Team:ULB-Brussels/modeling/42

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<div id="sousm">
<div id="sousm">
<a  href="https://2011.igem.org/Team:ULB-Brussels/modeling">Introduction</a>
<a  href="https://2011.igem.org/Team:ULB-Brussels/modeling">Introduction</a>
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<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/30">Phase at 30°C</a>
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<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/30">Transcriptional interference</a>
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<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/42">Phase at 42°C</a>
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<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/42">Insertion model</a>
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<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/comparison">Comparison with the Wet Lab work </a>
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<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/excision">Excision model</a>
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<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/loss">Loss of the pINDEL plasmid at 42°C</a>
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<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/comparison">Comparison with data</a>
<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/conclusion">Conclusion</a>
<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/conclusion">Conclusion</a>
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<div id="maintext">
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Modelling : Phase at 42°C </div>
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Modelling : Introduction </div>
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<h1>Phase at $42^\circ$C</h1>
 
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<h2>Preparation: electroporation and night culture</h2>
 
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<h1>Introduction</h1>
<p>
<p>
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Once the <em>E. Coli</em> population obtained after the phase at $30^\circ$C on arabinose (see section (\ref{Ph30})) reaches $1$ OD (at $600$nm), that is (almost) saturation, we move the bacteria in liquid (to have roughly $10^3$ per ml), and electropore them with the DNA fragment to insert (i.e. the gene X followed by the chloramphenicol resistance). The bacteria are then put in a culture with chloramphenicol, eliminating the ones that eventually would not have integrated the DNA fragment. That way, we obtain colony's of <em>E. Coli</em> having the fragment..
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The pINDEL plasmid can be divided into $2$ functional units:
 +
<ol>
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  <li>the IN function which is composed of the <em>gam</em>, <em>exo</em> and <em>bet</em> genes coding for the $\lambda$ Red recombinase system \cite{dat,yu}; and</li>
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  <li> the DEL function which is based on the <em>flp</em> gene encoding the FLP site-specific recombinase \cite{dat,yu}.</li>
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</ol>
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<p>
<p>
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Such a colony is then moved to a $30^\circ$C culture in $10$ml, where she grows until saturation (between $2\cdot10^9$ and $5\cdot10^9$ bacteria per ml). The solution is then diluted $100$ to $1000$ times, then cultivated, until it reaches an optic density (OD) (at $600$nm) of $0.2$ (which corresponds approximatively to $10^8$ bacteria). The bacteria are then put in presence of glucose at $42^\circ$C. The absence of arabinose desactivates Pbad (the promotor of the three-genes sequence $i$), and the presence of glucose reinforces this desactivation.
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The expression of $\lambda$ Red recombinase genes is under the control of the pBAD promoter.  This promoter is repressed by the AraC transcriptional regulator in absence of arabinose and activated by the same protein in the presence of arabinose. The<em>araC</em> gene is also encoded in the pINDEL plasmid.  The expression of the FLP recombinase is under the control of the $\lambda$ pR promoter.  This promoter is repressed at $30^\circ$C by the thermosensitive CI857 repressor which is also encoded in the pINDEL plasmid.  We will consider that expression of the <em>flp</em> gene is repressed at 90\% at $30^\circ$C, while at $42^\circ$C the <em>flp</em> gene is fully expressed. However it is reported that at this temperature, the activity of FLP is drastically reduced as compared to lower temperature \cite{buch}.
</p>
</p>
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<h2>Modelisation of the $42^\circ$C phase on glucose</h2>
 
<p>
<p>
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At initial time ($t=0$), the amount of bacteria is $N_0:=N(0)\approx10^8$. Like in section (\ref{Mod30}), we use a logistic model:
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In addition, pINDEL contains the <em>repA101ts</em> gene encoding the RepA101Ts protein and the origin of replication (<em>ori</em>) \cite{dat,yu}. The RepA101Ts protein initiates replication at $30^\circ$C by specifically binding to the ori. The RepA101Ts protein becomes rapidly inactive when the culture is shifted at 42¡C and is therefore not able to mediate replication initiation at this temperature. The pINDEL plasmid also contains the Amp resistance gene for plasmid selection.
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\begin{equation}
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\dot N=k_NN\left(1-\frac N{N_{max}}\right)
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\label{N42}\end{equation}
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where $N_{max}$ is the maximum amount of bacteria that the culture environment is able to contain and where $k_N$ corresponds to the growth rate one would observe in the limit where the saturation would be inexistent. Like in section (\ref{Mod30}), we have that the density of bacteria at dew point corresponds to a little more then $1$OD (at $600$nm), that is approximatively $N_{max}\approx2\cdot10^9$, and $k_N\approx \frac{\log{2}}{20\cdot60}\mbox{s}$.
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</p>
</p>
<p>
<p>
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Let us observe how $P$ evolves in time. At initial time in this phase, the average amount of Pindel plasmids per bacterium is $P_0:=P(0)\approx19$. The replication of those plasmids is activated by RepA101, non-stop produced by Pindel. The total amount of those enzymes thus follows the equation
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The Red recombinase promotes the insertion of a gene of interest (gene X) coupled to an antibiotic resistance gene flanked of FRT' sites (FRT'-Cm-FRT', our biobrick BBa\_K551000 for the selection of the insertion event in the bacterial chromosome.  FLP on the other hand is responsible for the site-specific excision of the antibiotic resistance gene, after insertion of the gene of interest, leaving a FRT' site. Thus, the IN and DEL functions are antagonist. Even under <em>flp</em> repression condition ($30^\circ$C), we cannot exclude that a small amount of FLP is produced due to the $\lambda$ pR promoter leakiness. This could drastically affect the frequency of insertion because excision of the Cm resistance gene could occur prior insertion of the X gene in the bacterial chromosome. To overcome this problem, we designed a particular configuration in which the IN and DEL functional units are encoded on the opposite strands and are facing each other. Our hypothesis is that the expression of the IN function (induced by arabinose) would inhibit the DEL function expression by a mechanism denoted as transcriptional interference. First, we will study by a computer simulation whether a potential transcriptional interference occurs between these 2 opposite-oriented functional units (see section (\ref{IntTranscr})).
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\begin{equation}
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\dot E_{tot}=C_EP-D_EE_{tot}
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\label{Etot42}\end{equation}
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in terms of the production rate $C_E$ of the enzyme per plasmid and of the natural deterioration rate $D_E$. However, at $42^\circ$C, the enzyme becomes quickly inactive. We obtain for the average active enzymes $E$ the relation:
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\begin{equation}
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\dot E=\dot E_{tot}-A_EE
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\label{E42}\end{equation}
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where $A_E$ is the natural deterioration rate of RepA101. We estimated $C_E\approx\ldots$, $A_E\approx\ldots$ and $D_E\approx\ldots$ (note that the value of $A_E$ is huge, relatively to the other parameters). At initial time, we can estimate that $E_0:=E(0)=E_{tot}(0)\approx\ldots$.
+
</p>
</p>
 +
<p>
 +
In our different models, we will consider a few parameters and we will estimate their values based on biological considerations. We will then analyze the coherence of our predictions together with the results of the experiments, and adapt the model if necessary.
 +
</p>
</div>
</div>

Revision as of 01:20, 22 September 2011

Modelling : Introduction

Introduction

The pINDEL plasmid can be divided into $2$ functional units:

  1. the IN function which is composed of the gam, exo and bet genes coding for the $\lambda$ Red recombinase system \cite{dat,yu}; and
  2. the DEL function which is based on the flp gene encoding the FLP site-specific recombinase \cite{dat,yu}.

The expression of $\lambda$ Red recombinase genes is under the control of the pBAD promoter. This promoter is repressed by the AraC transcriptional regulator in absence of arabinose and activated by the same protein in the presence of arabinose. ThearaC gene is also encoded in the pINDEL plasmid. The expression of the FLP recombinase is under the control of the $\lambda$ pR promoter. This promoter is repressed at $30^\circ$C by the thermosensitive CI857 repressor which is also encoded in the pINDEL plasmid. We will consider that expression of the flp gene is repressed at 90\% at $30^\circ$C, while at $42^\circ$C the flp gene is fully expressed. However it is reported that at this temperature, the activity of FLP is drastically reduced as compared to lower temperature \cite{buch}.

In addition, pINDEL contains the repA101ts gene encoding the RepA101Ts protein and the origin of replication (ori) \cite{dat,yu}. The RepA101Ts protein initiates replication at $30^\circ$C by specifically binding to the ori. The RepA101Ts protein becomes rapidly inactive when the culture is shifted at 42¡C and is therefore not able to mediate replication initiation at this temperature. The pINDEL plasmid also contains the Amp resistance gene for plasmid selection.

The Red recombinase promotes the insertion of a gene of interest (gene X) coupled to an antibiotic resistance gene flanked of FRT' sites (FRT'-Cm-FRT', our biobrick BBa\_K551000 for the selection of the insertion event in the bacterial chromosome. FLP on the other hand is responsible for the site-specific excision of the antibiotic resistance gene, after insertion of the gene of interest, leaving a FRT' site. Thus, the IN and DEL functions are antagonist. Even under flp repression condition ($30^\circ$C), we cannot exclude that a small amount of FLP is produced due to the $\lambda$ pR promoter leakiness. This could drastically affect the frequency of insertion because excision of the Cm resistance gene could occur prior insertion of the X gene in the bacterial chromosome. To overcome this problem, we designed a particular configuration in which the IN and DEL functional units are encoded on the opposite strands and are facing each other. Our hypothesis is that the expression of the IN function (induced by arabinose) would inhibit the DEL function expression by a mechanism denoted as transcriptional interference. First, we will study by a computer simulation whether a potential transcriptional interference occurs between these 2 opposite-oriented functional units (see section (\ref{IntTranscr})).

In our different models, we will consider a few parameters and we will estimate their values based on biological considerations. We will then analyze the coherence of our predictions together with the results of the experiments, and adapt the model if necessary.

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