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<li><a href="#topic1">Compartment Model for Muscone Inhalation</a></li>
<li><a href="#topic2">Topic2</a></li>
<li><a href="#topic3">ODE of MAPK pathway</a></li>
<li><a href="#topic4">Topic4</a></li>
<li><a href="#topic4">Lactic Acid Absorption Model</a></li>
</ul>
</div>
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<div class="col-lg-12">
<h2 id="topic3">
<h2>Ordinary Differential Equation of the signal transduction of the yeast MAPK pathway</h2>
<hr>
<h3>Model Description</h3>
<p>In our project, we express the muscone receptor (GPCR) on the yeast cell membrane. After a
certain concentration of muscone diffuses into the intestine and binds to the receptor, it
......@@ -971,28 +971,82 @@
<div class="row mt-4">
<div class="col-lg-12">
<h2 id="topic4">
<h2>Topic4</h2>
<h2>Lactic Acid Absorption Model</h2>
<hr>
<p>Tsinghua University is consistently ranked among the top universities in the Asia-Pacific according
to major international university rankings. Tsinghua University ranked No. 1 in China, the whole of
Asia-Oceania region and emerging countries according to the Times Higher Education, with its
industry income, research, and teaching performance indicator placed at 1st, 4th and 9th
respectively in the world. Internationally, Tsinghua was regarded as the most reputable Chinese
university by the Times Higher Education World Reputation Rankings where, it has ranked 8th globally
and 1st in the Asia-Pacific.</p>
<p>The Engineering Research Center for Navigation Technology is a relatively young institute in the
Department of Precision Instrument which was established in 2000, with the intention to "[pursue]
excellence in the research and development in the field of high-accuracy inertial instruments and
navigation technology, as well as in MEMS inertial sensor fields, and to provide advanced training
for future scientists and engineers in the field of inertial technology." Its research interests
cover high-accuracy inertial instruments and navigation technology, MEMS inertial sensors and
systems, and precise electro-mechanical control systems and their application. As of 2012, the area
of the center is 2900 square meters, including approximately 550 square meters of clean rooms.
Equipment and instruments in this center are worth over 50 million RMB (US$7.56 million).</p>
</div>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/figure/ibd-figure.jpg" alt="ibd_figure"
class="shadowed-image">
<h3>Model Description</h3>
<p>
Our project alleviates IBD symptoms by secreting lactic acid in the intestine to weaken
autoimmunity, but it may face two aspects of doubt: first, why can't lactic acid or lactic acid
bacteria probiotics be taken directly; second, will the considerable secretion of lactic acid cause
acidosis in the human body? We hope to model our project to describe how it has a better sustained
release effect compared to direct lactic acid consumption, more precise control compared to
probiotic intake, and to avoid adaptation of the immune system and gut microbiota. Additionally, we
need to develop a computational method to achieve precise control over lactic acid secretion to
regulate treatment time and prevent acidosis.
</p>
<h3>Basic Assumptions</h3>
<ol>
<li>Only the absorption process of lactic acid is described, without considering other effects of
lactic acid on the human body.</li>
<li>It is assumed that the location where lactic acid acts on immune cells is separated from the
intestinal environment.</li>
<li>It is assumed that the secretion rate of lactic acid is uniform, and activated yeast cells
secrete a total amount of lactic acid \(a\) within time \(t_0\), secreting \(\frac{a}{n}\) of
lactic acid in the time interval \(\frac{t_0}{n}\).</li>
</ol>
<h3>Model Equation</h3>
<h4>Direct Administration</h4>
<p>
In the case of direct lactic acid intake, the content of lactic acid in the intestine can be
described by the following equation:
</p>
<pre>
Qd=(Qd_0+a)e^{-(k_1+k_2)t}
</pre>
<strong>Explanation</strong>: The absorption rate is proportional to the concentration of lactic acid,
and the concentration of lactic acid declines in an exponential form.
<strong>Parameters</strong>:
<ul>
<li><em>Qd</em>: Remaining lactic acid content in the intestinal environment</li>
<li><em>Qd_0</em>: Initial lactic acid content in the intestinal environment</li>
<li><em>a</em>: Total amount of lactic acid ingested</li>
<li><em>k_1</em>: Absorption rate of lactic acid</li>
<li><em>k_2</em>: Rate at which lactic acid is eliminated due to metabolism and excretion</li>
<li><em>t</em>: Time</li>
</ul>
<h4>Induced Secretion</h4>
<p>
According to Fick's Law
</p>
<pre>
%
</pre>
<p>
The remaining lactic acid content in the intestinal environment has a recursive relationship over
time:
</p>
<pre>
Qd_i=(Qd_{i-1}+\frac{a}{n})e^{-(k_1+k_2)(t-(i-1)\frac{t_0}{n})}
</pre>
<p>
We can obtain the expression:
</p>
<pre>
Qd_i=\frac{a}{n}\sum_{m=1}^{i-1}e^{-(k_1+k_2)(mt-(j\frac{(m+2)(m+1)}{2}\frac{t_0}{n}))}
</pre>
<p>
TODO: Insert result graph
</p>
<p>
By simulating the absorption process of lactic acid, we can conclude that in the case of direct
administration, the concentration of lactic acid decreases exponentially over time, while in the
case of induced secretion, the concentration of lactic acid slowly increases over time and reaches
equilibrium after a certain period.
</p>
</div>
</div>
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