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− | <div id="page-heading" class="container-fluid page-heading" style="background-image: url(https://static.igem.org/mediawiki/2016/f/f4/T--BNU-China--project.jpg);"> | + | <div class="container-fluid page-heading" style="background-image: url(https://static.igem.org/mediawiki/2016/f/f4/T--BNU-China--project.jpg);"> |
− | <h3> MODELING </h3> | + | <h3> Background </h3> |
| </div> | | </div> |
− | <div style="background-image: url(https://static.igem.org/mediawiki/2016/e/e5/T--BNU-China--landingImage.jpg); background-size: 100%;">
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− | <div class="container page-story">
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− | <article id="modeling" class="col-lg-10 col-lg-offset-1 col-md-12 col-md-offset-0 col-sm-offset-0 col-sm-12">
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− | <header class="page-header">
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− | <h1>Modeling</h1>
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− | <small id="secondary-page-header">This is our Modeling Design</small>
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− | </header>
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− | <h2>Introduction</h2>
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− | <p>Microtubule is made up of 13 protofilaments. Now there is an widely accepted feature about the microtubule that microtubule has highly complicated dynamic instability. Under the fixed vitro cultures conditions, on the one hand, subunits will polymerize automatically forming the required structure when the condition is above the critical concentration; on the other hand, the microtubule will depolymerize into subunits when the condition is under the critical concentration. Apart from that, the single microtubule will always in the stage of polymerization and depolymerization.</p>
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− | <figure class="text-center">
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− | <img src="../img/paper/modeling/1.png" alt="this is a pic" width="60%">
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− | <figcaption>
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− | Fig.1 Our process
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− | </figcaption>
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− | </figure>
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− | <p><i>Tax</i>(Taxol), the efficient anti-cancer medicine, can promote the polymerization of the subunit and restrain the depolymerization of the microtubule, which can make the microtubule be in a stable condition and restrain the mitosis. Therefore, it’s important to study the tax’s mechanism of action during the microtubule’s dynamic assembling process. In order to research tax’s influence on this dynamic procedure from the microcosmic level, we analyze the dynamic procedure and build our mathematical model by four steps.</p>
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− | <ol>
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− | <li>
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− | Expound the theory of the microtubule’s depolymerization
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− | <br />
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− | Visual Simulation
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− | </li>
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− | <li>
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− | Verify tax’s influence degree about microtubule
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− | <br />
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− | Analysis of variance>
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− | </li>
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− | <li>
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− | Tax’s influence on the length of the microtubule
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− | <br />
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− | The probability distribution statistic of the Microtubule’s length
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− | </li>
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− | <li>
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− | Simulate tax’s mechanism of action to the microtubule
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− | <br />
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− | Differential equation modeling
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− | </li>
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− | </ol>
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− | <h2>One-way analysis of variance</h2>
| + | <div class="page-story"> |
− | <h3>1.0 - Theory of the one-way analysis of variance</h3>
| + | |
− | <p>By constructing the F-test statistics, we can use the one-way analysis of variance to study whether classification of the independent variable’s different levels can make significant influence on the variation of the continuous variable. If the levels have a significant influence, we can further give the 95% confidence interval of the dependent variable means under the different levels of the independent variable, and then we can analyze the degree of the different levels. But the precondition is that the data should satisfy the homogeneity of variance, in other words, the variance of the data should be the independent identically distributed. In the next part of the modeling, we will use the one-way analysis of variance to analyze the data, and then deal with the data.</p> | + | <article id="project" class="col-lg-10 col-lg-offset-1 col-md-12 col-md-offset-0 col-sm-offset-0 col-sm-12"> |
− | <h3>2.0 - The homogeneity test of variance</h3>
| + | <header class="page-header"> |
− | <p>We use the SPSS to do the homogeneity test of variance with the data we got, the outcome is shown in the figure below:</p>
| + | <h1>Background</h1> |
− | <figure class="text-center">
| + | </header> |
− | <img src="../img/paper/modeling/2.png" width="60%">
| + | |
− | <figcaption>
| + | <h2>Overview</h2> |
− | Fig.2 The figure of the data’s homogeneity test of variance
| + | <p>Cancer is a group of diseases involving abnormal cell growth with the potential to invade or spread to other parts of the body, and it is the second most common cause of death worldwide, leading to 14 million new cases and over 8 million deaths per year<sup><a href="https://2016.igem.org/Team:BNU-China/Project#ref-1">[1]</a></sup>. Besides, The financial costs of treating cancer were estimated at 1.16 trillion US dollars per year as of 2010. It has become one of the great challenges human is facing nowadays.</p> |
− | </figcaption>
| + | <figure class="text-center"> |
− | </figure>
| + | <img src="https://static.igem.org/mediawiki/2016/b/b2/T--BNU-China--cancer.jpg" width="65%"> |
− | <p>From the figure, we can see the data’s variance is XXX, nearly zero. Therefore, we can think the data meets the requirement about the homogeneity of variance and we can use the one-way analysis of variance to deal with the data.</p>
| + | <figcaption> |
− | <h3>3.0 - Construct the F-test statistics</h3>
| + | Fig.1 Death from cancer per million persons in 2012 |
− | <p>The independent variable is a classified variable which values 0 and 1 to describe whether the tax is added into the test tube. The dependent variable is the change of the micrutubule’ length, our modeling is shown below:</p>
| + | </figcaption> |
− | <p>
| + | </figure> |
− | $$ y = u_i + \varepsilon_{ij} $$
| + | <p>In order to conquer this serious problem, many medical scientists are devoted to exploit medicines that can target cancer cells. In 1962, paclitaxel was discovered in the bark of the Pacific yew, <i>Taxus brevifolia</i>, giving the name “paclitaxel”. Shortly after its discovery, taxanes have demonstrated a unique ability to palliate the symptoms of many types of advanced cancers, including carcinoma of the ovary, lung, head, neck, bladder, and esophagus. Good efficacy and little side effect quickly made the taxane class a most common addition to the chemotherapy against cancer in the past several decades.</p> |
− | </p>
| + | |
− | <p>y is the dependent variable, the change of the microtubule’s length. is the j observed value of the independent variable under the i level. is the mean of dependent variable under the I level. stands for the residual between dependent variable’s value and it’s mean value, also obey the normal distribution \(N(0, \sigma_i ^2)\) </p>
| + | |
− | <p>Then we construct the F test statistics. First, we define the quadratic sum of the residual:</p>
| + | |
− | <p>
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− | $$ SSE = \sum_{i=1}^k \sum_{j=1}^{n_i} (y_{ij}-\overline y_1)^2 $$
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− | </p>
| + | |
− | <p>
| + | |
− | And the quadratic sum of the elements:
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− | </p>
| + | |
− | <p>
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− | $$ SSA = \sum_{i=1}^k n_i (\overline y_{1}-\overline y)^2 $$
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− | </p>
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− | <p>SSA reflects the variance between different levels and the difference is made by the different elements; SSE reflects the variance in a certain level and this random difference is due to the selected sample’s random. For example, the measured length of the microtubule will be different when we add the TAX into the test tube.</p>
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− | <p>On the basis of the theory, our F test statistics is:</p>
| + | |
− | <p>
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− | $$ F = \frac{SSA/(n-k)}{SSE/(k-1)} \sim F(n-k, k-1) $$
| + | |
− | </p>
| + | |
− | <p>The numerator of the equation is a part of the dependent variable which can be explained by the change of the independent variable, while the denominator of the equation can be explained by other random elements except the change of the independent variable. The proportion of the change of independent variable in all change of the dependent variable becomes bigger, in other words, F has a higher value, independent variable influence dependent variable more.</p>
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− | <h3>4.0 - The F-test on the data</h3> | + | <figure class="text-center"> |
− | <p>The numerator of the equation is a part of the dependent variable which can be explained by the change of the independent variable, while the denominator of the equation can be explained by other random elements except the change of the independent variable. The proportion of the change of independent variable in all change of the dependent variable becomes bigger, in other words, F has a higher value, independent variable influence dependent variable more.</p>
| + | <img src="https://static.igem.org/mediawiki/2016/7/70/T--BNU-China--taxol2.jpg" width="65%" > |
− | <p>
| + | <figcaption> |
| + | Fig.2 Ball-and-stick model of the taxol |
| + | </figcaption> |
| + | </figure> |
| + | <p>The great commercial success of Paclitaxel and other anti-microtubule medicines has inspired pharmaceutical companies to extract and test similar compounds, farmers to grow related plants. So an effective method is being needed urgently to discover many other similar compounds. Moreover, testing the concentration of paclitaxel from fermentation broths or plants are in high demand.</p> |
| + | <p>How to test the taxol and screening other compounds?<br />We determine to use microtubule for assisting.</p> |
| + | <p>As we all know, the mechanism of taxol is to kill cancer cells by obstructing the function of microtubule and consequently blocking cell division. Microtubules are a kind of important cellular structure composed of two monomers: α-tubulin and β-tubulin. These hollow rod shaped proteins are required for many cellular activities including cell division and transportation.<sup><a href="https://2016.igem.org/Team:BNU-China/Project#ref-2">[2]</a></sup> A dynamic equivalence are found in microtubules, meaning that protein monomers are assembling and disassembling at every moment. The anti-microtubule agents can destroy the dynamic balance in microtubules, hence terminating cell mitosis and inducing the tumor cell apoptosis.</p> |
| + | <p>There are two types of anti-microtubule agents. One type inhibits assembly, such as vinca alkaloids, colchicine, podophyllotoxin and etc. The other type interferes disassembly, like taxanes and epothilones.</p> |
| + | <p>As for the discovery of anti-cancer compounds, we narrow down our sight to the anti-microtubule agents which are of great significance in cancer treatments.</p> |
| + | <p>As for our project this year, we modified the homo sapiens α-tubulin, ligated it with N/C terminal of the luciferase report gene fragments. Based on the principles of synthetic biology, we aimed to express the fusion proteins with α-tubulin and signaling residues. Then we made a kit containing the fusion α-tubulins and non-fusion β-tubulins with buffer which has an appropriate condition verified by experiments. We call the kit “taxolight”, and through which we can achieve these things below:</p> |
| + | <h3>Screening with high feasibility</h3> |
| + | <p>Anti-cancer agents especially paclitaxel have showed their powerful ability in clinical application. However, we still need to look for new drugs that are more effective.</p> |
| + | <p>The existing screening method of anti-microtubule agents needs to purify tubulins coming from mammalian brains. It heavily relies on the turbidity of tubulin solutions when they aggregate or disaggregate under certain temperatures <i>in vitro</i>. Once using this method, we can get a “S”-type standard aggregation curve based on the liquid OD value and the incubation time. Similarly, we can also get a standard disaggregation curve. When added different anti-microtubule agents, the aggregation/disaggregation curve will change correspondingly. Thus we can determine the role of the drug according to the change of curve.</p> |
| + | <p>The defects of this method are shown below:</p> |
| + | <ol> |
| + | <li>The operation of extracting and purifying tubulin from animal brain is very complicated, and the experiment must be done within an hour after killing the animal. At the same time, the price of reagents in this experiment is expensive. The experiment period is long which takes no less than 3 days.</li> |
| + | <li>The wave length of measuring OD is 350nm, which is between ultraviolet light and visible light and always leads to a huge deviation. Also, the requirement of the testing instruments is high, quartz containers are needed as well, which cost a lot.</li> |
| + | </ol> |
| + | <p>Our project avoids these drawbacks, and provides a new insight for the anti-microtubule drug screening. What we need is just a fluorescence microscope by using our kit.</p> |
| + | <p>Take paclitaxel as a control, we could test the fluorescence intensity of new medicine compared with paclitaxel's. In this way, further research and development of new anti-microtubule agents can be carried out easily than before.</p> |
| | | |
− | </p>
| + | <h3>Detection in high sensitivity</h3> |
− | <p>stands for that different values of the independent variable( whether the TAX is added into the tube or not) make no difference to the mean value of the dependent variable(microtubule’s length), in other words, the independent is not important to the dependent variable. Then we use \(R\) software to conduct F-test, the outcome is shown below:</p>
| + | <p>HPLC/RP-HPLC is one of the most common method to detect paclitaxel now. It relies on pumps to pass the sample through a column filled with solid adsorbent materials. Each component in the sample interacts differently with the adsorbent material, causing different flow rates and leading to the separation of the components as they flow out of the column.</p> |
− | <figure class="text-center">
| + | <figure class="text-center"> |
− | <img src="../img/paper/modeling/5.png" width="60%">
| + | <img src="https://static.igem.org/mediawiki/2016/c/c1/T--BNU-China--HPLC.jpg" width="65%"> |
− | <figcaption>
| + | <figcaption> |
− | Fig.3 Outcome of the F-test about the data
| + | Fig.3 The process of HPLC |
− | </figcaption>
| + | </figcaption> |
− | </figure>
| + | </figure> |
| + | <p>This is a time-consuming process which is very unfavorable to the studies in laboratory. For example, in a laboratory which producing paclitaxel from fungus, detecting the concentration of the product may delay experiment process if there were no paclitaxel at all. So we need to develop an effective method to rapidly detect whether taxanes exist or not before measuring concentration. Our kit can reach the goal in order to accelerate research progresses.</p> |
| + | <h3>Concentration detection</h3> |
| + | <p>Apart from our former achievements, optimization is also needed. An intensity-concentration database of certain medicines (e.g. paclitaxel) is being planned, then we can use our “taxolight” to determine the concentration of this certain medicine conveniently.</p> |
| + | <p>There is a limited issue that the sample solution must be ensured not containing other anti-microtubule agents. Nevertheless, it is still useful. For example, farmers who plant taxus can apply our kit to detect the concentration of taxanes in there plants. Moreover, factory can use our kit to test the concentration of taxol in their fermentation broth. In conclusion, our product can be popularized in many agent-specific tests.</p> |
| + | |
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− | <h2>Visual Simulation</h2>
| + | <div class="reference"> |
− | <p>We applied to programing visualization in this complex process based on certain laws of Microtubule dynamic instability.</p>
| + | |
− | <p>Tubulin is made up of two tubulin monomers which are nearly the same as each other. These two tubulin monomers are named α tubulin monomer and β tubulin monomer. Microtubule is made up of 13 protofilaments polymerized by tubulin dimers end to end. And microtubule can be the hollow tube with 13 protofilaments coiled into helix with each other, water in hollow part. The tube wall is 4~5nm thick.</p>
| + | |
− | <p>Tubulin dimers are incorporated into the growing lattice in the GTP-bound form and stochastically hydrolyze to GDP-tubulin, thus forming a GTP-cap. It is thought that the switching from growth to shrinkage occurs due to the loss of the GTP-cap.</p>
| + | |
− | <p>Caplow M<sup><a href="#ref-1">[1]</a></sup> research shows that when the cap structure of microtubule plus end subunit containing GDP- beta tubulin instead of GTP- beta tubulin, microtubule becomes unstable and will quickly depolymerize.</p>
| + | |
− | <figure class="text-center">
| + | |
− | <img src="../img/paper/modeling/3.png" width="60%">
| + | |
− | <figcaption>Fig.3 Microtubule dynamic instability</figcaption>
| + | |
− | </figure>
| + | |
− | <p>
| + | |
− | As is shown in the figure, there are two kinds of Dimer, called GDP and GTP, with blue and red two connected to the circular. These dimers have close relationship with each other, and there are three important modes of their action:
| + | |
− | </p>
| + | |
| <ol> | | <ol> |
− | <li> | + | <li id="ref-1">World Cancer Report 2014. World Health Organization. 2014. pp. Chapter 1.1. d5ISBN 9283204298.</li> |
− | GTP-tubulin dimer in endpoint can aggregate new GTP to make the single protofilament grow, and microtubules extend.
| + | |
− | </li>
| + | <li id="ref-2">Rowinsky EK, Donehower RC (Oct 1991). "The clinical pharmacology and use of anti-microtubule agents in cancer chemotherapeutics". Pharmacology.& Therapeutics. 52 (1): 35–84. doi:10.1016/0163-7258(91)90086-2. PMID 1687171.</li> |
− | <li> | + | |
− | At the same time, the endpoint GTP may also be made off, thereby protofilaments shorter.
| + | |
− | </li>
| + | |
− | <li>
| + | |
− | Any place of GTP (in addition to the right endpoints of the GTP) made made random hydrolyzed to GDP have a chance.
| + | |
− | </li>
| + | |
| </ol> | | </ol> |
− | <p>
| + | </div> |
− | We built a simple GUI interface to simulate the Microtubule dynamic instability. As for a tubulin, we can adjust the parameters of K, R, h, GDP and GTP to display number and length of tubulin in real time. Among them, K, h, R is the number obeying certain distributions.
| + | |
− | </p>
| + | </article> |
− | <p>
| + | |
− | According to above principles, we built the simulation process of the visual program in MATLAB@, Fig 2 is the schematic diagram of the principle of GTP hydrolysis. Among them means GTP, D means GDP, R means the probability of endpoint GTP polymerizing with new GTP, K means the probability of endpoint falling off, h means the probability of GTP hydrolysis into GDP. It should be noted that once GTP is transferred to GDP, it will not have polymerization, fall off, or hydrolysis, and will become stable state.
| + | </div> |
− | </p>
| + | |
− | <figure class="text-center">
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− | <img src="../img/paper/modeling/4.png" width="60%">
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− | <figcaption>Fig.4 Parameters of GTP-tubulin dimer hydrolysis</figcaption>
| + | |
− | </figure>
| + | |
− | </article>
| + | |
− | </div>
| + | |
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