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− | <section id="Overview" class=" mdl-components__page is-active"> | + | <section id="Overview" class=" mdl-components__page mdl-grid"> |
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| <div class="mdl-card__supporting-text"> | | <div class="mdl-card__supporting-text"> |
− |
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− | <h1>Flip-flop</h1>
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− | <br>
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− | <h2 id="intention-of-the-model">Intention of the Model</h2>
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− |
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− | According to our design of biological flip-flops, a recombinase-based device must be
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− | constructed, characterized and standardized. Recombinases can operate on sequences with
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− | recombination sites thus altering the direction of transcription. In this section we propose a
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− | model that characterize the process of gene recombination with ordinary differential equations
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− | (ODEs). Each reaction in the process is described with Hill or mas action kinetics. The aims of
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− | this model are listed as follows:
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− |
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− | <ol start="1">
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− | <script type="text/javascript">
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− | (function () {
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− |
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− | var doc_ols = document.getElementsByTagName("ol");
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− |
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− | for (i = 0; i < doc_ols.length; i++) {
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− | var ol_start = doc_ols[i].getAttribute("start") - 1;
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− | doc_ols[i].setAttribute("style", "counter-reset:ol " + ol_start + ";");
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− |
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− | }
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− |
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− | })();
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− | </script>
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− | <li rel="1">Estimate parameters in the model from experimental data and fine-tune the
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− | model.
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− | </li>
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− | <li rel="2">Simulate the sequence recombination process via recombinases. Show the changing
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− | of quantities of original and flipped sequences over time. Prove that the device can
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− | work as expected.
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− | </li>
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− | <li rel="3">Analyze the effects of varying recombinase production and degradation rates on
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− | the overall performance of the device.
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− | </li>
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− | <li rel="4">Assist in designing of the genetic circuit.</li>
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− | </ol>
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− |
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− | <h2 id="biological-basis">Biological Basis</h2>
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− |
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− | The sequence-flipping device is based on the integrase family of recombinases. On this page we
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− | focus only on the Bxb1 serine integrase, but the same dynamics model and analysis applies to two
| |
− | other types TP901 and PhiC31. Mechanism of serine integrases is well recorded in literature.<a
| |
− | href="#fn:footnote1" id="fnref:footnote1" title="See footnote" class="footnote">1</a>
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− |
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− |
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− | <h3 id="set-process">SET Process</h3>
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− |
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− | After transcription and translation of the Bxb1 recombinase gene, the proteins are expressed.
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− | Two Bxb1 monomers form a dimer. In dimerized form, the recombinase proteins can bind to attL and
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− | attR binding sites around the constitutive promoter J23119 on the reporter sequence. When both
| |
− | sites are occupied, synapse between the two sites can happen. This can enable flipping of the
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− | sequence and alter the direction of the promoter. The flipping process changes the direction of
| |
− | the reporter promoter and transforms the attB and attP sites in attL and attR. <br>
| |
− | In its initial direction, the promoter starts GFP transcription; after flipping, it turns to
| |
− | RFP. By measuring cell fluorescence with flow cytometry, we can quantify the ratio of flipped
| |
− | sequences (attL/R ratio). The data-fitting procedure relies on this key indicator.
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− |
| |
− |
| |
− | <h3 id="reset-process-with-integrase-rdf-fusion-protein">RESET Process with Integrase-RDF Fusion
| |
− | Protein</h3>
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− |
| |
− | 此处应有RDF机理。 <br>
| |
− | The following part describes species and reactions involved in different components of the
| |
− | model.
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− |
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− |
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− | <h2 id="model-composition">Model Composition</h2>
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− |
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− |
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− | <h3 id="pbad-arabinose-induced-protein-expression">pBAD – Arabinose-Induced Protein
| |
− | Expression</h3>
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− |
| |
− | We have decided to use an arabinose-induced promoter (pBAD) for the expression of recombinases
| |
− | on ColE1 vector. This promoter can be modelled as the following chemical system. <br>
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− | <span xmlns="http://www.w3.org/1999/xhtml" class="" rel="6c9f94ec126c51b116cc387738c9af0f"><span
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− | class="MathJax_SVG" id="MathJax-Element-67-Frame" role="textbox" aria-readonly="true"
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ypufJ+1CXADzFimnZ0lizSAxd3YGQWuNGMFump2wbTqz8lq8pxWBRS+yfpW/yamC28SJ2t8FCoshoChuFTAi9IH781Y2cda2/AJbfX+bFPgOhRosHUdunavTYHHTAHJGKRKl4WQgCBNMkCQcUpLWbwSvBDKuOdw62Edok0mWAAXwBuwwqWuapYBCQIGra5sfgQiggqBzH9zjeRix7LEOpSxXAQyQhaBC9ARuG6sYs8yKYVxL6V3TmDEdQd4Y2GiyWbBAuIInrTWwBrhissPgKeldty3ACdz8U5q4wmi5kRQM3bzJoRykTJ2lkH/jS5cDVOQZClT+4dbpH4JtwQxIIvQKF6mW1PgUhRwvriqcY+1x7OxIDtTrLEAAYUGkMUKlXGeAI6zw9JDKeI5e90+9fea5S95g9+dxTnOk5swi65YsHSbk9mPEiMzeopjYs0GPrgmAl7pokyJUa1UCYqcZWMHwpzlpXNWrdGsXxmjmcqPdAdGm4ypZLXLFPhpSWOpy7FSTlE64VncMVNB4hlAi7smpYqzjR9+7XBfxCPWYmUvtebdT1OgKXAFCjTYugJRu8umwCOnACGHVlnNHQKQOlAaQQnAADxoYudGWPnjA1AACkAF9yCCHNBCi5t9CJ4HQjQCD+EO2BHDwQVRkL26WsASQY7GmuY5Cw8TtGiCaa9pi4EWwhBLlcbS9kkj/qQm+Mgxs9L5JuucOQFSCTKNC7BLl0rCXNYf8j5hi3ZdLJyEJEkfliwWAgJnpRu6oBlBzrOEXG5b6Z5pLArGmitwma6G5kPIBbIIvt2aApekAPBBYcEiVeMByQ2sU2KiuB87s7KazlZVZ9Lf7M+atGbO8geEAFhLcUhpAarZS53tPIOynVaXWnxFDJezmclo6rvo43wZE4WGuFMKGi1BX814uuRqnJlGvZOWc9Y/gFDj6pixlwAkPuC3zD6alq7ZApaJRvBEyp38Nhdhtfy0tdjVS65799UUaApcmAINti5M0O6uKfCUUIAmmSBVa8kQzjLl+xoZvEdwAxw079DgZgzXWh8Ah/fyeyw7hCx/1/Q3xywZi9/9HZCZE0jQOtOEJ0Cbx+xdgllqs1PQIQRxZ8rsYUtzXaKP59b+DlCyoOkzv1f7zfnWgHhjIyAm7Z6SrdfTvFEKUAhklj97Ns9dAqoZhDmfrDniwbgZp9JC3JfMoUCSunzOTPaRCWkyq6B4LXGTFDNcgf1dvbufMOIdkTLjKiXf+dISB5YuwhQcnsmU9kATy5n5cBM2j4zhogAxtjynaUXTh+yieBCXSSC2lt0A1ljrJA/iomi8GbuaZR1q7KrnKII6TvNGD0MP++miQIOtp2u9e7ZNgabAeRRIQYcmeyvD4Xm991tNgcdNgaxZByBINCFWCZigRBAPxT0YyKjJdjIGlHudRDwUKrIZsgixHnHF5Var+Lf6eVz6/I2ygvKCQkRm0EySAayxLnMzzAQVNYlN1srTx+sN69mbDlCXNQCBLmCKxRpwBLKMn8uv2EvgypjMzVwyA6s5AFgsaZICpQtxJt4xJ+6VYlEl3qluzmkpo6gB+FjVeRZIqFHLWjzuHdSzawrcMAUabN3w4vXQmwJNgXujACFNMg5uiASrLHB8bwPoDzUFbpgCaflhVZJBE7BhGU83Oy6EwEi11KR1igsdqw+FBwDFyuV9hYcBFIlo5vIRNSGP78nu97zhhivRhvOrRh93Z32xEgNCvgUgiZ2S+CYTZkgAJHZMTBpXRcBKIh8WLi7NsiB61jjFn3IXFn8pSQjrmne4EnJd9n3/ZiHzN/yEayFLXabMT5flGrsKTOI/aKiQtHF36vcbPhQ99KeHAg22np617pk2BZoC51GAiw9tPO22DGqEO2nhW9A5j5791tNHAcBDUhtNTFK69Mo0KgkHaw3ANDduxd7jagywADjcARVMZ92ROEeSHhao2gfwBDixQgMlvifekxsyqxpQ513AKAGe9PCS8OhHUo9s3IeBHwk1WNAARHGcXBzFmWos3so+eE+sZzYukGLIxFzWDI6ytRoP6xfgJ/6t1gOURIN1TTp9CTI0c0ILz4vp7NYUaArcCAUuAbbEGXQl8xtZ8B7mE6NAn5MnRvqLfJiwmI1wthbndZGPdSdNgabAJgUAj1OLeNcae/W/64eAu6WzPT+/9P21Ma316btr4+jlbwpckgJccik2vrHvrkuS9XhfdwVbNES0M7LonCN8CICVjplJXmDqrTaCNO3aXnM50IbTjmc1+713buF387eOfOfn+iu3MP5Txkjo5sbCLeZVhltJ1oTh2iEuQNa8PA/Ox8cN/37njatKt6ZAU+B8ChAcZITba1mEWwzPUSskCwpL5tzEGs1Fepe+z+pBuF5qrCo1Jmlv/Pm7dN9c7Fg1sjbV0Xf7uabANSjg/GVyoq3+ncFM+nOOjHiNsT8NfeIZrzussGIIudXyzJANWKKWcxtZJ91ZOznLCVS8C9h6rwGyZNbhFnBOyxSoWQX+nD4ewjt8rZ87BOy1oqKp9fJvhRsJ5fy61dpQa+iWWwYWV//yW57P0tgFI/OtFxgt9bn03ktNml+pg8UCyBj1RiOTlZgfriTW3H45Irg9Nhr2fJoCl6CAtN2SGPCoWLNupMXAv7l94rlia8TvrAkJYoLcZ1y88PHat3MticGWkowChgsaHj/fAxRS6rtxd6sZPPfoIe26hAnqui0VE957v39vClyaAva3WDXnBJA6egYp1BWPVg+tBfVLr8r/60+GWi6u+JH/BrI0MocyC+h/TqNEIsOokYnPca3vdTxIyXPAlktDvIKgT4DrAw5+a35MAVQLZiO4BPlt32pzIfL3lk1JKljpZ2sjYNOuuszRT20c2YY0NYAE7/JHv8Vm3mqksPZ8wvBPv8V5bI3Z3nzn4eufz/HLN28pemmbZdXin8/PvmrdZY8CuJjvBUYLmFbzSaHQc7Tcj422PZ+mwKkUkJVN2mwFYWdFn4x1kg8QAAkaAArepPlNwVjWZud2qbFMef4dR1xQPpPFr91ZW40ShjBS+YWMeO5JAhA+cEp76yHgeEec0l200qd8t59tCmxRgPJRshDnxHmqTRIPSo2lM0gOojxQALuTDF1vj7HOk0nIo7JvapLLKK9wrnIf/1FqIRveJMlMtwMUOBVsAQqfPMCCWheCRM9tqtATODUFQKVMfQwuEh8YEe9UiCIIV+rWTPHqABDIHQBumBqNA4Gc8H5rTZAyFxft8wageCwgwoWioKSis9yLNMD5fUYK3qV5KrLpbLz8eN7FYp+nplsgNVDK8vUmfeHc2nbv8T4gCnBnkTABuMmmWDTrlOa+Ap54UCSP8neKEjx5y7rMXZgWPu8o78l+V/vZIoUi3e83HlD0V7a9UxtFpPv2NcaL5sELpFtT4KFQ4BVH4pC0nhjXs0dWRv9N3vGbVPjPKIOmtCDznWLlfShzvqVxSNjCG0djjQRyz23vGhG8l7Jl8e1z+3uq3jsFbDEdEzRp51m2Zm3GKYR7wyFwpgWAdcdBpBG59VY3t7lweSGAz818CQrZaFwdijWN60OkC9cWFrlcR9mkWHe47Nx6c0HQRKv/otHIUS4AX3sXhCxYLpe19bcfCISUDG/8yOL3bn3de/y3QwExk2JEM3aExZgia85qhz/J6satN5vsb7TyWw24UkspG6uU/rkU7jXKNPxCKm/Z6JYKVe/1QalTLXfShFfwt/d+/94UuDYFshB0fsfZIN9lBsX8O8UlgMX7J5sYRDXLul2HAhJiyJbJdVC7q2Wc0oeimDeTdebd9uXXGfrj6/UUsJWMHzCi6c9q7qdShfscIVYxwdoULfyyUzt7YM9zbwFIxRNkA6AkSJibCva0nYIXs9HQfvEDm9PacCQ34f5ZtVWevaU5rM3NXsRUCHMaFyL+yUddeDA5QApz8t4LFz6Ull21XJj6uzUFmgKnUUCqbdanbBLUUF4sKUNYhDL1uOeBNJr1Nbe+2aqU3ziizeUujjeyXEvRLXnQqU3qbzykWgx4DvCAuCWF3Knz7udviwKzaxkXXq5qS8kw3HXS6GfjycPCfK5b221R6v5HC9jyrCJzU0QJX+HSfJem7ALZXTK0x6BUvwstTnr3KNhyIBTr40rFT/4uVcv5svNfFyysBkY2F6cFvOVGy8MvNuOxZKWjVfjqhUkBZoSDdBHxyBowe4g0efOxD+Z1vHU/Xm5HNMipDUJ72rcqqB1ZD0UugSjJNBTDnJu6LYQnfu1ck85xMzoyjn6mKfBYKcBrgMtSti03O895PpukGRRFa1YqAgV3w8+MiFctcV/4O5BWayLN9HWvsaRR1ugHaDq1AWuUmi8e8Wnef0yeA6fSo59/mBSYrb/vVtxn5xGzJItZzkbhwcV2toI9zJne3qjeLiI+eAybVZElqhNzPaF1PAK2aOlpD8WacImQTYmm/5wmoJLrHM0jX/Sq8TuiMTznm/f5TnUf813xOpjJUh0yGktaoNcsA6S1RJeH3mS54faosQDVdbzluAKushQJ6eOc8+MGdGoDOtGFNgkgXWosnpJvoOUzh2B16nf6+abA00gBpTbcJdU1ULbQtQQW4mjF02bbc11PTw5KFpbu6r63pxh0pp3tc71AzANfpYDhflW9Bzoj4dO42x/mnJesvzx17PulpmD0C8oPkkdxOcx49oc5y9sdVc2L0B40T3gdj4CtZ40q64Z6V0Gan7y01ynMVheQu2QklJKSoCwNaW2sR6e6XHCP01dN1oFOrFV7fvcuSOAq25YLiXinqvGkcXitiPiKM/eEuASaDKk4Hay9uKIzP/Ndr6VLDhcCQIIWN9tdMhKiOxecOW2yrGKnJt0QmCvIfc54JEvPWiKWmvnLfGi9gaWvP4NYhMH3jAgXzFrRb+dAjJ92V4vxGUPsVx4xBey/LevLtaYufmopy5hzhzdt8SUJLZz/I1nKeARwQ0ovgpr1c2luNZGP3ym1gJiltNXGCsg5+8CNGIXqdUGIAbjWUl6rpff2JybUyDGnmz3LN+v6e0TEc8qE7hp3ca11736fLAWeRHFk56MqN/ay3X3kKJ+QlPL/b3ki2dzpeIw7fJb3jnRFxiDjkRnJXOemLjcOZ5Vccmofvm295tp//kbW2ZNZeZiZ/1btwJcdIS2pzBdLz1iSDa/F58i0p9Y/I2vuycK+4xvWaKZPruGpMl1dX3sA/633ibU1tiP95vrN81+7v7b2lv1krvpa3Qt7YMvAXSysWtqW1mJvo9NA6ktMErdEPuk13//RjITSrEvNy+ImeYHNJA0wgT8LxsqQIxuUb7iQBStvHQib1xwBJZvUoqmVxA2M6ZsrCOHFxce1ZKl5j1tgrb+0pYUUt8anPxtNaLWo7NGz/m78tKCYn3bNTD9caswTfbjToL3Mein0HM1IaIPmOgKZBBqF+IDNDAqX0U8GHH/XL0vR1joag30mqN24MBP7jVYbmGGhoilW2G92WbV+BKwaQ3dtbZB96oJCB4yQRvwIozhlb/SzTxcFXCL2OddUQjo3tGs1PNE/9jF3WWePllqcYrqrOIcUDuIH1KhiXUqreI7LmZRwCR/Qn6xZ3Na3Ws3257ktJU8tT+FZlyK3Qu8steRx3zIS/hAY8Gda+HxfXO5SjDFhyT3HOnWOS/XbjCQ86ekxz/OuCs9r7YXu98lRgIDIRfbfRsTz7nEYrL41O6YzW91661CcHS6HMohq+IPYLrLEXuPar0AveYk1jQzobJpzTTK21Q9ZkHxHgeGMEo7FMQF8a3xg7s84KMmNg3ePe5sLpH/IFEseLJS+eBoeJ8yETEiRYtw1jTqZGN/m/SWOlJfUrJgydsoWPNVaU+auuWDiP2q4al81ZMOvG/QnH5GdjYNrMj72/guyh7vEPOEANFPSSEw+GZesWuNdyVo5T3cBZZh/hFNkiETeTeQccxA/JomQuRxpCjPbR7yA7AP3Cbnf2NGCB4Jn7ME1byJ3lVAm35c3Af1YYslfylGRod2ba4q0HCfZlLLOP2ij6Qt/Xt+Vop0AACAASURBVIyL2wNbVXtIy28BjxJmJp4LCLo2OH7w6VKYyHvPrUN/Nq4sbg4eYtWWrh0uShlY/DvbViyU7FJAFLAFpFg8jACQ0BwSG9PBdND4+i+1urn9/rkDVGIKtQFGNhiBJBugiS7nWqMUFyS01+Zvn78y1rv8GcPEtPj/ole6FGbs2Vo2ovpNhw6jRM9MkZ6/p+a2xj3Mvy2NXxp9dd+sI3raY5K4AMoYASCGWdCaEwoVWKxtFmr21vsuNMx3MTGMKJPFOOhHLp9LfLv7eLwUsJ8+eigunNVz3b7XKEQZ9fwRU0R4yjpWnq/p0blFU1hkohm/z4U1XXB4eo2RdEYJBGInl5p7iydEde0jnMgUOjcgz2VsLNkIRltCaXpzuLO4zWtiUcw525oihgCD75onfnMkc2H2mdpo9HWfAK4zb++MhI/33N5lZu8+BD01O7nAXruRxZyP6uLq3HzswocJ52K1gKtsZCAlUrYaCxDB/LkDpEg+5l4na0hh7oxRhmeph6W+yInOrnNM8USoFkNPJgBuAAMlGjyz1syVRxYZ07eFf0g8QSAHvJxV8oKxVG8t4AyQA0IojGvLWE68DG1kKK71OfE39EzrHaWz2PH6DFkBf1+yhNVMpsZLniX3yJJcFco5JjxLjGhV9uKp5FQ8PjO+en6OW8XzeA5QoNdsk3IWkNUBOgAZbeoe0NfWHCq90AdIQv/PGGCVxxAluoyIeC2lGhyB11uPuQG7sAHZEti1F6wR8OZdbS17ePYFDxiHnAVkeWEnmZmR7Om/9fc94vT3wBa0CIhoUDL0fcTFY56kS9FiOJzpElFdNfL5IxkJHR6uJvrMgsoIi9gmb5MiYFpa9G2jVl/h/J4DZFOylpinAm1pHrXBbCquiDb4XoDhnKYX0+FKQoMCXFgkjMOGzmyFNqPnaDHvUmOsZp0xN0zIN2ZAscXYjvyGQbjsM3bPO+ZHsEuhxN+OWECBbUwMA/io8fF0pcRkpZS3jvWQu1BqnYcc89uO9cX8CFL+SQaE7l841iDX1AVRNf72jb2Zmmv92keY66kuAkfoWJ/xnYwJowVysXRrCtyVAvgst22XqAv50oHR+BiFlnNctdupLLGnabpZpGn8/H/WqmNpJmDQ8rqA3SkuJ5dkar7xU4LjUqOgwY/Ti8DcKPJ4Srgb8BXn/i3GpZhgD28nmO2dMePm3oSvpPb5lYaXRGYHdKnLfDhnM0zLFCFCmZTZJXprXdPN3kWe7sVpZcvvdkbCu56Mx/k+Wc6ecQ7IbTURxTVmPFuLyTIEaZ4pZII8g/gBZTdFguYMkrP2LHDkLmfPu5RFshiSE9zxrFQ8a/Ke9sySJcJ4yALOP2s5fpLlhRIIUdLqn+J3KRM0PuJdoMrc0LYCSnyB7EDmwYfwubTc40UZ2uFMk1E1Ls/4J5oR7r3D08mcU8lvLOQU/IWyCOgBEKxzAlzjJufN6dfnTNGAJN5o3P6Nd1JEGw+ZNBtvH7RMmQdAYv1Bvw8rvHm2YOLrPBOASnUOc60zZ4HxkBvJ7gCzvZPztB8YM7ayJCYYNXf0NI90oST7+o57SFvzcHCveI5xh6UP3dIQYu3sScB7DSvom+eFsVAMWh9z/oLx3Zr8ZbGPPbBVY5D2/NTXDnS6VUC/FtdE6+JWId3CEz6PNASSzUZjyYBwWaVsPFoTjMdCADGIMwdtOoR56S6l5wYGAcwMwN7Shi4BRwg3gSmfWIKF5m+QOcBirpUeR+a99oz5AyMOCk1NApi79FnfzTnSRLNqcR3MljEK+f+nuM8A2OlOSpDAeOw7dKJZAdJpdzEyDBFwqg3gpmnQMMKslp7PYHi07bQN2lKNOHuJxqwC9DVgdyl6Zj9cI1nkch8/luLel6ZT93c6BTIblcvVJXqNQPRq0U9rMEsX/uuCxVvxDvwuvRhoAKV79gwPAIKXy5MGNhVRLM2EjKXm/eqKSOjgNsIzgHJGX7XQsXG5FFm+CDVbjaXeuN0d+E4VZGiF8aRsgBUhpLbMznZqDSHfwvd4TlSQRih0D6XGmJaYoLbmJnP6Luk3HgsFCMcESvckoZBS41qtxhv7BqHZngQgKAbmM+jvFBAswnveG/iFc0r56d6ntK5uxawlZChtzdJL0eK8ZohFjaX3HgG/ev4sySxczih9nT3joIBZsrYT1IEMzfOUtFXJQs4GEDJMJGPV0AI4BkjNB6D0Nw1fBKqsIfmGTEsZyxMr4+SMCZ+breczEOYlwJiAZwKcqYgGgsjM6KnhLXjPnD0buCXvpVWtKoPq/kJrYTtkOo1cw8iRbpqsU1wZ6zzXvpn9AtzoY395b3YvryDKOwAQGW9ugBL5UnPvWMsa84c+5Mc1DMKixpUcLZZqjGVdRf2fDLagVCa3vPxoIFNgXZjL6p8yAw3tJ3/G2mbXjFME3FrfwQZ1wKFwF5HL1387cC6qJHJ+u1rs1go0z5fcFhCctY+0ES53QE8//EiZLnOzQsUOpQU+NThxi/aJ7s9J6LC3pknvpWKgc5ahU+IKuAPk4aDloaFyMDBamgfCEwskYE0Yqy21yP5GY50Mrz5DW4SRpbCyxCjmyujeX0vZvkenU3+vZwDjMe9zXXVP/XY///gpQPECuOA5LqvPuvCUgakERZRerEEEPsJSFg2uJTEAHxc6wYF2OsELAcHY0oKDj8+xXTn0tADl/4s5wDcIaekO4jfWMgIX4YQguBVQnn1RinlvKfaUEOtOTKXM7P5ds7OdmjUw3eznOBZeEYSDmhH11L4vvOTd3QOmgL2Zewnwp8i4hpJFSnHKnPkMAnw1bt1Z8qxYd2dwLxaGcp5rvbOmcTUENGpT75JQrS0pZViryApowd3PmZpjV2u8tHFRqtfasc4y4TqtUehI4b7UKg8kiHsHuMxGlsYPjUvDI8mC+DEPhASO1QDAmgakABsAF+8hrcqua/HxFQgDScAeELRUxH2WwZd4C5CUrpprheONjSKe3EtmS+8q68PQQkGf9K0hG+aQMvtM21qXDeCs2WTzWVY39LNevmkdl2JprV/WOyVn2V/VKyHBN1BVc0n4jt+sn28AffZTrpnfa31dv/N4QO//r21Ztuaiu+ckcGA2NEhuYSk81wEgck11fkpGwlrfAXq2cbmhsFBsNXExxmSzs3axJCyBE2MH1CymA0SbulbELWtO5XcJGy5HlzuTus0noQfXmGq2TV/aPQa0M6Wr/5xCBKsZbUua4vPDs5bolIyEtVaOdcR8aJn2NNAYGpO0dcTYKAWWtL01xf4ao8gU7Dmf+6z/wbpamfjSYd9aYHsr3bOObAQM6UgmoSN99TOXoQABA1C4RsPHgZbMpkrB4+Lcy3h1dCyUcDS5GhdfRS9ddlWrTglC+6vRarvMWLnw63SfrgLCVnxwZuvLOEd96odQ4bKnqU3X43OyicogS/tLQKwFWH2HJhhvz0RElHqEiNTUmzthYy1ed42m6WZv7PV+yOfnYrB3zUiYQftH15iW/klktjw6vlt8zr2051l0zrwob529TDIFbFCGfg/h75zOxztkGXdvLbtAQZruWaw4qZBwFliVKpDZ+nS68HqG/EWOqjGnzhuvHf0vFUVmVXeOMoZ8S0kOWOAjZMkaWz/HhFLWCKFZuzfxC3wjG3BRs0pTxuMLZBX3LyUxy6M+0UcDUilyeApoQBAwS3Gdrsy8dABRwry2xKPy7wmEWZLIR1mzb6Y9RTblVbYlsFUzuW7lF6gGEDQD+oEc6189yyiP0sq3Noe5r7UaYRR5GS6z5WI951SYPQ8YRHLv1SLb9hOMkl4ZS7G66ea5tSabhx3IcKDS330viHDpAOUl4eCnD3p9jgYEwMqDySfVIuzFL1UNokNMyHbw9vyAveeyzADBjB1YGjvzbqY0RwcX4loK78og9LXmQuKSs1krk+KG4vA95JbxaP6dQlMdLy0RzUsGym9pK+p7tVYOhsCi41Cm1mqNJvyogbEMql9yA813szip/8cAaCXq/rImzPpVyKk+1ddel6px8S2XVnXR3Pu+M8a1YKuxrmYsjMu4LWd7VL3+75h78j2uauekMT4ySt9JH/p8nhDzosF772JZ17e+UrAhFFC8UKzVQOuqicbvXZD4fNUgVldkSijndGlsAJVznBYwAh43GFpKViAeAzUZxlrQ/hLt8AKKIsLMWi2tWgpFH+iYgk0Cta2sbPN3M0kOmuh7SaHH+i84PptEHSlMH9kD8zOy7NKu7629+zmBq7i7h64UPIcW9/kOpZg7T0PPSyk85jm4jzNDmt+ABAoXypA5kdY58+cmBiRUQCWmiZC6FFKxV5cuxzC7Js5Ayfngdu+s4Jks5MBEbdXqfW5W5ll5TtDHV9YaK1TmIqDgAWyqK575Z+IM1ntnCmCseQQoxbhak7cphQEIvKDKQgwALIRpOVyiKysL/sktWQPu8MM1sJ1lfDxbE1rkXMlaQGDKrFteS9UAQoFNLtF/deubZbel5HVc9cjJyePtLWNYatVKtpXcYvbUA+DdMdU4g//PMbbVgmtdWCdzbRmR8GLA0HmDE+yVRb66pVlxqVV0foqLH6KwNAi4cyDXMjL5vgDDZAx7tVKS2KlB9P/GyOJig++5z2XGHu/5lsO6lLXE70yWqZ3dCtYmyNI2pLuldzPTzNLmqAcvGeFaGuFzGOGl30nhBhMl2KwljMAA0sLCTMsSuFcZvib2sIEJHoS1NQtizq0esL0smdWXlkBHk1ObMdNcVACM0bGc3UcadoIPl6psAGRqu46s5Vy75Mg7/czDooDzUjP23dfo7mohAbJSY0nQIjyKHa2xEHi7y9/5EofJpYnAVH3v56ycW3dN1Xii02xFn8HQFnCb6ZyxDnhcvVTrc3Mh17yA3T3iOQC1tZiGpXVNFyTvr2n/3ZM1Bu2uGQlnTfx97bf+zpOlAGBCQ3/XchBz5t5ZuZCxojnbI54uszBcrVbOpXMizsZ9TZB3j1dXPd8igwAzqfRdy1C6tQrkOcA0LRl7Vq2qoEm5kuxTLWVVYBeTyfJfM6l6r8ahkpukNScX1rWixMpaWbPgn3OagfAe7VkhMzyI3AGAVCv2XM/QGJbKH81ZqXkHia+fQzvQNRORWD/yzhwjdtSSZs7Vs2LvPptBtLVg8VrDDehPNszwnwxVIQsz2FCUA4vWghFiMyxoC2zNlq0lQXVt00pd60CwDkGOaxmZPCeWKTc2DcwR4FHrO7BSmORaMHWOUQYr1pC8tJZ8gfPZ2RRtQWrxvjrvmqgjD9sWiGNinn1K14L6nixr/r9fzyx91nHNsmcfYXQ17eeRjIQz095LyWw8s3VyKxC4Ws68m8k3Kl1pmTCcmpKUFgsDOjcV/ynrBtBXX2T7/xTtI6CWbk1r323L1ikrcj/PVssWfrBnZTh3VNY+NYTZh8uSAOBs3+W7/OgzIywgJZ5g5sNSHgNfqQVfuvznmNetmKSqPTWfOWYDn6cVzdgtFi/8O7OXbdExNes0lHjF2r3lzFGSZOPyw3ODJ4SLGVA7kvjIWGlsXd6UhmsxZVzRaYnz0r9rRkJj502xZ6lqy9a5p275vdmydS1lXo0PNxLWDXuTFn6OXz91hktlF+bkEnOCBmfQ/t0qgzBbtSSzEe9FlvKue5oMwpJM2bCk9K3xR/iRuOsj577SYFaGr8UK5TuztWku1DxnOgbCKJ5mgMFiRMmU6yWpRdanym/VjNdrPArAFKeqkadZtbiSLrW5NuxSPH6NZ8fTxDotgZOMdfUdc6R8Y3SYAXHtL7MVVrmyxvfqa6tsU7WA2ePWeyur4dLexX+tOXA7tzkuEZgjUwo98i17jDLPc7sy2xbYsoksdoKTUxJkyDDIquUyX/JBr5PyXA3+tTlqHNdMgLm+A62wy3Q2J8/vzah2CwzM8QPQ/JqVplrLfLPWZlna4DPo88xW5q1TmeEln0dXwhFtylp61fweE65Cqtn2ACSgbe1Tw7MVd1XnZD8B8tm2rIj2VWa31P+SEMQUbG/XPciyxTXpWm4edT5VYPV3Vts54+LWmrqEau2NvfXHIDpma49K9/s76w+f/Ws0ghdNbQYtCzbn1nEJQc/5zWyyLFwEo/lyrQlw7DseCPPFRLGR6ZR5HFDSLVl5MlNgehGslbiYL8mjmQEzfnTLk8EaAZAAa4JY/82VyPtLAsTauqabPa39UvB3vpdxp+muedeMhO5QcTdHG2GoY7aOUuvYc7MC5Nhb+08B0O6UrBvFWmF/XSpmSxIuyox0ZVurRzkrRbZSapvV/DxhndAOlFB0U4ASpNcUEuKZhDKkvInH4DWn3nXVqpKlaKqH17wCFJ1VET+79uEVwgLSHdc5z+zJ2Rfeb35ZegYAIBfVuc4WtDUeRf5MmQov8t9rSqMqEy/x0hmcbFnJGC+qqzO+jyfWRtYSKuSe0Jb4cjWk7OVKqN9cSxYyr9cMMP2+tDeX7hqAzL1EPnMGKDAOZ4XdAltzEOTR5BWZmcPFwDS6h/jm+lR77oqz1uRoitN6iIxprrWUizJbQ2x8AsWSVWcOWNTHHnDilufw1TTjWzFH++z1Ok9gDjRItDBZiHrrSzPo3MtIOGug17IJzt+sCTUIZrPJPp+fXZPElvCnXYoHnDXVazV0rkHpatlyMfC13mLu1xhD9/l4KZDBu84K955LZSOcz694Je6Bc6vxrLSxLMizVrqCo1kzXPur2lN/X+PjNU4zn+Pet6U8wfcJPNxatjwZcjy1LIq/4S+EpTU6zHQRm6kPmnf3y9bYWL4ohLI2jb46I+HjPbN3mRnFDYGWYtFZ4upUXdru0rd3qyub/wc0xNTM9VdT4Z7f26pTyvpOoZvKBIIsmYgFhdvxkSyiYoF8I71r5qLAR+Y9xxMdsSBXkMiChBZVMSE2kjVOA0wpcWcLX82o5zkAaU4xLw4PjRLkLvEocdksLUnHWidwnj+AZ59koqGlRBUzj18DzLMcDODjt7NCb+4PUK1lAMhs5p1JQoBF98WSBZ4SEdhJ9/u1rOJL665PwLxmB8+aZvl8dZH3N/2Taa3tWYqnvWw4FSXbvJDw3sZPMyFTpvoIe40JutYq2Qsuns3NTMx7GQgBR4uaB3ELoc9pwLdAw3wAjhQTnpkQ+sybbo9m9/F7Mok9S12OZTa/7/kK1wQk+tiyUOU35kxkxkYrvrQnaY9oPjLL25Yb7NKanJoVMMfokgPosgbc3lrVANUtrf5eP/17U2CmQK2z5XzWLEt3pVYVurgJ+f9ZSTDHPzirGSie3ycc8mTIgO4tASETUOS7FGgZmF7nw3UH/8lL229rsQb5XrqD14QbWzSa+RdFicubJ8hScdTaV7rZs6Yv0WTpu7X4ud/34hPuur79/u1R4D7qbFV3NxRays7m79ykhW2kFXopZXZSmBxFyM7EZVxyyZqnNMK3M5L1TM/Jnp1uvRnWsifD+CaAlVbKpYQVNaZoLdayeusAKpTCc7r+ym/WchtUJROeDNituTPXsjlrce+1P7ItRdScFt0azXKwOHku5XOrcWlLScjQE81zH2wlAmI1Q++0GC7xQ9YpCkAK7dldnnJfSvtsxkZhlm3OlM71OmugnbIvv/vZPbBV6yfZBFz8ahrO+aOJNgnFawHG8zuztnIvXqZqQblvuLD2XGLmQ7Tkm2pcxgzxEkry0NZ6L4SHqiWaXdrWajrUOdeARH+nrbBpLuGyhtnSGi/5n56yQdDLOtis0nbWgPe1fmZNwJ4Zv2YNWmMw87fmWLo111ZJNghirJF5cKvvr36qu9OsWdu6RLboqK6bQn4O7dEMkyyzWf/CfPhqXysz3Sl7oJ+9bQoAISy2Ug5LMeyyvGSr6cjXXOcqb1+70GtMV3XbySDkjDcQt5QJKHIeW2mdZ7eWPSVe1q/hGpmp7LfoBSRS9lRAh49lVratd9O92f1Fy3okNlT2QV4g2Y5a0C655t3Xw6aA+4OLFldh98ql21KmwS0lxuwxsqbwFLNZY20+ZiTa2Ro/QFTTic8JGvaAkr7F/NTvygiIx2TozB5gq95SnqU4qVb7OZ5rTbFSrf9rNKogt4I2IIGLKB5SXfC2LIlc6VgPWYXwXBbzWjcq6U6WSW8F8pznWHWAKzJy3ilVDgbyGA8kn5hb5ck1c6A5MJgYTwVzax5f7jZKakpta2UcWYBeRlpyMHBP5uPZwSAzhwGJDcOv07o1ZyafE5dJyGJt1hosxaizavXaA1s1swk/ceh6K1NcVtI+atUy8Fk74AC5gJZisGYXv6O++PMhWtKIsnqJUXPQLZKFr9lSmIKBSBlxstUidP4GbfNVXWveBRZzgZne/S0rbN+FOdJicOVjcuWvLTXquY2lkcXxqFXLdwA09EuQulUZfLZQrYHfefyzmXxpfJ7BjAhpNDOYMjobFwZASOR3zppVGeOcgt34CalH6UhL4nKxB5aKBy6tBcYAfGfcC0twBreeu3b9XlPAvhdg7uKjJT01bmGPgrOL+ZqVpRbgXBNcakwXxZOzQAvJfZu7NYXf0j2xp7mdk25sxfYSImnhCY54pzInR9qc4GfN0lb7ovEXQ0cJdNSq5f3Z+o73uafukuDkyBz7mdugQLrxE0IJ5tdos7sbBQpesxYvP2fGY/HlXjZngKbspKBMz6Ot0A3zkgRCfDghP/sS08RCnsWQ8RL391oZIXyHIhnvSgU6izjgYtzaVohKrfO5pvSvZxb/Qas5uYS5k/+y4PGSe6D6foA0RY6WBZbxdgoY9MAr8QTucBpZnAw3twqYgRR0qDHw+TzZhOEhFU/ZHwDJVRFvz3JOVfFGSe+dOU7Md/2WyqmM6Tcn8p+1IrtWsLUUUsRSSj41NgoosiTMgHeT87gW+gdQTC+1Ja+p2eti9pAjT1cAupVQjzyPBtwpyX6LRcT3wJaJ2AiQp7blsodYELoNe8QlLBeV4GsRampbG3kpoLOmCt8bT91ks6uKg+2igkIF7RkvBC8xgpowsuBokC80D9TRwDqcKbjMwM/za+ZTvsAOhMs50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src="data:image/png;base64,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"
| |
− | style="margin-top:0;margin-bottom:0;"></span></span></span></span></span> <br>
| |
− | The promoter pBAD binds to AraC and this represses transcription of mRNA. Arabinose will bind to
| |
− | AraC and form the Arab:AraC compound, allowing transcription to occur.
| |
− |
| |
− |
| |
− | <h4 id="assumptions">Assumptions</h4>
| |
− |
| |
− | We assume that:
| |
− |
| |
− | <ol start="1">
| |
− | <script type="text/javascript">
| |
− | (function () {
| |
− |
| |
− | var doc_ols = document.getElementsByTagName("ol");
| |
− |
| |
− | for (i = 0; i < doc_ols.length; i++) {
| |
− |
| |
− | var ol_start = doc_ols[i].getAttribute("start") - 1;
| |
− | doc_ols[i].setAttribute("style", "counter-reset:ol " + ol_start + ";");
| |
− |
| |
− | }
| |
− |
| |
− | })();
| |
− | </script>
| |
− | <li rel="1">AraC is always in large concentration</li>
| |
− | <li rel="2">AraC binding to arabinose occurs on a faster time scale to transcription</li>
| |
− | </ol>
| |
− |
| |
− | Therefore it is not necessary to consider individual concentrations of arabinose and AraC. We
| |
− | need only include the concentration of (Arab:AraC) complex in the model. The transcription rate
| |
− | constant K on the schematic diagram above is not a simple constant but described as a
| |
− | Michaelis-Mentin kinetics<a href="#fn:footnote4" id="fnref:footnote4" title="See footnote"
| |
− | class="footnote">2</a> equation below. <br>
| |
− | <span xmlns="http://www.w3.org/1999/xhtml" class="" rel="b718ab23c1be6a9bf2871313e4c69e7d"><span
| |
− | class="MathJax_SVG" id="MathJax-Element-70-Frame" role="textbox" aria-readonly="true"
| |
− | style="font-size: 100%; display: inline-block;"><span><img type="image/png"
| |
− | width="378.85"
| |
− | height="34.9875"
| |
− | longdesc="__SVG__undefined"
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"
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− | style="margin-top:0;margin-bottom:0;"></span></span></span>
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− | <br>
| |
− | Although pBAD system is known for rigidity<a href="#fn:footnote2" id="fnref:footnote2"
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− | title="See footnote" class="footnote">3</a>, we
| |
− | observed leaky expression in the experiments. So we add a basal translation level to describe
| |
− | leakiness. The basal expression level should be several orders of magnitude lower than the
| |
− | maximal level. <br>
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− | <span xmlns="http://www.w3.org/1999/xhtml" class="" rel="4134dfd69c8e208231d9bddaf3d96b5e"><span
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− | class="MathJax_SVG" id="MathJax-Element-71-Frame" role="textbox" aria-readonly="true"
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− | style="font-size: 100%; display: inline-block;"><span><img type="image/png"
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− | width="445.825"
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− | height="34.9875"
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− | longdesc="__SVG__undefined"
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"
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− | style="margin-top:0;margin-bottom:0;"></span></span></span>
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− | <br>
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| </div> | | </div> |
| </div> | | </div> |
− |
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| </section> | | </section> |
| <section id="Controller" class="mdl-components__page mdl-grid"> | | <section id="Controller" class="mdl-components__page mdl-grid"> |
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| <div class="mdl-card__supporting-text"> | | <div class="mdl-card__supporting-text"> |
− |
| |
− | <h1>Overview</h1>
| |
− | <br>
| |
− | <h2 id="pc0">Background</h2>
| |
− | In our design, after having designed the flip flop, the device can remember the information of
| |
− | its state, the next step is to transform the state into an actual function. To achieve this
| |
− | transformation, we first needed a “reader” to read out the current state. At this point the
| |
− | control unit comes into play. A control unit is a DNA sequence with recombinase sites whose
| |
− | expression is controlled by recom-binase and RDF by reversing or deleting a promoter and/or a
| |
− | terminator. To make the control unit reliable and predictable, we first need to be able to
| |
− | predict the behaviors of its “building blocks” (or “elements” in electrical engineering), from
| |
− | which we weave our engineer’s perspective into the biolog-ical system. However, we need to make
| |
− | some adaptations and adjustments to these “elements” to make them usable.
| |
− | <br><br>
| |
| | | |
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| <div class="mdl-card__supporting-text"> | | <div class="mdl-card__supporting-text"> |
| + | <h2 id="intention-of-the-model">Intention of the Model</h2> |
| + | We attempts to develop a framework of biological sequential circuits that are programmable. |
| + | The envisioned circuit is capable of both storing states in DNA and automatically running a |
| + | series of instructions in a specific order. According to our design, our bio-flip-flop has |
| + | two promoters, each triggered by an inducing signal. Therefore, if we would like to build an |
| + | automatic triggering system for the bio-flip-flop, we need at least two signals in our |
| + | clock. It is then self-evident to incorporate the classic structure in synthetic biology: |
| + | the repressilator.<br><br> This model serves as a proof of concept for such implementation. We |
| + | first |
| + | constructed an ordinary differential equation (ODE) system to describe the repressilator, |
| + | then we used two repressor proteins expressed by the repressilator to regulate the two |
| + | promoters. Finally we adjusted parameters and gave a simulation result as a proof of the |
| + | possibility of repressilator-driven bio-flip-flop. |
| | | |
− | <h1>Overview</h1> | + | |
− | <br>
| + | <br><br><h2>Biological Basis and Assumptions</h2> |
− | <h2 id="pc0">Background</h2>
| + | The |
− | In our design, after having designed the flip flop, the device can remember the information of | + | repressilator is a synthetic genetic regulatory network consisting of a ring-oscillator with |
− | its state, the next step is to transform the state into an actual function. To achieve this | + | three genes, each expressing a protein that represses the next gene in the loop.[^Footnote1] |
− | transformation, we first needed a “reader” to read out the current state. At this point the | + | This network was designed from scratch to exhibit a stable oscillation which is reported via |
− | control unit comes into play. A control unit is a DNA sequence with recombinase sites whose | + | the expression of green fluorescent protein, and hence acts like an electrical oscillator |
− | expression is controlled by recom-binase and RDF by reversing or deleting a promoter and/or a | + | system with fixed time periods. The repressilator consists of three genes connected in a |
− | terminator. To make the control unit reliable and predictable, we first need to be able to | + | feedback loop, such that each gene represses the next gene in the loop, and is repressed by |
− | predict the behaviors of its “building blocks” (or “elements” in electrical engineering), from | + | the previous gene.<br><br> |
− | which we weave our engineer’s perspective into the biolog-ical system. However, we need to make | + | <div align="center"><img src="https://static.igem.org/mediawiki/2017/8/80/Peking_modeling_fig_1.png" height="130px"/><br> |
− | some adaptations and adjustments to these “elements” to make them usable. | + | <strong>Fig.1. The genetic structure of the repressilator network</strong></div> |
| <br><br> | | <br><br> |
| + | We decided to implement our repressilator-triggered bio-flip-flop with two repressor proteins |
| + | regulating the two promoters’ transcription. The basis of ODE system construction is |
| + | illustrated as follows:<br><br> |
| + | |
| + | <div align="center"><img src="https://static.igem.org/mediawiki/2017/4/4a/Peking_modeling_fig_2.png" height="300px"/><br> |
| + | <strong>Fig.2. Schematic |
| + | drawing of the repressilator-driven bio-flip-flop </strong></div><br><br> |
| + | The upper promoter (X) is <span |
| + | class="math inline">\(P_{LtetO}\)</span> and is repressed by tetR protein. The lower |
| + | promoter (Y) is <span class="math inline">\(P_{R}\)</span> and is repressed by cI |
| + | protein.Simulation of bio-flip-flop starts at a later time than repressilator because the |
| + | expression levels of the repressor proteins at the beginning is not high enough. |
| + | |
| + | <br><br><h2 id="equations-and-parameters">Equations and Parameters</h2> |
| + | <h3 id="repressilator">Repressilator</h3> |
| + | The following table lists the reactions in the repressilator network. X, Y, Z represent LacI, |
| + | TetR and cI mRNAs, and PX, PY, PZ represent the corresponding proteins.<br><br> |
| + | |
| + | <div align="center"><img src="https://static.igem.org/mediawiki/2017/9/95/Peking_modelling_clock_table1.png" height="500px"/> |
| + | </div><br><br> |
| + | |
| + | |
| + | |
| + | |
| + | |
| + | Calculation of degradation rates are described as follows: <span class="math display">\[ |
| + | k_{dmRNA} = \frac{ln(2)}{\tau_{mRNA}} |
| + | \]</span> <span class="math display">\[ |
| + | k_{dprot} = \frac{ln(2)}{\tau_{protein}} |
| + | \]</span> <span class="math inline">\(\tau_{mRNA}\)</span> and <span class="math inline">\(\tau_{protein}\)</span> are |
| + | half lives of mRNA and protein. Calculation of maximum transcription rate: <span |
| + | class="math display">\[ |
| + | a_{tr} = 60(ps_a - ps_0) |
| + | \]</span> <span class="math inline">\(ps_a\)</span> is “tps active” and <span class="math inline">\(ps_0\)</span> is |
| + | “tps_repressive”. Calculation of translation rate: <span class="math display">\[ |
| + | k_{tl} = \frac{eff}{t_{ave}} |
| + | \]</span> <span class="math inline">\(eff\)</span> is translation efficiency and <span |
| + | class="math inline">\(t_{ave}\)</span> is average mRNA life time. <span |
| + | class="math inline">\(t_{ave} = \frac{\tau_{mRNA}}{ln(2)}\)</span><br><br> |
| + | |
| + | <h3>Transcription in bio-flip-flop</h3> The transcription kinetics in the bio-flip-flop were |
| + | modified to be repressed by repressors. These can be described by the following |
| + | equations: |
| + | |
| + | <br><br> |
| + | |
| + | <div align="center"><img src="https://static.igem.org/mediawiki/2017/9/95/Peking_modelling_clock_table2.png" height="100px"/> |
| + | </div><br><br> |
| + | |
| + | |
| + | <h2 id="simulation-results">Simulation Results</h2> |
| + | We conducted our simulation using Tellurium[^Footnote3], a Python-based simulation platform. |
| + | We first adjusted the parameters protein half life and mRNA half life (equivalently |
| + | transcription and translation of repressor proteins) to adjust oscillation period as the one |
| + | observed in the experiment. (此处链接到clock实验)<br><br> |
| + | |
| + | <div align="center"><img src="https://static.igem.org/mediawiki/2017/6/66/Peking_modeling_repressilator.png" height="400px"/> |
| + | <br><strong>Fig.1. Repressilator simulation results of tetR and cI protein</strong></div> |
| + | <br><br> |
| + | Then we incorporate the bio-flip-flop into the model, and we got the following simulation |
| + | results: <br><br> |
| + | |
| + | <div align="center"><img src="https://static.igem.org/mediawiki/2017/7/73/Peking_modeling_whole_rep_ff.png" height="400px"/> |
| + | <br><strong>Fig.2. Repressilator-driven |
| + | frequency divider simulation with two trigger signal groups</strong><br>X_F and Y_F have the same |
| + | meaning as those described in Recombinase section. (此处有超链接到第一个model子页面)</div> |
| + | <br><br> |
| + | |
| + | |
| + | |
| + | In this simulation |
| + | experiment, the flip-flop lost approximately 10% of its initial state after two trigger |
| + | signal groups. |
| | | |
| | | |
Line 540: |
Line 457: |
| </div> | | </div> |
| </section> | | </section> |
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| |
| | | |
| </div> | | </div> |