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{% extends "layout.html" %}
{% block title %}Model{% endblock %}
{% block page_content %}
<div class="sidebar">
<ul>
<li><a href="#description">Description</a></li>
<li><a href="#topic1">Inhalation</a></li>
<li><a href="#topic2">Binding</a></li>
<li><a href="#topic3">Secretion</a></li>
<li><a href="#topic4">Absorption</a></li>
</ul>
</div>
<div class="progress-container">
<svg class="progress-bar-circle" width="60" height="60">
<circle class="progress-circle" cx="30" cy="30" r="25" stroke-width="5" fill="transparent"></circle>
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<div class="progress-text">0%</div>
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<div class="row mt-4">
<div class="col-lg-12">
<h2 id="description">General Description of Modeling</h2>
<hr>
<p>Our model serves two main purposes:</p>
<ol>
<li><strong>Quantitative Description of Project Design</strong>: Due to safety considerations, we were
unable to conduct animal experiments to demonstrate the processes occurring during the operation of
the project. Modeling can help in understanding therapeutic pathways, provide a quantitative
perspective, and tell our story better.</li>
<li><strong>Computational Methods for Project Engineering</strong>: If the project can be carried out,
the model can help determine the parameters in the implementation process of the project, reduce the
calculation amount in the experimental process, connect the wet experimental independent system
, and make the design mathematically encapsulated as new components.</li>
</ol>
<p>Our model can be divided into four interconnected parts, representing the inhalation of muscone, its
binding
to receptors, intracellular signal transduction and lactate secretion triggered by receptor
activation, and the absorption of lactate. These models provide a comprehensive understanding of the
project and yield valuable computational results.</p>
</div>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/figure/ibd-figure.jpg" alt="ibd_figure"
class="shadowed-image">
</div>
</div>
<div class="row mt-4">
<div class="col-lg-12">
<h2 id="topic1">
<h2>Compartment Model for Muscone Inhalation</h2>
<hr>
<h3>Model Description</h3>
<p>The main focus of our project is the use of muscone as a signaling molecule to activate engineered
yeast in the gut for therapeutic purposes. Therefore, it is crucial to provide a quantitative
description and computational support for the diffusion of muscone in the body. This model describes
the entire process from the inhalation of muscone to its increased concentration in the intestinal
tract. We will establish a multi-compartment model that includes the following main processes:</p>
<ol>
<li><strong>Inhalation Process</strong>: Muscone is inhaled in the form of an aerosol into the
lungs.</li>
<li><strong>Pulmonary Process</strong>: Muscone distributes in the alveoli and may be exhaled,
adhered to, or permeated into the microvessels.</li>
<li><strong>Adhesion Process</strong>: A portion of muscone adheres to the respiratory mucosa and
then diffuses into the systemic circulation.</li>
<li><strong>Alveolar Microvessel Process</strong>: Muscone permeates into the alveolar microvessels
and gradually enters the systemic circulation.</li>
<li><strong>Systemic Circulation Process</strong>: Muscone distributes in the systemic circulation
and is transported to various parts of the body through the bloodstream.</li>
<li><strong>Intestinal Process</strong>: Muscone enters the target intestine through the mesenteric
microvascular network, where its concentration begins to increase.</li>
</ol>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/1-1.png" alt="Inhalation-1"
class="shadowed-image" style="width: 100%; max-width: 1000px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 2 Processes in the Inhalation
Model</p>
<p>Corresponding to the above processes, five compartments need to be established for simulation, where
\(t\) represents the time variable:</p>
<li><strong>Compartment 0</strong> (Alveolar Space, \(A\)): \(Q_A(t)\) represents the amount of
muscone
in the alveoli (\(\text {mg}\)).</li>
<li><strong>Compartment 1</strong> (Respiratory Mucosa, \(M\)): \(Q_M(t)\) represents the amount of
muscone adhered to the respiratory mucosa (\(\text {mg}\)).</li>
<li><strong>Compartment 2</strong> (Alveolar Capillaries, \(L\)): \(Q_L(t)\) represents the amount of
muscone in the alveolar capillaries (\(\text{mg}\)).</li>
<li><strong>Compartment 3</strong> (Systemic Circulation, \(C\)): \(Q_C(t)\) represents the amount of
muscone in the systemic circulation(\(\text{mg}\)).</li>
<li><strong>Compartment 4</strong> (Target Intestine, \(I\)): \(Q_I(t)\) represents the amount of
muscone in the intestine(\(\text{mg}\)).</li>
<p></p>
<h3>Initial Settings and Assumptions</h3>
<p>At \(t=0\), the amount of muscone in all compartments is \(0\).</p>
<p>Assuming that the total amount of inhaled muscone is \(Q_{\text{inhale}}\) (\(\text{mg}\)), which is
assumed to be \(100\text{mg}\). Only \(0.5\%\) of muscone enters the systemic circulation through
adhesion. In this model, since muscone only acts as a signaling molecule to activate yeast to
synthesize lactate, we only consider the metabolism and excretion of muscone in the systemic
circulation. We only focus on the short-term process of muscone appearing in the intestine from
scratch, and the subsequent process of reaching a certain concentration can be ignored.</p>
<h3>Model Equations</h3>
<h4>Inhalation Equation for Muscone</h4>
<p>
\[ V_{\text{inhale}}(t) =\frac{Q_{\text{inhale}}}{5}(u(t)-u(t-5)) \]
</p>
<p><strong>Explanation</strong>: This describes the rate equation for inhaling muscone over five
seconds,
where the total amount \( Q \) remains constant. The function \( u(t) \) is a step function, which
takes the value of \( \frac{Q_{\text{inhale}}}{5} \) from \( t=0s \) to \( t=5s \), and is \( 0 \)
otherwise, simulating the scenario of resting human respiration.</p>
<h4>Compartment 0: \( Q_A(t) \)</h4>
<p>
\[ \frac{dQ_A(t)}{dt} = V_{\text{inhale}}(t) - \left( k_{\text{exhale}} + k_{\text{perm}} \right)
Q_A(t) \]
</p>
<p><strong>Explanation</strong>: The amount of muscone in the alveoli increases through inhalation and
decreases due to exhalation, adhesion to the respiratory mucosa, and permeation into the alveolar
capillaries.</p>
<p><strong>Parameters</strong>:</p>
<ul>
<li>
\( k_{\text{exhale}} \): Since most of the muscone is rapidly exhaled, this value is relatively
large, taken as \( 10 \ \text{min}^{-1} \)
</li>
<li>
\( k_{\text{perm}} \): The rate of muscone permeation into the capillaries, affected by its
physicochemical properties, is taken as \( 0.005 \ \text{min}^{-1} \)
</li>
</ul>
<h4>Compartment 1: \( Q_M(t) \)</h4>
<p>
\[ \frac{dQ_M(t)}{dt} = 0.0005 \cdot k_{\text{adh}} V_{\text{inhale}}(t) - k_{\text{diffMC}} Q_M(t)
\]
</p>
<p><strong>Explanation</strong>: The increase in muscone on the mucosa comes from adhesion in the
alveoli, and the decrease is due to diffusion into the systemic circulation.</p>
<p><strong>Parameters</strong>:</p>
<ul>
<li>
\( k_{\text{adh}} \): The adhesion process is relatively slow, and only \( 0.5\% \) of muscone
enters the systemic circulation through this pathway, taken as \( 0.001 \ \text{min}^{-1} \)
</li>
<li>
\( k_{\text{diffMC}} \): Diffusion from the mucosa to the systemic circulation is slow, taken as
\( 0.01 \ \text{min}^{-1} \)
</li>
</ul>
<h4>Compartment 2: \( Q_L(t) \)</h4>
<p>
\[ \frac{dQ_L(t)}{dt} = k_{\text{perm}} Q_A(t) - k_{\text{diffLC}} Q_L(t) \]
</p>
<p><strong>Explanation</strong>: The increase in muscone in the alveolar capillaries comes from
permeation in the alveoli, and the decrease is due to diffusion into the systemic circulation.</p>
<p><strong>Parameters</strong>:</p>
<ul>
<li>
\( k_{\text{perm}} \): Same as Compartment 0
</li>
<li>
\( k_{\text{diffLC}} \): The diffusion rate from alveolar capillaries to the systemic
circulation is relatively slow, taken as \( 0.05 \ \text{min}^{-1} \)
</li>
</ul>
<h4>Compartment 3: \( Q_C(t) \)</h4>
<p>
\[ \frac{dQ_C(t)}{dt} = k_{\text{diffMC}} Q_M(t) + k_{\text{diffLC}} Q_L(t) - k_{\text{dist}}
Q_C(t) - k_{\text{excrete}} Q_C(t) \]
</p>
<p><strong>Explanation</strong>: The increase in muscone in the systemic circulation comes from the
input of mucosa and alveolar capillaries, and the decrease is due to distribution to the intestinal
mesenteric microvascular network and excretion through various routes.</p>
<p><strong>Parameters</strong>:</p>
<ul>
<li>
\( k_{\text{diffMC}} \): Same as Compartment 1
</li>
<li>
\( k_{\text{diffLC}} \): Same as Compartment 2
</li>
<li>
\( k_{\text{dist}} \): The rate constant of muscone distribution from the systemic circulation
to the intestinal mesenteric microvascular network, taken as \( 0.001 \ \text{min}^{-1} \)
</li>
<li>
\( k_{\text{excrete}} \): Muscone is excreted from the systemic circulation through epidermal
volatilization, urine, continuous respiration, etc., taken as \( 0.05 \ \text{min}^{-1} \)
</li>
</ul>
<h4>Compartment 4: \( Q_I(t) \)</h4>
<p>
\[ \frac{dQ_I(t)}{dt} = k_{\text{dist}} Q_C(t) - k_{move}Q_I(t) \]
</p>
<p><strong>Explanation</strong>: The increase in muscone in the intestine comes from the distribution of
the systemic circulation, and the decrease is due to metabolism and excretion through intestinal
fluid and peristalsis.</p>
<p>
\( k_{\text{dist}} \): Same as Compartment 3<br>
\( k_{move} \): The metabolism and excretion of muscone in the intestine, taken as \( 0.02 \
\text{min}^{-1} \)
</p>
<h3>System of Equations:</h3>
<p>In summary, we can write a system of ordinary differential equations and import it into MATLAB for
simulation:</p>
<p>
\[
\begin{align*}
Q_{\text{inhale}}(t) & = 100(mg)(Assumption) \\
V_{\text{inhale}}(t) & =\frac{Q_{\text{inhale}}}{5}(u(t)-u(t-5)) \\
\frac{dQ_A(t)}{dt} & = V_{\text{inhale}}(t) -\left( k_{\text{exhale}} + k_{\text{perm}} \right)
Q_A(t) \\
\frac{dQ_L(t)}{dt} & = k_{\text{perm}} Q_A(t) - k_{\text{diffLC}} Q_L(t) \\
\frac{dQ_M(t)}{dt} & = 0.0005\cdot k_{\text{adh}} V_{\text{inhale}}(t) - k_{\text{diffMC}} Q_M(t) \\
\frac{dQ_C(t)}{dt} & = k_{\text{diffMC}} Q_M(t) + k_{\text{diffLC}} Q_L(t) - k_{\text{dist}} Q_C(t)
-
k_{\text{excrete}} Q_C(t) \\
\frac{dQ_I(t)}{dt} & = k_{\text{dist}} Q_C(t)-k_{move}Q_I(t) \\
\end{align*}
\]
</p>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/1-2.png" alt="Inhalation-2"
class="shadowed-image" style="width: 100%; max-width: 1000px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 3 Stimulation Result of the
Muscone Inhalation Model</p>
<p>We simulated the distribution of muscone in the systemic circulation and obtained the concentration
change curve of muscone in the systemic circulation. According to the model, after one breath,
traces of muscone can spread into the intestine, similarly, the concentration change caused by
continuous muscone is simulated by changing the inhalation equation, and the concentration of
muscone in the intestine can be obtained in combination with experiment. Because
there is no animal experimental support, the data are manually drafted, and the calculation method
is more meaningful than the calculation results.</p>
<button id="Button1" onclick="toggleCodeSnippet1()">Inhalation.m</button>
<div id="codeSnippet1" class="code-snippet">% Define parameters
Q_inhale = 100; % mg
k_exhale = 10;
k_perm = 0.005;
k_adh = 0.001;
k_diffMC = 0.01;
k_diffLC = 0.05;
k_dist = 0.001;
k_excrete = 0.05;
k_move = 0.02;
% Define the time range
tspan = [0 300]; % From 0 to 5 minutes
initial_conditions = [0 0 0 0 0]; % The initial condition is 0
% solve ODE
[t, y] = ode45(@(t,y) odefun(t, y, Q_inhale, k_exhale, k_perm, k_adh, k_diffMC, k_diffLC, k_dist,
k_excrete, k_move), tspan, initial_conditions);
% calculate V_inhale
V_inhale = Q_inhale / 5 * (heaviside(t) - heaviside(t-5));
figure('Position', [100, 100, 1200, 1000]);
% V_inhale(t)
subplot(3,2,1)
plot(t, V_inhale)
title('V_{inhale}(t)')
xlabel('Time (s)')
ylabel('V_{inhale}')
% Q_A(t)
subplot(3,2,2)
plot(t, y(:,1))
title('Q_A(t)')
xlabel('Time (s)')
ylabel('Q_A')
% Q_L(t)
subplot(3,2,3)
plot(t, y(:,2))
title('Q_L(t)')
xlabel('Time (s)')
ylabel('Q_L')
% Q_M(t)
subplot(3,2,4)
plot(t, y(:,3))
title('Q_M(t)')
xlabel('Time (s)')
ylabel('Q_M')
% Q_C(t)
subplot(3,2,5)
plot(t, y(:,4))
title('Q_C(t)')
xlabel('Time (s)')
ylabel('Q_C')
% Q_I(t)
subplot(3,2,6)
plot(t, y(:,5))
title('Q_I(t)')
xlabel('Time (s)')
ylabel('Q_I')
sgtitle('Simulation Results')
% ODE
function dydt = odefun(t, y, Q_inhale, k_exhale, k_perm, k_adh, k_diffMC, k_diffLC, k_dist,
k_excrete, k_move)
V_inhale = Q_inhale / 5 * (heaviside(t) - heaviside(t-5));
dydt = zeros(5,1);
dydt(1) = V_inhale - (k_exhale + k_perm) * y(1); % dQ_A/dt
dydt(2) = k_perm * y(1) - k_diffLC * y(2); % dQ_L/dt
dydt(3) = 0.0005 * k_adh * V_inhale - k_diffMC * y(3); % dQ_M/dt
dydt(4) = k_diffMC * y(3) + k_diffLC * y(2) - k_dist * y(4) - k_excrete * y(4); % dQ_C/dt
dydt(5) = k_dist * y(4) - k_move * y(5); % dQ_I/dt
end</div>
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</div>
<div class="row mt-4">
<div class="col-lg-12">
<h2 id="topic2">
<h2>Molecular Dynamics Simulations of Muscone with its Receptor</h2>
<hr>
<p>One of the major contributions of our project was the development of a signaling pathway activated by
gas molecules acting as switches, so we were interested in the behavior of the muscone when bound to
its receptor. Molecular dynamics simulations can help us to visualize the binding process, track the
parameters of structural changes, protein folding, and receptor-ligand interactions, and demonstrate
their biological significance.</p>
<h3>1. Molecular Model Construction and Preparation</h3>
<ul>
<li>Before conducting molecular dynamics simulations, it is essential to accurately construct and
prepare the three-dimensional molecular model of the research object. In this study, our goal is
to simulate the interaction between muscone and the olfactory receptor Or5an6 (MOR215-1).</li>
</ul>
<h4>1. Constructing the Three-Dimensional Structures of Muscone and the Receptor:</h4>
<ul>
<li><strong>Muscone</strong>:</li>
<ul>
<li>Obtain the molecular structure information of muscone from the PubChem database. PubChem is
a widely used chemical information database that provides data on molecular structures,
chemical properties, and biological activities.</li>
<li>Molecular structure obtained from PubChem <a
href="https://pubchem.ncbi.nlm.nih.gov/compound/10947">link</a></li>
</ul>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/3-methylcyclopentadecanone.png"
alt="Muscone" class="shadowed-image" style="width: 50%; max-width: 500px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 4 The structural formula of
the Muscone</p>
<ul>
<li>Next, use the chemical modeling tool Avogadro to convert this structure into a PDB format
file (<code>muscone.pdb</code>) for further simulation and analysis. This step ensures that
the three-dimensional geometric structure of muscone is accurate and suitable for subsequent
molecular docking and dynamics simulations.</li>
<li>Avogadro converts to pdb format <code>muscone.pdb</code></li>
</ul>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/muscone.png" alt="Muscone"
class="shadowed-image" style="width: 50%; max-width: 500px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 5 The 3D geometry of Muscone
</p>
</ul>
<ul>
<li><strong>Receptor Or5an6 (MOR215-1)</strong>:
<ul>
<li>Retrieve the nucleic acid sequence of the MOR215-1 gene from the NCBI database and find
its protein sequence information. With support from Uniprot, further obtain the amino
acid sequence of this protein, which is an important component for subsequent docking
simulations. In addition, obtain the three-dimensional structural model of the Or5an6
receptor (<code>MOR215-1.pdb</code>) from the AlphaFold database, whose model quality is
widely recognized, especially in the field of protein structure prediction.</li>
<li>Nucleic acid sequence information in NCBI <a
href="https://www.ncbi.nlm.nih.gov/gene/258679">link</a></li>
<button id="Button2" onclick="toggleCodeSnippet2()">DNA sequence of Or5an6</button>
<div id="codeSnippet2" class="code-snippet">>NC_000085.7:12371629-12372576 Mus musculus strain C57BL/6J chromosome 19, GRCm39
ATGCCTGGAGGGAGGAATAGCACAGTCATCACCAAGTTCATCCTTGTGGGATTCTCAGATTTTCCAAAGC
TCAAGCTGGTTCTCTTTGTTATCTTCCTGGGAAGTTATCTCTCCACAGTGGTGTGGAACTTGGGCCTCAT
CATCTTGATTAGGATTGACCCTTACCTACACACACCTATGTACTTCTTCCTCAGCAATTTGTCATTTTTA
GATTTCTGTTACATTTCATCTACAACCCCTAAAATGCTCTCGGGATTCTTCCAGAAGTCTAAATCTATCT
CCTTTGTTGGGTGCACCATGCAGTACTTCATCTTCTCAAGCCTGGGTCTGTCCGAATGCTGCCTTCTGGC
AGCCATGGCTTATGACCGGTATGCTGCCATTTGTAATCCTCTTCTCTACACAGCCATCATGTCCCCGTCA
CTCTGTGTGCACATGGTGGTTGGAGCCTATAGTACTGGTCTCTTGGGTTCATTGATTCAACTGTGTGCTA
TACTTCAGCTCCATTTCTGTGGGCCAAATATTATAAACCATTTCTTTTGTGACCTGCCTCAGCTATTAGT
TCTTTCCTGCTCTGAAACCTTTCCCCTGCAAGTCTTGAAATTTGTAATAGCAGTGATTTTTGGGGTGGCA
TCTGTCATTGTTATCCTGATATCCTATGGTTATATCATTGGCACAATCCTGAATATCAGCTCAGTAGAAG
GTAGGTCCAAGGCATTCAATACCTGTGCCTCTCACCTGACAGCAGTCACCCTCTTTTTTGGATCAGGACT
CTTTGTCTATATGCGCCCCAGCTCCAACAGTTCCCAGGGTTATGACAAGATGGCTTCCGTGTTCTATACA
GTGGTGATTCCCATGTTGAATCCTCTGATTTATAGTCTCAGGAACAAGGAAATAAAAGATGCTCTTCAGA
GATGTAAAAATAAGTGCTTTTCTCAGTGCCACTGTTAG</div>
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<li>Protein sequence information in Uniprot <a
href="https://www.uniprot.org/uniprotkb/Q8VFV4/entry#sequences">link</a></li>
<button id="Button3" onclick="toggleCodeSnippet3()">Protein sequence of Or5an6</button>
<div id="codeSnippet3" class="code-snippet">>sp|Q8VFV4|O5AN6_MOUSE Olfactory receptor 5AN6 OS=Mus musculus OX=10090 GN=Or5an6
PE=2 SV=1
MPGGRNSTVITKFILVGFSDFPKLKLVLFVIFLGSYLSTVVWNLGLIILIRIDPYLHTPM
YFFLSNLSFLDFCYISSTTPKMLSGFFQKSKSISFVGCTMQYFIFSSLGLSECCLLAAMA
YDRYAAICNPLLYTAIMSPSLCVHMVVGAYSTGLLGSLIQLCAILQLHFCGPNIINHFFC
DLPQLLVLSCSETFPLQVLKFVIAVIFGVASVIVILISYGYIIGTILNISSVEGRSKAFN
TCASHLTAVTLFFGSGLFVYMRPSSNSSQGYDKMASVFYTVVIPMLNPLIYSLRNKEIKD
ALQRCKNKCFSQCHC</div>
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<li>Protein structure information in the AlphaFold database <a
href="https://alphafold.ebi.ac.uk/entry/Q8VFV4">link</a> <code>MOR215-1.pdb</code>
</li>
</ul>
</li>
</ul>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/or5an6.png"
alt="AF-Q8VFV4-F1-model_v4.pdb" class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 6 Protein structure of MOR215-1
</p>
<h4>2. System Preparation:</h4>
<ul>
<li>To study how muscone binds to the receptor, molecular docking tools such as AutoDock and Vina
are used to determine potential binding conformations and obtain docking data:
<ul>
<li>Mac software installation: AutoDock, Vina, XQuartz, MGLTools,</li>
<li>The 32-bit version of MGLTools cannot be used directly on Mac, but can be opened using
<code>open /Users/Shared/MGLTools/1.5.7/bin/adt</code>
</li>
<li><a href="https://mp.weixin.qq.com/s/yDN5DCvEnQdPGEPXL4NAwA">AutoDock</a> generates PDBQD
files: <code>MOR215_1.pdbqt</code> and <code>muscone.pdbqt</code>
<ul>
<li>In the same directory: <code>adt</code>, <code>autodock4</code>,
<code>autogrid4</code>, <code>vina</code>
</li>
</ul>
</li>
<li><a href="https://mp.weixin.qq.com/s/R8V7Hvag2OqTn4tLz3hGhg">Vina</a> configures the
docking parameter file <code>config.txt</code> in the same directory as follows (based
on actual coordinates), runs the docking simulation, and generates the file
<code>muscure.pdbqt</code>. This file records the possible binding modes of muscone with
the receptor at the defined coordinate position and dimensions
(<code>size_x, size_y, size_z</code>).
<button id="Button4" onclick="toggleCodeSnippet4()">config.txt</button>
<div id="codeSnippet4" class="code-snippet">receptor = MOR215_1.pdbqt
ligand = muscone.pdbqt
center_x = -0.112
center_y = -0.219
center_z = -2.092
size_x = 40
size_y = 40
size_z = 40
exhaustiveness= 8
out=muscure.pdbqt</div>
<script>
function toggleCodeSnippet4() {
var codeSnippet = document.getElementById("codeSnippet4");
var button = document.getElementById("Button4"); // 注意变量名通常使用小写开头
if (codeSnippet.style.display === "none") {
codeSnippet.style.display = "block";
button.textContent = "Collapse the code"; // 使用之前选中的按钮元素
} else {
codeSnippet.style.display = "none";
button.textContent = "Expand the code"; // 使用之前选中的按钮元素
}
}
</script>
<pre><code>./vina --config config.txt</code></pre>
Obtain <code>muscure.pdbqt</code>
</li>
</ul>
</li>
</ul>
<ul>
<li><strong>Visualization Structure Optimization and Inspection</strong>:
<ul>
<li>Use <a href="https://mp.weixin.qq.com/s/jPu-_iSX0h94Yxu3PO65zA">Pymol</a> to analyze the
generated docking structures, identify potential binding conformations, especially
focusing on interactions at amino acids Arg-51 and Tyr-271, and determine stable low
free energy conformations. Then extract this conformation as separate PDB files,
isolating <code>MOR.pdb</code> and <code>MUS.pdb</code>.
<ul>
<li>Open <code>muscure.pdbqt</code> and <code>MOR215-1.pdb</code></li>
<li>Select the appropriate conformation, display interactions
<code>Action - find - polar contacts - to any atoms</code>
</li>
<li>Add <code>Label</code>, export the image</li>
</ul>
</li>
<li>Alternative Conformations
<ul>
<li>Arg-51
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/dock1.png"
alt="Arg-51" class="shadowed-image"
style="width: 100%; max-width: 1000px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 7
Alternative Conformation with Arg-51</p>
</li>
<li>Tyr-271
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/dock2.png"
alt="Tyr-271" class="shadowed-image"
style="width: 100%; max-width: 1000px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 8
Alternative Conformation with Tyr-271</p>
</li>
<li>Select conformations with low free energy that are more likely, extract in pdb
format, isolating <code>MOR.pdb</code> and <code>MUS.pdb</code></li>
</ul>
</li>
</ul>
</li>
</ul>
<h3>2. Force field parameterization</h3>
<h4>1. Select Force Field:</h4>
<ul>
<li>To perform molecular dynamics simulations, it is necessary to choose an appropriate molecular
force field to describe the interactions between molecules within the system. CHARMM36 was
selected as the force field for protein and small molecule (musk ketone) interactions. However,
due to the absence of direct parameters for musk ketone in existing force fields, custom
parameters need to be generated to supplement it.</li>
</ul>
<h4>2. Generate Force Field Parameters:</h4>
<ul>
<li>Use Avogadro to convert to <code>.mol2</code> format, adjust file information, and then use the
software <a href="https://cgenff.com/">CGenFF</a> to generate its CHARMM36 force field parameter
file <code>MUS_fix.mol2</code> and parameter file <code>MUS.str</code>. This step includes
calculating the sorting of the chemical information file (<code>sort_mol2_bonds.pl</code>) to
ensure file correctness.</li>
</ul>
<pre><code>perl sort_mol2_bonds.pl MUS.mol2 MUS_fix.mol2</code></pre>
<h3>3. Preprocessing</h3>
<h4>1. Build the system:</h4>
<ul>
<li>Generate the topology file <code>MOR_processed.gro</code> for the receptor using GROMACS's
<code>pdb2gmx</code> command.
</li>
<pre><code>gmx pdb2gmx -f MOR.pdb -o MOR_processed.gro -ter</code></pre>
<li>Convert the force field parameters of muscone to a format recognizable by GROMACS to generate
its topology data using the CGenFF helper script.</li>
<pre><code>python cgenff_charmm2gmx_py3_nx2.py MUS MUS_fix.mol2 MUS.str charmm36-jul2022.ff</code></pre>
</ul>
<h4>2. Merge the system:</h4>
<ul>
<li>Prepare the complete solvent system required for simulations using the <code>editconf</code> and
<code>solvate</code> commands, merging the topology files of muscone <code>mus.gro</code> and
receptor <code>MOR_processed.gro</code> into a single system <code>complex.gro</code>.
</li>
<pre><code>gmx editconf -f mus_ini.pdb -o mus.gro
gmx editconf -f complex.gro -o newbox.gro -bt dodecahedron -d 1.0</code></pre>
<li>Solvate the system in solvent (such as water). From <code>topol.top</code>, it is known that the
net charge is 9; add counterions to neutralize the system.</li>
<pre><code>gmx editconf -f complex.gro -o newbox.gro -bt dodecahedron -d 1.0
gmx solvate -cp newbox.gro -cs spc216.gro -p topol.top -o solv.gro
gmx grompp -f ions.mdp -c solv.gro -p topol.top -o ions.tpr
gmx genion -s ions.tpr -o solv_ions.gro -p topol.top -pname NA -nname CL -neutral</code></pre>
<pre><code>[ molecules ]
; Compound #mols
Protein_chain_A 1
MUS 1
SOL 31227
CL 9</code></pre>
</ul>
<h4>3. Energy minimization:</h4>
<ul>
<li>Perform energy minimization on the overall system to eliminate unreasonable conflicts in the
initial geometry. Achieve rapid convergence of energy through the gradient descent algorithm and
ensure all atoms in the system are reasonably positioned within the force field. Analyze the
energy minimization results to ensure both the maximum force and potential energy are within
reasonable thresholds.</li>
<pre><code>gmx grompp -f em.mdp -c solv_ions.gro -p topol.top -o em.tpr
gmx mdrun -v -deffnm em
Steepest Descents converged to Fmax < 1000 in 1182 steps
Potential Energy = -1.5345670e+06
Maximum force = 8.9675085e+02 on atom 4987
Norm of force = 1.3456365e+01</code></pre>
<pre><code>gmx energy -f em.edr -o potential.xvg
#11 0
xmgrace potential.xvg
dit xvg_show -f potential.xvg</code></pre>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/potential.png" alt="potential"
class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 9 Potential Energy
Minimization</p>
</ul>
<h3>4. Molecular Dynamics Simulation</h3>
<h4>1. System Equilibration:</h4>
<ul>
<li>To achieve thermal and mechanical equilibrium of the system, simulations are conducted in two
stages: NVT (constant temperature) and NPT (constant pressure) equilibration. The system
temperature is gradually increased to the target of 300K to reach stable conditions, while
analyzing the curves of temperature, pressure, and density over time to ensure the stability of
the system.</li>
</ul>
<pre><code>gmx grompp -f nvt.mdp -c em.gro -r em.gro -p topol.top -n index.ndx -o nvt.tpr
gmx mdrun -deffnm nvt
gmx energy -f nvt.edr -o temperature.xvg
#16 0
dit xvg_show -f temperature.xvg</code></pre>
<img src="2.temperature.png" alt="">
<img src="temperature.png" alt="">
<pre><code>gmx grompp -f npt.mdp -c nvt.gro -t nvt.cpt -r nvt.gro -p topol.top -n index.ndx -o npt.tpr -maxwarn 1
gmx mdrun -deffnm npt
gmx energy -f npt.edr -o pressure.xvg
#17 0
gmx energy -f npt.edr -o density.xvg
#23 0
dit xvg_show -f temperature.xvg</code></pre>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/pressure.png" alt="pressure"
class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 10 Curve of the pressure over
time
</p>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/density.png" alt="density"
class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 11 Curve of the density over time
</p>
<h4>2. Production Simulation:</h4>
<ul>
<li>Under the conditions of equilibrium, a long-term production simulation is conducted. This
simulation observes the time evolution characteristics of the dynamic interactions between
muscone and the receptor, typically requiring simulation times ranging from hundreds of
nanoseconds to several microseconds to ensure the reliability and reproducibility of the
results. By sampling key frame data of the system during the dynamic process, it aids in further
analyzing the intermolecular interactions and dynamic conformational changes.</li>
</ul>
<pre><code>gmx grompp -f md.mdp -c npt.gro -t npt.cpt -p topol.top -n index.ndx -o md_0_10.tpr
gmx mdrun -deffnm md_0_10</code></pre>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/mds.png" alt="MDS"
class="shadowed-image" style="width: 100%; max-width: 1000px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 12 Molecular dynamics simulation
process
</p>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/mds-result.png" alt="density"
class="shadowed-image" style="width: 100%; max-width: 1000px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 13 Results of the molecular
dynamics simulations
</p>
<h3>5. Post-Processing and Analysis</h3>
<ul>
<li>After the completion of molecular dynamics simulations, detailed post-processing and analysis of
the data is a key step in understanding the behavior of molecular systems. This section will
demonstrate the use of GROMACS tools to analyze trajectory data, and visualize it using VMD and
PyMOL.</li>
</ul>
<h4>1. Trajectory Analysis:</h4>
<p>To gain deeper insights into the interactions between muscone and the receptor, visualization tools
are used to make the simulation process intuitive, identifying key interaction sites and structural
changes.</p>
<ul>
<li>Using the <code>gmx trjconv</code> tool, the calculated trajectory data is centered and periodic
boundary conditions are removed, generating the centered trajectory file
<code>md_0_10_center.xtc</code> and its initial frame <code>start.pdb</code>.
</li>
</ul>
<pre><code>gmx trjconv -s md_0_10.tpr -f md_0_10.xtc -o md_0_10_center.xtc -center -pbc mol -ur compact
#1 0
gmx trjconv -s md_0_10.tpr -f md_0_10_center.xtc -o start.pdb -dump 0
#0</code></pre>
<ul>
<li>In PyMOL, key interactions of the protein-ligand system can be visualized through selection and
rotation commands, identifying important residues and binding pockets that play significant
roles during the simulation process.</li>
</ul>
<pre><code># Pymol
select water, resn SOL
select ions, resn CL
select protein, not water and not ions
select ligand, resn MUS
deselect
cmd.rotate('x', 45)
cmd.rotate('y', 45)</code></pre>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/start.png" alt="start.pdb"
class="shadowed-image" style="width: 100%; max-width: 1000px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 14 Visualization of the
protein-ligand system
</p>
<ul>
<li>Finally, generate a fitted trajectory file suitable for analysis and animation production.</li>
</ul>
<pre><code>gmx trjconv -s md_0_10.tpr -f md_0_10_center.xtc -o md_0_10_fit.xtc -fit rot+trans
#4 0
gmx trjconv -s md_0_10.tpr -f md_0_10_fit.xtc -o traj.pdb -dt 10
#0</code></pre>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/muscure.gif" alt="Trajectory Analysis"
class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 15 Trajectory Analysis
</p>
<h4>2. RMSD (Root Mean Square Deviation) Analysis</h4>
<ul>
<li>RMSD provides a fundamental metric for measuring structural deviation during the simulation
process. By calculating the deviation of structures at different time points, it is possible to
assess the stability of the system.</li>
</ul>
<pre><code>gmx distance -s md_0_10.tpr -f md_0_10_center.xtc -select 'resname "MUS" and name O plus resid 51 and name NH1' -oall
gmx make_ndx -f em.gro -o index.ndx
> 13 & a O
> 1 & r 51 & a NH1
> 1 & r 51 & a CZ
> 20 | 21 | 22
> q
gmx angle -f md_0_10_center.xtc -n index.ndx -ov angle.xvg
gmx make_ndx -f em.gro -n index.ndx
> 13 & ! a H*
> name MUS_Heavy
> q
gmx rms -s em.tpr -f md_0_10_center.xtc -n index.ndx -tu ns -o rmsd_mus.xvg
xmgrace rmsd_mus.xvg
dit xvg_show -f rmsd_mus.xvg
xmgrace rmsd_mus.xvg</code></pre>
<ul>
<li>From the RMSD curve, it can be observed that the system stabilizes after approximately 1
nanosecond, with a fluctuation range of around 1.3 Å. This indicates that the structures of the
protein and ligand remained relatively stable throughout the simulation process, with no
significant conformational changes occurring, supporting the potential biological significance
of the results.</li>
</ul>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/rmsd.png" alt="RMSD Plot"
class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 16 RMSD Analysis
</p>
<h4>3. Radius of Gyration (Rg) Calculation</h4>
<ul>
<li>The radius of gyration (Rg) is used to assess the compactness of a protein and is an important
indicator of protein folding or unfolding.</li>
<li>If the protein folding is stable, its radius of gyration Rg will maintain a relatively stable
value. If the protein unfolds, its Rg will change over time.</li>
</ul>
<pre><code>gmx gyrate -s md_0_10.tpr -f md_0_10_fit.xtc -o gyrate.xvg
#1
xmgrace gyrate.xvg</code></pre>
<ul>
<li>In the simulation, the Rg value of the protein remained between 2.2 and 2.25 nanometers,
indicating that the protein maintained a compact folded state during the simulation period at
300 K, with no significant unfolding or expansion occurring.</li>
</ul>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/gr1.png"
alt="Additional Radius of Gyration Plot" class="shadowed-image"
style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 17 Radius of Gyration Calculation
</p>
<h4>4. Protein-Ligand Interaction Energy</h4>
<ul>
<li>By calculating the Coulomb and Lennard-Jones interaction energies within the system, the binding
energy between musk ketone and the receptor is quantified.</li>
</ul>
<pre><code>gmx make_ndx -f em.gro -o index.ndx
> 1 | 13
gmx grompp -f ie.mdp -c npt.gro -t npt.cpt -p topol.top -n index.ndx -o ie.tpr
gmx mdrun -deffnm ie -rerun md_0_10.xtc -nb cpu
gmx energy -f ie.edr -o interaction_energy.xvg
Energy Average Err.Est. RMSD Tot-Drift
-------------------------------------------------------------------------------
Coul-SR:Protein-MUS 0.0439222 0.38 2.88794 1.41131 (kJ/mol)
LJ-SR:Protein-MUS -81.3724 1.6 9.75743 1.99715 (kJ/mol)
#21 | 22
xmgrace interaction_energy.xvg
dit xvg_show -f interaction_energy.xvg</code></pre>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/energy.png"
alt="Interaction Energy Plot" class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 18 Protein-Ligand Interaction
Energy
</p>
<ul>
<li>The calculation results show that the Lennard-Jones interaction dominates in stable binding,
averaging -81.37 kJ/mol, indicating that hydrophobic interactions play a central role in the
binding between the ligand and the receptor.</li>
</ul>
</div>
</div>
<div class="row mt-4">
<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
activates the receptor, which in turn activates the G protein. The G protein dissociates into α and
βγ subunits, with the βγ subunit releasing and activating Ste20 and the scaffold protein Ste5. Ste5
can undergo oligomerization and other behaviors, recruiting Ste11, Ste7, and Fus3 near the plasma
membrane. The cascade reaction is initiated by Ste20, and the signal is transmitted along the
Ste11-Ste7-Fus3 cascade. Fus3 activates the transcription factor pFUS1, and the downstream gene is
LahA, which expresses lactate dehydrogenase LDH, catalyzing the conversion of pyruvate to lactate.
This model simulates the changes in the concentrations and phosphorylation states of molecules in
the signaling transduction pathway by writing out chemical reactions and converting them into
ordinary differential equations, in order to obtain the quantitative relationship between muscone
activation and lactate secretion. The model includes the following main processes:</p>
<ol>
<li><strong>Activation of Muscone Receptor</strong>: The muscone receptor Ste2, derived from
mouse olfactory epithelium, is a G protein-coupled receptor (GPCR) that is expressed on the cell
membrane and receives signals. Its domains consist of α, β, and γ, where the Gα subunit is
called Gpa1, and the Gα and Gγ subunits are Ste4 and Ste18, respectively, both anchored in the
cell membrane, without discussing the scenario of their separation. After binding with muscone,
Gpa1 will release Ste4-Ste18.</li>
<li><strong>Formation of Scaffold</strong>: The released Ste4-Ste18 can bind to Ste5, and the Ste5
protein can undergo dimerization, oligomerization, and other behaviors, forming a scaffold near
the cell membrane and recruiting proteins related to the cascade phosphorylation.</li>
<li><strong>Cascade Reaction</strong>: The scaffold composed of Ste5 can recruit Ste11 (MAPKKK),
Ste7 (MAPKK), and Fus3 (MAPK). Each of these three proteins has multiple phosphorylation
modification sites, and the efficiency of catalyzing phosphorylation varies under different
modification scenarios. Furthermore, the three proteins independently bind to Ste5, and a
reaction can only occur when two adjacent proteins are simultaneously present on the scaffold,
making this signaling pathway highly specific.</li>
<li><strong>Activation of pFUS1</strong>: The transcription factor pFUS1 is activated by Fus3, and
the downstream gene is LahA, which expresses lactate dehydrogenase to produce lactate.</li>
</ol>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/mapk.png" alt="MAPK Pathway"
class="shadowed-image" style="width: 50%; max-width: 500px;">
</div>
<h3>Basic Assumptions</h3>
<ol>
<li>Since the model only simulates the signal transduction shortly after muscone activation, it
does not consider protein synthesis and degradation, assuming that the concentrations of each
protein remain stable during this time.</li>
<li>It is assumed that all proteins involved in the cascade reaction have the same dephosphorylation
rate, denoted by \(k_{cat_{dephosph}}\).</li>
<li>The behavior of all molecules in the system is random and not influenced by environmental
factors.</li>
</ol>
<h3>Model Equations</h3>
<h4>Activation of muscone Receptor</h4>
<strong>Reactions</strong>:
<div>
<p>
\[
\begin{align*}
\text{Pheromone} + \text{Ste2} & \rightarrow \text{PheromoneSte2} \\
\text{PheromoneSte2} & \rightarrow \text{Pheromone} + \text{Ste2} \\
\text{PheromoneSte2} + \text{Gpa1Ste4Ste18} & \rightarrow \text{PheromoneSte2Gpa1Ste4Ste18} \\
\text{PheromoneSte2Gpa1Ste4Ste18} & \rightarrow \text{PheromoneSte2Gpa1} + \text{Ste4Ste18} \\
\text{PheromoneSte2Gpa1} & \rightarrow \text{PheromoneSte2} + \text{Gpa1} \\
\text{Gpa1} + \text{Ste4Ste18} & \rightarrow \text{Gpa1Ste4Ste18}
\end{align*}
\]
</p>
</div>
<strong>Explanation</strong>
<p>
After Ste2 binds with muscone, it interacts with the G protein, causing the exchange of GDP
bound to the G protein with GTP in the cytoplasm, releasing Ste4 and Ste18. After Gpa1 catalyzes the
conversion of GTP to GDP, it can return to the cytoplasm and rebind, forming a G protein trimer.
Since the original signaling pathway is the yeast pheromone signaling pathway, with the ligand being
the pheromone, this section uses Pheromone to represent the molecules that activate the receptor.
</p>
<strong>Ordinary Differential Equations</strong>
<div>
<p>
\[
\begin{align*}
\frac{d{P}}{dt} & = k_{off_{PS}}{PS} - k_{on_{PS}}{P}*{S} \\
\frac{d{S}}{dt} & = k_{off_{PS}}{PS} - k_{on_{PS}}{P}*{S} \\
\frac{d{PS}}{dt} & = k_{on_{PS}}{P}*{S} + k_{off_{SG}} {PSG} \\
& \quad - k_{off_{PS}}{PS} - k_{on_{SG}}{PS} * {GSS} \\
\frac{d{GSS}}{dt} & = k_{on_{GS}}{SS} * {G} - k_{on_{SG}}{PS} * {GSS} \\
\frac{d{PSGSS}}{dt} & = k_{on_{SG}}{PS} * {GSS} - k_{on_{GS}}{PSGSS} \\
\frac{d{PSG}}{dt} & = k_{on_{GS}}{PSGSS} - k_{off_{SG}} {PSG} \\
\frac{d{SS}}{dt} & = k_{on_{GS}}{PSGSS} - k_{on_{GS}}{SS} * {G} \\
\frac{d{G}}{dt} & = k_{off_{SG}} {PSG} - k_{on_{GS}}{SS} * {G} \\
\end{align*}
\]
</p>
</div>
<strong>Variables</strong>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">Table 1: Variables of Receptor
Activation Model</p>
<table>
<thead>
<tr>
<th>Variable</th>
<th>Represents Molecule</th>
<th>Concentration (\(\mu M\))</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(P\)</td>
<td>Pheromone</td>
<td>-</td>
</tr>
<tr>
<td>\(S\)</td>
<td>Ste2</td>
<td>\(0.287\)</td>
</tr>
<tr>
<td>\(PS\)</td>
<td>PheromoneSte2</td>
<td>-</td>
</tr>
<tr>
<td>\(GSS\)</td>
<td>Gpa1Ste4Ste18</td>
<td>-</td>
</tr>
<tr>
<td>\(PSGSS\)</td>
<td>PheromoneSte2Gpa1Ste4Ste18</td>
<td>-</td>
</tr>
<tr>
<td>\(PSG\)</td>
<td>PheromoneSte2Gpa1</td>
<td>-</td>
</tr>
<tr>
<td>\(SS\)</td>
<td>Ste4Ste18</td>
<td>\(2\times 10^{-4}\)</td>
</tr>
<tr>
<td>\(G\)</td>
<td>Gpa1</td>
<td>\(2\times 10^{-4}\)</td>
</tr>
</tbody>
</table>
<strong>Parameters</strong>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">Table 2: Parameters of Receptor
Activation Model</p>
<table>
<thead>
<tr>
<th>Parameter</th>
<th>Meaning</th>
<th>Value</th>
<th>Unit</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(k_{on_{PS}}\)</td>
<td>Binding rate of Pheromone to Ste2</td>
<td>\(0.185\)</td>
<td>\({\mu M}^{-1} \cdot s^{-1}\)</td>
</tr>
<tr>
<td>\(k_{off_{PS}}\)</td>
<td>Dissociation rate of PheromoneSte2</td>
<td>\(1 \times 10^{-3}\)</td>
<td>\(s^{-1}\)</td>
</tr>
<tr>
<td>\(k_{on_{SG}}\)</td>
<td>Binding rate of PheromoneSte2 to Gpa1Ste4Ste18</td>
<td>-</td>
<td>\({\mu M}^{-1} \cdot s^{-1}\)</td>
</tr>
<tr>
<td>\(k_{off_{SG}}\)</td>
<td>Dissociation rate of PheromoneSte2Gpa1</td>
<td>-</td>
<td>\(s^{-1}\)</td>
</tr>
<tr>
<td>\(k_{on_{GS}}\)</td>
<td>Binding rate of Gpa1 to Ste4Ste18</td>
<td>-</td>
<td>\({\mu M}^{-1} \cdot s^{-1}\)</td>
</tr>
<tr>
<td>\(k_{off_{GS}}\)</td>
<td>Dissociation rate of PheromoneGpa1Ste4Ste18</td>
<td>-</td>
<td>\(s^{-1}\)</td>
</tr>
</tbody>
</table>
<strong>Initial Conditions</strong>
<p>
There are \(0.3{\mu M}\) of Pheromone and \(1{\mu M}\) of inactive G proteins. Known variables are
entered, other variables are set to zero, and unknown parameters are defined. After starting the
simulation, reactions occur according to the equations listed.
</p>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/3-1.png" alt="Receptor Activation"
class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 19 Receptor Activation</p>
<button id="Button5" onclick="toggleCodeSnippet5()">receptor.m</button>
<div id="codeSnippet5" class="code-snippet">% parameter setting
kon_PS = 0.185;
koff_PS = 1e-3;
kon_SG = 0.1;
koff_GS = 0.1;
koff_SG = 0.1;
kon_GS = 0.01;
% initial value setting
Pheromone = 0.3;
Ste2 = 0.287;
Pheromone_Ste2 = 0.0;
Gpa1_Ste4Ste18 = 1.0;
Pheromone_Ste2_Gpa1_Ste4Ste18 = 0.0;
Pheromone_Ste2_Gpa1 = 0.0;
Ste4Ste18 = 2e-4;
Gpa1 = 2e-4;
% time setting
tspan = [0 500];
% Define the systems of ordinary differential equations
odefun = @(t, y) [ koff_PS*y(3)-kon_PS*y(1)*y(2);
koff_PS*y(3)-kon_PS*y(1)*y(2);
kon_PS*y(1)*y(2)+koff_SG*y(6)-koff_PS*y(3)-kon_SG*y(3)*y(4);
kon_GS*y(7)*y(8)-kon_SG*y(3)*y(4);
kon_SG*y(3)*y(4)-koff_GS*y(5);
koff_GS*y(5)-koff_SG*y(6);
koff_GS*y(5)-kon_GS*y(7)*y(8);
koff_SG*y(6)-kon_GS*y(7)*y(8);
];
% Find the numerical solution of the system of ordinary differential equations
[t, Y] = ode45(odefun, tspan,
[Pheromone,Ste2,Pheromone_Ste2,Gpa1_Ste4Ste18,Pheromone_Ste2_Gpa1_Ste4Ste18,Pheromone_Ste2_Gpa1,Ste4Ste18,Gpa1,]);
% plot the results
figure;
plot(t, Y(:,1), 'DisplayName', 'Pheromone', 'LineWidth', 2); hold on;
plot(t, Y(:,2), 'DisplayName', 'Ste2', 'LineWidth', 2);
plot(t, Y(:,3), 'DisplayName', 'PS', 'LineWidth', 2);
plot(t, Y(:,4), 'DisplayName', 'GS', 'LineWidth', 2);
plot(t, Y(:,5), 'DisplayName', 'PSGS', 'LineWidth', 2);
plot(t, Y(:,6), 'DisplayName', 'PSG', 'LineWidth', 2);
plot(t, Y(:,7), 'DisplayName', 'Ste4Ste18', 'LineWidth', 2);
plot(t, Y(:,8), 'DisplayName', 'Gpa1', 'LineWidth', 2);
xlabel('Time');
ylabel('Concentration');
title('Dynamics of Variables Over Time');
legend('show');
grid on;</div>
<script>
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<h4>Formation of the Scaffold</h4>
<strong>Reactions</strong>:
<div>
\[
\begin{align*}
Ste5 + Ste5 & \leftrightarrows Ste5Ste5 \\
Ste4Ste18Ste5 + Ste5 & \leftrightarrows Ste4Ste18Ste5Ste5 \\
Ste4Ste18Ste5 + Ste4Ste18Ste5 & \leftrightarrows Ste4Ste18Ste5Ste5Ste4Ste18 \\
Ste4Ste18 + Ste5 & \leftrightarrows Ste4Ste18Ste5 \\
Ste4Ste18 + Ste5Ste5 & \leftrightarrows Ste4Ste18Ste5Ste5 \\
Ste4Ste18 + Ste4Ste18Ste5Ste5 & \leftrightarrows Ste4Ste18Ste5Ste5Ste4Ste18 \\
\end{align*}
\]
</div>
<p><strong>Explanation</strong>: The binding of Ste4Ste18 with Ste5 and the oligomerization of Ste5 is a
process that is not completely independent. Many equations can be derived through combinations, but
here
we only consider the dimerization process, and each reaction is reversible. Since Ste5 actually
binds to
Ste4, we abbreviate Ste5 as S5 and Ste4 as S4 in the equations.</p>
<p></p><strong>Ordinary Differential Equations</strong>:</p>
<div>
\[
\begin{align*}
\frac{d{S5}}{dt} & = -2 k_{on_{S5:S5}}{S5}^2 + 2 k_{off_{S5:S5}}{S55} \\
& \quad -k_{on_{S4:S5}}{S5}*{S4} + k_{off_{S4:S5}}{S45} \\
& \quad -k_{on_{S4S5:S5}}{S5}*{S45}+k_{off_{S4S5:S5}}{S5}*{S455}\\
\frac{d{S55}}{dt} & = k_{on_{S5:S5}} {S5}^2- k_{off_{S5:S5}}{S55} \\
& \quad - k_{on_{S4:S5S5}} {S4}* {S55} + k_{off_{S4:S5S5}} {S455} \\
\frac{d{S45}}{dt} & = k_{on_{S4:S5}}{S5}*{S4}- k_{off_{S4:S5}} {S45} \\
& \quad -k_{on_{S4S5:S5}}{S5}*{S45}+k_{off_{S4S5:S5}}{S5}*{S455}\\
& \quad -2 k_{on_{S4S5:S5S4}}{S45}^2 + 2 k_{off_{S4S5:S5S4}}{S4554} \\
\frac{d{S455}}{dt} & = k_{on_{S4:S5S5}} {S4}* {S55} - k_{off_{S4:S5S5}} {S455} \\
& \quad +k_{on_{S4S5:S5}}{S5}*{S45}-k_{off_{S4S5:S5}}{S5}*{S455}\\
& \quad -k_{on_{S4:S5S5S4}}{S455}*{S4}+k_{off_{S4:S5S5S4}}{S4554}\\
\frac{d{S4554}}{dt} & = k_{on_{S4:S5S5S4}}{S455}*{S4}-k_{off_{S4:S5S5S4}}{S4554}\\
& \quad +k_{on_{S4S5:S5S4}}{S45}^2 - k_{off_{S4S5:S5S4}}{S4554} \\
\frac{d{S4}}{dt} & = -k_{on_{S4:S5}}{S5}*{S4}+ k_{off_{S4:S5}} {S45} \\
& \quad - k_{on_{S4:S5S5}} {S4}* {S55} + k_{off_{S4:S5S5}} {S455} \\
& \quad -k_{on_{S4:S5S5S4}}{S455}*{S4}+k_{off_{S4:S5S5S4}}{S4554}\\
\end{align*}
\]
</div>
<strong>Variables</strong>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">Table 3: Variables of Scaffold
Formation Model</p>
<table>
<thead>
<tr>
<th>Variable</th>
<th>Represents Molecule</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(S5\)</td>
<td>Ste5</td>
</tr>
<tr>
<td>\(S55\)</td>
<td>Ste5Ste5</td>
</tr>
<tr>
<td>\(S45\)</td>
<td>Ste4Ste18Ste5</td>
</tr>
<tr>
<td>\(S455\)</td>
<td>Ste4Ste18Ste5Ste5</td>
</tr>
<tr>
<td>\(S4554\)</td>
<td>Ste4Ste18Ste5Ste5Ste4Ste18</td>
</tr>
<tr>
<td>\(S4\)</td>
<td>Ste4Ste18</td>
</tr>
</tbody>
</table>
<strong>Parameters</strong>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">Table 4: Parameters of Scaffold
Formation Model</p>
<table>
<thead>
<tr>
<th>Parameter</th>
<th>Meaning</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(k_{on_{S5:S5}}\)</td>
<td>Binding rate of Ste5 and Ste5</td>
</tr>
<tr>
<td>\(k_{off_{S5:S5}}\)</td>
<td>Dissociation rate of Ste5:Ste5</td>
</tr>
<tr>
<td>\(k_{on_{S4:S5}}\)</td>
<td>Binding rate of Ste4Ste18 and Ste5</td>
</tr>
<tr>
<td>\(k_{off_{S4:S5}}\)</td>
<td>Dissociation rate of Ste4Ste18:Ste5</td>
</tr>
<tr>
<td>\(k_{on_{S4S5:S5}}\)</td>
<td>Binding rate of Ste4Ste18Ste5 and Ste5</td>
</tr>
<tr>
<td>\(k_{off_{S4S5:S5}}\)</td>
<td>Dissociation rate of Ste4Ste18Ste5:Ste5</td>
</tr>
<tr>
<td>\(k_{on_{S4:S5S5}}\)</td>
<td>Binding rate of Ste4Ste18 and Ste5Ste5</td>
</tr>
<tr>
<td>\(k_{off_{S4:S5S5}}\)</td>
<td>Dissociation rate of Ste4Ste18:Ste5Ste5</td>
</tr>
<tr>
<td>\(k_{on_{S4:S5S5S4}}\)</td>
<td>Binding rate of Ste4Ste18Ste5Ste5 and Ste4Ste18</td>
</tr>
<tr>
<td>\(k_{off_{S4:S5S5S4}}\)</td>
<td>Dissociation rate of Ste4Ste18Ste5Ste5:Ste4Ste18</td>
</tr>
<tr>
<td>\(k_{on_{S4S5:S5S4}}\)</td>
<td>Binding rate of Ste4Ste18Ste5 and Ste4Ste18Ste5</td>
</tr>
<tr>
<td>\(k_{off_{S4S5:S5S4}}\)</td>
<td>Dissociation rate of Ste4Ste18Ste5:Ste5Ste4Ste18</td>
</tr>
</tbody>
</table>
<strong>Initial conditions</strong>
<p>Assume that before signal transduction starts, there are only free Ste5 and just released Ste4Ste18
in the cell, with concentrations both equal to 1, and parameters are assumed. After starting the
simulation, reactions occur according to the listed equations, and after a period of time, the
concentrations reach equilibrium.</p>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/3-2.png" alt="Scaffold Formation"
class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 20 Scaffold Formation</p>
<button id="Button6" onclick="toggleCodeSnippet6()">scaffold.m</button>
<div id="codeSnippet6" class="code-snippet">% parameter setting
kon_S5S5 = 0.1;
koff_S5S5 = 0.01;
kon_S4S5_S5 = 0.05;
koff_S4S5_S5 = 0.01;
kon_S4S5_S5S4 = 0.03;
koff_S4S5_S5S4 = 0.01;
kon_S4S5 = 0.2;
koff_S4S5 = 0.1;
kon_S4_S5S5 = 0.1;
koff_S4_S5S5 = 0.05;
kon_S4_S5S5S4 = 0.05;
koff_S4_S5S5S4 = 0.02;
% initial value setting
Ste5 = 1.0;
Ste5_Ste5 = 0.0;
Ste4Ste18_Ste5 = 0.0;
Ste4Ste18_Ste5_Ste5 = 0.0;
Ste4Ste18_Ste5_Ste5_Ste4Ste18 = 0.0;
Ste4Ste18 = 1.0;
% time setting
tspan = [0 100];
% Define the systems of ordinary differential equations
odefun = @(t, y) [
-2*kon_S5S5*y(1)^2+2*koff_S5S5*y(2)-kon_S4S5*y(1)*y(6)+koff_S4S5*y(3)-kon_S4S5_S5*y(1)*y(3)+koff_S4S5_S5*y(4);
kon_S5S5*y(1)^2-koff_S5S5*y(2)-kon_S4_S5S5*y(2)*y(6)+koff_S4_S5S5*y(4);
kon_S4S5*y(1)*y(6)-koff_S4S5*y(3)-kon_S4S5_S5*y(1)*y(3)+koff_S4S5_S5*y(4)-2*kon_S4S5_S5S4*y(3)^2+2*koff_S4S5_S5S4*y(5);
kon_S4_S5S5*y(2)*y(6)-koff_S4_S5S5*y(4)+kon_S4S5_S5*y(1)*y(3)-koff_S4S5_S5*y(4)-kon_S4_S5S5S4*y(4)*y(6)+koff_S4_S5S5S4*y(5);
kon_S4_S5S5S4*y(4)*y(6)-koff_S4_S5S5S4*y(5)+kon_S4S5_S5S4*y(3)^2-koff_S4S5_S5S4*y(5);
-kon_S4S5*y(1)*y(6)+koff_S4S5*y(3)-kon_S4_S5S5*y(2)*y(6)+koff_S4_S5S5*y(4)-kon_S4_S5S5S4*y(4)*y(6)+koff_S4_S5S5S4*y(5);
];
% Find the numerical solution of the system of ordinary differential equations
[t, Y] = ode45(odefun, tspan, [Ste5, Ste5_Ste5, Ste4Ste18_Ste5, Ste4Ste18_Ste5_Ste5,
Ste4Ste18_Ste5_Ste5_Ste4Ste18, Ste4Ste18]);
% plot the results
figure;
plot(t, Y(:,1), 'DisplayName', 'Ste5', 'LineWidth', 2); hold on;
plot(t, Y(:,2), 'DisplayName', 'Ste5Ste5', 'LineWidth', 2);
plot(t, Y(:,3), 'DisplayName', 'Ste4Ste18Ste5', 'LineWidth', 2);
plot(t, Y(:,4), 'DisplayName', 'Ste4Ste18Ste5Ste5', 'LineWidth', 2);
plot(t, Y(:,5), 'DisplayName', 'Ste4Ste18Ste5Ste5Ste4Ste18', 'LineWidth', 2);
plot(t, Y(:,6), 'DisplayName', 'Ste4Ste18', 'LineWidth', 2);
xlabel('Time');
ylabel('Concentration');
title('Dynamics of Variables Over Time');
legend('show');
grid on</div>
<script>
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<h4>Cascading Reactions</h4>
<p><strong>Reactions</strong>:</p>
<div>
<p>
\[
\begin{align*}
Ste5_{off_{Ste11}} + Ste11_{off} & \leftrightarrows Ste5Ste11 \\
Ste5_{off_{Ste7}} + Ste7_{off} & \leftrightarrows Ste5Ste7 \\
Ste5_{off_{Fus3}} + Fus3_{off} & \leftrightarrows Ste5Fus3 \\
\end{align*}
\]
</p>
<p>
\[
\begin{align*}
Ste11 & \xrightarrow {Ste20} Ste11_{pS} \\
Ste11_{pS} & \xrightarrow {Ste20} Ste11_{pSpS} \\
Ste11_{pSpS} & \xrightarrow {Ste20} Ste11_{pSpSpT} \\
\end{align*}
\]
</p>
<p>
\[
\begin{align*}
Ste7 & \xrightarrow {Ste11_{pS},Ste11_{pSpS},Ste11_{pSpSpT}} Ste7_{pS} \\
Ste7_{pS} & \xrightarrow {Ste11_{pS},Ste11_{pSpS},Ste11_{pSpSpT}} Ste7_{pSpT}\\
\end{align*}
\]
</p>
<p>
\[
\begin{align*}
Fus3 & \xrightarrow {Ste7_{pS},Ste7_{pSpT}} Fus3_{pY} \\
Fus3 & \xrightarrow {Ste7_{pS},Ste7_{pSpT}} Fus3_{pT} \\
Fus3_{pY} & \xrightarrow {Ste7_{pS},Ste7_{pSpT}} Fus3_{pYpT} \\
Fus3_{pT} & \xrightarrow {Ste7_{pS},Ste7_{pSpT}} Fus3_{pYpT} \\
\end{align*}
\]
</p>
</div>
<h2>Explanation</h2>
<p>Only the Ste5 bound to the scaffold has significance in recruiting Ste11, Ste7, and Fus3, and the
binding to these three proteins is independent. Therefore, the Ste5 on the scaffold can be treated
as three copies to calculate its binding with Ste11, Ste7, and Fus3 separately. The three proteins
are activated through cascading phosphorylation initiated by Ste20, and the conditions for the
reactions to occur are that the kinases are activated and bound to the scaffold. Each protein has
different forms of phosphorylation modifications, which may have different catalytic reaction rates;
thus, they need to be listed separately.</p>
<h2>Ordinary Differential Equations</h2>
<p>The forms of multiple reactions are similar; here, only a portion is selected for demonstration.</p>
<p>Taking Ste11 as an example to illustrate the binding of the kinase with Ste5:</p>
<div>
<p>
\[
\begin{align*}
\frac{dSte5_{off_{Ste11}}}{dt} & = k_{off_{Ste5Ste11}}Ste5Ste11 -
k_{on_{Ste5Ste11}}Ste5_{off_{Ste11}} * Ste11_{off} \\
\frac{dSte11_{off}}{dt} & = k_{off_{Ste5Ste11}}Ste5Ste11 - k_{on_{Ste5Ste11}}Ste5_{off_{Ste11}}
* Ste11_{off} \\
\frac{dSte5Ste11}{dt} & = - k_{off_{Ste5Ste11}}Ste5Ste11 + k_{on_{Ste5Ste11}}Ste5_{off_{Ste11}}
* Ste11_{off} \\
\end{align*}
\]
</p>
</div>
<h2>Variables</h2>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">Table 5: Variables of Ste11 Binding
Model</p>
<table>
<thead>
<tr>
<th>Variable</th>
<th>Represents Molecule</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(Ste5_{off_{Ste11}}\)</td>
<td>Unbound kinase Ste5</td>
</tr>
<tr>
<td>\(Ste11_{off}\)</td>
<td>Unbound scaffold Ste11</td>
</tr>
<tr>
<td>\(Ste5Ste11\)</td>
<td>Bound Ste5 and Ste11</td>
</tr>
</tbody>
</table>
<h2>Parameters</h2>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">Table 6: Parameters of Ste11 Binding
Model</p>
<table>
<thead>
<tr>
<th>Parameter</th>
<th>Meaning</th>
<th>Units</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(k_{off_{Ste5Ste11}}\)</td>
<td>Dissociation rate of Ste5Ste11</td>
<td>\({s}^{-1}\)</td>
</tr>
<tr>
<td>\(k_{on_{Ste5Ste11}}\)</td>
<td>Association rate of Ste5 and Ste11</td>
<td>\({\mu M}^{-1}·s^{-1}\)</td>
</tr>
</tbody>
</table>
<p>Using Ste11 catalyzing the phosphorylation of Ste7 as an example to illustrate the phosphorylation
process:</p>
<div>
<p>
\[
\frac{dSte7_{pS}}{dt} =
kcat_{Ste11pS{Ste7_{pS}}}Ste11_{pS}*\frac{Ste5Ste11}{Ste11_{total}}*\frac{Ste5Ste7}{Ste7_{total}}*\frac{Ste7_{pS}}{Ste7_{total}}+\ldots
\]
</p>
</div>
<h2>Variables</h2>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">Table 7: Variables of Ste7
Phosphorylation Model</p>
<table>
<thead>
<tr>
<th>Variable</th>
<th>Represents Molecule</th>
</tr>
</thead>
<tbody>
<tr>
<td>\(Ste7_{pS}\)</td>
<td>Phosphorylated Ste7 at S359</td>
</tr>
<tr>
<td>\(Ste11_{pS}\)</td>
<td>Phosphorylated Ste11 at S302</td>
</tr>
<tr>
<td>\(Ste5Ste11\)</td>
<td>Ste11 bound to Ste5</td>
</tr>
<tr>
<td>\(Ste5Ste7\)</td>
<td>Ste7 bound to Ste5</td>
</tr>
<tr>
<td>\(Ste7_{total}\)</td>
<td>Total amount of Ste7</td>
</tr>
</tbody>
</table>
<h2>Parameters</h2>
<p>\(kcat_{Ste11pS{Ste7_{pS}}}\): Represents the catalytic efficiency in this case.</p>
<h2>Initial Conditions</h2>
<p>The concentrations of the three kinases are known, assuming their initial state has not undergone
phosphorylation. Some enzyme activity parameters are known, and other parameters are roughly
estimated to the same order of magnitude.</p>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/3-3.png"
alt="Combination of kinases and scaffold" class="shadowed-image"
style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 21 Combination of kinases and
scaffold</p>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/3-4.png" alt="Ste11 phosphorylation"
class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 22 Ste11 phosphorylation</p>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/3-5.png" alt="Ste11 phosphorylation"
class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 23 Ste7 phosphorylation</p>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/3-6.png" alt="Fus3 phosphorylation"
class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 24 Fus3 phosphorylation</p>
<button id="Button7" onclick="toggleCodeSnippet7()">cascade.m</button>
<div id="codeSnippet7" class="code-snippet">% initial value setting
scaffold_Ste5 = 0.5;
Ste5_off_Ste11 = scaffold_Ste5;
Ste11_off = 0.2;
Ste5_Ste11 = 0.0;
Ste5_off_Ste7 = scaffold_Ste5;
Ste7_off = 0.05;
Ste5_Ste7 = 0.0;
Ste5_off_Fus3 = scaffold_Ste5;
Fus3_off = 0.088;
Ste5_Fus3 = 0.0;
Ste11 = Ste11_off;
Ste11_pS = 0;
Ste11_pSpS = 0;
Ste11_pSpSpT = 0;
Ste7 = Ste7_off;
Ste7_pS = 0;
Ste7_pSpT = 0;
Fus3 = Fus3_off;
Fus3_pY = 0;
Fus3_pT = 0;
Fus3_pYpT = 0;
% parameter setting
kon_Ste5_Ste11 = 0.1; % Ste5_off_Ste11 + Ste11_off -> Ste5_Ste11
koff_Ste5_Ste11 = 0.2; % Ste5_Ste11 -> Ste5_off_Ste11 + Ste11_off
kon_Ste5_Ste7 = 0.3; % Ste5_off_Ste7 + Ste7_off -> Ste5_Ste7
koff_Ste5_Ste7 = 0.4; % Ste5_Ste7 -> Ste5_off_Ste7 + Ste7_off
kon_Ste5_Fus3 = 0.5; % Ste5_off_Fus3 + Fus3_off -> Ste5_Fus3
koff_Ste5_Fus3 = 0.6; % Ste5_Fus3 -> Ste5_off_Fus3 + Fus3_off
kcat_Ste20Ste11_pS = 1.8438; % Ste11 -> Ste11_pS
kcat_Ste20Ste11pS_pS = 1.8438; % Ste11_pS -> Ste11_pSpS
kcat_Ste20Ste11pSpS_pT = 1.8438; % Ste11_pSpS -> Ste11_pSpSpT
kcat_Ste11pSSte7_pS = 1; % Ste11_pS + Ste7 -> Ste7_pS
kcat_Ste11pSSte7pS_pT = 0.5; % Ste11_pS + Ste7_pS -> Ste7_pSpT
kcat_Ste11pSpSSte7_pS = 2; % Ste11_pSpS + Ste7 -> Ste7_pS
kcat_Ste11pSpSSte7pS_pT = 1.5; % Ste11_pSpS + Ste7_pS -> Ste7_pSpT
kcat_Ste11pSpSpTSte7_pS = 3; % Ste11_pSpSpT + Ste7 -> Ste7_pS
kcat_Ste11pSpSpTSte7pS_pT = 2.5; % Ste11_pSpSpT + Ste7_pS -> Ste7_pSpT
kcat_Ste5Ste7pSFus3_pY = 2.6079; % Ste7_pS + Fus3 -> Fus3_pY
kcat_Ste5Ste7pSFus3_pT = 2.6079; % Ste7_pS + Fus3 -> Fus3_pT
kcat_Ste5Ste7pSFus3pY_pT = 2.6079; % Ste7_pS + Fus3_pY -> Fus3_pYpT
kcat_Ste5Ste7pSFus3pT_pY = 2.6079; % Ste7_pS + Fus3_pT -> Fus3_pYpT
kcat_Ste5Ste7pSpTFus3_pY = 0.86812; % Ste7_pSpT + Fus3 -> Fus3_pY
kcat_Ste5Ste7pSpTFus3_pT = 6.7879; % Ste7_pSpT + Fus3 -> Fus3_pT
kcat_Ste5Ste7pSpTFus3pY_pT = 3.5252; % Ste7_pSpT + Fus3_pY -> Fus3_pYpT
kcat_Ste5Ste7pSpTFus3pT_pY = 1.5; % Ste7_pSpT + Fus3_pT -> Fus3_pYpT
kcat_dephosph = 0.1;
% time setting
tspan = [0 40];
% Define the systems of ordinary differential equations
odefun = @(t, y) [
koff_Ste5_Ste11*y(3)-kon_Ste5_Ste11*y(1)*y(2); % Ste5_off_Ste11 y(1)
koff_Ste5_Ste11*y(3)-kon_Ste5_Ste11*y(1)*y(2); % Ste11_off y(2)
-koff_Ste5_Ste11*y(3)+kon_Ste5_Ste11*y(1)*y(2); % Ste5_Ste11 y(3)
koff_Ste5_Ste7*y(6)-kon_Ste5_Ste7*y(4)*y(5); % Ste5_off_Ste7 y(4)
koff_Ste5_Ste7*y(6)-kon_Ste5_Ste7*y(4)*y(5); % Ste7_off y(5)
-koff_Ste5_Ste7*y(6)+kon_Ste5_Ste7*y(4)*y(5); % Ste5_Ste7 y(6)
koff_Ste5_Fus3*y(9)-kon_Ste5_Fus3*y(7)*y(8); % Ste5_off_Fus3 y(7)
koff_Ste5_Fus3*y(9)-kon_Ste5_Fus3*y(7)*y(8); % Fus3_off y(8)
-koff_Ste5_Fus3*y(9)+kon_Ste5_Fus3*y(7)*y(8); % Ste5_Fus3 y(9)
-kcat_Ste20Ste11_pS*scaffold_Ste5*(y(3)*y(10)/(y(2)+y(3))^2)+kcat_dephosph*y(11); % Ste11 y(10)
kcat_Ste20Ste11_pS*scaffold_Ste5*(y(3)*y(10)/(y(2)+y(3))^2)-kcat_Ste20Ste11pS_pS*scaffold_Ste5*(y(3)*y(11)/(y(2)+y(3))^2)-kcat_dephosph*y(11)+kcat_dephosph*y(12);
% Ste11_pS y(11)
kcat_Ste20Ste11pS_pS*scaffold_Ste5*(y(3)*y(11)/(y(2)+y(3))^2)-kcat_Ste20Ste11pSpS_pT*scaffold_Ste5*(y(3)*y(12)/(y(2)+y(3))^2)-kcat_dephosph*y(12)+kcat_dephosph*y(13);
% Ste11_pSpS y(12)
kcat_Ste20Ste11pSpS_pT*scaffold_Ste5*(y(3)*y(12)/(y(2)+y(3))^2)-kcat_dephosph*y(13); % Ste11_pSpSpT
y(13)
-kcat_Ste11pSSte7_pS*y(11)*(y(3)/(y(2)+y(3)))*(y(6)*y(14)/(y(5)+y(6))^2)-kcat_Ste11pSpSSte7_pS*y(12)*(y(3)/(y(2)+y(3)))*(y(6)*y(14)/(y(5)+y(6))^2)-kcat_Ste11pSpSpTSte7_pS*y(13)*(y(3)/(y(2)+y(3)))*(y(6)*y(14)/(y(5)+y(6))^2)+kcat_dephosph*y(15);
% Ste7 y(14)
kcat_Ste11pSSte7_pS*y(11)*(y(3)/(y(2)+y(3)))*(y(6)*y(14)/(y(5)+y(6))^2)-kcat_Ste11pSSte7pS_pT*y(11)*(y(3)/(y(2)+y(3)))*(y(6)*y(15)/(y(5)+y(6))^2)+kcat_Ste11pSpSSte7_pS*y(12)*(y(3)/(y(2)+y(3)))*(y(6)*y(14)/(y(5)+y(6))^2)-kcat_Ste11pSpSSte7pS_pT*y(12)*(y(3)/(y(2)+y(3)))*(y(6)*y(15)/(y(5)+y(6))^2)+kcat_Ste11pSpSpTSte7_pS*y(13)*(y(3)/(y(2)+y(3)))*(y(6)*y(14)/(y(5)+y(6))^2)-kcat_Ste11pSpSpTSte7pS_pT*y(13)*(y(3)/(y(2)+y(3)))*(y(6)*y(15)/(y(5)+y(6))^2)-kcat_dephosph*y(15)+kcat_dephosph*y(16);
% Ste7_pS y(15)
kcat_Ste11pSSte7pS_pT*y(11)*(y(3)/(y(2)+y(3)))*(y(6)*y(15)/(y(5)+y(6))^2)+kcat_Ste11pSpSSte7pS_pT*y(12)*(y(3)/(y(2)+y(3)))*(y(6)*y(15)/(y(5)+y(6))^2)+kcat_Ste11pSpSpTSte7pS_pT*y(13)*(y(3)/(y(2)+y(3)))*(y(6)*y(15)/(y(5)+y(6))^2)-kcat_dephosph*y(16);
% Ste7_pSpT y(16)
-kcat_Ste5Ste7pSFus3_pY*y(15)*(y(6)/(y(5)+y(6)))*(y(9)*y(17)/(y(8)+y(9))^2)-kcat_Ste5Ste7pSFus3_pT*y(15)*(y(6)/(y(5)+y(6)))*(y(9)*y(17)/(y(8)+y(9))^2)-kcat_Ste5Ste7pSpTFus3_pY*y(16)*(y(6)/(y(5)+y(6)))*(y(9)*y(17)/(y(8)+y(9))^2)-kcat_Ste5Ste7pSpTFus3_pT*y(16)*(y(6)/(y(5)+y(6)))*(y(9)*y(17)/(y(8)+y(9))^2)+kcat_dephosph*y(18)+kcat_dephosph*y(19);
% Fus3 y(17)
kcat_Ste5Ste7pSFus3_pY*y(15)*(y(6)/(y(5)+y(6)))*(y(9)*y(17)/(y(8)+y(9))^2)-kcat_Ste5Ste7pSFus3pY_pT*y(15)*(y(6)/(y(5)+y(6)))*(y(9)*y(18)/(y(8)+y(9))^2)+kcat_Ste5Ste7pSpTFus3_pY*y(16)*(y(6)/(y(5)+y(6)))*(y(9)*y(17)/(y(8)+y(9))^2)-kcat_Ste5Ste7pSpTFus3pY_pT*y(16)*(y(6)/(y(5)+y(6)))*(y(9)*y(18)/(y(8)+y(9))^2)-kcat_dephosph*y(18)+kcat_dephosph*y(20);
% Fus3_pY y(18)
kcat_Ste5Ste7pSFus3_pT*y(15)*(y(6)/(y(5)+y(6)))*(y(9)*y(17)/(y(8)+y(9))^2)-kcat_Ste5Ste7pSFus3pT_pY*y(15)*(y(6)/(y(5)+y(6)))*(y(9)*y(19)/(y(8)+y(9))^2)+kcat_Ste5Ste7pSpTFus3_pT*y(16)*(y(6)/(y(5)+y(6)))*(y(9)*y(17)/(y(8)+y(9))^2)-kcat_Ste5Ste7pSpTFus3pT_pY*y(16)*(y(6)/(y(5)+y(6)))*(y(9)*y(19)/(y(8)+y(9))^2)-kcat_dephosph*y(19)+kcat_dephosph*y(20);
% Fus3_pT y(19)
kcat_Ste5Ste7pSFus3pY_pT*y(15)*(y(6)/(y(5)+y(6)))*(y(9)*y(18)/(y(8)+y(9))^2)+kcat_Ste5Ste7pSFus3pT_pY*y(15)*(y(6)/(y(5)+y(6)))*(y(9)*y(19)/(y(8)+y(9))^2)+kcat_Ste5Ste7pSpTFus3pY_pT*y(16)*(y(6)/(y(5)+y(6)))*(y(9)*y(18)/(y(8)+y(9))^2)+kcat_Ste5Ste7pSpTFus3pT_pY*y(16)*(y(6)/(y(5)+y(6)))*(y(9)*y(19)/(y(8)+y(9))^2)-2*kcat_dephosph*y(20);
% Fus3_pYpT y(20)
];
% Find the numerical solution of the system of ordinary differential equations
[t, Y] = ode45(odefun, tspan, [Ste5_off_Ste11; Ste11_off; Ste5_Ste11; Ste5_off_Ste7; Ste7_off;
Ste5_Ste7; Ste5_off_Fus3; Fus3_off; Ste5_Fus3; Ste11; Ste11_pS; Ste11_pSpS; Ste11_pSpSpT; Ste7;
Ste7_pS; Ste7_pSpT; Fus3; Fus3_pY; Fus3_pT; Fus3_pYpT]);
figure;
hold on;
plot(t, Y(:, 1), 'LineWidth', 2, 'DisplayName', 'Ste5_{off_{Ste11}}');
plot(t, Y(:, 2), 'LineWidth', 2, 'DisplayName', 'Ste11_{off}');
plot(t, Y(:, 3), 'LineWidth', 2, 'DisplayName', 'Ste5Ste11');
plot(t, Y(:, 4), 'LineWidth', 2, 'DisplayName', 'Ste5_{off_{Ste7}}');
plot(t, Y(:, 5), 'LineWidth', 2, 'DisplayName', 'Ste7_{off}');
plot(t, Y(:, 6), 'LineWidth', 2, 'DisplayName', 'Ste5Ste7');
plot(t, Y(:, 7), 'LineWidth', 2, 'DisplayName', 'Ste5_{off_{Fus3}}');
plot(t, Y(:, 8), 'LineWidth', 2, 'DisplayName', 'Fus3_{off}');
plot(t, Y(:, 9), 'LineWidth', 2, 'DisplayName', 'Ste5Fus3');
xlabel('Time (t)');
ylabel('Concentration');
title('Variable Change Graph');
legend show;
grid on;
hold off;
figure;
hold on;
plot(t, Y(:, 10), 'LineWidth', 2, 'DisplayName', 'Ste11');
plot(t, Y(:, 11), 'LineWidth', 2, 'DisplayName', 'Ste11_{pS}');
plot(t, Y(:, 12), 'LineWidth', 2, 'DisplayName', 'Ste11_{pSpS}');
plot(t, Y(:, 13), 'LineWidth', 2, 'DisplayName', 'Ste11_{pSpSpT}');
xlabel('Time (t)');
ylabel('Concentration');
title('Ste11 Variable Change Graph');
legend show;
grid on;
hold off;
figure;
hold on;
plot(t, Y(:, 14), 'LineWidth', 2, 'DisplayName', 'Ste7');
plot(t, Y(:, 15), 'LineWidth', 2, 'DisplayName', 'Ste7_{pS}');
plot(t, Y(:, 16), 'LineWidth', 2, 'DisplayName', 'Ste7_{pSpT}');
xlabel('Time (t)');
ylabel('Concentration');
title('Ste7 Variable Change Graph');
legend show;
grid on;
hold off;
figure;
hold on;
plot(t, Y(:, 17), 'LineWidth', 2, 'DisplayName', 'Fus3');
plot(t, Y(:, 18), 'LineWidth', 2, 'DisplayName', 'Fus3_{pY}');
plot(t, Y(:, 19), 'LineWidth', 2, 'DisplayName', 'Fus3_{pT}');
plot(t, Y(:, 20), 'LineWidth', 2, 'DisplayName', 'Fus3_{pYpT}');
xlabel('Time (t)');
ylabel('Concentration');
title('Fus3 Variable Change Graph');
legend show;
grid on;
hold off;</div>
<script>
function toggleCodeSnippet7() {
var codeSnippet = document.getElementById("codeSnippet7");
var button = document.getElementById("Button7"); // 注意变量名通常使用小写开头
if (codeSnippet.style.display === "none") {
codeSnippet.style.display = "block";
button.textContent = "Collapse the code"; // 使用之前选中的按钮元素
} else {
codeSnippet.style.display = "none";
button.textContent = "Expand the code"; // 使用之前选中的按钮元素
}
}
</script>
</div>
</div>
<div class="row mt-4">
<div class="col-lg-12">
<h2 id="topic4">
<h2>lactate Absorption Model</h2>
<hr>
<h3>Model Description</h3>
<p>
Our project alleviates IBD symptoms by secreting lactate in the intestine to weaken
autoimmunity, but it may face two aspects of doubt: first, why can't lactate or lactate
bacteria probiotics be taken directly; second, will the considerable secretion of lactate 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 lactate 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 lactate secretion to
regulate treatment time and prevent acidosis.
</p>
<h3>Basic Assumptions</h3>
<ol>
<li>Only the absorption process of lactate is described, without considering other effects of
lactate on the human body.</li>
<li>It is assumed that the location where lactate acts on immune cells is separated from the
intestinal environment.</li>
<li>It is assumed that the secretion rate of lactate is uniform, and activated yeast cells
secrete a total amount of lactate \(a\) within time \(t_0\), secreting \(\frac{a}{n}\) of
lactate in the time interval \(\frac{t_0}{n}\).</li>
</ol>
<h3>Model Equation</h3>
<p>
According to Fick's law :
</p>
<p>
\[
\frac{dQd}{dt} = -D \frac{dC}{dx}
\]
</p>
<p>
</p>
Because the distance between diffusion is very small, the concentration difference between the two sides
of the system replaces the concentration gradient, so this formula can be simplified to:
</p>
<p>
\[
\frac{dQd}{dt} = K\times Qd
\]
</p>
<h4>Direct Administration</h4>
<p>In the case of direct lactate intake, the content of lactate in the intestine can be
described by the following equation:</p>
<p>
\[ Q_d = (Q_{d_0} + a)e^{-(k_1 + k_2)t} \]
</p>
<p><strong>Explanation</strong>: The absorption rate is proportional to the concentration of lactic
acid, and the concentration of lactate declines in an exponential form.</p>
<p><strong>Parameters</strong>:</p>
<ul>
<li>\( Q_d \): Remaining lactate content in the intestinal environment</li>
<li>\( Q_{d_0} \): Initial lactate content in the intestinal environment</li>
<li>\( a \): Total amount of lactate ingested</li>
<li>\( k_1 \): Absorption rate of lactate</li>
<li>\( k_2 \): Rate at which lactate is eliminated due to metabolism and excretion</li>
<li>\( t \): Time</li>
</ul>
<h4>Induced Secretion</h4>
<p>The remaining lactate content in the intestinal environment has a recursive relationship over
time:</p>
<p>
\[ Q_{d_i} = \left(Q_{d_{i-1}} + \frac{a}{n}\right)e^{-(k_1 + k_2)(t - (i-1)\frac{t_0}{n})} \]
</p>
<p>We can obtain the expression:</p>
<p>
\[ Q_{d_i} = \frac{a}{n} \sum_{m=1}^{i-1} e^{-(k_1 + k_2)\left(mt - \left(j \frac{(m+2)(m+1)}{2}
\frac{t_0}{n}\right)\right)} \]
</p>
<div class="image-container">
<img src="https://static.igem.wiki/teams/5187/wiki-model-fig/4-1.png" alt="Lactate Absorption"
class="shadowed-image" style="width: 80%; max-width: 800px;">
</div>
<p style="text-align: center; font-size: 0.9em; margin-top: 10px;">fig 25 Lactate Absorption</p>
<button id="Button8" onclick="toggleCodeSnippet8()">lactate.m</button>
<div id="codeSnippet8" class="code-snippet">% Parameter settings
Qd0 = 0; % Initial lactic acid level
a = 50; % Total amount of lactic acid administered
k1 = 0.1; % Absorption rate of lactic acid
k2 = 0.05; % Metabolism and excretion rate of lactic acid
t0 = 20; % Total time
n = 10; % Number of induced secretions
time_step = 0.1; % Time step
% Time array
t = 0:time_step:t0;
% Direct administration simulation
Qd_direct = (Qd0 + a) * exp(-(k1 + k2) * t);
% Induced secretion simulation
Qd_induced = zeros(1, length(t));
for i = 1:n
% Calculate the time point for each induced secretion
current_time = (i-1) * (t0 / n);
if current_time <= t0
% Update concentration
for j = 1:length(t)
if t(j) >= current_time
Qd_induced(j) = Qd_induced(j) + a/n * exp(-(k1 + k2) * (t(j) - current_time));
end
end
end
end
% Plot results
figure;
hold on;
plot(t, Qd_direct, 'r-', 'LineWidth', 2, 'DisplayName', 'Direct Administration');
plot(t, Qd_induced, 'b-', 'LineWidth', 2, 'DisplayName', 'Induced Secretion');
xlabel('Time (t)');
ylabel('Intestinal Lactate Level (Qd)');
title('Lactate Concentration Change Curve');
legend;
grid on;
hold off;</div>
<script>
function toggleCodeSnippet8() {
var codeSnippet = document.getElementById("codeSnippet8");
var button = document.getElementById("Button8"); // 注意变量名通常使用小写开头
if (codeSnippet.style.display === "none") {
codeSnippet.style.display = "block";
button.textContent = "Collapse the code"; // 使用之前选中的按钮元素
} else {
codeSnippet.style.display = "none";
button.textContent = "Expand the code"; // 使用之前选中的按钮元素
}
}
</script>
<p>By simulating the absorption process of lactate, we can conclude that in the case of direct
administration, the concentration of lactate decreases exponentially over time, while in the
case of induced secretion, the concentration of lactate slowly increases over time and reaches
equilibrium after a certain period.</p>
</div>
</div>
</body>
</html>
{% endblock %}