MatlabR2020a, both initial condition and boundary
-                        condition were supposed to be provided.
-                    </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>
-                        $$
-                        \left.c(t, r)\right|_{t=0}=\left\{\begin{array}{ll}
-& r \neq 0 \\
-                        c_{o} & r=0
-                        \end{array}\right.
-                        $$
-                    </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">
-                        <img src="https://static.igem.org/mediawiki/2020/8/8f/T--ZJU-China--wiki_mode_fig7.png"></img>
-                        <h6>Fig. 5 a) Concentration field of magnetosome in tissue fluid b) Magnetosome diffused in the
-                            tumor issue capillaries around it.</h6>
-                    </div>
-                    <br>
-                    <h3>Detection and Combination with HER2</h3>
-                    <p>
-                        To describe the combination and degradation with HER2, we have a model about modified
-                        magnetosomes in vivo. Assuming that there is no other way to clear magnetosomes and 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 processes are as follows.
-                        Parameter names and chemical equations can be found in the appendix.
-                    </p>
-                    <br>
-                    <p>
-                        $$\frac{d}{dt}F=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ -k_{2} \cdot H \cdot F +k_{-2} \cdot FH$$
-                        $$\frac{d}{dt}Z=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ -k_{1} \cdot FH \cdot Z+k_{-1} \cdot
-                        ZFH-P$$
-                        $$\frac{d}{dt}FZ=k_{1} \cdot F \cdot Z-k_{-1} \cdot FZ -k_{2} \cdot H \cdot FZ+k_{-2} \cdot
-                        ZFH-P$$
-                        $$\frac{d}{dt}H=-k_{2} \cdot H \cdot F+k_{-2} \cdot FH -k_{2} \cdot H \cdot FZ+k_{-2} \cdot
-                        ZFH$$
-                        $$\frac{d}{dt}FH=k_{2} \cdot H \cdot F-k_{-2} \cdot FH -k_{1} \cdot FH \cdot Z+k_{-1} \cdot
-                        ZFH$$
-                        $$\frac{d}{dt}ZFH=k_{1} \cdot FH \cdot Z-k_{-1} \cdot ZFH+k_{2} \cdot H \cdot FZ-k_{-2} \cdot
-                        ZFH-P$$
-                    </p>
-                    <br>
-                    <p>
-                        We can see in the result that the process of combination finished very quickly (Fig.6a), while
-                        the total number of the magnetosomes decreases gradually because of the phagocytosis process
-                        (Fig.6b), and the concentration of magnetosomes is <b>one tenth</b> of what it was before after around
-                        <b>120</b> minutes. We also have results with different concentration of magnetosomes injected
-                        (Fig.6c), which shows the combination in a short of time with different injection concentration
-                        of modified magnetosomes.
-                    </p>
-                    <br>
-                    <div class="imgbox">
-                        <img src="https://static.igem.org/mediawiki/2020/c/cb/T--ZJU-China--wiki_model_fig6a_new.png"></img>
-                        <h6>a</h6>
-                    </div>
-                    <br>
-                    <div class="imgbox">
-                        <img src="https://static.igem.org/mediawiki/2020/4/44/T--ZJU-China--wiki_model_fig6b_new.png"></img>
-                        <h6>b</h6>
-                    </div>
-                    <div class="imgbox">
-                        <img src="https://static.igem.org/mediawiki/2020/a/ae/T--ZJU-China--wiki_model_fig6c_new.png"></img>
-                        <h6>c</h6>
-                    </div>
-                    <div class="imgbox">
-                        <h6>Fig. 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 short time
-                            after injection</h6>
-                    </div>
-                    <br>
-                    <br>
-                </div>
-            </div>
-            <div class="section appd" id="appd">
-                <div class="container1">
-                    <h2>Appendix</h2>
-                    <p>
-                        Please consult the following file for a clearer understanding of the formulation of the model.
-                    </p>
-                    <br>
-                    <div class="imgbox">
-                        <embed src="https://static.igem.org/mediawiki/2020/6/67/T--ZJU-China--wiki_model_app.pdf" width="750"
-                            height="600">
-                    </div>
-                </div>
-            </div>
-            <div class="section our-team" id="our-team">
-                <div class="container1">
-                    <h2>Reference</h2>
-                    <p>
-                        [1] Stamatakis, M., & Mantzaris, N. V. (2009). Comparison of deterministic and stochastic models
-                        of the lac operon genetic network. Biophysical journal, 96(3), 887–906.
-                        https://doi.org/10.1016/j.bpj.2008.10.028
-                    </p>
-                    <br>
-                    <p>
-                        [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 mouse
-                        fibroblasts in vitro. Letters in applied microbiology, 45(1), 75–81.
-                        https://doi.org/10.1111/j.1472-765X.2007.02143.x
-                    </p>
-                    <br>
-                    <p>
-                        [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 transfer
-                        regime and the effect of fluid viscosity. Chemical Engineering Science, 223, 115734.
-                        https://doi.org/10.1016/j.ces.2020.115734
-                    </p>
-                    <br>
-                    <br>
-                </div>
-            </div>
-        </div>
-    </div>
-    <div class="top-arrow">
-        <a href="#" id="scroll" style="display:block ;"><i class="fa fa-angle-up"
-                style="font-size:36px;color:pink"></i></a>
-    </div>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsjquerymin&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jspropermin&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsboot&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsowl&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jseasing&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jstype&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsq1&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jswow&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsaos&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsway&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jscounter&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsven&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jssel&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsmenu&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jscustom1&action=raw&ctype=text/javascript"></script>
-    <script>
-        $document.ready(function () {
-            $("#HQ_page").attr('id', "");
-});
-    </script>
-    <script>
-        var typed = new Typed('#typed', {
-            stringsElement: '#typed-strings',
-            typeSpeed: 100,
-            backSpeed: 100,
-            loop: true,
-            smartBackspace: true,
-        });
-    </script>
-    <script>
-        function topMao(target) {
-            $('html, body').animate({ scrollTop: $(target).offset().top - 170 }, 500);//130为锚点到距顶部的距离，500为执行时间
-            return true;
-        }
-    </script>
-    <script>
-        var topBegin = $("#accordion").offset().top;  //获取导航栏（class='positionMiddleNav'）离视口的高度
-        $(window).scroll(function () {  //scroll事件
-            var win_top = $(this).scrollTop(); //获取滚动条位置
-            var _top = $("#accordion").offset().top; //获取当前导航栏距视口高度
-            console.log(win_top, 'aa');
-            console.log(_top, 'cc');
-            if (win_top >= _top - 150) {
-                $("#accordion").css({ position: "fixed", top: "10em" });
-            }
-            if (win_top < topBegin) { //因为导航栏距视口高度在定位发生后是变化的 ，
-                //所以当导航栏回到原位置时保持先前状态需要将滚动条位置与最先前的导航栏位置进行对比
-                $("#accordion").css({ position: "absolute" });
-            }
-        })
-    </script>
-    <script>
-        function displaywindowsize() {
-            var w = document.documentElement.clientWidth;
-            var h = document.documentElement.clientHeight;
-            if (w < 1100 && w > 800) {
-                $("#accordion").css({ left: "2%" });
-                $("#accordion").css({ display: "block" });
-            }
-            else if (w < 800) {
-                $("#accordion").css({ display: "none" });
-            }
-            else {
-                $("#accordion").css({ left: "10%" });
-                $("#accordion").css({ display: "block" });
-            }
-        }
-        window.addEventListener("resize", displaywindowsize);
-        displaywindowsize();
-    </script>
-</body>
-</html>
-<html lang="en">
-<style>
-    /* CLEAR DEFAULT SETTINGS **************************************************/
-    #sideMenu,
-    #top_title,
-    .patrollink,
-    #firstHeading,
-    #home_logo,
-    #sideMenu {
-        display: none;
-    }
-    #content {
-        padding-left: 0px;
-        width: 100%;
-        margin-top: 10px;
-        padding-top: 0px;
-        padding-bottom: 0px;
-        margin-bottom: -10px;
-        margin-right: 0px;
-        margin-left: 0px;
-        border: none;
-    }
-    body,
-    html {
-        background-image: url('https://static.igem.org/mediawiki/2020/9/9e/T--ZJU-China--wiki_back2.png');
-        width: 100%;
-        height: 100%;
-    }
-    #top {
-        display: none;
-    }
-    #bodyContent a[href ^="https://"],
-    .link-https {
-        padding-right: 0px;
-    }
-    #bodyContent p {
-        font-size: large;
-    }
-    #bodyContent h1,
-    h2,
-    h3,
-    h4,
-    h5,
-    h6 {
-        font-family: 'Nunito', sans-serif;
-    }
-    #bodyContent ul {
-        margin: 0 0 0 0;
-        list-style-image: url();
-    }
-</style>
-<head>
-    <meta charset="utf-8">
-    <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
-    <title>Model</title>
-    <link rel="stylesheet" type="text/css"
-        href="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/CSS&action=raw&ctype=text/css" />
-    <!-- <link href="assets/css/style.css" rel="stylesheet"> -->
-    <link rel="stylesheet" type="text/css"
-        href="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/CSS/barcss/site&action=raw&ctype=text/css" />
-    <link rel="stylesheet" type="text/css"
-        href="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/CSS/barcss/jquery&action=raw&ctype=text/css" />
-    <link rel="stylesheet" href="https://cdn.staticfile.org/font-awesome/4.7.0/css/font-awesome.css">
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/jquery&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/code&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/scroll.js&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/lightbox&action=raw&ctype=text/javascript"></script>
-    <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/JS/barjs/main&action=raw&ctype=text/javascript"></script>
-    <script src="https://2020.igem.org/common/MathJax-2.5-latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
-    <!-- HTML5 shim and Respond.js for IE8 support of HTML5 elements and media queries -->
-    <!--[if lt IE 9]>
-    <script src="https://oss.maxcdn.com/html5shiv/3.7.2/html5shiv.min.js"></script>
-    <script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
-    <![endif]-->
-    <style>
-        p {
-            font_size: 40px;
-        }
-    </style>
-    <style>
-        .MathJax nobr>span.math>span {
-            border-left-width: 0 !important
-        }
-        ;
-    </style>
-</head>
-<body style="background-image: url('https://static.igem.org/mediawiki/2020/9/9e/T--ZJU-China--wiki_back2.png');">
-    <!-- Pre Loader Area start -->
-    <div id="preloader">
-        <div class="loader"></div>
-    </div>
-    <!-- Pre Loader Area End -->
-    <div class="navigation">
-        <ul>
-            <li>
-                <a href="#Cloning" style="background-color: #f6b37f;"
-                    class="nav-active rounded"><span>Overview</span></a>
-            </li>
-            <li>
-                <a href="#about" style="background-color: #7ecef4;" class="rounded"><span>PART Ⅰ</span></a>
-            </li>
-            <li>
-                <a href="#services" style="background-color: #f19ec2;" class="rounded"><span>PART Ⅱ</span></a>
-            </li>
-            <li>
-                <a href="#showcase" style="background-color:#eb6877;" class="rounded"><span>PART Ⅲ</span></a>
-            </li>
-            <li>
-                <a href="#appd" style="background-color:#d197f7;" class="rounded"><span>Appendix</span></a>
-            </li>
-            <li>
-                <a href="#our-team" style="background-color: #cce198" class="rounded"><span>Reference</span></a>
-            </li>
-        </ul>
-    </div>
-    <section class="menu-section-area">
-        <!-- Navigation -->
-        <nav class="navbar navbar-expand-lg fixed-top d-none d-sm-none d-md-block d-lg-block d-xl-block" id="mainNav"
-            style="background-image: url('https://static.igem.org/mediawiki/2020/b/b9/T--ZJU-China--wiki_navback2.png');">
-            <div class="container">
-                <a class="navbar-brand" href="index.html" style="left:-10%;margin:-20px"><img
-                        src="https://static.igem.org/mediawiki/2020/7/7f/T--ZJU-China--temt.png" class="img-fluid"
-                        width="150px"></a>
-                <div class="collapse navbar-collapse" id="navbarResponsive">
-                    <ul class="navbar-nav text-capitalize ml-auto">
-                        <li class="nav-item dropdown-box" style="background-color:pink;;opacity: 0.9;">
-                            <a class="nav-link js-scroll-trigger" href="index.html">Home</a>
-                        </li>
-                        <li class="nav-item dropdown-box" style="background-color: coral;;opacity: 0.9;">
-                            <a class="nav-link" href="#">Team</a>
-                            <ul class="dropdown-list">
-                                <li><a href="team.html">Team Members</a></li>
-                                <li><a href="domain.html">Attributions</a></li>
-                            </ul>
-                        </li>
-                        <li class="nav-item dropdown-box" style="background-color:cornflowerblue;;opacity: 0.9;">
-                            <a class="nav-link" href="#">Project</a>
-                            <ul class="dropdown-list">
-                                <li><a href="domain.html">Description</a></li>
-                                <li><a href="background.html">Background</a></li>
-                                <li><a href="domain.html">Design</a></li>
-                                <li><a href="experiment.html">Experiment</a></li>
-                                <li><a href="hosting.html">Result</a></li>
-                                <li><a href="hosting.html">Demonstrate</a></li>
-                            </ul>
-                        </li>
-                        <li class="nav-item dropdown-box" style="background-color:dodgerblue;opacity: 0.9;">
-                            <a class="nav-link" href="#">Modeling</a>
-                            <ul class="dropdown-list">
-                                <li><a href="services.html">Overview</a></li>
-                                <li><a href="services-classic.html">xxx Model</a></li>
-                            </ul>
-                        </li>
-                        <li class="nav-item dropdown-box" style="background-color:darkslateblue;opacity: 0.9;">
-                            <a class="nav-link" href="#">Parts</a>
-                            <ul class="dropdown-list">
-                                <li><a href="about.html">Measurement</a></li>
-                                <li><a href="pricing-table.html">Improvement</a></li>
-                                <li><a href="login.html">New Parts</a></li>
-                            </ul>
-                        </li>
-                        <li class="nav-item dropdown-box" style="background-color:indianred;opacity: 0.9;">
-                            <a class="nav-link" href="#">Human</a>
-                            <ul class="dropdown-list">
-                                <li><a href="safety.html">Safety</a></li>
-                                <li><a href="blog-classic.html">Human Practice</a></li>
-                            </ul>
-                        </li>
-                        <li class="nav-item dropdown-box" style="background-color:orchid;opacity: 0.9;">
-                            <a class="nav-link" href="#">Application</a>
-                            <ul class="dropdown-list">
-                                <li><a href="blog-grid.html">Hardware</a></li>
-                                <li><a href="blog-classic.html">Software</a></li>
-                            </ul>
-                        </li>
-                    </ul>
-                </div>
-            </div>
-        </nav>
-        <!-- Navigation -->
-        <!-- Mobile Menu Start -->
-        <nav class="mobile_menu hidden d-none">
-            <a href="index.html"><img class="mobile-logo"
-                    src="https://static.igem.org/mediawiki/2020/7/7f/T--ZJU-China--temt.png" alt="Logo"></a>
-            <ul class="nav navbar-nav navbar-right menu">
-                <li class="dropdown active">
-                    <a>Home</a>
-                </li>
-                <li class="dropdown">
-                    <a>Team</a>
-                    <ul class="sub_menu">
-                        <li><a href="team.html">Team Members</a></li>
-                        <li><a href="domain.html">Attributions</a></li>
-                    </ul>
-                </li>
-                <li class="dropdown">
-                    <a>Project</a>
-                    <ul class="sub_menu">
-                        <li><a href="domain.html">Description</a></li>
-                        <li><a href="background.html">Background</a></li>
-                        <li><a href="domain.html">Design</a></li>
-                        <li><a href="domain.html">Experiment</a></li>
-                        <li><a href="domain.html">Result</a></li>
-                        <li><a href="domain.html">Demonstrate</a></li>
-                    </ul>
-                </li>
-                <li class="dropdown">
-                    <a>Modeling</a>
-                    <ul class="sub_menu">
-                        <li><a href="domain.html">Overview</a></li>
-                        <li><a href="domain.html">xxx Model</a></li>
-                    </ul>
-                </li>
-                <li class="dropdown">
-                    <a>Parts</a>
-                    <ul class="sub_menu">
-                        <li><a href="domain.html">Measurement</a></li>
-                        <li><a href="domain.html">Improvement</a></li>
-                        <li><a href="domain.html">New Parts</a></li>
-                    </ul>
-                </li>
-                <li class="dropdown">
-                    <a>Human</a>
-                    <ul class="sub_menu">
-                        <li><a href="safety.html">Safety</a></li>
-                        <li><a href="blog-classic.html">Human Practice</a></li>
-                    </ul>
-                </li>
-                <li class="dropdown">
-                    <a>Application</a>
-                    <ul class="sub_menu">
-                        <li><a href="blog-grid.html">Hardware</a></li>
-                        <li><a href="blog-classic.html">Software</a></li>
-                    </ul>
-                </li>
-            </ul>
-        </nav>
-        <!-- Mobile Menu End -->
-    </section>
-    <!--Main Menu/ Mobile Menu Section-->
-    <div class="pagename">
-        <h1>Model</h1>
-    </div>
-    <div id="scrollable">
-        <div class="pagestyle"
-            style="background-image: url('https://static.igem.org/mediawiki/2020/c/cd/T--ZJU-China--wiki_navback.jpg');top:120px;">
-            <div class="section Cloning" id="Cloning">
-                <div class="container1">
-                    <h2>Overview</h2>
-                    <p>
-                        To understand the production of targeted antibody and modified magnetosomes, as well as the combination
-                        and disaggregation of them, we have established some in-vivo and in-vitro models.
-                    </p>
-                    <br>
-                    <p>
-                        Our modeling work is comprised of three parts.
-                    </p>
-                    <p>
-) We used two models to describe the <b>reactions in <i>E.coli</i> and magnetotactic bacteria</b> separately.
-                    </p>
-                    <p>
-) We used a deterministic model to determine the <b>combination and disaggregation of scFv-Fc and
-                        modified magnetosomes in vitro</b>.
-                    </p>
-                    <p>
-) We used two models to describe <b>the movements of modified magnetosomes and its combination with HER2 in vivo</b>.
                      </p>
@@ Line 1,320: / Line 327: @@
                  <div class="container1">
-                     <h2 style="line-height:1.5;">PART Ⅰ Deterministic Model to Compute the Production of scFv and
+                     <h2 style="line-height:1.5;">PART Ⅰ Deterministic model to compute the production of ScFv and modified magnetosomes</h2>
-                        Modified Magnetosomes</h2>
                      <p>
-                         To product scFv and modified magnetosomes, we introduced the plasmid containing the target gene
+                         To product ScFv and modified magnetosomes, we introduced the plasmid containing the target gene into E. coli and magnetotactic bacteria respectively, and finally understood the
-                        into <i>E.coli</i> and magnetotactic bacteria respectively, and finally understood the final yield of
+                        final yield of the target product by simulating their metabolic processes respectively.
-                        the target product by simulating their metabolic processes respectively.
                      </p>
-                     <h3><b>E. coli</b></h3>
+                     <h3>E. coli</h3>
                      <p>
-                         In <i>E.coli</i>, T7 RNA polymerase is placed under a <a>lac</a> Operon, which can be induced by IPTG. The
+                         In E. coli, T7 RNA polymerase is placed under a lac Operon, which can be induced by IPTG. The production of the target protein, ScFv-Fc, is controlled by T7 promoter (Fig.1a)
-                        production of the target protein, scFv-Fc, is controlled by T7 promoter (Fig.1a) <a
+                        <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)
-                            href="#our-team"><sup>[1]</sup></a>. The combination between T7 RNA polymerase and T7
+                         describing these processes are shown as follows, and parameter names and chemical equations can be found in the appendix.
-                        promoter is determined by Hill function. The ordinary differential equations (ODEs) describing
-                         these processes are shown as follows, and parameter names and chemical equations can be found in
-                        the appendix.
                      </p>
@@ Line 1,344: / Line 346: @@
                          \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
+                         \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}\\
-                        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}
-                         \frac{d}{dt}R_{2E}&= 2 \cdot k_{2R} \cdot R_{E}^{2}-2 \cdot k_{-2R} \cdot R_{2E}-k_{r} \cdot
+                         \cdot I_{E}^{2} \\& + k_{-dr1} \cdot I_{2}R_{2E}-\lambda_{R2} \cdot R_{2E}\\
-                        R_{2 E} \cdot O_{E} +k_{-r} \cdot \left(O_{total}-O_{E}\right)-k_{dr1} \cdot R_{2E} \cdot
+                         \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}
-                         I_{E}^{2} \\& + k_{-dr1} \cdot I_{2}R_{2E}-\lambda_{R2} \cdot R_{2E}\\
+                        \cdot I_{2}R_{2E}\\
-                         \frac{d}{dt}O_{E}&=-k_{r} \cdot R_{2E} \cdot O_{E}+k_{-r} \cdot
+                         \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
-                        \left(O_{total}-O_{E}\right)+k_{dr2} \cdot \left(O_{total}-O_{E}\right) \cdot I_{E}^{2}-k_{-dr2}
+                         \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}\\
-                        \cdot O_{E} \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}
-                         \frac{d}{dt}I_{E}&= -2 \cdot k_{dr1} \cdot R_{2E} \cdot I_{E}^{2} +2 \cdot k_{-dr1} \cdot
+                         \cdot I_{2}R_{2E} \\&-\lambda_{I2R2} \cdot I_{2}R_{2E}\\
-                        I_{2}R_{2E}-2 \cdot k_{dr2} \cdot \left(O_{total}-O_{E}\right) \cdot I_{E}^{2} \\&+2 \cdot
+                         \frac{d}{dt}MY_{E}&=\alpha_{0} \cdot \left(O_{total}-O_{E}\right) +\alpha_{1} \cdot O_{E} -\lambda_{MY} \cdot MY_{E}\\
-                         k_{-dr2} \cdot O_{E} \cdot I_{2}R_{2 E}+k_{ft} \cdot YI_{exE}+k_{t} \cdot
+                         \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}\\
-                        \left(I_{ex}-I_{E}\right)+2 \cdot \lambda_{I2R2} \cdot I_{2}R_{2E}\\
+                         \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}I_{2}R_{2E}&=k_{dr1} \cdot R_{2E} \cdot I_{E}^{2} -k_{-dr1} \cdot I_{2}R_{2E}
+                         \frac{d}{dt}MT7_{E}&=\alpha_{0} \cdot \left(O_{total}-O_{E}\right)+\alpha_{1} \cdot O_{E} -\lambda_{MT7} \cdot MT7_{E}\\
-                        +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
+                         \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}\\
-                        \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}
                          \end{align}
@@ Line 1,376: / Line 367: @@
                      <br>
                      <p>
-                         According our modeling result, although there’s a peak before adding IPTG, the production cannot
+                         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
-                        be maintained during a long period of time. Only after adding IPTG, the concentration of the
+                        concentration of the target protein in the bacteria is maintained at 1.3069×10<sup>4</sup> nM.
-                        target protein in the bacteria is maintained at <b>1.3069×10<sup>4</sup> nM</b>.
                      </p>
                      <br>
@@ Line 1,394: / Line 384: @@
                      <br>
                      <div class="imgbox">
-                         <h6>Fig.1 Induced expression of scFv-Fc
+                         <h6>Fig.1 Induced expression of ScFv-Fc
-                             a) Schematic diagram of the model b) Dynamics of target protein. Horizontal axis shows the
+                             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
-                            length of time. Vertical axis demonstrates the amount of protein (scFv-Fc) within the
+                             the system.</h6>
-                             system.</h6>
                      </div>
-                     <h3>Magnetotactic Bacteria</h3>
+                     <h3>Magnetotactic bacteria</h3>
                      <p>
-                         In magnetotactic bacteria, target protein (mamC-ZZ) is placed under a lac Opera, and the
+                         In magnetotactic bacteria, target protein (mamC-Zz) is placed under a lac Opera, and the repressor protein LacI is stably expressed in the cell, 2 molecules of LacI will form a
-                        repressor protein LacI is stably expressed in the cell, 2 molecules of LacI will form a dimer
+                         dimer which binds to LacO DNA fragment and represses the expression of target protein (Fig. 2a). When IPTG is added and transported into the cell, IPTG molecules will bind with
-                         which binds to LacO DNA fragment and represses the expression of target protein (Fig. 2a). When
+                        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
-                        IPTG is added and transported into the cell, IPTG molecules will bind with LacI and inhibit its
+                        will be localized to the magnetosome membrane by intracellular transport. The ordinary differential equations (ODEs) describing these processes are shown as follows, parameter
-                        binding to LacO. In this way, target protein can be rescued from suppression <a
+                        names and chemical equations can be found in the appendix.
-                            href="#our-team"><sup>[1]</sup></a>.. We assume that all target proteins 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.
                      </p>
                      <br>
@@ Line 1,419: / Line 404: @@
                              \begin{align}
                              \frac{d}{d t}MR_{M} &= \alpha_MR \cdot O_{total} - \lambda_{MR} \cdot MR_{M}\\
-                             \frac{d}{dt}R_{M}&=\beta_{R} \cdot MR_{M} -2 \cdot k_{2R} \cdot R_{M}^2 +2 \cdot k_{-2R}
+                             \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}\\
-                            \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
-                             \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 I_{M}^{2} \\&+k_{-dr1} \cdot I_{2}R_{2M}-\lambda_{R2} \cdot R_{2M}\\
-                            R_{2M} \cdot O_{M} +k_{-r} \cdot \left(O_{total}-O_{M}\right)-k_{dr1} \cdot R_{2M} \cdot
+                             \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}
-                            I_{M}^{2} \\&+k_{-dr1} \cdot I_{2}R_{2M}-\lambda_{R2} \cdot R_{2M}\\
+                            \cdot I_{2}R_{2M}\\
-                             \frac{d}{dt}O_{M}&=-k_{r} \cdot R_{2M} \cdot O_{M}+k_{-r} \cdot
+                             \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}
-                            \left(O_{total}-O_{M}\right)+k_{dr2} \cdot \left(O_{total}-O_{M}\right) \cdot
+                            \\&+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}\\
-                            I_{M}^{2}-k_{-dr2} \cdot O_{M} \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}
-                             \frac{d}{dt}I_{M}&=-2 \cdot k_{dr1} \cdot R_{2M} \cdot I_{M}^{2} +2 \cdot k_{-dr1} \cdot
+                             \cdot I_{2}R_{2M} \\&-\lambda_{I2R2} \cdot I_{2}R_{2M}\\
-                            I_{2}R_{2M}-2 \cdot k_{dr2} \cdot \left(O_{total}-O_{M}\right) \cdot I_{M}^{2} \\&+2 \cdot
+                             \frac{d}{dt}MY_{M}&=\alpha_{0} \cdot \left(O_{total}-O_{M}\right) +\alpha_{1} \cdot O_{M} -\lambda_{MY} \cdot MY_{M}\\
-                            k_{-dr2} \cdot O_{M} \cdot I_{2}R_{2M}+k_{ft} \cdot YI_{exM}+k_{t} \cdot
+                             \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}\\
-                            \left(I_{ex}-I_{M}\right)+2 \cdot \lambda_{I2R2} \cdot I_{2}R_{2M}\\
+                             \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}I_{2}R_{2M}&=k_{dr1} \cdot R_{2M} \cdot I_{M}^{2} -k_{-dr1} \cdot I_{2}R_{2M}
+                             \frac{d}{dt}MZ_{M}&=\alpha_{0} \cdot \left(O_{total}-O_{M}\right)+\alpha_{1} \cdot O_{M} -\lambda_{MZ} \cdot MZ_{M}\\
-                            +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}
@@ Line 1,452: / Line 427: @@
                      <p>
-                         According to our modeling result, the final concentration of target protein mamC-ZZ is
+                         According to our modeling result, the final concentration of target protein mamC-Zz is 2.3625×10<sup>3</sup> nM. Since the concentration of magnetosomes extracted from the
-                        <b>2.3625×10<sup>3</sup> nM</b>. Since the concentration of magnetosomes extracted from the culture
+                         culture medium whose OD600 reaches 1 is 172ug per milliliter <a href="#our-team"><sup>[2]</sup></a>, the average concentration of magnetosomes is 46.83 per cell, and there are
-                         medium whose OD600 reaches <b>1</b> is <b>172ug per milliliter</b> <a href="#our-team"><sup>[2]</sup></a>, the
+                        an average of 24.31 target protein mamC-Zz on each magnetosome when assuming that all target proteins are localized to the magnetosome membrane.
-                        average concentration of magnetosomes is <b>46.83</b> per cell, and there are 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.
                      </p>
                      <br>
@@ Line 1,474: / Line 446: @@
                      <div class="imgbox">
                          <h6>
-                             Fig. 2 Induced expression of mamC-ZZ a) Schematic diagram of the model b) Dynamics of target
+                             Fig. 2 Induced expression of mamC-Zz a) Schematic diagram of the model b) Dynamics of target protein. Horizontal axis shows the length of time. Vertical axis demonstrates
-                            protein. Horizontal axis shows the length of time. Vertical axis demonstrates the amount of
+                             the amount of protein (mamC-Zz) within the system.
-                             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 in vitro</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 ZZ domain so that these
-                        two parts will combine and work together. Assuming that there’s no factor causing target protein
-                        degradation in vitro, the ordinary differential equations (ODEs) describing these processes are
-                        shown as follows.
-                    </p>
-                    <br>
-                    <p>
-                        $$\frac{d}{dt}F=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ$$
-                        $$\frac{d}{dt}Z=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ$$
-                        $$\frac{d}{dt}FZ=k_{1} \cdot F \cdot Z-k_{-1} \cdot FZ$$
-                    </p>
-                    <br>
-                    <p>
-                        From the modeling result, we can see the reaction between 10mg/ml modified magnetosomes and
-ug/ml scFv-Fc is very fast and the production rate is relatively high (Fig. 3).
-                    </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>Fig. 3 Combination of scFv-Fc and modified magnetosomes (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 class="section showcase" id="showcase">
-                <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>
-                    <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>
-                        According to Fick’s First Law, eddy diffusion caused by natural convection is calculated by
-                        \(J_{2}=D_{n} \times \frac{\partial c}{\partial r}\\\).
-                    </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>Fig. 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>
-                    <br>
-                    <p>
-                        To solve the following PDE with the help of MatlabR2020a, both initial condition and boundary
-                        condition were supposed to be provided.
-                    </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>
-                        $$
-                        \left.c(t, r)\right|_{t=0}=\left\{\begin{array}{ll}
-& r \neq 0 \\
-                        c_{o} & r=0
-                        \end{array}\right.
-                        $$
-                    </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">
-                        <img src="https://static.igem.org/mediawiki/2020/8/8f/T--ZJU-China--wiki_mode_fig7.png"></img>
-                        <h6>Fig. 5 a) concentration field of magnetosome in tissue fluid b) Magnetosome diffused in the
-                            tumor issue capillaries around it.</h6>
-                    </div>
-                    <br>
-                    <h3>Detection and combination with HER2</h3>
-                    <p>
-                        To describe the combination and degradation with HER2, we have a model about modified
-                        magnetosomes in vivo. Assuming that there is no other way to clear magnetosomes and 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 processes are as follows.
-                        Parameter names and chemical equations can be found in the appendix.
-                    </p>
-                    <br>
-                    <p>
-                        $$\frac{d}{dt}F=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ -k_{2} \cdot H \cdot F +k_{-2} \cdot FH$$
-                        $$\frac{d}{dt}Z=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ -k_{1} \cdot FH \cdot Z+k_{-1} \cdot
-                        ZFH-P$$
-                        $$\frac{d}{dt}FZ=k_{1} \cdot F \cdot Z-k_{-1} \cdot FZ -k_{2} \cdot H \cdot FZ+k_{-2} \cdot
-                        ZFH-P$$
-                        $$\frac{d}{dt}H=-k_{2} \cdot H \cdot F+k_{-2} \cdot FH -k_{2} \cdot H \cdot FZ+k_{-2} \cdot
-                        ZFH$$
-                        $$\frac{d}{dt}FH=k_{2} \cdot H \cdot F-k_{-2} \cdot FH -k_{1} \cdot FH \cdot Z+k_{-1} \cdot
-                        ZFH$$
-                        $$\frac{d}{dt}ZFH=k_{1} \cdot FH \cdot Z-k_{-1} \cdot ZFH+k_{2} \cdot H \cdot FZ-k_{-2} \cdot
-                        ZFH-P$$
-                    </p>
-                    <br>
-                    <p>
-                        We can see in the result that the process of combination finished very quickly (Fig.6a), while
-                        the total number of the magnetosomes decreases gradually because of the phagocytosis process
-                        (Fig.6b), and the concentration of magnetosomes is one tenth of what it was before after around
-minutes. We also have results with different concentration of magnetosomes injected
-                        (Fig.6c), which shows the combination in a short of time with different injection concentration
-                        of modified magnetosomes.
-                    </p>
-                    <br>
-                    <div class="imgbox">
-                        <img src="https://static.igem.org/mediawiki/2020/c/cb/T--ZJU-China--wiki_model_fig6a_new.png"></img>
-                        <h6>a</h6>
-                    </div>
-                    <br>
-                    <div class="imgbox">
-                        <img src="https://static.igem.org/mediawiki/2020/4/44/T--ZJU-China--wiki_model_fig6b_new.png"></img>
-                        <h6>b</h6>
-                    </div>
-                    <div class="imgbox">
-                        <img src="https://static.igem.org/mediawiki/2020/a/ae/T--ZJU-China--wiki_model_fig6c_new.png"></img>
-                        <h6>c</h6>
-                    </div>
-                    <div class="imgbox">
-                        <h6>Fig. 6 a) Magnetosome binding in a short time b) Metabolism of magnetosomes in the body for
-                            a long time c) The combination of different con6>a</h6>
-                    </div>
-                    <br>
-                    <div class="imgbox">
-                        <img src="https://static.igem.org/mediawiki/2020/5/5d/T--ZJU-China--wiki_model_fig2b_new.png"></img>
-                        <h6>b</h6>
-                    </div>
-                    <br>
-                    <div class="imgbox">
-                        <h6>
-                            Fig. 2 Induced expression of mamC-ZZ 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>
@@ Line 1,800: / Line 459: @@
              <div class="section services" id="services">
                  <div class="container1">
-                     <h2 style="line-height:1.5;">PART Ⅱ Deterministic model to determine the combination and
+                     <h2 style="line-height:1.5;">PART Ⅱ Deterministic model to determine the combination and disaggregation of SCFV-Fc and modified magnetosomes in vitro</h2>
-                        disaggregation of scFv-Fc and modified magnetosomes in vitro</h2>
                      <br>
                      <br>
                      <p>
-                         After scFv-Fc and modified magnetosomes being produced in <a>E. coli</a> and magnetotactic bacteria,
+                         After ScFv-Fc and modified magnetosomes being produced in E. coli and magnetotactic bacteria, they are extracted from cells and purified. Fc domain can combine with Zz domain
-                        they are extracted from cells and purified. Fc domain can combine with ZZ domain so that these
+                        so that these two parts will combine and work together. Assuming that there’s no factor causing target protein degradation in vitro, the ordinary differential equations (ODEs)
-                        two parts will combine and work together. Assuming that there’s no factor causing target protein
+                        describing these processes are shown as follows.
-                        degradation in vitro, the ordinary differential equations (ODEs) describing these processes are
-                        shown as follows.
                      </p>
                      <br>
@@ Line 1,822: / Line 478: @@
                      <br>
                      <p>
-                         From the modeling result, we can see the reaction between 10mg/ml modified magnetosomes and
+                         From the modeling result, we can see the reaction between 10mg/ml modified magnetosomes and 100ug/ml ScFv-Fc is very fast and the production rate is relatively high (Fig. 3).
-ug/ml ScFv-Fc is very fast and the production rate is relatively high (Fig. 3).
                      </p>
@@ Line 1,829: / Line 484: @@
                      <div class="imgbox">
                          <img src="https://static.igem.org/mediawiki/2020/e/ef/T--ZJU-China--wiki_model_fig3b_new.png"></img>
-                         <h6>Fig. 3 Combination of scFv-Fc and modified magnetosomes (the blue line refers to the
+                         <h6>Fig. 3 combination of ScFv-Fc and modified magnetosomes ( the blue line refers to the combination product of ScFv-Fc and modified magnetosomes, and the orange line refers
-                            combination product of scFv-Fc and modified magnetosomes, and the orange line refers to pure
+                             to pure magnetosomes)</h6>
-                             magnetosomes)</h6>
                      </div>
@@ Line 1,843: / Line 497: @@
              <div class="section showcase" id="showcase">
                  <div class="container1">
-                     <h2 style="line-height:1.5;">PART Ⅲ Kinetic Model to Simulate the Diffusion and Binding of Modified
+                     <h2 style="line-height:1.5;">PART Ⅲ Kinetic model to simulate the diffusion and binding of modified magnetosomes inside the tumor</h2>
-                        Magnetosomes inside the Tumors</h2>
                      <br>
                      <br>
@@ Line 1,851: / Line 504: @@
                      <br>
                      <p>
-                         It could be assumed that the magnetosome injected collect around the tumor if exists, since our
+                         It could be assumed that the magnetosome injected collect around the tumor if exists, since our magnetosome has been proved to stick to her-2 produced by breast cancer cells
-                        magnetosome has been proved to stick to HER2 produced by breast cancer cells specifically. As
+                        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
-                        magnetosome enters into tissue fluid from blood, its concentration changes with time and the
+                         of magnetosome’s concentration field to explain the process intuitively by image.
-                        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
+                         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. Four respects were considered, involving motions with the flow of tissue fluid,
+                        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
-                        eddy diffusion caused by natural convection, mass transfer due to the difference of
+                        to a molecular in size.
-                        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
+                         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
-                        three-dimension gradient. That is to say, small particles were assumed to diffuse evenly to
+                        evenly to different directions and scalars were calculated instead of vectors.
-                        different directions and scalars were calculated instead of vectors.
                      </p>
                      <br>
@@ Line 1,880: / Line 528: @@
                      <p>
-                         Macroscopic methods could be useful to solve the problem. Use J to represent the diffusion flux.
+                         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
-                        It is easy to infer motions with the flow of tissue fluid as \(J_{1}=ub \times \frac{\partial
+                        \frac{\partial c}{\partial r}\\\).
-                        c}{\partial r}\\\).
                      </p>
                      <br>
@@ Line 1,890: / Line 537: @@
                      <br>
                      <p>
-                         According to Fick’s First Law, eddy diffusion caused by natural convection is calculated by
+                         According to Fick’s First Law, eddy diffusion caused by natural convection is calculated by \(J_{2}=D_{n} \times \frac{\partial c}{\partial r}\\\).
-                        \(J_{2}=D_{n} \times \frac{\partial c}{\partial r}\\\).
                      </p>
                      <br>
                      <p>
-                         On top of that, natural convection is very weak in both capillaries and tissue fluid flows. We
+                         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 \(J_{2} \approx 0\\\).
-                        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
+                         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
-                        transfer coefficient was in need, for the expression, \(J_{3}=k_{c} \times \frac{\partial
+                        \frac{\partial c}{\partial r}\\\).
-                        c}{\partial r}\\\).
                      </p>
                      <br>
                      <p>
-                         We used Chaoqun Yao(2020)’s experiment kc data of 1:1 silicone oil-water mixture, to whose
+                         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
-                        viscosity blood and tissue fluid similar<a href="#our-team"><sup>[3]</sup></a>. A model was
+                        model was built for the relationship between the rate of flow and kc. Microsoft Office Excel was employed to finish the task.
-                        built for the relationship between the rate of flow and kc. Microsoft Office Excel was employed
-                        to finish the task.
                      </p>
                      <br>
@@ Line 1,920: / Line 562: @@
                      <br>
                      <p>
-                         Now we could get the value of Q in our situation. This way, the value of kc could be assumed
+                         Now we could get the value of Q in our situation. This way, the value of kc could be assumed roughly.
-                        roughly.
                      </p>
                      <br>
@@ Line 1,930: / Line 571: @@
                      <br>
                      <p>
-                         Dispersion effect also led to the diffusion of magnetosome in tumor tissue. It could be
+                         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:
-                        estimated the same way as eddy diffusion caused by natural convection:
                      </p>
                      <br>
@@ Line 1,968: / Line 608: @@
                      <br>
                      <p>
-                         $$\frac{\partial c}{\partial t}=\frac{\partial J}{\partial r}+u_{a} \nabla
+                         $$\frac{\partial c}{\partial t}=\frac{\partial J}{\partial r}+u_{a} \nabla \boldsymbol{c}_{\boldsymbol{o}}$$
-                        \boldsymbol{c}_{\boldsymbol{o}}$$
                      </p>
@@ Line 1,975: / Line 614: @@
                      <p>
-                         To solve the following PDE with the help of MatlabR2020a, both initial condition and boundary
+                         To solve the following PDE with the help of MatlabR2020a, both initial condition and boundary condition were supposed to be provided.
-                        condition were supposed to be provided.
                      </p>
                      <br>
                      <p>
-                         We should provide the relationship between r and c under the circumstance that t-0, when
+                         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
-                        diffusion hadn’t happened in our model. At the very beginning, magnetosome collect in the
+                         the capillary and it is presumed that there was seldom magnetosome in tissue fluid.
-                         capillary and it is presumed that there was seldom magnetosome in tissue fluid.
                      </p>
                      <br>
@@ Line 1,997: / Line 634: @@
                      <br>
                      <p>
-                         In comparison to the initial condition, this time we’re required to explain how t influences c
+                         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
-                        at the time of rmin=0 and rmax=10, embodying the probable size of the tumor. Soon we found the
+                        we found the condition invalid. At last we expand rmax=100 to produce the image.
-                        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
+                         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
-                        taking place at the original location where diffusion started precisely and in detail. A highly
+                        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.
-                        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>
@@ Line 2,014: / Line 648: @@
                      <br>
                      <p>
-                         Simultaneously, we assumed that when diffusion flux caught the brim space, co would be small
+                         Simultaneously, we assumed that when diffusion flux caught the brim space, co would be small enough to be ignored.
-                        enough to be ignored.
                      </p>
                      <br>
@@ Line 2,025: / Line 658: @@
                      <div class="imgbox">
                          <img src="https://static.igem.org/mediawiki/2020/8/8f/T--ZJU-China--wiki_mode_fig7.png"></img>
-                         <h6>Fig. 5 a) concentration field of magnetosome in tissue fluid b) Magnetosome diffused in the
+                         <h6>Fig. 5 a) concentration field of magnetosome in tissue fluid b) Magnetosome diffused in the tumor issue capillaries around it.</h6>
-                            tumor issue capillaries around it.</h6>
                      </div>
@@ Line 2,033: / Line 665: @@
                      <p>
-                         To describe the combination and degradation with HER2, we have a model about modified
+                         To describe the combination and degradation with HER2, we have a model about modified magnetosomes in vivo. Assuming that there is no other way to clear magnetosomes and
-                        magnetosomes in vivo. Assuming that there is no other way to clear magnetosomes and ScFv-Fc in
+                        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
-                        the tissue fluid except for phagocytosis by macrophages and the phagocytosis is at a constant
+                        processes are as follows. Parameter names and chemical equations can be found in the appendix.
-                        rate, the ordinary differential equations (ODEs) describing these processes are as follows.
-                        Parameter names and chemical equations can be found in the appendix.
                      </p>
                      <br>
                      <p>
                          $$\frac{d}{dt}F=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ -k_{2} \cdot H \cdot F +k_{-2} \cdot FH$$
-                         $$\frac{d}{dt}Z=-k_{1} \cdot F \cdot Z+k_{-1} \cdot FZ -k_{1} \cdot FH \cdot Z+k_{-1} \cdot
+                         $$\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$$
-                        ZFH-P$$
+                         $$\frac{d}{dt}FZ=k_{1} \cdot F \cdot Z-k_{-1} \cdot FZ -k_{2} \cdot H \cdot FZ+k_{-2} \cdot ZFH-P$$
-                         $$\frac{d}{dt}FZ=k_{1} \cdot F \cdot Z-k_{-1} \cdot FZ -k_{2} \cdot H \cdot FZ+k_{-2} \cdot
+                         $$\frac{d}{dt}H=-k_{2} \cdot H \cdot F+k_{-2} \cdot FH -k_{2} \cdot H \cdot FZ+k_{-2} \cdot ZFH$$
-                        ZFH-P$$
+                         $$\frac{d}{dt}FH=k_{2} \cdot H \cdot F-k_{-2} \cdot FH -k_{1} \cdot FH \cdot Z+k_{-1} \cdot ZFH$$
-                         $$\frac{d}{dt}H=-k_{2} \cdot H \cdot F+k_{-2} \cdot FH -k_{2} \cdot H \cdot FZ+k_{-2} \cdot
+                         $$\frac{d}{dt}ZFH=k_{1} \cdot FH \cdot Z-k_{-1} \cdot ZFH+k_{2} \cdot H \cdot FZ-k_{-2} \cdot ZFH-P$$
-                        ZFH$$
-                         $$\frac{d}{dt}FH=k_{2} \cdot H \cdot F-k_{-2} \cdot FH -k_{1} \cdot FH \cdot Z+k_{-1} \cdot
-                        ZFH$$
-                         $$\frac{d}{dt}ZFH=k_{1} \cdot FH \cdot Z-k_{-1} \cdot ZFH+k_{2} \cdot H \cdot FZ-k_{-2} \cdot
-                        ZFH-P$$
@@ Line 2,057: / Line 682: @@
                      <br>
                      <p>
-                         We can see in the result that the process of combination finished very quickly (Fig.6a), while
+                         We can see in the result that the process of combination finished very quickly (Fig.6a), while the total number of the magnetosomes decreases gradually because of the
-                        the total number of the magnetosomes decreases gradually because of the phagocytosis process
+                         phagocytosis process (Fig.6b), and the concentration of magnetosomes is one tenth of what it was before after around 120 minutes. We also have results with different
-                         (Fig.6b), and the concentration of magnetosomes is one tenth of what it was before after around
+                        concentration of magnetosomes injected (Fig.6c), which shows the combination in a short of time with different injection concentration of modified magnetosomes.
-minutes. We also have results with different concentration of magnetosomes injected
-                        (Fig.6c), which shows the combination in a short of time with different injection concentration
-                        of modified magnetosomes.
                      </p>
                      <br>
@@ Line 2,085: / Line 707: @@
                      <div class="imgbox">
-                         <h6>Fig. 6 a) Magnetosome binding in a short time b) Metabolism of magnetosomes in the body for
+                         <h6>Fig. 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
-                            a long time c) The combination of different concentrations of magnetosomes in a short time
+                            short time after injection</h6>
-                            after injection</h6>
                      </div>
@@ Line 2,116: / Line 737: @@
                      <br>
                      <div class="imgbox">
-                         <embed src="https://static.igem.org/mediawiki/2020/6/67/T--ZJU-China--wiki_model_app.pdf" width="750"
+                         <embed src="https://static.igem.org/mediawiki/2020/6/67/T--ZJU-China--wiki_model_app.pdf" width="750" height="600">
-                            height="600">
                      </div>
@@ Line 2,127: / Line 747: @@
                      <h2>Reference</h2>
                      <p>
-                         [1] Stamatakis, M., & Mantzaris, N. V. (2009). Comparison of deterministic and stochastic models
+                         [1] Stamatakis, M., & Mantzaris, N. V. (2009). Comparison of deterministic and stochastic models of the lac operon genetic network. Biophysical journal, 96(3), 887–906.
-                        of the lac operon genetic network. Biophysical journal, 96(3), 887–906.
                          https://doi.org/10.1016/j.bpj.2008.10.028
                      </p>
                      <br>
                      <p>
-                         [2] Xiang, L., Wei, J., Jianbo, S., Guili, W., Feng, G., & Ying, L. (2007). Purified and
+                         [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
-                        sterilized magnetosomes from Magnetospirillum gryphiswaldense MSR-1 were not toxic to mouse
+                         mouse fibroblasts in vitro. Letters in applied microbiology, 45(1), 75–81. https://doi.org/10.1111/j.1472-765X.2007.02143.x
-                         fibroblasts in vitro. Letters in applied microbiology, 45(1), 75–81.
-                        https://doi.org/10.1111/j.1472-765X.2007.02143.x
                      </p>
                      <br>
                      <p>
-                         [3] Yao, C., Ma, H., Zhao, Q., Liu, Y., Zhao, Y., & Chen, G. (2020). Mass transfer in
+                         [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
-                        liquid-liquid Taylor flow in a microchannel: Local concentration distribution, mass transfer
+                         transfer regime and the effect of fluid viscosity. Chemical Engineering Science, 223, 115734. https://doi.org/10.1016/j.ces.2020.115734
-                         regime and the effect of fluid viscosity. Chemical Engineering Science, 223, 115734.
-                        https://doi.org/10.1016/j.ces.2020.115734
                      </p>
                      <br>
@@ Line 2,156: / Line 771: @@
      <div class="top-arrow">
-         <a href="#" id="scroll" style="display:block ;"><i class="fa fa-angle-up"
+         <a href="#" id="scroll" style="display:block ;"><i class="fa fa-angle-up" style="font-size:36px;color:pink"></i></a>
-                style="font-size:36px;color:pink"></i></a>
      </div>
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsjquerymin&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsjquerymin&action=raw&ctype=text/javascript"></script>
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jspropermin&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsboot&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jspropermin&action=raw&ctype=text/javascript"></script>
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsowl&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jseasing&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsboot&action=raw&ctype=text/javascript"></script>
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jstype&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsq1&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsowl&action=raw&ctype=text/javascript"></script>
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jswow&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsaos&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jseasing&action=raw&ctype=text/javascript"></script>
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsway&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jstype&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsq1&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jswow&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsaos&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsway&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jscounter&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jscounter&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsven&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsven&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jssel&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jssel&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsmenu&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jsmenu&action=raw&ctype=text/javascript"></script>
-     <script type="text/javascript"
+     <script type="text/javascript" src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jscustom1&action=raw&ctype=text/javascript"></script>
-        src="https://2020.igem.org/wiki/index.php?title=Template:ZJU-China/jscustom1&action=raw&ctype=text/javascript"></script>
      <script>

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