Team:Imperial College London/Project Gene Modelling

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<h1>Modelling</h1>
<h1>Modelling</h1>
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<h2>I. INTRODUCTION</h2>
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<p style="font-size:1.3em;"><a href="#" onClick="ddaccordion.collapseall('technology'); return false">Collapse all</a>  | <a href="#" onClick="ddaccordion.expandall('technology'); return false">Expand all</a></p>
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<p>The gene guard device involves three proteins:</p>
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<div class="technology">1. Introduction</div>
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<p>1) Holin is a protein forms pore complexes in the inner-membrane and this pores allow endolysin to move into periplasmic space. </p>
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<div class="thelanguage">
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<p>2) Endolysin is an enzyme that could break down the cell wall and causes cell lysis. </p>
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<p>The Gene Guard device involves three proteins:</p>
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<p>3) Anti-holin binds to holin and prevent from forming pores. </p>
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<p>1. <b>Holin</b> is a protein that forms pore complexes in the inner membrane of bacteria and these pores allow endolysin to move into the periplasmic space. </p>
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<p>2. <b>Endolysin</b> is an enzyme that can break down the cell wall and induce cell lysis. </p>
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<p>3. <b>Anti-holin</b> binds to holin and prevents it from forming pores. </p>
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<p>Our system will have holin and endolysin genes together with axuin genes and chemoreceptor genes on the plasmids, and anti-holin genes on the genome under control of strong promoter. The production of anti-holin will prevent cell lysis of the genetic modified bacteria by deactivating holin. If the plasmid get horizontal transferred to a different cell without anti-holin on its genome(e.g. any wild type soil bacteria), the expression of holin and endolysin will induce cell lysis and hence prevent it from keeping the plasmid containing auxin gene.
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<p>Our system will have the holin and endolysin genes together with the Phyto-Route and the Auxin Xpress genes on the plasmid, and the anti-holin gene on the genome under the control of a strong promoter. The production of anti-holin will prevent cell lysis of the genetically modified (GM) bacteria by deactivating holin. If the plasmid is transferred to a different bacterium without anti-holin on its genome (<i>e.g.</i> any wild type soil bacteria), the expression of holin and endolysin will induce cell lysis. This will prevent the spread of the AuxIn plasmid, containing the Phyto-Route and Auxin Xpress genes, to naturally occurring soil bacteria.</p>
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<br>
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<br>
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<h2>II. OBJECTIVES</h2>
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<p>    The key to the success of this device is the right ratio of holin and anti-holin production such that the anti-holin can deactivate all the holin produced in our genetic modified bacteria, and the holin expression level in wild type bacteria is high enough to induce cell lysis. As the gene expression is controlled by both promoter strength and ribosome binding site (RBS) strength, therefore modeling of gene guard is important for helping us to choose appropriate promoters and ribosome binding site (RBS) to inhibit and optimize cell behavior in our genetic modified cell and soil bacteria respectively. </p>
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<br>
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<h2>III. DESCRIPTION</h2>
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<p>  The modeling of gene guard consists two parts, one is the holin production in wild type bacteria and the other part is the deactivation of holin by anti-holin in genetic modified bacteria. Since all the genes in our system are constitutively expressed, thereby we only consider steady state. </p>
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<br>
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<h3>1. Holin production in wild type soil bacteria</h3>
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<p>This part of modeling focused on deriving the relationships between promoter strength and RBS strength of holin on single plasmid. In order to model this, the following assumptions were made: </p>
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<p style="text-align:right;font-size:1.3em;"><a href="#" class="collapseLink" onClick="ddaccordion.collapseone('technology', 0); return false">Collapse</a></p>
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<p>1) After plasmid transfer and duplication, there will be 50 copies of plasmids in one bacterium. </p>
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</div>
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<p>2) The literature indicates that cell lysis happens at holin concentration equals to 1000/cell[1]. </p>
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<p>Based on above assumptions, the kinetics of cell lysis in wild type bacteria was modeled using ordinary differential equations (ODEs) for the holin mRNA and holin (Equation 1). In equation 1, P<sub>holin</sub>represents promoter strength for holin genes, K<sub>holin</sub> is the RBS stregth of holin, &gamma;'<sub>mRNA</sub> is the degradation rate of mRNA in wild type bacteria, and &gamma;'<sub>protein</sub> is the degradation rate of protein in wild type bacteria.</p>
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<p><img src = "https://static.igem.org/mediawiki/2011/7/77/Picture2.png" /></p>
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<div class="technology">2. Objectives</div>
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<p>At steady state (i.e. d[ ] /dt = 0), rearrange Equation 1 with [Holin] = 1000, we obtained an expression for P_(holin) K_(holin) as shown in Equation 2: </p>
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<div class="thelanguage">
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<p>   The key to the success of this device is the correct ratio of holin and anti-holin production such that the anti-holin can deactivate all the holin produced in our modified bacteria, and the holin expression level in wild type bacteria is high enough to induce cell lysis. As gene expression is controlled by promoter strength and ribosome binding site (RBS) strength, modelling of the Gene Guard is important to help us choose a promoter and RBS of appropriate strength. </p>
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<p ><img src="https://static.igem.org/mediawiki/2011/thumb/8/82/GMB.png/800px-GMB.png"alt="" width="430" height="55" />
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<p style="text-align:right;font-size:1.3em;"><a href="#" class="collapseLink" onClick="ddaccordion.collapseone('technology', 1); return false">Collapse</a></p>
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</div>
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<div class="technology">3. Description</div>
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<div class="thelanguage">
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<p>  The modelling of the Gene Guard consists of two parts, one is the holin production in wild type bacteria and the other is the deactivation of holin by anti-holin in our modified bacteria. Since all the genes in our system are constitutively expressed, we only consider the steady state. </p>
<br>
<br>
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<h3>2. Holin inhibition in Genetic Modified bacteria</h3>
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<h4>Holin production in wild type soil bacteria</h4>
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<p>    In genetic modified bacteria the promoter strength and RBS strength of anti-holin on the genome should be stronger than promoter strength and RBS strength of holin on single plasmid such that all the holin produced by 300 copies of plasmids should be inhibited, where 300 is the maximum number of plasmids can be in single bacterium. In this system, the anti-holin can bind to holin to form dimer, which is defined as the deactivated holin. The mechanism in the genetic modified bacteria can be described in following ODEs in Equation 3.</p>
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<p><img src="https://static.igem.org/mediawiki/2011/thumb/d/de/E1.png/800px-E1.png"alt=""  
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<p>This part of the modelling is focused on deriving the relationships between promoter strength and RBS strength of holin on a single plasmid. In order to model this, the following assumptions were made: </p>
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<p><img src="https://static.igem.org/mediawiki/2011/1/11/Tt3.png"alt=""  />
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<p>1) Gene Guard is contained on a pSB1C3 plasmid which contains pUC19-derived pMB1 replication origin (~100-300 molecules per cell)<sup>[5]</sup>. The number of plasmids in bacteria ranges from 100 to 300 per cell. To make sure the promoter and RBS are strong enough for the holin/endolysin to be effective, we underestimated the number of plasmids in soil bacteria to be 50, although they will always have at least 100. Therefore our system should work whenever the number of plasmids in a soil bacterium is greater than 50.  </p>
 +
<p>2) The literature indicates that cell lysis occurs at a holin concentration equal to 1000 molecules/cell<sup>[1],[5],[6]</sup>, therefore we used this as the threshold concentration for cell lysis in our system. </p>
 +
<p>3)      Since the construct used to characterise the Pveg promoter last year contains a mutation, we assume that the<b> <a href= "http://partsregistry.org/wiki/index.php?title=Part:BBa_K515010">Pveg2</a></b> promoter we used for anti-holin has same the strength as Pveg.
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<p>Based on these assumptions, the kinetics of cell lysis in wild type bacteria was modelled using ordinary differential equations (ODEs) for the holin mRNA and holin protein (Equation 1). At steady state (<i>i.e.</i> d[mRNA<sub>holin</sub>] /dt = 0 and d[holin]/dt = 0), rearranging Equation 1 with [holin] = 1000, we obtained an expression for P<sub>holin</sub> K<sub>holin</sub> as shown in Equation 2.</p>
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<p>    Again at steady state with d[]/dt = 0, we obtained an equation of holin concentration (Equation 4).  </p>
 
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<p > <img src="https://static.igem.org/mediawiki/2011/e/e7/T4.png"alt="" width="795" height="231" />
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<p><img src = "https://static.igem.org/mediawiki/2011/3/36/C1.png" /></p>
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<br>
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<br>
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<h4>Holin inhibition in our modified bacteria</h4>
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<h2>IV. RESULTS</h2>
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<p>   In our bacteria the strength of the promoter and RBS controlling expression of anti-holin on the genome should be higher than that of holin on a single plasmid, such that all the holin produced by 300 plasmid copies (the maximum copy number in a single bacterium) can be inhibited. In our system, anti-holin binds to holin to form a dimer, which is defined as the deactivated holin. The mechanism in our modified bacteria is described by Equation 3. We defined the ratio of promoter and RBS strength for anti-holin and holin respectively as "m", as seen in Equation 4.</p>
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<p><img src="https://static.igem.org/mediawiki/2011/8/85/G2.png"/></p>
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<p style="text-align:right;font-size:1.3em;"><a href="#" class="collapseLink" onClick="ddaccordion.collapseone('technology', 2); return false">Collapse</a></p>
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</div>
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<div class="technology">4. Results and discussion</div>
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<div class="thelanguage">
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<p>    By varying the ratio m in Equation 4, we found that the holin concentration in GM bacteria decreased to zero at ratio m ≥ 300 (see Figure 1). Then, we tested m = 400 with the anti-holin promoter (<a href="http://partsregistry.org/wiki/index.php?title=Part:BBa_K515104">J23100</a>) we have with strength 13.1 pg RNA/min/μg substrate DNA, the result is displayed in Figure 2.</P>
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<div class="imgbox" style="width:820px;margin:0 auto;">
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<img class="border" src="https://static.igem.org/mediawiki/2011/4/45/G3.png" width="800px" />
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<p><i> Figure 1: The holin concentration in GM bacteria vs. ratio m (m = (P<sub>anti-holin</sub>K<sub>anti-holin</sub>)/(P<sub>holin</sub>K<sub>holin</sub>)). This graph shows that the intracellular concentration of holin remains at zero if m > 300. (Modelling by Imperial College London iGEM team 2011).</i></p>
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</div>
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<p>    By varying the ratio m in equation 4, we obtained that the holin concentration in genetic modified bacteria decreased to zero at ratio m ≥ 400 (see Figure 1). Then, we tested m = 400 with the anti-holin promoter we have with strength 13.1pg RNA/min/μg substrate DNA using ODEs shown in Equation 1 and 3, the result (Figure 2) shown that all the holin in the cell are inhibited as the holing concentration remains at 0 all the time, while the holin concentration in wild type bacteria reaches 1000 per cell after 5000 seconds.
 
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<p>    <img src="https://static.igem.org/mediawiki/2011/thumb/b/b3/Tt5.png/775px-Tt5.png"alt=""  />
 
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<p>    <b>Fig.1 The holin concentration against the ratio m</b>
 
<br>
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<p>   <img src="https://static.igem.org/mediawiki/2011/thumb/5/51/Tt6.png/800px-Tt6.png"alt="" />
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<p>   <b>Fig.2 Evolution of anti-holin and hoin in genetic modified and wild type bacteria agiainst time(s)</b>
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<img class="border" src="https://static.igem.org/mediawiki/2011/c/c5/Fig_2.png" width="800px" />
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<p><i> Figure 2: The evolution of different protein species vs. time at m = 400. All the holin proteins in the GM cell are inhibited as the holin concentration remains at 0 all the time, while the holin concentration in wild type bacteria reaches 1000 per cell after 5000 seconds.(Modelling by Imperial College London iGEM team 2011).</i></p>
 +
</div>
<br>
<br>
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<p>In summary, the modelling of gene guard informed us that the promoter strength and RBS strength for holin and anti-holin can be arbitrarily chosen as long as their ratio (<i>i.e.</i> P<sub>anti-holin</sub>K<sub>anti-holin</sub>)/(P<sub>holin</sub>K<sub>holin</sub>) >300), to make it certain, the ratio value 400 was selected for our project.
<br>
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<h2>V. PARAMETERS</h2>
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<p>   <img src="https://static.igem.org/mediawiki/2011/8/8f/Ggtable.png" />
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<div class="technology">5. Parameters</div>
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<div class="thelanguage">
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<h2>VI. MATLAB CODE</h2>
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<p>   <img src="https://static.igem.org/mediawiki/2011/f/ff/Ggparameter2.png" /></p>
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<h2>VII. REFERENCE</h2>
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<p>  [1] Christos G. Savva, Jill S. Dewey, John Deaton, Rebecca L. White, Douglas K. Struck, Andreas Holzenburg and Ry Young. The holin of bacteriophage lambda forms rings with large diameter. Molecular Microbiology 69(4), 784–793. 2008.
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<div class="technology">6. Matlab code</div>
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<p>  [2] http://ctb.pku.edu.cn/main/2011course/Network%20motifs/Sneppen%202010/pdf
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<div class="thelanguage">
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<p>  [3] A. G. ndling., M. D. Manson, R. Young (2001)‘Holins kill without warning’ 9348–9352 PNAS July 31, 2001 vol. 98 u no. 16
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<p><a href="https://static.igem.org/mediawiki/2011/3/3a/Gene_Guard.zip"><img src="https://static.igem.org/mediawiki/2011/8/8c/ICL_DownloadIcon.png" width="180px" /></a></p>
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<div class="technology">7. References</div>
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<div class="thelanguage">
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<p>  [1] Shetty Rp, Endy D, Knight TF Jr (2008) Engineering Biobrick vectors from biobrick parts. <i>J Biol Eng.</i>Apr 14;2:5. doi: 10.1186/1754-1611-2-5</p>
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<p>  [2]  Savva GG, Dewey JS, Deaton J, White RL, Struck DK, Holzenburg A and Young R (2008) The holin of bacteriophage lambda forms rings with large diameter. <i>Molecular Microbiology</i> <b>69(4):</b> 784–793.</p>
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<p>  [3] K. Nath, A.L. Koch (1971) Protein degradation in E. coli. The journal of biological chemistry vol. 246, No. 22, Issue of November 25, pp 6956-6967,1971</p>
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<p>  [4] Gründling et al. (2001) Holins kill without warning. <i>PNAS</i> <b>98(16):</b> 9348-9352</p>
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<p>  [5] Young, Ry, Ing-Nang Wang and William D. Roof. “Phages will out: strategies of host cell lysis.” Trends in Microbiology 2000; 8(3):120-8.</p>
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<p>  [6] Christos G. Savva, Jill S. Dewey, John Deaton, Rebecca L. White, Douglas K. Struck, Andreas Holzenburg and Ry Young. The holin of bacteriophage lambda forms rings with large diameter. Molecular Microbiology 69(4), 784–793. 2008.</p>
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M3: Design
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<a href="https://2011.igem.org/Team:Imperial_College_London/Project_Gene_Assembly" style="text-decoration:none;color:#728F1D;float:right;">
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M3: Assembly
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Latest revision as of 23:39, 16 October 2011




Module 3: Gene Guard

Containment is a serious issue concerning the release of genetically modified organisms (GMOs) into the environment. To prevent horizontal gene transfer of the genes we are expressing in our chassis, we have developed a system based on the genes encoding holin, anti-holin and endolysin. We are engineering anti-holin into the genome of our chassis, where it acts as an anti-toxin, and holin and endolysin on plasmid DNA. In the event of horizontal gene transfer with a soil bacterium, holin and endolysin will be transferred without anti-holin, rendering the recipient cell non-viable and effectively containing the Auxin Xpress and Phyto-Route genes in our chassis.




Modelling

Collapse all | Expand all

1. Introduction

The Gene Guard device involves three proteins:

1. Holin is a protein that forms pore complexes in the inner membrane of bacteria and these pores allow endolysin to move into the periplasmic space.

2. Endolysin is an enzyme that can break down the cell wall and induce cell lysis.

3. Anti-holin binds to holin and prevents it from forming pores.

Our system will have the holin and endolysin genes together with the Phyto-Route and the Auxin Xpress genes on the plasmid, and the anti-holin gene on the genome under the control of a strong promoter. The production of anti-holin will prevent cell lysis of the genetically modified (GM) bacteria by deactivating holin. If the plasmid is transferred to a different bacterium without anti-holin on its genome (e.g. any wild type soil bacteria), the expression of holin and endolysin will induce cell lysis. This will prevent the spread of the AuxIn plasmid, containing the Phyto-Route and Auxin Xpress genes, to naturally occurring soil bacteria.

Collapse

2. Objectives

The key to the success of this device is the correct ratio of holin and anti-holin production such that the anti-holin can deactivate all the holin produced in our modified bacteria, and the holin expression level in wild type bacteria is high enough to induce cell lysis. As gene expression is controlled by promoter strength and ribosome binding site (RBS) strength, modelling of the Gene Guard is important to help us choose a promoter and RBS of appropriate strength.

Collapse

3. Description

The modelling of the Gene Guard consists of two parts, one is the holin production in wild type bacteria and the other is the deactivation of holin by anti-holin in our modified bacteria. Since all the genes in our system are constitutively expressed, we only consider the steady state.


Holin production in wild type soil bacteria

This part of the modelling is focused on deriving the relationships between promoter strength and RBS strength of holin on a single plasmid. In order to model this, the following assumptions were made:

1) Gene Guard is contained on a pSB1C3 plasmid which contains pUC19-derived pMB1 replication origin (~100-300 molecules per cell)[5]. The number of plasmids in bacteria ranges from 100 to 300 per cell. To make sure the promoter and RBS are strong enough for the holin/endolysin to be effective, we underestimated the number of plasmids in soil bacteria to be 50, although they will always have at least 100. Therefore our system should work whenever the number of plasmids in a soil bacterium is greater than 50.

2) The literature indicates that cell lysis occurs at a holin concentration equal to 1000 molecules/cell[1],[5],[6], therefore we used this as the threshold concentration for cell lysis in our system.

3) Since the construct used to characterise the Pveg promoter last year contains a mutation, we assume that the Pveg2 promoter we used for anti-holin has same the strength as Pveg.

Based on these assumptions, the kinetics of cell lysis in wild type bacteria was modelled using ordinary differential equations (ODEs) for the holin mRNA and holin protein (Equation 1). At steady state (i.e. d[mRNAholin] /dt = 0 and d[holin]/dt = 0), rearranging Equation 1 with [holin] = 1000, we obtained an expression for Pholin Kholin as shown in Equation 2.


Holin inhibition in our modified bacteria

In our bacteria the strength of the promoter and RBS controlling expression of anti-holin on the genome should be higher than that of holin on a single plasmid, such that all the holin produced by 300 plasmid copies (the maximum copy number in a single bacterium) can be inhibited. In our system, anti-holin binds to holin to form a dimer, which is defined as the deactivated holin. The mechanism in our modified bacteria is described by Equation 3. We defined the ratio of promoter and RBS strength for anti-holin and holin respectively as "m", as seen in Equation 4.

Collapse

4. Results and discussion

By varying the ratio m in Equation 4, we found that the holin concentration in GM bacteria decreased to zero at ratio m ≥ 300 (see Figure 1). Then, we tested m = 400 with the anti-holin promoter (J23100) we have with strength 13.1 pg RNA/min/μg substrate DNA, the result is displayed in Figure 2.


Figure 1: The holin concentration in GM bacteria vs. ratio m (m = (Panti-holinKanti-holin)/(PholinKholin)). This graph shows that the intracellular concentration of holin remains at zero if m > 300. (Modelling by Imperial College London iGEM team 2011).


Figure 2: The evolution of different protein species vs. time at m = 400. All the holin proteins in the GM cell are inhibited as the holin concentration remains at 0 all the time, while the holin concentration in wild type bacteria reaches 1000 per cell after 5000 seconds.(Modelling by Imperial College London iGEM team 2011).


In summary, the modelling of gene guard informed us that the promoter strength and RBS strength for holin and anti-holin can be arbitrarily chosen as long as their ratio (i.e. Panti-holinKanti-holin)/(PholinKholin) >300), to make it certain, the ratio value 400 was selected for our project.

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5. Parameters
6. Matlab code
7. References

[1] Shetty Rp, Endy D, Knight TF Jr (2008) Engineering Biobrick vectors from biobrick parts. J Biol Eng.Apr 14;2:5. doi: 10.1186/1754-1611-2-5

[2] Savva GG, Dewey JS, Deaton J, White RL, Struck DK, Holzenburg A and Young R (2008) The holin of bacteriophage lambda forms rings with large diameter. Molecular Microbiology 69(4): 784–793.

[3] K. Nath, A.L. Koch (1971) Protein degradation in E. coli. The journal of biological chemistry vol. 246, No. 22, Issue of November 25, pp 6956-6967,1971

[4] Gründling et al. (2001) Holins kill without warning. PNAS 98(16): 9348-9352

[5] Young, Ry, Ing-Nang Wang and William D. Roof. “Phages will out: strategies of host cell lysis.” Trends in Microbiology 2000; 8(3):120-8.

[6] Christos G. Savva, Jill S. Dewey, John Deaton, Rebecca L. White, Douglas K. Struck, Andreas Holzenburg and Ry Young. The holin of bacteriophage lambda forms rings with large diameter. Molecular Microbiology 69(4), 784–793. 2008.

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M3: Design M3: Assembly