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Modelling : Introduction

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Introduction

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

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

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.

In addition, pINDEL contains the repA101ts gene encoding the RepA101Ts protein and the origin of replication (ori). 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.

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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 <a href="https://2011.igem.org/Team:ULB-Brussels">Home</a>
 <a href="https://2011.igem.org/Team:ULB-Brussels/project">Project</a>
-<a id="couleur"   href="https://2011.igem.org/Team:ULB-Brussels/modeling">Modeling</a>
+<a  id="couleur"   href="https://2011.igem.org/Team:ULB-Brussels/modeling">Modelling</a>
 <a href="https://2011.igem.org/Team:ULB-Brussels/human">Human practice</a>
-<a href="https://2011.igem.org/Team:ULB-Brussels/Results">Results</a>
+<a href="https://2011.igem.org/Team:ULB-Brussels/Discussion">Discussion</a>
 <a href="https://2011.igem.org/Team:ULB-Brussels/parts">Parts</a>
 <a href="https://2011.igem.org/Team:ULB-Brussels/safety">Safety</a>
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 <div id="sousm">
-<a  href="https://2011.igem.org/Team:ULB-Brussels/modeling">Introduction</a>
+<div id="gris"><a  href="https://2011.igem.org/Team:ULB-Brussels/modeling">Introduction</a></div>
-<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/30">Phase at 30°C</a>
+<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/30">Transcriptional interference</a>
-<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/42">Phase at 42°C</a>
+<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/42">Insertion model</a>
-<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/comparison">Comparison with the Wet Lab work </a>
+<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/excision">Excision model</a>
+<a href="https://2011.igem.org/Team:ULB-Brussels/modeling/loss">Loss of the pINDEL plasmid at 42°C</a>
+<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>
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-			Modeling : Introduction			</div>
+			Modelling : Introduction			</div>
 			<div id="maint">
+NB : If it is your first visit on our wiki and you cannot see the mathematical formulae on a page, please refresh it.
+<h1>Introduction</h1>
 <p>
-We will consider a population of <em>Escherichia Coli</em>, that possesses the Pindel plasmid, inserted beforehand by electroporation. The replication origin (ORI) of this plasmid is activated by RepA101, a constitutive enzyme, produced by the plasmid itself; at $42^\circ$C, this enzyme (RepA101) becomes rapidly inactive. Also, the plasmid includes a three-gene sequence coding for proteins (gam, exo and bet) inducing the insertion, by Red recombinase, of a gene "X" (at which we added, as a control, a resistance gene to chloramphenicol) in the bacterial DNA. The promotor of this three-gene sequence, Pbad, is activated by arabinose. Pindel includes in addition a coding sequence for flippase, whose promotor (lambda phage pR promotor) is blocked by a thermo-sensible repressor (at $42^\circ$C, the promotor isn't repressed at all, whereas at $30^\circ$C it is almost completely repressed, to $\ldots\%$). Those two sequences follow each other, but are encrypted in opposite directions, which eventually leads to an interference phenomenal. Furthermore, flippase, originally coming from yeast, is entirely active at $30^\circ$C, but is disabled at $42^\circ$C. Red recombinase recognizes the gene sequence to insert (the "X" gene followed by the resistance gene) and insert them in the bacteria's genome, while flippase excise the resistance to chloramphenicol package.
+The pINDEL plasmid can be divided into $2$ functional units:
+<ol>
+  <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; and</li>
+  <li> the DEL function which is based on the <em>flp</em> gene encoding the FLP site-specific recombinase.</li>
+</ol>
 </p>
 <p>
-At start, we place bacteria possessing Pindel at $30^\circ$C on arabinose. The Red recombinase genes are then expressed because of the presence of arabinose. In parallel, a small amount of flippase is produced: in section (2.1), we will study, by a computer simulation, the interference that occurs during the transcription of those two opposite-oriented genes, which will give us an idea of the probability that the flippase sequence eventually is transcribed. Nevertheless, we do expect that the amount of flippase produced remains low. After a while, those bacteria are electroporated in order to insert the X gene.
+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.
 </p>
 <p>
-By testing the resistance to chloramphenicol, we can determine which colonies have integrated the X gene, coupled with the resistance gene. We take some of those bacteria and place them at $42^\circ$C on glucose. Flippase is then fully produced, and is able to excise the chloramphenicol-resistance package. At the same time, the RepA101 enzyme, allowing the Pindel plasmid to reproduce is strongly suppressed, and becomes fast completely inactive. In consequence, the total number of plasmids remains constant; and the increase in population will dilute that amount of plasmids among the bacteria, leaving most of them without any plasmid. In the same way, flippase stops being produced, and therefore, by natural degradation, disappears. We thus obtain a population possessing the X gene, but devoid of the chloramphenicol resistance nor the Pindel plasmid.
+In addition, pINDEL contains the <em>repA101ts</em> gene encoding the RepA101Ts protein and the origin of replication (<em>ori</em>). 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.
 </p>
 <p>
-It is this whole process that we will try to model here. In our model, we consider a few different parameters, of which we will estimate the values, based on biological considerations. Afterwards, we will analyze the coherence of our predictions together with the results of the experiments, or if necessary, adapt the model itself.
+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.
 </p>
 <p>
-Let us begin with a proper definition of the different biological functions we are to study:
+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.
-<ul>
-  <li>$N$ : total amount of bacteria per ml in the considered population;</li>
-  <li>$P$ : average amount of Pindel plasmids per bacterium;</li>
-  <li>$E_{tot}$ : average amount of RepA101 enzymes per bacterium;</li>
-  <li>$E$ : average amount of RepA101 enzymes active per bacterium;</li>
-  <li>$F$ : average amount of flippase per bacterium;</li>
-  <li>$G_i (i=1,2,3)$ : average amount of the protein $i$ for the Red recombinase, per bacterium.</li>
-</ul>
 </p>