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− | <span style="color:black;font-family:comfort;font-size:16px;""><b>Working:</b> The engineered cells that will be degrading the antibiotics can die due to numerous reasons. When they die, they release the plasmid containing the antibiotic resistance gene into the environment. The wild population can take up these plasmids and can gain resistance to the antibiotics that we are trying to degrade. The cells replicate at a rate 𝝀 and follow a logistic growth curve. There is an intrinsic death rate in the population that we take as 𝛿. We have not considered any degradation rate of DNA in the environment as this would be the worst case scenario. In the single gene system the cells B upon death release the plasmid G into the environment. This contains the gene that can degrade the antibiotic and confer resistance. When the wild population of cells C come in contact with G they can uptake this genetic material which would lead to the formation of an AMR mutant in the population called | + | <span style="color:black;font-family:comfort;font-size:16px;""><b>Working:</b> The engineered cells that will be degrading the antibiotics can die due to numerous reasons. When they die, they release the plasmid containing the antibiotic resistance gene into the environment. The wild population can take up these plasmids and can gain resistance to the antibiotics that we are trying to degrade. The cells replicate at a rate 𝝀 and follow a logistic growth curve. There is an intrinsic death rate in the population that we take as 𝛿. We have not considered any degradation rate of DNA in the environment as this would be the worst case scenario. In the single gene system the cells B upon death release the plasmid G into the environment. This contains the gene that can degrade the antibiotic and confer resistance. When the wild population of cells C come in contact with G they can uptake this genetic material which would lead to the formation of an AMR mutant in the population called B<sub>1</sub>. In the working of the single gene system we keep track of the number of B<sub>1</sub> cells that are formed in the environment. The differential equations follow from this.</span> |
<p style="color:black;font-family:comfort;font-size:16px;"> | <p style="color:black;font-family:comfort;font-size:16px;"> | ||
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<table class="tableizer-table"> | <table class="tableizer-table"> | ||
<thead><tr class="tableizer-firstrow"><th>PARAMETER</th><th>DESCRIPTION</th><th>VALUE</th><th>UNITS</th><th>REFERENCE</th></tr></thead><tbody> | <thead><tr class="tableizer-firstrow"><th>PARAMETER</th><th>DESCRIPTION</th><th>VALUE</th><th>UNITS</th><th>REFERENCE</th></tr></thead><tbody> | ||
− | <tr><td> | + | <tr><td>𝜆</td><td>Growth rate</td><td>0.03</td><td>hr</td><td>[2]</td></tr> |
− | <tr><td> | + | <tr><td>𝛿</td><td>Death rate</td><td>0.005</td><td>hr 1</td><td>[3]</td></tr> |
− | <tr><td> | + | <tr><td>r</td><td>Transformation rate</td><td>10<sup>-8</sup></td><td>[5]</td>[4]</tr> |
− | <tr><td>N cap</td><td>Population cap</td><td> | + | <tr><td>N<sub>cap</sub></td><td>Population cap</td><td>10<sup>9</sup></td><td>cells/mL</td><td>Chosen for this</td></tr> |
</tbody></table> | </tbody></table> | ||
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<thead><tr class="tableizer-firstrow"><th>SPECIES</th><th>DESCRIPTION</th><th>UNITS</th></tr></thead><tbody> | <thead><tr class="tableizer-firstrow"><th>SPECIES</th><th>DESCRIPTION</th><th>UNITS</th></tr></thead><tbody> | ||
<tr><td>B</td><td>Engineered Cells</td><td>cells/mL</td></tr> | <tr><td>B</td><td>Engineered Cells</td><td>cells/mL</td></tr> | ||
− | <tr><td>B | + | <tr><td>B<sub>1</sub></td><td>Cells with plasmid G<sub>1</sub></td><td>cells/mL</td></tr> |
− | <tr><td>B 2</td><td>Cells with plasmid G | + | <tr><td>B<sub>2</sub></td><td>Cells with plasmid G<sub>2</sub></td><td>cells/mL</td></tr> |
− | <tr><td>B | + | <tr><td>B<sub>3</sub></td><td>Final Transformation mutant</td><td>cells/mL</td></tr> |
− | <tr><td>G | + | <tr><td>G<sub>1</sub></td><td>Plasmid 1</td><td>plasmid/mL</td></tr> |
− | <tr><td>G | + | <tr><td>G<sub>2</sub></td><td>Plasmid 2</td><td>plasmid/ml</td></tr> |
<tr><td>C</td><td>Wild population</td><td>cell/mL</td></tr> | <tr><td>C</td><td>Wild population</td><td>cell/mL</td></tr> | ||
</tbody></table> | </tbody></table> | ||
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<tr><td>T</td><td>Transconjugant</td><td>cells/mL</td></tr> | <tr><td>T</td><td>Transconjugant</td><td>cells/mL</td></tr> | ||
<tr><td>D</td><td>Donor</td><td>cells/mL</td></tr> | <tr><td>D</td><td>Donor</td><td>cells/mL</td></tr> | ||
− | <tr><td>RT</td><td>Mating Pair between Recipients and Transconjugant</td><td>Mating pair/mL</td></tr> | + | <tr><td>I<sub>RT</sub></td><td>Mating Pair between Recipients and Transconjugant</td><td>Mating pair/mL</td></tr> |
− | <tr><td>I TT</td><td>Mating pair between two transconjugant</td><td>Mating pair/mL</td></tr> | + | <tr><td>I<sub>TT</sub></td><td>Mating pair between two transconjugant</td><td>Mating pair/mL</td></tr> |
− | <tr><td>RD</td><td>Mating pair between Recipients and Donor</td><td>Mating pair/mL</td></tr> | + | <tr><td>I<sub>RD</sub></td><td>Mating pair between Recipients and Donor</td><td>Mating pair/mL</td></tr> |
− | <tr><td>TD</td><td>Mating pair between Transconjugant and Donor</td><td>Mating pair/mL</td></tr> | + | <tr><td>I<sub>TD</sub></td><td>Mating pair between Transconjugant and Donor</td><td>Mating pair/mL</td></tr> |
</tbody></table> | </tbody></table> | ||
</center> | </center> | ||
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<table class="tableizer-table"> | <table class="tableizer-table"> | ||
<thead><tr class="tableizer-firstrow"><th>PARAMETER</th><th>DESCRIPTION</th><th>VALUE</th><th>UNITS</th><th>REFERENCE</th></tr></thead><tbody> | <thead><tr class="tableizer-firstrow"><th>PARAMETER</th><th>DESCRIPTION</th><th>VALUE</th><th>UNITS</th><th>REFERENCE</th></tr></thead><tbody> | ||
− | <tr><td> | + | <tr><td>𝜆</td><td>Growth rate</td><td>0.03</td><td>hr<sup>-1</sup></td><td>[3]</td></tr> |
− | <tr><td> | + | <tr><td>𝛿</td><td>Death rate</td><td>0.005</td><td>hr<sup>-1</sup></td><td>[4]</td></tr> |
− | <tr><td> | + | <tr><td>𝛄</td><td>DNA transfer rate</td><td>15</td><td>hr<sup>-1</sup></td><td>[5]</td></tr> |
− | <tr><td>K</td><td>Mating pair formation rate</td><td>1.0 * 10- | + | <tr><td>K<sub>1</sub></td><td>Mating pair formation rate</td><td>1.0 * 10<sup>-8</sup></td><td>hr<sup>-1</sup></td><td>[6]</td></tr> |
− | <tr><td>K 2</td><td>Mating pair dissociation rate</td><td>200</td><td>hr</td><td>[6]</td></tr> | + | <tr><td>K<sub>2</sub></td><td>Mating pair dissociation rate</td><td>200</td><td>hr<sup>-1</sup></td><td>[6]</td></tr> |
− | <tr><td>N cap</td><td>Population cap</td><td> | + | <tr><td>N<sub>cap</sub></td><td>Population cap</td><td>10<sup>10</sup></td><td>cells/mL</td><td>Arbitrarily Chosen</td></tr> |
</tbody></table> | </tbody></table> | ||
</center> | </center> | ||
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<tr><td>ph_br_n</td><td>Burst size per lysed bacterium</td><td>250</td><td>-</td></tr> | <tr><td>ph_br_n</td><td>Burst size per lysed bacterium</td><td>250</td><td>-</td></tr> | ||
<tr><td>ph_fr_tp</td><td>Fraction of tp in burst</td><td>0.02</td><td>-</td></tr> | <tr><td>ph_fr_tp</td><td>Fraction of tp in burst</td><td>0.02</td><td>-</td></tr> | ||
− | <tr><td>ph_d</td><td>Fractional extracellular deactivation rate of phage virions/tp</td><td>0.0745</td><td>h-1</td></tr> | + | <tr><td>ph_d</td><td>Fractional extracellular deactivation rate of phage virions/tp</td><td>0.0745</td><td>h<sup>-1</sup></td></tr> |
− | <tr><td>ph_cir_n</td><td>No. of circulating virions/tp</td><td> | + | <tr><td>ph_cir_n</td><td>No. of circulating virions/tp</td><td>10<sup>7</sup></td><td>-</td></tr> |
− | <tr><td>MOI</td><td>No. of circulating virions/tp per bacterium</td><td>ph_cir_n/N</td><td>-</td></tr> | + | <tr><td>MOI</td><td>No. of circulating virions/tp per bacterium</td><td>ph_cir_n/N<sub>cap</sub></td><td>-</td></tr> |
<tr><td>pr_inf_hit</td><td>Probability of virion/tp injecting the carried genetic material into the bacterium given absorption</td><td>0.8</td><td>-</td></tr> | <tr><td>pr_inf_hit</td><td>Probability of virion/tp injecting the carried genetic material into the bacterium given absorption</td><td>0.8</td><td>-</td></tr> | ||
<tr><td>pr_inf</td><td>Probability of infection for a growing susceptible or lysogen not immune to other enteric phages</td><td>1 - exp(MOl*pr_inf_hit)</td><td>-</td></tr> | <tr><td>pr_inf</td><td>Probability of infection for a growing susceptible or lysogen not immune to other enteric phages</td><td>1 - exp(MOl*pr_inf_hit)</td><td>-</td></tr> | ||
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<tr><td>b_fr_lys_in</td><td>Fraction of lysogens in inflowing bacteria</td><td>0.05</td><td>-</td></tr> | <tr><td>b_fr_lys_in</td><td>Fraction of lysogens in inflowing bacteria</td><td>0.05</td><td>-</td></tr> | ||
<tr><td>b_fr_lys_en</td><td>Fraction of lysogens in enteric bacteria (start)</td><td>0.013</td><td>-</td></tr> | <tr><td>b_fr_lys_en</td><td>Fraction of lysogens in enteric bacteria (start)</td><td>0.013</td><td>-</td></tr> | ||
− | <tr><td>k</td><td>growth rate of bacteria,</td><td>0.03</td><td>h | + | <tr><td>k</td><td>growth rate of bacteria,</td><td>0.03</td><td>h<sup>-1</sup></td></tr> |
− | <tr><td>d</td><td>death rate of bacteria,</td><td>0.005</td><td>h-1</td></tr> | + | <tr><td>d</td><td>death rate of bacteria,</td><td>0.005</td><td>h<sup>-1</sup></td></tr> |
− | <tr><td>N</td><td>Population cap</td><td> | + | <tr><td>N</td><td>Population cap</td><td>10<sup>10</sup></td><td>-</td></tr> |
<tr><td>g_n</td><td>No. of AMR gene copies per bacterium</td><td>1</td><td>-</td></tr> | <tr><td>g_n</td><td>No. of AMR gene copies per bacterium</td><td>1</td><td>-</td></tr> | ||
<tr><td>pr_gpick_gntr _pl</td><td>Probability tp picks plasmid bearing AMR gene, per lytic cycle per bacterium</td><td>0.02</td><td>-</td></tr> | <tr><td>pr_gpick_gntr _pl</td><td>Probability tp picks plasmid bearing AMR gene, per lytic cycle per bacterium</td><td>0.02</td><td>-</td></tr> | ||
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<table class="tableizer-table"> | <table class="tableizer-table"> | ||
<thead><tr class="tableizer-firstrow"><th>SPECIES</th><th>DESCRIPTION</th><th>UNITS</th></tr></thead><tbody> | <thead><tr class="tableizer-firstrow"><th>SPECIES</th><th>DESCRIPTION</th><th>UNITS</th></tr></thead><tbody> | ||
− | <tr><td>N 1</td><td>Newly Infected bacteria of subpopulation 1 (Wild Population)</td><td>cells/mL</td></tr> | + | <tr><td>N<sub>1</sub></td><td>Newly Infected bacteria of subpopulation 1 (Wild Population)</td><td>cells/mL</td></tr> |
− | <tr><td>N | + | <tr><td>N<sub>2</sub></td><td>Newly Infected bacteria of subpopulation 2 (Coli Kaze)</td><td>cells/mL</td></tr> |
− | <tr><td>N | + | <tr><td>N<sub>3</sub></td><td>Susceptible bacteria of subpopulation 1 (Wild Population)</td><td>cells/mL</td></tr> |
− | <tr><td>N | + | <tr><td>N<sub>4</sub></td><td>Susceptible bacteria of subpopulation 2 (Coli Kaze)</td><td>cells/mL</td></tr> |
− | <tr><td>N | + | <tr><td>N<sub>5</sub></td><td>Immune Lysogen of subpopulation 1 (Wild Population)</td><td>cells/mL</td></tr> |
− | <tr><td>N | + | <tr><td>N<sub>6</sub></td><td>Immune Lysogen of subpopulation 2 (Coli Kaze)</td><td>cells/mL</td></tr> |
− | <tr><td>N | + | <tr><td>N<sub>7</sub></td><td>Bacteria processing tp in subpopulation 1 (Wild Population)</td><td>cells/mL</td></tr> |
− | <tr><td> | + | <tr><td>N<sub>8</sub></td><td>Bacteria processing tp in subpopulation 2 (Coli Kaze)</td><td>cells/mL</td></tr> |
− | <tr><td>N | + | <tr><td>N<sub>9</sub></td><td>Bacteria of subpopulation 1 (Wild Population) in Direct Lytic cycle</td><td>cells/mL</td></tr> |
− | <tr><td>N 10</td><td>Bacteria of subpopulation 2 (Coli Kaze) in Direct Lytic cycle</td><td>cells/mL</td></tr> | + | <tr><td>N<sub>10</sub></td><td>Bacteria of subpopulation 2 (Coli Kaze) in Direct Lytic cycle</td><td>cells/mL</td></tr> |
− | <tr><td>N 11</td><td>Bacteria of subpopulation 1 (Wild Population) in Induced Lytic cycle</td><td>cells/mL</td></tr> | + | <tr><td>N<sub>11</sub></td><td>Bacteria of subpopulation 1 (Wild Population) in Induced Lytic cycle</td><td>cells/mL</td></tr> |
− | <tr><td>N 12</td><td>Bacteria of subpopulation 2 (Coli Kaze) in Induced Lytic cycle</td><td>cells/mL</td></tr> | + | <tr><td>N<sub>12</sub></td><td>Bacteria of subpopulation 2 (Coli Kaze) in Induced Lytic cycle</td><td>cells/mL</td></tr> |
− | <tr><td>N 13</td><td>Virions</td><td>virions/ml</td></tr> | + | <tr><td>N<sub>13</sub></td><td>Virions</td><td>virions/ml</td></tr> |
</tbody></table> | </tbody></table> | ||
</center> | </center> |
Revision as of 19:54, 27 October 2020