Team:Grenoble/Projet/Modelling/Stochastic

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<html>
<html>
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<div class="body">
<div class="body">
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<div class="left">
<div class="left">
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    <h1>Modelling - Stochastic</h1>
 
-
        <p>
 
-
With precedent modelling, we get the deterministic behavior of our system. All the parameters are precisely known and the solution obtained is always the same
 
-
whatever the number of simulation is. However, in the switch area, the choice between one of the two state is randomly made by bacterias.
 
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That's why, we need a modelling which is taking into account the randomness of the choice of the state.
 
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    </p>
 
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    <div  class="blocbackground" id="Random_Aspect">
 
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    <h2>Sensitivity to noise</h2>
 
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    <p>
 
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In a first time, we just used the deterministic model. The gradient of IPTG and the homogenous concentration of aTc are modeled by a
 
-
normal distribution with for standard deviation a predetermined percentage of the distribution average.
 
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    </p>
 
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    <table class="nobordure">
 
-
<tr>
 
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<td><a href="https://static.igem.org/mediawiki/2011/8/83/Conc_det.png"><img src="https://static.igem.org/mediawiki/2011/8/83/Conc_det.png" class="centerwide" style="box-shadow: none"/></a>
 
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<div class="legend">
 
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<strong>Figure 1:</strong>
 
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Logarithmic gradient of IPTG and aTc repartition on the plate with deterministic modelling
 
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</div></td>
 
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<td><a href="https://static.igem.org/mediawiki/2011/2/2c/Conc_sto.png"><img src="https://static.igem.org/mediawiki/2011/2/2c/Conc_sto.png" class="centerwide" style="box-shadow: none"/></a>
 
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<div class="legend">
 
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<strong>Figure 2:</strong>
 
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Logarithmic gradient of IPTG and aTc repartition on the plate with random deterministic modelling
 
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</div>
 
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</td>
 
-
</tr></br>
 
-
<tr>
 
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<td><a href="https://static.igem.org/mediawiki/2011/4/49/Switch_det.png"><img src="https://static.igem.org/mediawiki/2011/4/49/Switch_det.png" class="centerwide" style="box-shadow: none"/></a>
 
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<div class="legend">
 
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<strong>Figure 3:</strong>
 
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Concentration of both repressor on the plate with deterministic modelling.
 
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</div></td>
 
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<td><a href="https://static.igem.org/mediawiki/2011/8/8f/Switch_Stoc.png"><img src="https://static.igem.org/mediawiki/2011/8/8f/Switch_Stoc.png" class="centerwide" style="box-shadow: none"/></a>
 
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<div class="legend">
 
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<strong>Figure 4:</strong>
 
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Concentration of both repressor on the plate with random deterministic modelling.
 
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</div>
 
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</td>
 
-
</tr>
 
-
</table>
 
-
<p>
 
-
With the random model, fluctuations in the system are more present. This affects the quality of the switch.
 
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That's why is important to take into account the stochastic aspect (random and probalistic studies) of the system.
 
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In our stochastic model, we used gillespie algorithm. An often used one in stochastic modelling.
 
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</p>
 
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</div>
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<h2>Two new translational regulation mechanisms!</H2>
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<div  class="blocbackground" id="Gillespie_algorithm">
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    <h2>Gillespie algorithm</h2>
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      <p>
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-
During a chemical reaction, the molecules move at random in the medium obeying brownian motion,
+
-
and reactions happen randomly in the medium. On a macroscopic scale, the reactions can be seen
+
-
as deterministic, and the statistical properties are summarized by constants in classical ODEs.
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-
However, at a cell's scale, the influence of the randomness of the reactions is no longer
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negligible, especially for biosensors. For an efficient measurement biosensor systems must provide
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the expected precision of the measure.
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      </p>
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      <p>
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-
IMAGEEUH
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      </p>
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      <p>
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Each reaction has a certain probability to occur in an interval of time, and this probability
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depends, for example, on the concentration of reactant species in the medium and on the affinity
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constants of the reactions.
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      </p>
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-
      <p>
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-
In his algorithm Gillespie uses propensity theory to describe the behaviour of such a medium. Each
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reaction occuring in the cell, like construction or destruction of a protein, has a certain
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propensity. These propensities depend on the reactants concentrations and on other molecules in the
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cell (e.g. : The production of a protein from a gene placed after a pLac promoter depends on the
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concentrations of lacI and/or IPTG molecules in the cell).
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      </p>
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-
      <ol>
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-
<li>Propensity functions and the Gillespie Algorithm</li>
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<p>
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-
  Our stochastic model only describes the stochastic behaviour of the Toggle switch genetical network.
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  The toggle switch is the core of our system, it is the most sensitive part of the network and sets
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  the precision, the behaviour and the limits of our system.
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</p>
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<p>
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  The propensity functions used in our models are derived from the ODEs we have already written for
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-
  deterministic modelling :
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</p>
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<table class="nobordure">
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-
<tr>
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  <td><big>Chemical reaction</big></td>
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  <td><big>Propensity</big></td>
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</tr>
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<tr>
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 +
<div class="blocbackground">
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  <td>
 
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    <math >
 
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      <mrow>
 
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<mi>&Phi;</mi>
 
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<mo>&rarr;</mo>
 
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<mi>TetR</mi>
 
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      </mrow>
 
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    </math>
 
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  </td>
 
 +
<h3>A post-transcriptional regulation system for our toggle switch</h3>
 +
<p>The toggle developed by the marmot’s team will switch the bacteria to a sender or reciever phenotype
-
  <td>
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depending on the relative amounts of two inducers: mercury (or tetracycline) in the sample and IPTG, our reference which is comprised
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  <math >
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-
  <mrow>
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  <mfrac>
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  <mrow>
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    <msub>
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-
    <mi>k</mi>
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-
  <mi>plac</mi>
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    </msub>
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-
   
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-
      <mrow>
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-
<msub>
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-
<mi>P</mi>
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      <mi>lac total</mi>
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</msub>
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      </mrow>
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  </mrow>
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  <mrow>
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    <mi>1 +</mi>
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-
    <msup>
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-
  <mrow>
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    <mfenced open="(" close=")" separators=",">
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      <mrow>
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-
<mfrac>
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  <mrow>
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-
   
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-
      <mrow>
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<mi>lacI</mi>
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-
      </mrow>
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-
   
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  </mrow>
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  <mrow>
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    <mi>1 +</mi>
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    <mfrac>
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      <mrow>
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-
+
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  <mrow>
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    <mi>IPTG</mi>
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  </mrow>
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      </mrow>
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      <mrow>
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<msub>
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<mi>K</mi>
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      <mi>lacI - IPTG</mi>
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</msub>
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      </mrow>
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    </mfrac>
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  </mrow>
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</mfrac>
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      </mrow>
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    </mfenced>
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  </mrow>
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  <msub>
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  <mi>n</mi>
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<mi>plac</mi>
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  </msub>
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    </msup>
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  </mrow>
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</mfrac>
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      </mrow>
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    </math>
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-
    </td>
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 +
as a linear gradient in our sensor. Bacteria are thus exposed to IPTG before they encounter the inducer contained in the sample and hence
-
  </tr>
+
all cells will be in the receiver phenotype induced by IPTG. To avoid this bias, we want to keep the amount of LacI repressor as low as
-
  <tr>
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-
    <td>
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      <math >
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      <mrow>
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-
<mi>TetR</mi>
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-
<mo>&rarr;</mo>
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-
<mi>&Phi;</mi>
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      </mrow>
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      </math>
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    </td>
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    <td>
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      <math >
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      <mrow>
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-
<msub>
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-
<mi>&delta;</mi>
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-
      <mi>TetR</mi>
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-
</msub>
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-
<mi>TetR</mi>
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-
      </mrow>
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-
      </math>
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    </td>
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 +
possible until the sample to analyse is added.</p>
-
    </tr>
+
<p>To achieve this, we decided to develop a translational regulation system that allows to control the onset of the synthesis of both
-
    <tr>
+
-
      <td>
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-
<math >
+
-
  <mrow>
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-
    <mi>&Phi;</mi>
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-
    <mo>&rarr;</mo>
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-
    <mi>lacI</mi>
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-
  </mrow>
+
-
</math>
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-
      </td>
+
 +
repressors (LacI and MerR/TetR). This regulation mechanism should allow, upon triggering, to rapidly increase the amount of a
 +
protein within a cell. </p>
-
      <td>
+
<p>We investigated two mechanisms that are well documented in the literature and that can be extracted from different microorganisms.
-
<math >
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-
  <mrow>
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-
    <mfrac>
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      <mrow>
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-
<msub>
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-
<mi>k</mi>
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      <mi>pTet</mi>
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-
</msub>
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-
+
-
  <mrow>
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-
    <msub>
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-
    <mi>P</mi>
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-
  <mi>Tet total</mi>
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-
    </msub>
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-
  </mrow>
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-
+
-
      </mrow>
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-
      <mrow>
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-
<mi>1 +</mi>
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-
<msup>
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-
      <mrow>
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-
<mfenced open="(" close=")" separators=",">
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-
  <mrow>
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-
    <mfrac>
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-
      <mrow>
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-
+
-
  <mrow>
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-
    <mi>TetR</mi>
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-
  </mrow>
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-
+
-
      </mrow>
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-
      <mrow>
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-
<mi>1 +</mi>
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-
<mfrac>
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-
  <mrow>
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-
   
+
-
      <mrow>
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-
<mi>aTc</mi>
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-
      </mrow>
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-
   
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-
  </mrow>
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  <mrow>
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    <msub>
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    <mi>K</mi>
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  <mi>TetR - aTc</mi>
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    </msub>
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  </mrow>
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</mfrac>
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      </mrow>
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    </mfrac>
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  </mrow>
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</mfenced>
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      </mrow>
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      <msub>
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      <mi>n</mi>
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    <mi>pTet</mi>
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      </msub>
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</msup>
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      </mrow>
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    </mfrac>
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  </mrow>
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</math>
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      </td>
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-
     
+
 +
The first one is from Pseudomonas aeruginosa and comprises two RNA sequences and a protein, RsmA. The second one, the RpoS regulation
-
    </tr>
+
system, is from E. coli, and it involves a hairpin leader sequence and an inducible regulatory small RNA. </p>
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    <td>
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      <math >
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      <mrow>
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<mi>lacI</mi>
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<mo>&rarr;</mo>
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<mi>&Phi;</mi>
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      </mrow>
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      </math>
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    </td>
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    <td>
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      <math >
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      <mrow>
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<msub>
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<mi>&delta;</mi>
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      <mi>lacI</mi>
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</msub>
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<mi>lacI</mi>
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      </mrow>
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      </math>
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    </td>
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-
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-
   
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</table>
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<p>
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  The parameters are the same as those used in ODEs and can be found on the
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  <a href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Parameters"> parameters page.</a>
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  In our Matlab code the propensities are computed at each time step in the file Stochastic_model.m.
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</p>
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<p>
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  Then a pseudo-random number is generated in the interval [0;1] with Matlab function rand(). This
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  number will set which one of the reactions will occur during this iteration, or time step. The interval
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  of time that separates each iteration is set by the sum of all propensities. If all reactions have very
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  high propensities, many iterations will happen in a certain amount of time – And many iterations means
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  many reactions as well. By contrary, if all propensities are low, few reactions will occur during the same
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  amount of time. The time interval is then inversely proportionnal to the sum of all propensities.
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</p>
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<p>
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  This is the core of the algorithm. It can be found in the file Gillespie.m
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  The species concentrations are finally changed according to the reaction fixed
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  by the random number and the loop keeps running until the ending time of the
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  simulation is reached (ending time fixed by the user).
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</p>
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<p>Reference : Daniel T. Gillespie (1977). "Exact Stochastic Simulation of Coupled Chemical Reactions".
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The Journal of Physical Chemistry 81 (25): 2340–2361</p>
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<p>Daniel T. Gillespie (1976). "A General Method for Numerically Simulating the Stochastic Time Evolution
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of Coupled Chemical Reactions". Journal of Computational Physics 22 (4): 403–434</p>
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<li>Runs and statistical properties</li>
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<p>
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  In a Gillespie simulation, the information brought by a few instances of the Gillespie simulation is
+
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  enough to get the general behaviour of the genetical system.
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  However, it is not sufficient when the information that we want is the mean or the variance of the
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  concentrations in each species.
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</p>
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<p>
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  In this case a great number of runs is necessary to have a correct estimate of the expected values.
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  This is why we had to write a Matlab code to iterate a great number of runs. This part of the code
+
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  can be found in the file Main_gillespie.m.
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</p>
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<p>
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  Once the runs are computed through Gillespie algorithm, we have to extract the information from them.  
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  In this purpose we wrote the Hist.m, test.m and Dynamicdistros.m files. These files are specific to
+
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  our system, we hope they can give an idea of how to analyse the results obtained via our Gillespie
+
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  code, but they are not as easily understandable as other files.
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</p>
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<p>
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  Once the datasets are obtained we have to extract its statistical properties. Refer to the next
+
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  section for more information.
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</p>
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      </ol>
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-
           
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      <p>IMPORTANT NOTE:</p>
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      <p>
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  We tried to write a Matlab code that is as easily adaptable to any other system as possible.
+
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  However, because of the lack of time and the great amount of work it requires, we could not
+
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  build a completely generic MATLAB function handler for Gillespie simulations. We provide the source codes
+
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  <a href="http://igemgrenoble-files.perso.sfr.fr/2011/MATLAB_Archives/">here</a> of the Matlab
+
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  stochastic scripts for our simulations and tried to comment them as much as possible. Note that,
+
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  if you want to adapt our code to a completely different system, only the Stochastic_model.m and
+
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  parameters.mat files need to be changed, but a good understanding of the whole code is necessary.
+
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      </p>
+
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</div>
+
<p>We isolated and cloned the RsmA translational regulation system from <i>Pseudomonas aeruginosa</i>
-
+
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<div class="blocbackground" id="Stats">
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    <h2>Mean, standard deviation and statistical properties</h2>
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      <p>
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To get the number of bacteria and the minimal step for the IPTG gradient we get, we need to compute
+
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the mean and the standard deviation of each of the two species of the toggle switch.
+
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      </p>
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      <p>
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X1 and X2 are here the matrices which will represent the two toggle switch ways in each bacterium on
+
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the whole plate. On eahc point of the plate are wells containing a great number of bacteria. Each way in each
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bacterium is a random variable. The X matrices are then matrices of nb<SUB>cells</SUB>*nb<SUB>cell/well</SUB>
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random variables.
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      </p>
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      <p>
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Thanks to stochastic modelling we can obtain the mean and variance in each of the nb<SUB>wells</SUB> wells on
+
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the plate.
+
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+
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      <img src="https://static.igem.org/mediawiki/2011/d/df/Mean1.png" class="centerwide"/>
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      </p>
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      <p>
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To design our final device we need to know the width of the interface between the two ways of the toggle switch.
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We also need to know the number of bacteria needed in the wells to have a proper measurement.
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      </p>
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      <p>
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The interface which will be the colored part of our plate will turn red when populations in way 1 and populations
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in way 2 are in presence on the same point on the plate.
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We then need to know the statistical properties of the (X<SUB>1</SUB>X<SUB>2</SUB>)<SUB>well</SUB> random variable.<br/>
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      <img src="https://static.igem.org/mediawiki/2011/b/bb/Mean2.png" class="centerwide"/>
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      </p>
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      <p>
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(µ<SUB>X1X2</SUB>(well) is of course not continuous but discrete, we just want to highlight the deviation problem caused
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by σ<SUB>X1X2</SUB>(well))
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      </p>
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      <p>We want to know µ<SUB>X1X2</SUB>(well) and σ<SUB>X1X2</SUB>(well) to obtain respectively :</p>
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      <ol>
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<li>
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  The width of the "gaussian" function of µ<SUB>X1X2</SUB>(well) to set the minimal definition (the ΔIPTG between wells)
+
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  of our final device
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</li>
+
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<li>
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  The minimum number of bacteria we want in the wells.
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</li>
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<p>
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  We have nb<SUB>cell/well</SUB> independant random variables with the same probability density function. According to
+
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  central limit theorem, the mean of X<SUB>1</SUB>X<SUB>2</SUB> = (X<SUB>1</SUB>X<SUB>2 cell1</SUB> +
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  X<SUB>1</SUB>X<SUB>2 cell2</SUB> + ... + X<SUB>1</SUB>X<SUB>2 celln</SUB>) / n is µ<SUB>X1X2</SUB>(well) and its
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  standard deviation is σ<SUB>X1X2</SUB>(well)/<math><mrow><msqrt><mi>n</mi></msqrt></mrow></math>.
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  The width of the gaussian is therefore easily calculable (µ<SUB>X1X2</SUB>(well) = µ<SUB>X1</SUB>(well) +
+
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  µ<SUB>X2</SUB>(well)), but it's not that easy for the standard deviation σ<SUB>X1X2</SUB>(well)
+
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</p>
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<p>
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  If we consider Y1 and Y2 two random variables correlated, with known mean and variance (µ<SUB>1</SUB>, µ<SUB>2</SUB>,
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  σ<SUB>1</SUB>, σ<SUB>2</SUB>)<br/>
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-
  Var(Y<SUB>1</SUB>Y<SUB>2</SUB>) = E[(Y<SUB>1</SUB>Y<SUB>2</SUB> - E[(Y<SUB>1</SUB>Y<SUB>2</SUB>])<SUP>2</SUP>]<br/>
+
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  = E[(Y<SUB>1</SUB>Y<SUB>2</SUB>)<SUP>2</SUP> -2E[Y<SUB>1</SUB>Y<SUB>2</SUB>]Y<SUB>1</SUB>Y<SUB>2</SUB> +
+
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  E[Y<SUB>1</SUB>Y<SUB>2</SUB>]<SUP>2</SUP>]<br/>
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  = E[(Y<SUB>1</SUB>Y<SUB>2</SUB>)] -2(µ<SUB>1</SUB>µ<SUB>2</SUB>)<SUP>2</SUP> + µ<SUB>1</SUB>µ<SUB>2</SUB>
+
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</p>
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<p>
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  and E[(Y<SUB>1</SUB>Y<SUB>2</SUB>)] is not reductible to function of µ<SUB>1</SUB> and µ<SUB>2</SUB>. To obtian this value
+
-
  we then needed to create a composite random variable X<SUB>3</SUB> wich will be calculated during for each run of our
+
-
  MATLAB stochastic algorithm (see previous section).<br/>
+
-
  x<SUB>3</SUB> = x<SUB>1</SUB> * x<SUB>2</SUB><br/>
+
-
  We can thus get the variance and mean of X<SUB>1</SUB>X<SUB>2</SUB> (X<SUB>3</SUB>) through simulation.
+
-
  If we want to get an error inferior to 10% for example around the µ<SUB>X1X2</SUB>(well) curve, the number of bacteria n
+
-
  needed will be n so that :
+
-
  <math display="block">
+
-
  <mrow>
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    <mfrac>
+
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      <mrow>
+
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<msub>
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<mi>&sigma;</mi>
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      <msub>
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      <mi>X</mi>
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    <mn>3</mn>
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      </msub>
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-
</msub>
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<mfenced open="(" close=")" separators=",">
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  <mrow>
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    <mi>well</mi>
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  </mrow>
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</mfenced>
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      </mrow>
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      <mrow>
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-
<msqrt>
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  <mi>n</mi>
+
-
</msqrt>
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      </mrow>
+
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    </mfrac>
+
-
    <mo>/</mo>
+
-
    <msub>
+
-
    <mi>µ</mi>
+
-
  <mi>X1X2</mi>
+
-
    </msub>
+
-
    <mfenced open="(" close=")" separators=",">
+
-
      <mrow>
+
-
<mi>well</mi>
+
-
      </mrow>
+
-
    </mfenced>
+
-
    <mo>&lt;</mo>
+
-
    <mi>10%</mi>
+
-
  </mrow>
+
-
  </math>
+
-
  With such a precision we can then calculate the IPTG definition between the wells.
+
-
</p>
+
-
+
-
</div>
+
(BBa_K545005, BBa_K545006, BBa_K545007, BBa_K545008), and part of the RpoS system from E. coli (BBa_K545666).  </p>
 +
<h3>The RsmA translational regulation system</H3>
-
+
<ul><ol><h3>How does it work?</h3></ol></ul>
-
<div id="selector">
+
-
<form method="get" >
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  <input type="button" value="< PREVIOUS <" onclick="document.location = '/Team:Grenoble/Projet/Modelling/Deterministic';" />
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    <optgroup label="Modelling Homepage">
 
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    <option value="#Content" >Table of content</option>
 
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    </optgroup>
 
-
    <optgroup label="Deterministic Modelling" >
+
<p>The RsmA regulation system of Pseudomonas has homologs in many other bacteria, like CsrA of Escherichia coli1, for example. It is basically composed of:
-
                               
+
-
                                    <option value="/Deterministic#Our_EquationsTS" >Our equations - Toggle switch</option>
+
-
                                    <option value="/Deterministic#Our_EquationsQS" >Our equations - Quorum sensing</option>
+
<ul><li>A leader sequence at the 5’ end of the mRNAs of the genes to be regulated. Many different sequences exist depending on the gene to regulate.</li>
-
                               
+
-
                                    <option value="/Deterministic#Our_algorithms" >Our algorithms</option>
+
-
                               
+
-
                                    <option value="/Deterministic#Isoclines">Isoclines and Hysteresis</option>
+
-
                               
+
-
                                   
+
-
                            </optgroup>
+
-
                       
+
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                            <optgroup label="Stochastic Modelling">
+
-
                               
+
-
                                    <option value="/Stochastic#Geof" selected="selected">Geof's</option>
+
-
                               
+
-
                                    <option value="/Stochastic#Gillespie_algorithm">Gillespie algorithm</option>
+
-
                               
+
-
                                    <option value="/Stochastic#Stats">Mean, standard deviation and stats</option>
+
-
                            </optgroup>
+
<li>A regulatory protein named RsmA that binds to a GGA motif within the stem-loop structure of the transcribed leader sequences2. When RsmA is bound to the mRNA, the latter cannot be translated and is degraded.</li>
-
                            <optgroup label="Parameters">
+
<li>An inducible small RNA – the one we use is called rsmY – which sequesters the RsmA protein, having a greater affinity for it than the transcribed gene leader sequences.</li></ul>
-
                           
+
-
    <option value="/Parameters">Our parameters</option>
+
-
    </optgroup>
+
-
                            <optgroup label="Results">
+
</p>
-
    <option value="/Results#Validation">Validation of our Network</option>
+
<p>Using this system, the cell transcribes genes of which the translation is more or less repressed by RsmA, depending on their leader sequence (Fig 1). The strength of the repression depends on the stem-loop conformation of the leader sequence as well as on the number of GGA repeats that constitute binding sites for RsmA (see also Fig 3 + 4)</p>
-
    <option value="/Results#Device">Device specificities</option>
+
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    </optgroup>
 
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                    </select>
 
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                    <input type="hidden" name="id2" value="0" />
 
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                    <input type="submit" value="Go!" />
 
-
  <input type="button" value="> NEXT >" onclick="document.location = '/Team:Grenoble/Projet/Modelling/Parameters';" />
 
-
            </form>
+
 
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            </div>
+
<p><center><a href="https://static.igem.org/mediawiki/2011/f/fe/Rsma_off.png"><img height="350px"src="https://static.igem.org/mediawiki/2011/f/fe/Rsma_off.png"alt="logo iGEM"/></center>
 +
 
 +
<div class="legend"> <strong>Figure 1 :</strong></a> When no trigger comes from the environment, the translation of genes carrying a leader sequence (LS) containing stem-loops and GGA motifs is repressed by RsmA. The ribosome cannot bind on the RBS and the mRNA is not translated.</div></p>
 +
 
 +
<p>When the transcription of rsmY is triggered, the rsmY RNA acts as an activator by sequestering the RsmA repressor and allowing
 +
 
 +
the ribosome access to the messenger to be translated (see Fig 2).</p>
 +
 
 +
<p><center><a href="https://static.igem.org/mediawiki/2011/9/90/Rsma_on.png"><img height="400px" src="https://static.igem.org/mediawiki/2011/9/90/Rsma_on.png"alt="logo iGEM"/></center><div class="legend"> <strong> Figure 2 :</strong></a> When the transcription of rsmY is triggered, the RsmA protein is sequestered, which allows the translation of genes carrying an RsmA-controlled leader Sequence.</div></p>
 +
 
 +
<ul><ol><h3>Fha1 and magA operon leader sequences </h3></ol></ul>
 +
 
 +
<p>A microarray analysis revealed that RsmA regulates about 60 genes from two to more than one hundred fold3! Most of those genes are involved in secretion, or pili biogenesis. We decided to work on the leader sequences of magA and fha1. They are not strongly inhibited by RsmA, but are well documented, and the biobricks we made will be useful for our host lab.</p>
 +
 
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<p><center><a href="https://static.igem.org/mediawiki/2011/6/64/Fha_sequence.png"><img height="350px" src="https://static.igem.org/mediawiki/2011/6/64/Fha_sequence.png"alt="logo iGEM"/></center>
 +
 
 +
<div class="legend"> <strong>Figure 3 :</strong></a> Secondary structure of the leader sequence of fha1, identified as a direct target for RsmA regulation. The downstream sequence codes for a scaffold protein of the “type 6” secretion system. Highlighted are the ribosome-binding site (RBS) and the GGA motifs (Brenic and Lory, 2009). PA0081 is the sequence ID of the Pseudomonas genome project website (<a href="http://www.pseudomonas.com/">http://www.pseudomonas.com/<a/>)</div></p>
 +
 
 +
 
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<p>
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<center>
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<a href="https://static.igem.org/mediawiki/2011/f/fd/Regulation_rsma6.png"><img height="200px" src="https://static.igem.org/mediawiki/2011/f/fd/Regulation_rsma6.png"/>
 +
 
 +
</center>
 +
 
 +
<div class="legend">
 +
 
 +
<strong>
 +
 
 +
Figure 4 :</strong></a>Secondary srtucture of the magA operon leader sequence, also identified as a direct target of RsmA regulation. The operon contains a macrobuline-like protein (Brenic and Lory, 2009). The ribosome-binding site (RBS) is highlighted. PA4492 is the sequence ID of the Pseudomonas genome project website (<a href="http://www.pseudomonas.com/">http://www.pseudomonas.com/</a>)
 +
 
 +
</div>
 +
 
 +
</p>
 +
 
 +
 
 +
 
 +
 
 +
 
 +
 
 +
 
 +
 
 +
 
 +
<ul><li><h3>The rpoS regulation system</h3></ul></li>
 +
 
 +
<p>When nutrients become scarce, bacteria need to quickly shut down the expression of many genes an activate others. A major global regulator of this growth transition is RpoS, an alternative sigma factor (also called sigmaS). The RNA polymerase holoenzyme containing RpoS recognizes a new set of promoters and thus changes the global transcriptional program in an appropriate manner.</p>
 +
 
 +
<p>Because of the central role of RpoS, its expression is tightly regulated. Much of this regulation is exerted at the level of translation. The mechanism has been intensely studied and we can therefore exploit the system to create a new biobrick that provides an on-off switch for the translation of target genes.</p>
 +
 
 +
 +
 
 +
<p>The 5'-untranslated RNA (5'-UTR) of the rpoS gene adopts a particular secondary structure that places the ribosome binding site into a double-stranded region and therefore prevents recognition by the ribosome5. A small RNA, called dsrA, is produced when the cells enter starvation. This RNA interacts with the 5'-UTR of the rpoS RNA and induces a change in its secondary structure that liberates the RBS and thus stimulates the translation of rpoS 6⁠.</p>
 +
 
 +
<p>We have amplified the rpoS leader sequence by PCR and cloned it into PSB1C3. </p>
 +
 
 +
 +
 
 +
 +
 
 +
<p><ul><li>1. Timmermans, J. & Melderen, L.V. Post-transcriptional global regulation by CsrA in bacteria. Cellular and Molecular Life Sciences 2897-2908(2010).doi:10.1007/s00018-010-0381-z </li></p>
 +
 
 +
<p><li>2. Mercante, J. et al. Molecular Geometry of CsrA ( RsmA ) Binding to RNA and Its Implications for Regulated Expression. Journal of Molecular Biology 392, 511-528(2009).</li> </p>
 +
 
 +
<p><li>3. Brencic, A. & Lory, S. Determination of the regulon and identification of novel mRNA targets of Pseudomonas aeruginosa RsmA. Molecular Microbiology 72, 612-632(2009). </li></ul></p>
 +
 
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Revision as of 19:03, 23 October 2011

Grenoble 2011, Mercuro-Coli iGEM




Two new translational regulation mechanisms!

A post-transcriptional regulation system for our toggle switch

The toggle developed by the marmot’s team will switch the bacteria to a sender or reciever phenotype depending on the relative amounts of two inducers: mercury (or tetracycline) in the sample and IPTG, our reference which is comprised as a linear gradient in our sensor. Bacteria are thus exposed to IPTG before they encounter the inducer contained in the sample and hence all cells will be in the receiver phenotype induced by IPTG. To avoid this bias, we want to keep the amount of LacI repressor as low as possible until the sample to analyse is added.

To achieve this, we decided to develop a translational regulation system that allows to control the onset of the synthesis of both repressors (LacI and MerR/TetR). This regulation mechanism should allow, upon triggering, to rapidly increase the amount of a protein within a cell.

We investigated two mechanisms that are well documented in the literature and that can be extracted from different microorganisms. The first one is from Pseudomonas aeruginosa and comprises two RNA sequences and a protein, RsmA. The second one, the RpoS regulation system, is from E. coli, and it involves a hairpin leader sequence and an inducible regulatory small RNA.

We isolated and cloned the RsmA translational regulation system from Pseudomonas aeruginosa (BBa_K545005, BBa_K545006, BBa_K545007, BBa_K545008), and part of the RpoS system from E. coli (BBa_K545666).

The RsmA translational regulation system

      How does it work?

The RsmA regulation system of Pseudomonas has homologs in many other bacteria, like CsrA of Escherichia coli1, for example. It is basically composed of:

  • A leader sequence at the 5’ end of the mRNAs of the genes to be regulated. Many different sequences exist depending on the gene to regulate.
  • A regulatory protein named RsmA that binds to a GGA motif within the stem-loop structure of the transcribed leader sequences2. When RsmA is bound to the mRNA, the latter cannot be translated and is degraded.
  • An inducible small RNA – the one we use is called rsmY – which sequesters the RsmA protein, having a greater affinity for it than the transcribed gene leader sequences.

Using this system, the cell transcribes genes of which the translation is more or less repressed by RsmA, depending on their leader sequence (Fig 1). The strength of the repression depends on the stem-loop conformation of the leader sequence as well as on the number of GGA repeats that constitute binding sites for RsmA (see also Fig 3 + 4)

logo iGEM
Figure 1 : When no trigger comes from the environment, the translation of genes carrying a leader sequence (LS) containing stem-loops and GGA motifs is repressed by RsmA. The ribosome cannot bind on the RBS and the mRNA is not translated.

When the transcription of rsmY is triggered, the rsmY RNA acts as an activator by sequestering the RsmA repressor and allowing the ribosome access to the messenger to be translated (see Fig 2).

logo iGEM
Figure 2 : When the transcription of rsmY is triggered, the RsmA protein is sequestered, which allows the translation of genes carrying an RsmA-controlled leader Sequence.

      Fha1 and magA operon leader sequences

A microarray analysis revealed that RsmA regulates about 60 genes from two to more than one hundred fold3! Most of those genes are involved in secretion, or pili biogenesis. We decided to work on the leader sequences of magA and fha1. They are not strongly inhibited by RsmA, but are well documented, and the biobricks we made will be useful for our host lab.

logo iGEM
Figure 3 : Secondary structure of the leader sequence of fha1, identified as a direct target for RsmA regulation. The downstream sequence codes for a scaffold protein of the “type 6” secretion system. Highlighted are the ribosome-binding site (RBS) and the GGA motifs (Brenic and Lory, 2009). PA0081 is the sequence ID of the Pseudomonas genome project website (http://www.pseudomonas.com/)

Figure 4 :Secondary srtucture of the magA operon leader sequence, also identified as a direct target of RsmA regulation. The operon contains a macrobuline-like protein (Brenic and Lory, 2009). The ribosome-binding site (RBS) is highlighted. PA4492 is the sequence ID of the Pseudomonas genome project website (http://www.pseudomonas.com/)

  • The rpoS regulation system

When nutrients become scarce, bacteria need to quickly shut down the expression of many genes an activate others. A major global regulator of this growth transition is RpoS, an alternative sigma factor (also called sigmaS). The RNA polymerase holoenzyme containing RpoS recognizes a new set of promoters and thus changes the global transcriptional program in an appropriate manner.

Because of the central role of RpoS, its expression is tightly regulated. Much of this regulation is exerted at the level of translation. The mechanism has been intensely studied and we can therefore exploit the system to create a new biobrick that provides an on-off switch for the translation of target genes.

The 5'-untranslated RNA (5'-UTR) of the rpoS gene adopts a particular secondary structure that places the ribosome binding site into a double-stranded region and therefore prevents recognition by the ribosome5. A small RNA, called dsrA, is produced when the cells enter starvation. This RNA interacts with the 5'-UTR of the rpoS RNA and induces a change in its secondary structure that liberates the RBS and thus stimulates the translation of rpoS 6⁠.

We have amplified the rpoS leader sequence by PCR and cloned it into PSB1C3.

  • 1. Timmermans, J. & Melderen, L.V. Post-transcriptional global regulation by CsrA in bacteria. Cellular and Molecular Life Sciences 2897-2908(2010).doi:10.1007/s00018-010-0381-z

  • 2. Mercante, J. et al. Molecular Geometry of CsrA ( RsmA ) Binding to RNA and Its Implications for Regulated Expression. Journal of Molecular Biology 392, 511-528(2009).

  • 3. Brencic, A. & Lory, S. Determination of the regulon and identification of novel mRNA targets of Pseudomonas aeruginosa RsmA. Molecular Microbiology 72, 612-632(2009).

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