Difference between revisions of "Team:USP-Brazil/Model"

(Replaced content with "{{USP-Brazil/teste}} {{USP-Brazil/GenswitchBootstrapCSS}}")
Line 2: Line 2:
  
 
{{USP-Brazil/GenswitchBootstrapCSS}}
 
{{USP-Brazil/GenswitchBootstrapCSS}}
 +
 +
 +
 +
 +
<html>
 +
<!-- MathJax (LaTeX for the web) -->
 +
<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_SVG.js" async>
 +
</script>
 +
<script type="text/x-mathjax-config">
 +
MathJax.Hub.Config({
 +
        SVG: { linebreaks: { automatic: true } }
 +
});
 +
</script>
 +
<head>
 +
<style>
 +
body {
 +
  margin: 0;
 +
  font-family: "Lato", sans-serif;
 +
}
 +
 +
.btn_expand {
 +
position: relative;
 +
width: 100%;
 +
padding: 0.75%;
 +
background-color: rgb (237, 95, 166);
 +
cursor: pointer;
 +
font-size:0.9em;
 +
box-sizing: border-box;
 +
border-radius: 5px;
 +
color: #f054a4
 +
border: 1px solid #d7d7d7;
 +
transition: border 0.1s ease-in-out, color 0.2s ease-in-out;
 +
 +
}
 +
 +
.carousel{
 +
    background: #2f4357;
 +
    margin-top: 20px;
 +
}
 +
.carousel-item{
 +
    text-align: center;
 +
    min-height: 280px; /* Prevent carousel from being distorted if for some reason image doesn't load */
 +
}
 +
.bs-example{
 +
margin: 20px;
 +
 +
}
 +
.carousel-imagepix{
 +
  max-height:450px;
 +
  min-width: 100%;
 +
 
 +
}
 +
* {
 +
  box-sizing: border-box;
 +
}
 +
 +
.column {
 +
  float: left;
 +
  width: 50%;
 +
  padding: 5px;
 +
}
 +
 +
/* Clearfix (clear floats) */
 +
.row::after {
 +
  content: "";
 +
  clear: both;
 +
  display: table;
 +
}
 +
div.a {
 +
  text-align: center;
 +
}
 +
 +
body {
 +
  margin: 0;
 +
  font-family: "Lato", sans-serif;
 +
}
 +
 +
.btn_expand {
 +
position: relative;
 +
width: 100%;
 +
padding: 0.75%;
 +
background-color: rgb (237, 95, 166);
 +
cursor: pointer;
 +
font-size:0.9em;
 +
box-sizing: border-box;
 +
border-radius: 5px;
 +
color: #f054a4
 +
border: 1px solid #d7d7d7;
 +
transition: border 0.1s ease-in-out, color 0.2s ease-in-out;
 +
 +
}
 +
 +
.carousel{
 +
    background: #2f4357;
 +
    margin-top: 20px;
 +
}
 +
.carousel-item{
 +
    text-align: center;
 +
    min-height: 280px; /* Prevent carousel from being distorted if for some reason image doesn't load */
 +
}
 +
.bs-example{
 +
margin: 20px;
 +
 +
}
 +
.carousel-imagepix{
 +
  max-height:450px;
 +
  min-width: 100%;
 +
 
 +
}
 +
 +
</style>
 +
</head>
 +
<body>
 +
<div class="row">
 +
<div class = "col-sm-1"></div>
 +
<div class = "col-sm-10">
 +
<p style = "text-align: left">
 +
With our project we aimed to create a system that could alternate between different states. And for that we created a circuit that utilizes a negative feedback loop combined with recombinases generating a switch (For further details go to the page (LINK)).
 +
</p>
 +
<p style = "text-align: left">
 +
To show that this concept can work with the circuit that we have in mind, we develop a model to simulate the expected behaviour of the system. But also, we had another problem: Which inhibitors we should use? If we choose inhibitors too weak for our system, the entire inversion system will collapse If we use an inhibitor that is too strong, we can be stuck in only one state.</p>
 +
<p style = "text-align: left">
 +
So, with that in mind, we develop a simple differential equation model, that allows us to predict the behaviour of our systems and, therefore, guiding our project.
 +
</p>
 +
</div>
 +
</div>
 +
</div>
 +
 +
<div class = "a">
 +
 
 +
    <h1 style= "color:rgba(50, 0, 188, 0.8);"> The Model</h1>
 +
 +
</div>
 +
<div class="row">
 +
<div class = "col-sm-1"></div>
 +
<div class = "col-sm-10">
 +
<p style = "text-align: left">At first, we had two initial choices of models: A boolean or a system of ODEs. The boolean could allow us to see the behaviour of our system, however since we are interested in finding not only the simulation of our circuit, but also with the behaviour in a continuous way, we choose to go with the ODEs. So, based in our design, we develop the following model:</p>
 +
<p style = "text-align: left">We created a visual representation of our circuits in 3 different sub-topics:
 +
<br>&nbsp; &nbsp; &nbsp;Promoter inversion; Promoter repression; Light promoter repression
 +
<br>These diagrams represent our ODEs and makes easier to understand and visualize them, we these representations:
 +
<ul>
 +
<li>Sphere – Variable of the system</li>
 +
<li>Line – Relation between the systems</li>
 +
<li>Arrow - indicates the directionality of the system (back of the arrow decreases and front of the arrow grows</li>
 +
<li>Bar (In the line) – Indicates no decreasing of the variable with the line</li>
 +
</ul></p>
 +
 +
INSERT FIGURE
 +
<p style = "text-align: left">
 +
We already represented our system of equations, where the variables are pS_ for the promoter State 1 ou 2, L_ for the light promoters, pS_r and L_r are the repressed promoters, Rc_ are the recombinases, Rs_ are the repressors and Rp_ are the promoters. (For a quicker look at the variables and parameters, check the table at the end of the page). So, from that we can write the ODEs.
 +
<br>&nbsp; And finally, our equations are the following:
 +
 +
$$\frac{dpS1}{dt} = RcB*i*(pS2+pS2r) + pS1r*\delta  - pS1(RcA*i + Rs2*fr2)    \\
 +
$$\frac{dpS2}{dt} = RcA*i*(pS1+pS1r) + pS2r*\delta  - pS2(RcB*i + Rs1*fr1) \\
 +
$$\frac{dL1}{dt} = L1r*\delta - L1*Rs2*fr2 \;|| \; \frac{dL2}{dt} = L2r*\delta - L2*Rs1*fr1 \\
 +
$$\frac{dpS1r}{dt} = pS1*Rs2*fr2 - pS1r*(\delta + RcA*i) \;||\; \frac{dpS2r}{dt} = pS2*Rs1*fr1 - pS2r*(\delta + RcB*i) \\
 +
$$\frac{dRcA}{dt} = L1*l*\alpha - \mu*RcA \;||\; \frac{dRcB}{dt} = L2*l*\alpha - \mu*RcB \\
 +
$$\frac{dRp1}{dt} = pS1*\alpha - \mu*Rp1 \;||\; \frac{dRp2}{dt} = pS2*\alpha - \mu*Rp2 \\
 +
$$\frac{dL1r}{dt} = -L1r*\delta + L1*Rs2*fr2 \;||\; \frac{dL2r}{dt} = -L2r*\delta + L2*Rs1*fr1 \\
 +
$$\frac{dRs1}{dt} = (pS1+L1)*\alpha + (pS2r+L2r)*\delta*\varphi - \mu*Rs1 \;||\; \frac{dRs2}{dt} = (pS2+L2)*\alpha + (pS1r+L1r)*\delta*\varphi - \mu*Rs2 $$
 +
 +
</p>
 +
 +
</div>
 +
</div>
 +
</div>
 +
 
 +
</div>
 +
 +
 +
 +
 +
</body>
 +
</html>
 +
 +
<html>

Revision as of 01:46, 22 October 2019



Sticky Animated Navigation Bar



With our project we aimed to create a system that could alternate between different states. And for that we created a circuit that utilizes a negative feedback loop combined with recombinases generating a switch (For further details go to the page (LINK)).

To show that this concept can work with the circuit that we have in mind, we develop a model to simulate the expected behaviour of the system. But also, we had another problem: Which inhibitors we should use? If we choose inhibitors too weak for our system, the entire inversion system will collapse If we use an inhibitor that is too strong, we can be stuck in only one state.

So, with that in mind, we develop a simple differential equation model, that allows us to predict the behaviour of our systems and, therefore, guiding our project.

The Model

At first, we had two initial choices of models: A boolean or a system of ODEs. The boolean could allow us to see the behaviour of our system, however since we are interested in finding not only the simulation of our circuit, but also with the behaviour in a continuous way, we choose to go with the ODEs. So, based in our design, we develop the following model:

We created a visual representation of our circuits in 3 different sub-topics:
     Promoter inversion; Promoter repression; Light promoter repression
These diagrams represent our ODEs and makes easier to understand and visualize them, we these representations:

  • Sphere – Variable of the system
  • Line – Relation between the systems
  • Arrow - indicates the directionality of the system (back of the arrow decreases and front of the arrow grows
  • Bar (In the line) – Indicates no decreasing of the variable with the line

INSERT FIGURE

We already represented our system of equations, where the variables are pS_ for the promoter State 1 ou 2, L_ for the light promoters, pS_r and L_r are the repressed promoters, Rc_ are the recombinases, Rs_ are the repressors and Rp_ are the promoters. (For a quicker look at the variables and parameters, check the table at the end of the page). So, from that we can write the ODEs.
  And finally, our equations are the following: $$\frac{dpS1}{dt} = RcB*i*(pS2+pS2r) + pS1r*\delta - pS1(RcA*i + Rs2*fr2) \\ $$\frac{dpS2}{dt} = RcA*i*(pS1+pS1r) + pS2r*\delta - pS2(RcB*i + Rs1*fr1) \\ $$\frac{dL1}{dt} = L1r*\delta - L1*Rs2*fr2 \;|| \; \frac{dL2}{dt} = L2r*\delta - L2*Rs1*fr1 \\ $$\frac{dpS1r}{dt} = pS1*Rs2*fr2 - pS1r*(\delta + RcA*i) \;||\; \frac{dpS2r}{dt} = pS2*Rs1*fr1 - pS2r*(\delta + RcB*i) \\ $$\frac{dRcA}{dt} = L1*l*\alpha - \mu*RcA \;||\; \frac{dRcB}{dt} = L2*l*\alpha - \mu*RcB \\ $$\frac{dRp1}{dt} = pS1*\alpha - \mu*Rp1 \;||\; \frac{dRp2}{dt} = pS2*\alpha - \mu*Rp2 \\ $$\frac{dL1r}{dt} = -L1r*\delta + L1*Rs2*fr2 \;||\; \frac{dL2r}{dt} = -L2r*\delta + L2*Rs1*fr1 \\ $$\frac{dRs1}{dt} = (pS1+L1)*\alpha + (pS2r+L2r)*\delta*\varphi - \mu*Rs1 \;||\; \frac{dRs2}{dt} = (pS2+L2)*\alpha + (pS1r+L1r)*\delta*\varphi - \mu*Rs2 $$