Team:Valencia/Modeling

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</p><p>Our main sponsors:
 
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</p><p>Our institutions:
 
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<p>"Water Colicin Cleaner: disinfected water by E. coli"</p>
 
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<p>The aim of our team is to develop a biological alternative for disinfecting contaminated water using synthetic biology. We will kill targeted pathogens by means of antimicrobial peptides in Escherichia coli. The activity of these proteins will be controlled by a biological pH-stat that will use cyanobacteria to control pH.
 
-
We plan to deliver a DIY kit that will help people that struggle to find pathogen-free drinking water avoiding important diseases, such as cholera, diarrhea and typhoid fever, ending in more than 2 million deaths in the last year according to the WHO Guidelines for Drinking-Water Quality (World Health Organization, 2011).
 
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<a href="/images/3/32/Albuferavalencia.jpg" class="image" title="Valencia MarsTransition.jpg"><img alt="" src="/wiki/images/3/32/Albuferavalencia.jpg" width="690" height="300" border="0" /></a>
 
-
</p><p><br />
 
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</p><p>T.1
 
-
</p><p>T.2
 
-
</p><p>T.3
 
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</p><p>T.4
 
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</p>
 
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<a name="The_Valencia_IGEM_Team_2010"></a><h1> <span class="mw-headline">The Valencia IGEM Team 2010</span></h1>
 
-
<div class="floatright"><span><a href="/Image:Valencia_logo_loco_200.png" class="image" title="Valencia logo loco 200.png"><img alt="" src="/wiki/images/thumb/7/7f/Valencia_logo_loco_200.png/180px-Valencia_logo_loco_200.png" width="50" height="50" border="0" /></a></span></div>
 
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<p>T.6
 
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<br />
 
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</p>
 
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<a name="News"></a><h1> <span class="mw-headline">News</span></h1>
 
-
<div class="floatright"><span><a href="/Image:Valencia_nasa.jpg" class="image" title="NASA"><img alt="NASA" src="/wiki/images/thumb/a/a1/Valencia_nasa.jpg/140px-Valencia_nasa.jpg" width="50" height="50" border="0" /></a></span></div>
 
-
<ul><li>02/11/2011 - Meeting with David Bergner, Deputy Chief of the <a href="http://spacebiosciences.arc.nasa.gov/" class="external text" title="http://spacebiosciences.arc.nasa.gov/" rel="nofollow">Division of Space Biosciences</a>, from <a href="http://www.nasa.gov/centers/ames/home/index.html" class="external text" title="http://www.nasa.gov/centers/ames/home/index.html" rel="nofollow">NASA Ames Research Center</a>. Discussed synthetic biology application in space bioscience.
 
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<div class="floatleft"><span><a href="/Image:Valencia_jamboree.jpg" class="image" title="Jamboree 2010"><img alt="Jamboree 2010" src="/wiki/images/thumb/b/b1/Valencia_jamboree.jpg/200px-Valencia_jamboree.jpg" width="200" height="133" border="0" /></a></span></div>
 
-
<p><b>Jamboree 2010 Highlights</b>
 
-
</p><p><a href="/Image:Valencia_gold_medal.jpg" class="image" title="Image:valencia_gold medal.jpg"><img alt="Image:valencia_gold medal.jpg" src="/wiki/images/4/44/Valencia_gold_medal.jpg" width="50" height="30" border="0" /></a>
 
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<b>Valencia Team in the News</b>
 
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<h2>pH variations with light</h2>
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                          title="Recent changes in pages linked from this page [k]" accesskey="k">Related changes</a></li>
+
<p>We have successfully simulated the behaviour of pH changes in response to irradiation on cyanobacteria <i>Synechocystis</i> sp. PCC 6803, as you can see by this graph:
 +
<center><div><span><a href="https://static.igem.org/mediawiki/2011/f/fd/VLC_Resultat.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/f/fd/VLC_Resultat.png" width="800" align="center" border="0" /></a></span></div></center></p>
 +
<b>Why is this important?</b>
 +
<p>A model is not good or wrong, is more or less useful. Our model apart from making us think about the causes and relationships among the effects involved in this mechanism, has help us understand some results of the <a href="https://2011.igem.org/Team:Valencia/Project2" TARGET="_blank" title="pH variations">pH variations</a> in our pH-stat.</p>
 +
<b>How have done this?</b>
 +
<p>First of all, we have to think on the physics of the behaviour we wanted to describe. We have light arriving upon a cyanobacteria and pH changing more or less proportionately to the time of irradiation.</p>
 +
<p>Thus, we have a light input and a pH variation output.</p>
 +
<center><div><span><a href="https://static.igem.org/mediawiki/2011/9/90/VLC_Un_escalo.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/9/90/VLC_Un_escalo.png" width="800" align="center" border="0" /></a></span></div></center>
 +
<p>Now we need a transfer function that giving a light input delivers and output such as the one observed. To that purpose we can observe that the response (pH variation) behaves like a first order system with a lagging time.</p><br>
 +
<p>We work on the frequency plane (using Laplace transforms). Thus, transfer function of a first order system with a lagging time is such as:</p><br>
 +
<center><div><span><a href="https://static.igem.org/mediawiki/2011/a/a6/VLC_Eq1.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/a/a6/VLC_Eq1.png" width="400" align="center" border="0" /></a></span></div></center>
 +
<p>Using the transfer function of the system we can get the response such as:</p><br>
 +
y(t) = pH - pH<sub>0</sub><br>
 +
y(s)= L [y(t)] where L[] function is Laplace transform<br>
 +
y(s) = G(s)·u(s)<br>
 +
<p>With the experimental data we have obtained the parameters values:</p><br>
 +
<center><div><span><a href="https://static.igem.org/mediawiki/2011/9/93/VLC_Param.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/9/93/VLC_Param.png" width="400" align="" border="0" /></a></span></div></center><br>
 +
And with them we can adjust almost perfectly the experimental upwards dynamics:<br>
 +
<center><div><span><a href="https://static.igem.org/mediawiki/2011/6/6c/VLC_Realisim.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/6/6c/VLC_Realisim.png" width="500" align="" border="0" /></a></span></div></center><br>
 +
We assume that the dynamics downwards should have the same underlying physics, so parameters should remain the same, we obtain a theoretical simulation and tallies real data:<br>
 +
<center><div><span><a href="https://static.igem.org/mediawiki/2011/4/41/VLC_Baixada.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/4/41/VLC_Baixada.png" width="800" align="" border="0" /></a></span></div></center>
 +
As we can see, they are pretty much equivalent.<br>
 +
Anyway, let's consider now more than one peak. If we have different pulses of light, it's straight ofrward to think that we'll have different peaks of pH variations, but, if we look closer to the time series, we observe that gain response is weaker as time goes by and the basal value follows a slow, but constant upward tendency.<br>
 +
<center><div><span><a href="https://static.igem.org/mediawiki/2011/4/47/VLC_Llarga.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/4/47/VLC_Llarga.png" width="700" align="" border="0" /></a></span></div></center><br>
 +
In order to model this behaviour we'll use two functions:<br>
 +
On one hand a buffering function that will multiply the response function
 +
<center><div><span><a href="https://static.igem.org/mediawiki/2011/f/fe/VLC_At.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/f/fe/VLC_At.png" width="150" align="" border="0" /></a></span></div></center><br>
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On the other hand a function that models appropriately the increase of a basal point is the following one and should be added to the response function.
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<center><div><span><a href="https://static.igem.org/mediawiki/2011/4/48/VLC_Bt.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/4/48/VLC_Bt.png" width="200" align="" border="0" /></a></span></div></center><br>
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As we have done before, we can calculate the following parameters:
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<center><div><span><a href="https://static.igem.org/mediawiki/2011/3/31/VLC_Tresparam.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/3/31/VLC_Tresparam.png" width="300" align="" border="0" /></a></span></div></center><br>
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With them, we can get the final equations:<br>
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y(s) = G(s)·u(s)<br>
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+
y(s)= L<sup>-1</sup>[y(s)]  (reversed Laplace transform)<br>
 +
Y(t) = y(t)·A(t)+B(t)<br>
 +
pH=Y(t) + pH<sub>0</sub><br><br>
 +
Function y(t) is not easy to describe as it is a stepwise function depending of the time of the simulation, it is like:
 +
<center><div><span><a href="https://static.igem.org/mediawiki/2011/1/13/VLC_Yt.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/1/13/VLC_Yt.png" width="875" align="" border="0" /></a></span></div></center>
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Now, just run the set of equations and plot the results accordingly and you have the graph:
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<center><div><span><a href="https://static.igem.org/mediawiki/2011/f/fd/VLC_Resultat.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/f/fd/VLC_Resultat.png" width="800" align="center" border="0" /></a></span></div></center>
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<h2>Bacteriocin efficiency on killing bacteria</h2>
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<p>It is really important to understand the bacterias resistance against antimicrobial peptides for many bioremediation and health applications. With the following modeling, we want to know which is the response from our pathogens towards different bacteriocins concentrations and deduce which is the approximated amount of peptides needed to kill around the whole culture, which is 0.7µM of bacteriocin in our simulation.</p>
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<center><div><span><a href="https://static.igem.org/mediawiki/2011/3/34/Pepti.png" class="image" ><img alt="" src="https://static.igem.org/mediawiki/2011/3/34/Pepti.png" width="800" align="center" border="0" /></a></span></div></center>
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The model above consists of a logistic regression with following expression:
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<center><IMG SRC="https://static.igem.org/mediawiki/2011/1/14/Valeqmodel1.JPG" ALT="Overall Setup"></center>
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where we simulate the % of targeted killed bacteria vs the concentration of peptides.
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The fitting of the experimental values has an AIC of 49,27.<br/><br/>
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<center><IMG SRC="https://static.igem.org/mediawiki/2011/c/cd/Valeqmodel2.JPG" ALT="Overall Setup"></center>
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Own experimental values where not validated, so similar results have been taken for the model from an external source: </br></br>
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"Clavanin permeabilizes target membranes via two distinct ph-dependent mechanisms", Ellen J. M. van Kan.

Latest revision as of 03:47, 22 September 2011



Modeling

pH variations with light

We have successfully simulated the behaviour of pH changes in response to irradiation on cyanobacteria Synechocystis sp. PCC 6803, as you can see by this graph:

Why is this important?

A model is not good or wrong, is more or less useful. Our model apart from making us think about the causes and relationships among the effects involved in this mechanism, has help us understand some results of the pH variations in our pH-stat.

How have done this?

First of all, we have to think on the physics of the behaviour we wanted to describe. We have light arriving upon a cyanobacteria and pH changing more or less proportionately to the time of irradiation.

Thus, we have a light input and a pH variation output.

Now we need a transfer function that giving a light input delivers and output such as the one observed. To that purpose we can observe that the response (pH variation) behaves like a first order system with a lagging time.


We work on the frequency plane (using Laplace transforms). Thus, transfer function of a first order system with a lagging time is such as:


Using the transfer function of the system we can get the response such as:


y(t) = pH - pH0
y(s)= L [y(t)] where L[] function is Laplace transform
y(s) = G(s)·u(s)

With the experimental data we have obtained the parameters values:



And with them we can adjust almost perfectly the experimental upwards dynamics:

We assume that the dynamics downwards should have the same underlying physics, so parameters should remain the same, we obtain a theoretical simulation and tallies real data:
As we can see, they are pretty much equivalent.
Anyway, let's consider now more than one peak. If we have different pulses of light, it's straight ofrward to think that we'll have different peaks of pH variations, but, if we look closer to the time series, we observe that gain response is weaker as time goes by and the basal value follows a slow, but constant upward tendency.

In order to model this behaviour we'll use two functions:
On one hand a buffering function that will multiply the response function

On the other hand a function that models appropriately the increase of a basal point is the following one and should be added to the response function.

As we have done before, we can calculate the following parameters:

With them, we can get the final equations:
y(s) = G(s)·u(s)
y(s)= L-1[y(s)] (reversed Laplace transform)
Y(t) = y(t)·A(t)+B(t)
pH=Y(t) + pH0

Function y(t) is not easy to describe as it is a stepwise function depending of the time of the simulation, it is like:
Now, just run the set of equations and plot the results accordingly and you have the graph:


Bacteriocin efficiency on killing bacteria

It is really important to understand the bacterias resistance against antimicrobial peptides for many bioremediation and health applications. With the following modeling, we want to know which is the response from our pathogens towards different bacteriocins concentrations and deduce which is the approximated amount of peptides needed to kill around the whole culture, which is 0.7µM of bacteriocin in our simulation.



The model above consists of a logistic regression with following expression:
Overall Setup
where we simulate the % of targeted killed bacteria vs the concentration of peptides. The fitting of the experimental values has an AIC of 49,27.

Overall Setup


Own experimental values where not validated, so similar results have been taken for the model from an external source:

"Clavanin permeabilizes target membranes via two distinct ph-dependent mechanisms", Ellen J. M. van Kan.