Team:LCG-UNAM-Mexico/Modeling

From 2008.igem.org

(Difference between revisions)
Line 14: Line 14:
<!--
<!--
.Estilo1 {color: #5C743D}
.Estilo1 {color: #5C743D}
 +
.style1 {font-size: 9px}
 +
.style2 {
 +
color: #5C743D;
 +
font-size: 14px;
 +
font-weight: bold;
 +
}
 +
.style3 {
 +
font-size: 14px;
 +
color: #5C743D;
 +
}
-->
-->
</style>
</style>
Line 83: Line 93:
   &nbsp;<br /> </td>
   &nbsp;<br /> </td>
     <td width="42">&nbsp;</td>
     <td width="42">&nbsp;</td>
-
     <td colspan="4" valign="top"><img src="https://static.igem.org/mediawiki/2008/7/70/Head_spacer.gif" alt="" width="305" height="1" border="0" /><br />
+
     <td colspan="4" valign="top"><div align="center"><img src="https://static.igem.org/mediawiki/2008/7/70/Head_spacer.gif" alt="" width="305" height="1" border="0" /><br />
-
&nbsp;<br />
+
      &nbsp;<br />
-
 
+
     
-
&nbsp;<br />
+
      &nbsp;<img src="https://static.igem.org/mediawiki/2008/5/5b/Model1a.jpg" /> <img src="https://static.igem.org/mediawiki/2008/4/43/Model2.jpg" /> <img src="https://static.igem.org/mediawiki/2008/7/7f/Model3.jpg" /><br>
-
        <table border="0" cellspacing="0" cellpadding="2" width="590">
+
      <img src="https://static.igem.org/mediawiki/2008/9/99/Ribbon435773498.gif" alt="ribbon" width="579" height="9" /><br />
 +
    </div>
 +
      <table border="0" cellspacing="0" cellpadding="2" width="590">
             <tr>
             <tr>
-
           <td class="pageName">Modeling</td>
+
           <td class="pageName"><div align="center">
 +
            <p>Modeling the system </p>
 +
          </div></td>
         </tr>
         </tr>
         <tr>
         <tr>
-
           <td class="bodyText"><p align="justify"><br>
+
           <td class="bodyText"><p align="justify">The objective of our modelling is to accurately describe and predict the behavior of the system and its response given an inducing signal. Also, we aim to better know and understand the&nbsp; system through the  identification of critical parameters and species, and thus be able to  obtain the desired dynamics.<br />
-
            We are using MatLab to simulate our system. We have already done a first approximation which did not contain real parameteres; however we tried to keep the system consistent within itself. Don't know what we're talking about? Take a look at our <a href="https://2008.igem.org/Team:LCG-UNAM-Mexico/Project" title="Project Description">project description</a>. </p>
+
              Our system is composed of 13 species and 11 coupled biochemical reactions that completely describe it. This can be represented through a set of ordinary differential equations (ODEs). The simulations were done using Simbiology, a package from Matlab.</p>
-
             <p align="justify">&nbsp;</p>
+
            <p align="center"> <img alt="Iwig 2006" src="https://static.igem.org/mediawiki/2008/4/47/Diagrama3.jpg"> </p>
-
             <p><strong>Metabolites and enzymes relevant to the model </strong></p>
+
             <p align="justify" class="style1"><strong><em>FIG 1</em>:</strong> Our system is conformed by two regulation mechanisms. The first mechanism is the one controlled by us through AHL. LuxR and AiiA compete to bind AHL when it enters the cell. AiiA efficiently degrades AHL, while LuxR and AHL form a dimer. This dimer serves as an activator of cI*, which represses RcnA. The second of these mechanisms is the natural regulation of RcnA in response to the intracellular nickel concentration. When there is no nickel inside the cell, RcnR represses RcnA. However, when nickel enters the cell, it forms a dimer with RcnR and changes its conformation so it no longer represses RcnA. RcnA is then free to start pumping Ni  out of the cell. We are keeping this because it is damaging to the  bacteria to have the pump always on, and otherwise it would need a  constant supply of AHL.<br>
-
             <table width="585" border="0">
+
              <br>
 +
            </p>
 +
             <p class="style3"><strong>Metabolites and enzymes relevant to the model </strong></p>
 +
             <table width="585" border="0" bordercolor="#75923C">
               <tr>
               <tr>
-
                 <td width="132"><ol>
+
                 <td width="170"><ol>
-
                  <li> AiiA</li>
+
                    <li> AiiA </li>
-
                  <li>AHL</li>
+
                              <li> AHL </li>
-
                  <li>LuxR</li>
+
                              <li> LuxR </li>
-
                  <li>AHL:LuxR</li>
+
                              <li> AHL:LuxR </li>
-
                  <li>cI*</li>
+
                              <li> (AHL:LuxR):(AHL:LUXR)<br>
-
                  <li>ρ</li>
+
                              </li>
-
                  <li>ρ:cI*</li>
+
                              <li> ρcI </li>
-
                  <li>RcnA</li>
+
                              <li> CI </li>
-
                  <li>Ni[int]</li>
+
                              <li> CI:CI </li>
-
                  <li>Ni[ext]</li>
+
                              <li> ρ </li>
-
                  <li>Unk</li>
+
                              <li> RcnA </li>
 +
                              <li> Ni[int]</li>
 +
                              <li> Ni[ext] </li>
 +
                              <li> Unk</li>
                 </ol>                </td>
                 </ol>                </td>
-
                 <td width="443" valign="top"><p>Acyl-Homoserine Lactone Lactonase<br>
+
                 <td width="405" valign="top" bordercolor="1"><p>Acyl-Homoserine Lactone Lactonase<br>
-
                  Acyl-Homoserine Lactone<br>
+
Acyl-Homoserine Lactone<br>
-
                  Transcriptional Activator<br>
+
Transcriptional Activator<br>
-
                  Complex formed by AHL and LuxR<br>
+
Complex formed by AHL and LuxR<br>
-
                  λ phage repressor (cI) modified with a LVA tail for quick degradation<br>
+
Dimer of AHL:LuxR complexes<br>
-
                  <em>rcnA</em> promoter<br>
+
cI* promoter, inducible by the dimer of AHL:LuxR complexes<br>
-
                  Complex formed by cI* repressor and <em>rcnA</em> promoter <br>  
+
λ phage repressor (CI) modified with a LVA tail for quick degradation<br>
-
                  <em>Escherichia coli</em> nickel efflux pump<br>
+
Repressor, dimer of CI molecules<br>
-
                  Intracellular nickel<br>
+
<em>rcnA</em> promoter, modified to be repressible by CI:CI<br>
-
                  Extracellular nickel
+
<em>Escherichia coli</em> nickel efflux pump<br>
-
                  <br>
+
Intracellular nickel<br>
-
                  Unknown nickel import channel <br>
+
Extracellular nickel<br>
 +
Unknown nickel import channel<br>
                 </p>                </td>
                 </p>                </td>
               </tr>
               </tr>
             </table>
             </table>
-
             <p>&nbsp;</p>
+
             <br>
-
             <p><strong>Reactions</strong></p>
+
            <br>
-
             <table width="585" border="0">
+
             <p><strong><span class="style3">Reactions</span><br>
-
              <tr>
+
              </strong><br>
-
                <td width="206" valign="top"><ol>
+
              You can click on the next image to see a table of our reactions with their kinetics.</p>
-
                    <li>AiiA + AHL <strong>-&gt;</strong> AiiA </li>
+
             <p><img src="https://static.igem.org/mediawiki/2008/1/12/Bichem_react_table.PNG" alt="Table of biochemical reactions" width="581" height="279"><span class="style1"><br>
-
                    <li>AHL + LuxR <strong>&lt;--&gt;</strong> AHL:LuxR </li>
+
                <strong>* </strong>The equations are numbered like this because those we  had initially defined evolved into this final list throughout the  summer. We didn't want to change all references made to these equations  so we just adjusted the numbering.<br>
-
                    <li>AHL:LuxR <strong>-&gt;</strong> AHL:LuxR + cI*</li>
+
            </span><br>
-
                    <li>cI* <strong>-&gt;</strong> Ø</li>
+
            </p>
-
                    <li>ρ + cI* <strong>&lt;-&gt;</strong> ρ:cI*</li>
+
            <p class="style2">Ordinary Differential Equations</p>
-
                    <li>ρ <strong>-&gt;</strong> ρ + RcnA</li>
+
            <p align="justify">We are taking into account the following set of ODEs, based on the biochemical reactions above. This set  accurately and completely describes our model. Please click on the image to see a higher resolution.</p>
-
                    <li>RcnA + Ni[int] <strong>-&gt;</strong> RcnA + Ni[ext]</li>
+
            <p align="center"><br>
-
                    <li>RcnA <strong>-&gt;</strong> Ø</li>
+
              <img src="https://static.igem.org/mediawiki/2008/6/63/Equationa.PNG" alt="Set of ODEs"></p>
-
                    <li>Unk +  Ni[ext] <strong>-&gt;</strong> Unk + Ni[int]</li>
+
            <p><strong><span class="style3"><br>
-
                </ol></td>
+
              Assumptions of the model </span><br>
-
                <td width="369" valign="top"><p>Degradation of AHL by AiiA<br>
+
               <br>
-
                  Complex formation and dissociation between AHL and LuxR<br>
+
             </strong></p>
-
                  Transcription activation
+
             <div id="lev4">
-
                of cI* by AHL and LuxR complex<br>
+
              <ol>
-
                Natural degradation of cI*<br>
+
                <li>
-
                Complex formation and dissociation between
+
                  <div align="justify"> <strong>Once there is nickel in the medium, RcnR no longer participates in the pump’s regulation.</strong> If there’s nickel in the medium, we can assume that RcnR is always coupled with a Ni molecule, so it will not be capable of repressing RcnA (The few RcnR molecules in the cell will cause noise, but this  will be indistinguishable from the pump’s normal behavior). [1]<strong></strong> </div>
-
ρ and cI*<br>
+
                </li>
-
                RcnA production<br>
+
                <li> <strong>Cell membrane permeability to AHL is not considered inside the model.</strong> The model assumes all AHL enters the cell, however the concentration  needed in the model to obtain the desired results is changed by us  accordingly. [2]<br>
-
                Nickel efflux by RcnA<br>
+
                 </li>
-
                Natural degradation of RcnA
+
                <li>
-
                <br>
+
                  <div align="justify"> <strong>All decrease in AHL concentration is due to AiiA.</strong> We consider the natural degradation of AHL to be unimportant given the time taken to make the analysis (AHL half-life is long, from 3 to 24 hours). [3] </div>
-
                Nickel import by the unknown channel
+
                </li>
-
</p></td>
+
                <li>
-
               </tr>
+
                  <div align="justify"> <strong>The change in the transcription of cI* is only dependent on AHL concentration.</strong> There’s a basal production of cI*, however the change will always be due to the AHL concentration given that production of LuxR is constitutive. </div>
-
             </table>
+
                </li>
-
            <p>&nbsp;</p>
+
                <li>
-
             <p><strong>Assumptions of the model </strong></p>
+
                  <div align="justify"> <strong>It is a homogeneous system.</strong> This means that the coefficients of the equations are constant (so we don’t have compartmentalization). </div>
-
            <ol>
+
                </li>
-
              <li>
+
                <li>
-
                <div align="justify"><strong>Once there is nickel in the medium, RcnR no longer participates in the pump’s regulation.</strong> If there’s nickel in the medium, we can assume that RcnR is always coupled with a Ni molecule, so it will not be capable of repressing RcnA (The few RcnR molecules in the cell will cause noise, but this  will be indistinguishable from the pump’s normal behavior).</div>
+
                  <div align="justify"> <strong>The quantity of nickel used by the cell is negligible compared to the concentrations in and out of the cell.</strong> This means we don’t need to include an equation describing the change in the Ni concentration due to cell consumption in the time used by the experiment. [1] </div>
-
              </li>
+
                </li>
-
              <li>
+
                <li>
-
                 <div align="justify"><strong>All decrease in AHL concentration is due to AiiA.</strong> We consider the natural degradation of AHL to be unimportant given the time taken to make the analysis (AHL half-life is long, from 3 to 24 hours).</div>
+
                  <div align="justify"> <strong>The  production of RcnR, LuxR and AiiA is constitutive and their concentrations have reached the steady state at the beginning of the  experiment.</strong> </div>
-
              </li>
+
                </li>
-
              <li>
+
                <li>
-
                <div align="justify"><strong>The change in the transcription of cI* is only dependent on AHL concentration.</strong> There’s a basal production of cI*, however the change will always be due to the AHL concentration given that production of LuxR is constitutive. </div>
+
                  <div align="justify"> <strong>NikABCDE will not play a role in our model.</strong> NikABCDE serves to import nickel to the cell, however it only works in anaerobic conditions and our experiment will be made in aerobic conditions. This therefore implies that the nickel import will only take place by the unknown mechanism, which nonetheless is constant and constitutive. [1] </div>
-
              </li>
+
                </li>
-
              <li>
+
              </ol>
-
                <div align="justify"><strong>It is a homogeneous system.</strong> This means that the coefficients of the equations are constant (so we don’t have compartmentalization). </div>
+
              <strong>References</strong><br>
-
              </li>
+
             </div>
-
              <li>
+
            <div id="lev4">
-
                <div align="justify"><strong>The quantity of nickel used by the cell is negligible compared to the concentrations in and out of the cell.</strong> This means we don’t need to include an equation describing the change in the Ni concentration due to cell consumption in the time used by the experiment.</div>
+
              <p> 1- Nickel homeostasis in Escherichia coli – the rcnR-rcnA efflux pathway and its linkage to NikR function Jeffrey S. Iwig, Jessica L. Rowe and Peter T. Chivers* Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St Louis, MO, 63110, USA. Molecular Microbiology (2006) 62(1), 252–262 doi:10.1111/j.1365-2958.2006.05369.x </p>
-
              </li>
+
              <p>2- Biological Sciences - Biophysics: Tianhai Tian and Kevin Burrage Stochastic models for regulatory networks of the genetic toggle switch PNAS 2006 103:8372-8377; published ahead of print May 19, 2006, doi:10.1073/pnas.0507818103 </p>
-
              <li>
+
              <p>3- http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/parts/BBa_I13207 </p>
-
                <div align="justify"><strong>The  production of RcnR, LuxR and AiiA is constitutive and their concentrations have reached the steady state.</strong> </div>
+
              <p><br>
-
              </li>
+
              </p>
-
              <li>
+
              <p> </p>
-
                <div align="justify"><strong>NikABCDE will not play a role in our model.</strong> NikABCDE serves to import nickel to the cell, however it only works in anaerobic conditions and our experiment will be made in aerobic conditions. This therefore implies that the nickel import will only take place by the unknown mechanism, which nonetheless is constant and constitutive.</div>
+
            </div></td>
-
              </li>
+
-
            </ol>
+
-
             <p align="justify" class="Estilo1">We still need to state here, why can we assume  these things?</p>
+
-
            <p align="justify" class="Estilo1">&nbsp;</p></td>
+
         </tr>
         </tr>
-
  <td class="pageName">Modeling details </td>
+
    <td class="pageName"><div align="center">Parameters &amp; kinetics </div></td>
         <tr>
         <tr>
-
           <td valign="top" class="bodyText"><p><br>
+
           <td valign="top" class="bodyText"><p align="justify"><br>
-
              <strong>Pending</strong>: cI* and AHL:LuxR dimerization, should we include them in the model? </p>
+
The complete model uses 18 kinetic parameters and 11 biochemical  reactions. We got 13 of these parameters researching the literature,  and of the other 5 we estimated 2. The remaining 3 we adjusted to the  observed results. Reaction kinetics were gotten from the literature,  and if no evidence was found then we assumed it to be Law of Mass  Action.<br>
-
             <p>Details coming soon! <br>
+
<br>
-
            </p></td>
+
1. Degradation of AHL by AiiA <br>
 +
          </p>
 +
             <p align="justify"><br>
 +
              </p></td>
</tr>
</tr>
-
         <tr>
+
         <td class="pageName">Modeling details </td>
-
          <td valign="top" class="bodyText">&nbsp;</td>
+
-
        </tr>
+
     </table>
     </table>
         <br />
         <br />

Revision as of 06:50, 27 October 2008

LCG-UNAM-Mexico:Modeling

Header image
iGEM 2008 TEAM
line decor
  
line decor

 
 
 
  

 
 
ribbon

Modeling the system

The objective of our modelling is to accurately describe and predict the behavior of the system and its response given an inducing signal. Also, we aim to better know and understand the  system through the identification of critical parameters and species, and thus be able to obtain the desired dynamics.
Our system is composed of 13 species and 11 coupled biochemical reactions that completely describe it. This can be represented through a set of ordinary differential equations (ODEs). The simulations were done using Simbiology, a package from Matlab.

Iwig 2006

FIG 1: Our system is conformed by two regulation mechanisms. The first mechanism is the one controlled by us through AHL. LuxR and AiiA compete to bind AHL when it enters the cell. AiiA efficiently degrades AHL, while LuxR and AHL form a dimer. This dimer serves as an activator of cI*, which represses RcnA. The second of these mechanisms is the natural regulation of RcnA in response to the intracellular nickel concentration. When there is no nickel inside the cell, RcnR represses RcnA. However, when nickel enters the cell, it forms a dimer with RcnR and changes its conformation so it no longer represses RcnA. RcnA is then free to start pumping Ni out of the cell. We are keeping this because it is damaging to the bacteria to have the pump always on, and otherwise it would need a constant supply of AHL.

Metabolites and enzymes relevant to the model

  1. AiiA
  2. AHL
  3. LuxR
  4. AHL:LuxR
  5. (AHL:LuxR):(AHL:LUXR)
  6. ρcI
  7. CI
  8. CI:CI
  9. ρ
  10. RcnA
  11. Ni[int]
  12. Ni[ext]
  13. Unk

Acyl-Homoserine Lactone Lactonase
Acyl-Homoserine Lactone
Transcriptional Activator
Complex formed by AHL and LuxR
Dimer of AHL:LuxR complexes
cI* promoter, inducible by the dimer of AHL:LuxR complexes
λ phage repressor (CI) modified with a LVA tail for quick degradation
Repressor, dimer of CI molecules
rcnA promoter, modified to be repressible by CI:CI
Escherichia coli nickel efflux pump
Intracellular nickel
Extracellular nickel
Unknown nickel import channel


Reactions

You can click on the next image to see a table of our reactions with their kinetics.

Table of biochemical reactions
* The equations are numbered like this because those we had initially defined evolved into this final list throughout the summer. We didn't want to change all references made to these equations so we just adjusted the numbering.

Ordinary Differential Equations

We are taking into account the following set of ODEs, based on the biochemical reactions above. This set accurately and completely describes our model. Please click on the image to see a higher resolution.


Set of ODEs


Assumptions of the model

  1. Once there is nickel in the medium, RcnR no longer participates in the pump’s regulation. If there’s nickel in the medium, we can assume that RcnR is always coupled with a Ni molecule, so it will not be capable of repressing RcnA (The few RcnR molecules in the cell will cause noise, but this will be indistinguishable from the pump’s normal behavior). [1]
  2. Cell membrane permeability to AHL is not considered inside the model. The model assumes all AHL enters the cell, however the concentration needed in the model to obtain the desired results is changed by us accordingly. [2]
  3. All decrease in AHL concentration is due to AiiA. We consider the natural degradation of AHL to be unimportant given the time taken to make the analysis (AHL half-life is long, from 3 to 24 hours). [3]
  4. The change in the transcription of cI* is only dependent on AHL concentration. There’s a basal production of cI*, however the change will always be due to the AHL concentration given that production of LuxR is constitutive.
  5. It is a homogeneous system. This means that the coefficients of the equations are constant (so we don’t have compartmentalization).
  6. The quantity of nickel used by the cell is negligible compared to the concentrations in and out of the cell. This means we don’t need to include an equation describing the change in the Ni concentration due to cell consumption in the time used by the experiment. [1]
  7. The production of RcnR, LuxR and AiiA is constitutive and their concentrations have reached the steady state at the beginning of the experiment.
  8. NikABCDE will not play a role in our model. NikABCDE serves to import nickel to the cell, however it only works in anaerobic conditions and our experiment will be made in aerobic conditions. This therefore implies that the nickel import will only take place by the unknown mechanism, which nonetheless is constant and constitutive. [1]
References

1- Nickel homeostasis in Escherichia coli – the rcnR-rcnA efflux pathway and its linkage to NikR function Jeffrey S. Iwig, Jessica L. Rowe and Peter T. Chivers* Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St Louis, MO, 63110, USA. Molecular Microbiology (2006) 62(1), 252–262 doi:10.1111/j.1365-2958.2006.05369.x

2- Biological Sciences - Biophysics: Tianhai Tian and Kevin Burrage Stochastic models for regulatory networks of the genetic toggle switch PNAS 2006 103:8372-8377; published ahead of print May 19, 2006, doi:10.1073/pnas.0507818103

3- http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/parts/BBa_I13207


Parameters & kinetics


The complete model uses 18 kinetic parameters and 11 biochemical reactions. We got 13 of these parameters researching the literature, and of the other 5 we estimated 2. The remaining 3 we adjusted to the observed results. Reaction kinetics were gotten from the literature, and if no evidence was found then we assumed it to be Law of Mass Action.

1. Degradation of AHL by AiiA


Modeling details

 
 
             

Retrieved from "http://2008.igem.org/Team:LCG-UNAM-Mexico/Modeling"