http://2013.igem.org/wiki/index.php?title=Team:British_Columbia/Modeling&feed=atom&action=historyTeam:British Columbia/Modeling - Revision history2024-03-28T17:47:52ZRevision history for this page on the wikiMediaWiki 1.16.5http://2013.igem.org/wiki/index.php?title=Team:British_Columbia/Modeling&diff=364108&oldid=prevYm10201002: /* == */2014-08-07T12:49:26Z<p><span class="autocomment">==</span></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>======</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>===<ins class="diffchange diffchange-inline">Substrate Utilization</ins>===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Bacteria require a substrate for growth, and the depletion of this substrate is proportional to the growth rate of the uninfected bacteria and the amount of bacteria. Although the infected bacteria do not multiply when infected, the infected cells may consume substrate to generate energy needed to replicate the phage. Although it may be the case that the bacteria simply recycle intracellular material, a substrate utilization term ($\gamma$) for the infected cells is added (if the bacteria do in fact recycle intracellular material, it follows that this value will be 0). Moreover, when cells lyse, the re-solubilized cytoplasmic contents can be metabolized by other bacteria and will add to the amount of nutrients available. Thus, the equation for substrate utilization rate is:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Bacteria require a substrate for growth, and the depletion of this substrate is proportional to the growth rate of the uninfected bacteria and the amount of bacteria. Although the infected bacteria do not multiply when infected, the infected cells may consume substrate to generate energy needed to replicate the phage. Although it may be the case that the bacteria simply recycle intracellular material, a substrate utilization term ($\gamma$) for the infected cells is added (if the bacteria do in fact recycle intracellular material, it follows that this value will be 0). Moreover, when cells lyse, the re-solubilized cytoplasmic contents can be metabolized by other bacteria and will add to the amount of nutrients available. Thus, the equation for substrate utilization rate is:</div></td></tr>
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</table>Ym10201002http://2013.igem.org/wiki/index.php?title=Team:British_Columbia/Modeling&diff=364107&oldid=prevYm10201002: /* Deterministic Model - modeling bacterial growth under phage predation */2014-08-07T12:47:31Z<p><span class="autocomment">Deterministic Model - modeling bacterial growth under phage predation</span></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>===<del class="diffchange diffchange-inline">Substrate Utilization</del>===</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>======</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Bacteria require a substrate for growth, and the depletion of this substrate is proportional to the growth rate of the uninfected bacteria and the amount of bacteria. Although the infected bacteria do not multiply when infected, the infected cells may consume substrate to generate energy needed to replicate the phage. Although it may be the case that the bacteria simply recycle intracellular material, a substrate utilization term ($\gamma$) for the infected cells is added (if the bacteria do in fact recycle intracellular material, it follows that this value will be 0). Moreover, when cells lyse, the re-solubilized cytoplasmic contents can be metabolized by other bacteria and will add to the amount of nutrients available. Thus, the equation for substrate utilization rate is:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Bacteria require a substrate for growth, and the depletion of this substrate is proportional to the growth rate of the uninfected bacteria and the amount of bacteria. Although the infected bacteria do not multiply when infected, the infected cells may consume substrate to generate energy needed to replicate the phage. Although it may be the case that the bacteria simply recycle intracellular material, a substrate utilization term ($\gamma$) for the infected cells is added (if the bacteria do in fact recycle intracellular material, it follows that this value will be 0). Moreover, when cells lyse, the re-solubilized cytoplasmic contents can be metabolized by other bacteria and will add to the amount of nutrients available. Thus, the equation for substrate utilization rate is:</div></td></tr>
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</table>Ym10201002http://2013.igem.org/wiki/index.php?title=Team:British_Columbia/Modeling&diff=361674&oldid=prevJoelkumlin: /* Probabilistic Model */2013-10-29T03:56:31Z<p><span class="autocomment">Probabilistic Model</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Probabilistic Model==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Probabilistic Model==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>For the <del class="diffchange diffchange-inline">numerical </del>simulation of co-cultures we utilized the cell programming language gro, which was developed by the Klavins Lab at the University of Washington [2]. The model considers two strains of bacteria on a two-dimensional plane under attack of one virus. One strain (green) contains a specific spacer element for the "control" phage and is granted immunity, whereas the other strain (yellow) is susceptible to phage infection. In the simulation, susceptible bacteria entering regions with high phage concentrations are very likely to become infected and upon lysis increase the phage concentration of that region. Below is a timeseries illustrating the control of susceptible cells with phage addition over the course of one batch cycle. Here, the amount of viable susceptible cells remaining over time can be controlled by adjusting the starting phage-to-bacteria ratio, allowing for optimal product formation. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>For the <ins class="diffchange diffchange-inline">probabilistic </ins>simulation of co-cultures we utilized the cell programming language gro, which was developed by the Klavins Lab at the University of Washington [2]. The model considers two strains of bacteria on a two-dimensional plane under attack of one virus. One strain (green) contains a specific spacer element for the "control" phage and is granted immunity, whereas the other strain (yellow) is susceptible to phage infection. In the simulation, susceptible bacteria entering regions with high phage concentrations are very likely to become infected and upon lysis increase the phage concentration of that region. Below is a timeseries illustrating the control of susceptible cells with phage addition over the course of one batch cycle. Here, the amount of viable susceptible cells remaining over time can be controlled by adjusting the starting phage-to-bacteria ratio, allowing for optimal product formation. </div></td></tr>
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</table>Joelkumlinhttp://2013.igem.org/wiki/index.php?title=Team:British_Columbia/Modeling&diff=361580&oldid=prevMvanins: /* Population Dynamics Modeling */2013-10-29T03:54:18Z<p><span class="autocomment">Population Dynamics Modeling</span></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><br/><b>Figure 1:</b> <del class="diffchange diffchange-inline">Model schematic</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><br/><b>Figure 1:</b> <ins class="diffchange diffchange-inline">Schematic of the model system where both strains are immunized against common environmental phages and the abundance of one can be modulated by the addition of a control phage.</ins></div></td></tr>
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</table>Mvaninshttp://2013.igem.org/wiki/index.php?title=Team:British_Columbia/Modeling&diff=361451&oldid=prevClawson: /* Extending to Co-culture */2013-10-29T03:51:13Z<p><span class="autocomment">Extending to Co-culture</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Extending to Co-culture===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Extending to Co-culture===</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The end goal of our project is to tune product formation of two or more compounds by adding phage to a batch reactor. Our extension to co-cultures considers the situation where vanillin and cinnamaldehyde strains have both been engineered with <del class="diffchange diffchange-inline">the </del>CRISPR immunity to an environmental phage. Additionally, the vanillin producing strain has been engineered with immunity to a control phage, whereas the cinnamaldehyde is susceptible. Since both strains contain the CRISPR <del class="diffchange diffchange-inline">system </del>and an engineered metabolic pathway it is not entirely unreasonable to assume that growth rates are similar. Let our bacterial cultures be $X$ for cinnamaldehyde and $Z$ for vanillin. Our equations become:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The end goal of our project is to tune product formation of two or more compounds by adding phage to a batch reactor. Our extension to co-cultures considers the situation where vanillin and cinnamaldehyde strains have both been engineered with <ins class="diffchange diffchange-inline">"</ins>CRISPR immunity<ins class="diffchange diffchange-inline">" </ins>to an environmental phage. Additionally, the vanillin producing strain has been engineered with immunity to a control phage, whereas the cinnamaldehyde is susceptible. Since both strains contain the CRISPR <ins class="diffchange diffchange-inline">assembly </ins>and an engineered metabolic pathway<ins class="diffchange diffchange-inline">, </ins>it is not entirely unreasonable to assume that <ins class="diffchange diffchange-inline">their </ins>growth rates are similar. Let our bacterial cultures be $X$ for cinnamaldehyde and $Z$ for vanillin. Our equations become:</div></td></tr>
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</table>Clawsonhttp://2013.igem.org/wiki/index.php?title=Team:British_Columbia/Modeling&diff=361354&oldid=prevClawson: /* Extending to Co-culture */2013-10-29T03:48:49Z<p><span class="autocomment">Extending to Co-culture</span></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><html><p>We use Matlab to solve this system of equations. This model demonstrates how phage can be used to control product formation. However, to know whether or not the model is representative of our systems behaviour, we must first have a qualitative understanding of our expected results. As the initial MOI increases, the cinnamaldehyde producing strain (susceptible to control phage infection) will collapse faster than at a lower MOI. If we assume that the production rates of vanillin and cinnamaldehyde equal during growth without phage, then we expect the product formation curves to separate with increasing MOI. Figure 5 shows that our model run at two <del class="diffchange diffchange-inline"> </del>different MOI's (two orders of magnitude apart), <del class="diffchange diffchange-inline">notice that the model </del>predicts the qualitative trends we were expecting to see. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><html><p>We use Matlab to solve this system of equations. This model demonstrates how phage can be used to control product formation. However, to know whether or not the model is representative of our systems behaviour, we must first have a qualitative understanding of our expected results. As the initial MOI increases, the cinnamaldehyde producing strain (susceptible to control phage infection) will collapse faster than at a lower MOI. If we assume that the production rates of vanillin and cinnamaldehyde equal during growth without phage, then we expect the product formation curves to separate with increasing MOI. Figure 5 shows that our model<ins class="diffchange diffchange-inline">, </ins>run at two different MOI's (two orders of magnitude apart), predicts the qualitative trends we were expecting to see. </div></td></tr>
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</table>Clawsonhttp://2013.igem.org/wiki/index.php?title=Team:British_Columbia/Modeling&diff=361264&oldid=prevClawson: /* Extending to Co-culture */2013-10-29T03:46:48Z<p><span class="autocomment">Extending to Co-culture</span></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><html><p>We use Matlab to solve this system of equations. This model demonstrates how phage can be used to control product formation. However, to know whether or not the model is representative of our systems behaviour, we must first have a qualitative understanding of our expected results. As the initial MOI <del class="diffchange diffchange-inline">of the control phage </del>increases, the cinnamaldehyde producing strain will collapse faster than at a lower MOI. If we assume that the production rates of vanillin and cinnamaldehyde equal during growth without phage, then we expect the product formation curves to separate with increasing MOI. Figure 5 shows that our model run at two different MOI's (two orders of magnitude apart), notice that the model predicts the qualitative trends we were expecting to see. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><html><p>We use Matlab to solve this system of equations. This model demonstrates how phage can be used to control product formation. However, to know whether or not the model is representative of our systems behaviour, we must first have a qualitative understanding of our expected results. As the initial MOI increases, the cinnamaldehyde producing strain <ins class="diffchange diffchange-inline">(susceptible to control phage infection) </ins>will collapse faster than at a lower MOI. If we assume that the production rates of vanillin and cinnamaldehyde equal during growth without phage, then we expect the product formation curves to separate with increasing MOI. Figure 5 shows that our model run at two different MOI's (two orders of magnitude apart), notice that the model predicts the qualitative trends we were expecting to see. </div></td></tr>
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</table>Clawsonhttp://2013.igem.org/wiki/index.php?title=Team:British_Columbia/Modeling&diff=361153&oldid=prevClawson: /* Extending to Co-culture */2013-10-29T03:43:44Z<p><span class="autocomment">Extending to Co-culture</span></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><html><p>We use Matlab to solve this system of equations. This model <del class="diffchange diffchange-inline">expects to show </del>how phage can be used to control product formation, <del class="diffchange diffchange-inline">but </del>to know whether or not the model <del class="diffchange diffchange-inline">paints the right picture </del>we must first have a qualitative understanding of <del class="diffchange diffchange-inline">what we are expecting to see</del>. As the initial MOI of the control phage increases, the cinnamaldehyde producing strain will collapse faster than at a lower MOI. If we assume that the production rates of vanillin and cinnamaldehyde equal during growth without phage, then we expect the product formation curves to separate with increasing MOI. Figure 5 shows that our model run at two different MOI's (two orders of magnitude apart), notice that the model predicts the qualitative trends we were expecting to see. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><html><p>We use Matlab to solve this system of equations. This model <ins class="diffchange diffchange-inline">demonstrates </ins>how phage can be used to control product formation<ins class="diffchange diffchange-inline">. However</ins>, to know whether or not the model <ins class="diffchange diffchange-inline">is representative of our systems behaviour, </ins>we must first have a qualitative understanding of <ins class="diffchange diffchange-inline">our expected results</ins>. As the initial MOI of the control phage increases, the cinnamaldehyde producing strain will collapse faster than at a lower MOI. If we assume that the production rates of vanillin and cinnamaldehyde equal during growth without phage, then we expect the product formation curves to separate with increasing MOI. Figure 5 shows that our model run at two different MOI's (two orders of magnitude apart), notice that the model predicts the qualitative trends we were expecting to see. </div></td></tr>
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</table>Clawsonhttp://2013.igem.org/wiki/index.php?title=Team:British_Columbia/Modeling&diff=361054&oldid=prevClawson: /* Probabilistic Model */2013-10-29T03:41:25Z<p><span class="autocomment">Probabilistic Model</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Probabilistic Model==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Probabilistic Model==</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>For the numerical simulation of co-cultures we utilized the cell programming language gro, which was developed by the Klavins Lab at the University of Washington [2]. The model considers two strains of bacteria on a two-dimensional plane under attack of one virus. One strain (green) contains a specific spacer element for the "control" phage and is granted immunity, whereas the other <del class="diffchange diffchange-inline">stain </del>(yellow) is susceptible to phage infection. In the simulation, susceptible bacteria entering regions with high phage concentrations are very likely to become infected and upon lysis increase the phage concentration of that region. Below is a timeseries illustrating the control of susceptible cells with phage addition over the course of one batch cycle. Here, the amount of viable susceptible cells remaining over time can be controlled by adjusting the starting phage-to-bacteria ratio, allowing for optimal product formation. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>For the numerical simulation of co-cultures we utilized the cell programming language gro, which was developed by the Klavins Lab at the University of Washington [2]. The model considers two strains of bacteria on a two-dimensional plane under attack of one virus. One strain (green) contains a specific spacer element for the "control" phage and is granted immunity, whereas the other <ins class="diffchange diffchange-inline">strain </ins>(yellow) is susceptible to phage infection. In the simulation, susceptible bacteria entering regions with high phage concentrations are very likely to become infected and upon lysis increase the phage concentration of that region. Below is a timeseries illustrating the control of susceptible cells with phage addition over the course of one batch cycle. Here, the amount of viable susceptible cells remaining over time can be controlled by adjusting the starting phage-to-bacteria ratio, allowing for optimal product formation. </div></td></tr>
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</table>Clawsonhttp://2013.igem.org/wiki/index.php?title=Team:British_Columbia/Modeling&diff=360977&oldid=prevClawson: /* Substrate Utilization */2013-10-29T03:39:12Z<p><span class="autocomment">Substrate Utilization</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Substrate Utilization===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>===Substrate Utilization===</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Bacteria require a substrate for growth, and the depletion of this substrate is proportional to the growth rate of the uninfected bacteria and the amount of bacteria. Although the infected bacteria do not multiply when infected, the infected cells may <del class="diffchange diffchange-inline">use up </del>substrate to <del class="diffchange diffchange-inline">gain the </del>energy needed to replicate the phage. Although it may be the case that the bacteria simply recycle intracellular material, a substrate utilization term ($\gamma$) for the infected cells is <del class="diffchange diffchange-inline">utilized </del>(if the bacteria do in fact recycle intracellular material, it follows that this value will be 0). Moreover, when cells lyse, the <del class="diffchange diffchange-inline">cell materials </del>can be metabolized by other bacteria and will add to the amount of nutrients available. Thus, the equation for substrate utilization rate is:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Bacteria require a substrate for growth, and the depletion of this substrate is proportional to the growth rate of the uninfected bacteria and the amount of bacteria. Although the infected bacteria do not multiply when infected, the infected cells may <ins class="diffchange diffchange-inline">consume </ins>substrate to <ins class="diffchange diffchange-inline">generate </ins>energy needed to replicate the phage. Although it may be the case that the bacteria simply recycle intracellular material, a substrate utilization term ($\gamma$) for the infected cells is <ins class="diffchange diffchange-inline">added </ins>(if the bacteria do in fact recycle intracellular material, it follows that this value will be 0). Moreover, when cells lyse, the <ins class="diffchange diffchange-inline">re-solubilized cytoplasmic contents </ins>can be metabolized by other bacteria and will add to the amount of nutrients available. Thus, the equation for substrate utilization rate is:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\begin{align}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\begin{align}</div></td></tr>
</table>Clawson