Team:Brown/Modeling/Parameters

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# K_m represents the ligand’s dissociation constant
# K_m represents the ligand’s dissociation constant
-
= Players =
+
<html>
-
 
+
<h1 id="players"
-
The following are the players that are used in the modeling of our circuit:
+
>Players</h1
-
 
+
><p
-
== Transcription factors ==
+
>The following are the players that are used in the modeling of our circuit:</p
-
 
+
><h2 id="transcription-factors"
-
# LovTAP
+
>Transcription factors</h2
-
# LovTAP* (After light-induced conformational change)
+
><ol
-
# tetR
+
><li
-
# Mnt
+
  ><p
-
# AraC
+
    >LovTAP</p
-
# LacI
+
    ></li
-
# CI
+
  ><li
-
# CI434
+
  ><p
-
# GAL4
+
    >LovTAP* (After light-induced conformational change)</p
-
 
+
    ></li
-
== Reporters ==
+
  ><li
-
 
+
  ><p
-
# S1
+
    >tetR</p
-
# S2
+
    ></li
-
# S3
+
  ><li
-
# S4
+
  ><p
-
 
+
    >Mnt</p
-
== Constants ==
+
    ></li
-
 
+
  ><li
-
The following are the constants for which we need to find online or determine experimentally:
+
  ><p
-
 
+
    >AraC</p
-
# <math>\delta = \left\{
+
    ></li
 +
  ><li
 +
  ><p
 +
    >LacI</p
 +
    ></li
 +
  ><li
 +
  ><p
 +
    >CI</p
 +
    ></li
 +
  ><li
 +
  ><p
 +
    >CI434</p
 +
    ></li
 +
  ><li
 +
  ><p
 +
    >GAL4</p
 +
    ></li
 +
  ></ol
 +
><h2 id="reporters"
 +
>Reporters</h2
 +
><ol
 +
><li
 +
  ><p
 +
    >S1</p
 +
    ></li
 +
  ><li
 +
  ><p
 +
    >S2</p
 +
    ></li
 +
  ><li
 +
  ><p
 +
    >S3</p
 +
    ></li
 +
  ><li
 +
  ><p
 +
    >S4</p
 +
    ></li
 +
  ></ol
 +
><h2 id="constants"
 +
>Constants</h2
 +
><p
 +
>The following are the constants for which we need to find online or determine experimentally:</p
 +
><ol
 +
><li
 +
  ><p
 +
    ><span class="math"
 +
      >$\delta = \left\{
     \begin{array}{ll}
     \begin{array}{ll}
-
         0 & \mbox{without light}\\
+
         0 &amp; \mbox{without light}\\
-
         1 & \mbox{with light}
+
         1 &amp; \mbox{with light}
     \end{array}
     \end{array}
-
\right.</math>
+
\right.$</span
-
# <math>c</math> represents the rate of conformation change from LovTAP to LovTAP* under 470nm light.
+
      ></p
-
 
+
    ></li
-
== Parameters ==
+
  ><li
-
 
+
  ><p
-
<ol>
+
    ><span class="math"
-
<li><p><math>\alpha_x</math> represents the <math>x</math>th synthesis rate <math>\left(\dfrac{\text{nanomoles}}{\text{min}}\right)</math>.<br />
+
      ><em
-
<math>\alpha=\left(\text{rate of transcription}\right)\times\left(\text{rate of translation}\right)</math><br />
+
>c</em
-
For promoters for which reliable data is not available, we assume an average ''E. coli'' transcription speed to be 70 nucleotides/second = 4,200 nucleotides/min, and an average translation speed of 40 amino acids/second = 2400, which is then further regulated by the appropriate ribosome binding site, represented as a normalized constant. Thus, we use the following equation to calculate unknown synthesis rates[0]: <math>\alpha = \left(\frac{4200}{\text{gene length}}\right)\times\left(\frac{2400\times\text{RBS Strength}}{\text{protein length}}\right) </math></p>
+
></span
-
 
+
      > represents the rate of conformation change from LovTAP to LovTAP* under 470nm light.</p
-
<p><math>\alpha_1</math> LovTAP synthesis rate constant <math>= 1.06432\times10^{-13}</math> nanomoles. <math>\alpha_2</math> tetR synthesis rate constant <math>= 1.15318\times10^{-13}</math> nanomoles. <math>\alpha_3</math> Mnt synthesis rate constant <math>= 6.0562\times*10^{-13}</math> nanomoles. <math>\alpha_4</math> AraC synthesis rate constant <math>= 5.99989\times10^{-14}</math> nanomoles. <math>\alpha_5</math> LacI synthesis rate constant <math>= 3.94791\times10^{-14}</math> nanomoles. <math>\alpha_6</math> CI synthesis rate constant <math>= 8.93023\times10^{-14}</math> nanomoles. <math>\alpha_7</math> CI434 synthesis rate constant <math>= 1.2236\times10^{-13}</math> nanomoles. <math>\alpha_8</math> [check]SupD synthesis rate constant <math>= 1.2236\times10^{-13}</math> nanomoles. <math>\alpha_9</math> [check]T7ptag synthesis rate constant <math>= 1.2236\times10^{-13}</math> nanomoles. <math>\alpha_{10}</math> [check]GAL4 synthesis rate constant <math>= 1.06432\times10^{-13}</math> nanomoles.</p>
+
    ></li
-
 
+
  ></ol
-
<p><math>\alpha_{11}</math> S1 synthesis rate constant <math>= 9.68992\times10^{-14}</math> nanomoles. <math>\alpha_{12}</math> S2 synthesis rate constant <math>= 9.68992\times10^{-14}</math> nanomoles. <math>\alpha_{13}</math> S3 synthesis rate constant <math>= 9.68992\times10^{-14}</math> nanomoles. <math>\alpha_{14}</math> S4 synthesis rate constant <math>= 9.68992\times10^{-14}</math> nanomoles.</p></li>
+
><h2 id="parameters"
-
<li><p><math>\beta_x </math> represents <math>x</math>th basal (un-induced or un-repressed) synthesis rate of a given promoter. We assume that, for all promoters, this is equal to 1% of the synthesis rate constant. <math>\forall x \ \beta_x = 0.1\alpha_x</math></p></li>
+
>Parameters</h2
-
<li><p><math>\mu_x</math> represents the degradation rate of a given protein. When the degredation rate is unknown, we assume a decay of 0.012 proteins/min (half-life of one hour) <math>\mu_1= 0.0453</math> Rate of LovTAP degredation <math>(1/sec)</math><math>\mu_2= 0.0453</math> Rate of LovTAP* degredation <math>(1/sec)</math><math>\mu_3 = 0.0453</math> tetR degredation <math>(1/sec)</math><math>\mu_4= 0.0453</math> Rate of Mnt degredation <math>(1/sec)</math><math>\mu_5= 0.0453</math> Rate of AraC degredation <math>(1/sec)</math><math>\mu_6= 0.0453</math> Rate of LacI degredation <math>(1/sec)</math><math>\mu_7= 0.0453</math> Rate of CI degredation <math>(1/sec)</math><math>\mu_8= 0.0453</math> Rate of CI434 degredation <math>(1/sec)</math><math>\mu_9= 00453</math> Rate of SupD degredation <math>(1/sec)</math><math>\mu_{10}= 0.0453</math> Rate of T7ptag degredation <math>(1/sec)</math><math>\mu_{11}= 0.012</math> Rate of T7 polymerase degredation <math>(1/sec)</math><math>\mu_{12}= 0.012</math> Rate of GAL4 degredation <math>(1/sec)</math><math>\mu_{13}= 0.012</math> Rate of S1 degredation <math>(1/sec)</math><math>\mu_{14}= 0.012</math> Rate of S2 degredation <math>(1/sec)</math><math>\mu_{15}= 0.012</math> Rate of S3 degredation <math>(1/sec)</math><math>\mu_{16}= 0.012</math> Rate of S4 degredation <math>(1/sec)</math></p></li>
+
><ol
-
<li><p><math>n_x</math> represents the hill coefficient for a given protein. <math>n_1 = 1</math> for LovTAP*</p>
+
><li
-
 
+
  ><p
-
<p><math>n_2 = 3</math> for tetR)</p>
+
    ><span class="math"
-
 
+
      >α<sub
-
<p><math>n_3 = 2</math> for CI</p>
+
><em
-
 
+
  >x</em
-
<p><math>n_4 = 2</math> for CI434</p>
+
  ></sub
-
 
+
></span
-
<p><math>n_5 = 2</math> Hill coefficient of GAL4</p>
+
      > represents the <span class="math"
-
 
+
      ><em
-
<p><math>n_6 = 2</math> Hill coefficient of AraC</p>
+
>x</em
-
 
+
></span
-
<p><math>n_7 = 2</math> Hill coefficient of T7</p>
+
      >th synthesis rate <span class="math"
-
 
+
      >$\left(\dfrac{\text{nanomoles}}{\text{min}}\right)$</span
-
<p><math>n_8 = 2</math> Hill coefficient of LacI</p>
+
      >.<br
-
 
+
      /> <span class="math"
-
<p><math>n_9 = 1</math> Hill coefficient of Mnt</p>
+
      >α = (<em
-
</li>
+
>rate of transcription</em
-
<li><p><math>K_x</math> represents, for a given protein, the ligand concentration producing half occupation (ligand concentration occupying half of the binding sites) in nanomoles. This is also the infamous &quot;microscopic dissociation constant&quot;. <math>K_{d1} = 142</math> for LovTAP*</p>
+
>) × (<em
-
 
+
>rate of translation</em
-
<p><math>K_{d2} = 0.179</math> for tetR</p>
+
>)</span
-
 
+
      ><br
-
<p><math>K_{d3} = 50</math> for CI</p>
+
      /> For promoters for which reliable data is not available, we assume an average <em
-
 
+
      >E. coli</em
-
<p><math>K_{d4} = 40</math> for CI434</p>
+
      > transcription speed to be 70 nucleotides/second = 4,200 nucleotides/min, and an average translation speed of 40 amino acids/second = 2400, which is then further regulated by the appropriate ribosome binding site, represented as a normalized constant. Thus, we use the following equation to calculate unknown synthesis rates[0]: <br
-
 
+
      /><span class="math"
-
<p><math>K_{d5} = 0.5</math> for GAL4</p>
+
      >$\alpha = \left(\frac{4200}{\text{gene length}}\right)\times\left(\frac{2400\times\text{RBS Strength}}{\text{protein length}}\right) $</span
-
 
+
      ><br
-
<p><math>K_{d6} = 14</math> for AraC</p>
+
      /></p
-
 
+
    ><p
-
<p><math>K_{d7} = 2</math> for T7</p>
+
    ><span class="math"
-
 
+
      >α<sub
-
<p><math>K_{d8} = 800</math>for LacI</p>
+
>1</sub
-
 
+
></span
-
<p><math>K_{d9} = 50</math> for Mnt</p>
+
      > LovTAP synthesis rate constant <span class="math"
-
</li>
+
      > = 1. 06432 × 10<sup
-
<li><p><math>c</math> <math>c_1 = 20.20</math>, which represents the rate of light-induced LovTAP to LovTAP* conformation change <math>(1/sec)</math> <math>c_2 = 20.20</math> which represents the rate of the reaction SupD + T7ptag <math>\rightarrow</math> T7</p></li>
+
> - 13</sup
-
<li><p><math>\delta = \left\{
+
></span
 +
      > nanomoles. <span class="math"
 +
      >α<sub
 +
>2</sub
 +
></span
 +
      > tetR synthesis rate constant <span class="math"
 +
      > = 1. 15318 × 10<sup
 +
> - 13</sup
 +
></span
 +
      > nanomoles. <span class="math"
 +
      >α<sub
 +
>3</sub
 +
></span
 +
      > Mnt synthesis rate constant <span class="math"
 +
      > = 6. 0562 ×  * 10<sup
 +
> - 13</sup
 +
></span
 +
      > nanomoles. <span class="math"
 +
      >α<sub
 +
>4</sub
 +
></span
 +
      > AraC synthesis rate constant <span class="math"
 +
      > = 5. 99989 × 10<sup
 +
> - 14</sup
 +
></span
 +
      > nanomoles. <span class="math"
 +
      >α<sub
 +
>5</sub
 +
></span
 +
      > LacI synthesis rate constant <span class="math"
 +
      > = 3. 94791 × 10<sup
 +
> - 14</sup
 +
></span
 +
      > nanomoles. <span class="math"
 +
      >α<sub
 +
>6</sub
 +
></span
 +
      > CI synthesis rate constant <span class="math"
 +
      > = 8. 93023 × 10<sup
 +
> - 14</sup
 +
></span
 +
      > nanomoles. <span class="math"
 +
      >α<sub
 +
>7</sub
 +
></span
 +
      > CI434 synthesis rate constant <span class="math"
 +
      > = 1. 2236 × 10<sup
 +
> - 13</sup
 +
></span
 +
      > nanomoles. <span class="math"
 +
      >α<sub
 +
>8</sub
 +
></span
 +
      > [check]SupD synthesis rate constant <span class="math"
 +
      > = 1. 2236 × 10<sup
 +
> - 13</sup
 +
></span
 +
      > nanomoles. <span class="math"
 +
      >α<sub
 +
>9</sub
 +
></span
 +
      > [check]T7ptag synthesis rate constant <span class="math"
 +
      > = 1. 2236 × 10<sup
 +
> - 13</sup
 +
></span
 +
      > nanomoles. <span class="math"
 +
      >α<sub
 +
>10</sub
 +
></span
 +
      > [check]GAL4 synthesis rate constant <span class="math"
 +
      > = 1. 06432 × 10<sup
 +
> - 13</sup
 +
></span
 +
      > nanomoles.</p
 +
    ><p
 +
    ><span class="math"
 +
      >α<sub
 +
>11</sub
 +
></span
 +
      > S1 synthesis rate constant <span class="math"
 +
      > = 9. 68992 × 10<sup
 +
> - 14</sup
 +
></span
 +
      > nanomoles. <span class="math"
 +
      >α<sub
 +
>12</sub
 +
></span
 +
      > S2 synthesis rate constant <span class="math"
 +
      > = 9. 68992 × 10<sup
 +
> - 14</sup
 +
></span
 +
      > nanomoles. <span class="math"
 +
      >α<sub
 +
>13</sub
 +
></span
 +
      > S3 synthesis rate constant <span class="math"
 +
      > = 9. 68992 × 10<sup
 +
> - 14</sup
 +
></span
 +
      > nanomoles. <span class="math"
 +
      >α<sub
 +
>14</sub
 +
></span
 +
      > S4 synthesis rate constant <span class="math"
 +
      > = 9. 68992 × 10<sup
 +
> - 14</sup
 +
></span
 +
      > nanomoles.</p
 +
    ></li
 +
  ><li
 +
  ><p
 +
    ><span class="math"
 +
      >β<sub
 +
><em
 +
  >x</em
 +
  ></sub
 +
></span
 +
      > represents <span class="math"
 +
      ><em
 +
>x</em
 +
></span
 +
      >th basal (un-induced or un-repressed) synthesis rate of a given promoter. We assume that, for all promoters, this is equal to 1% of the synthesis rate constant. <br
 +
      /><span class="math"
 +
      >∀ <em
 +
>x</em
 +
> β<sub
 +
><em
 +
  >x</em
 +
  ></sub
 +
> = 0. 1α<sub
 +
><em
 +
  >x</em
 +
  ></sub
 +
></span
 +
      ><br
 +
      /></p
 +
    ></li
 +
  ><li
 +
  ><p
 +
    ><span class="math"
 +
      >μ<sub
 +
><em
 +
  >x</em
 +
  ></sub
 +
></span
 +
      > represents the degradation rate of a given protein. When the degredation rate is unknown, we assume a decay of 0.012 proteins/min (half-life of one hour) <span class="math"
 +
      >μ<sub
 +
>1</sub
 +
> = 0. 0453</span
 +
      > Rate of LovTAP degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>2</sub
 +
> = 0. 0453</span
 +
      > Rate of LovTAP* degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>3</sub
 +
> = 0. 0453</span
 +
      > tetR degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>4</sub
 +
> = 0. 0453</span
 +
      > Rate of Mnt degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>5</sub
 +
> = 0. 0453</span
 +
      > Rate of AraC degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>6</sub
 +
> = 0. 0453</span
 +
      > Rate of LacI degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>7</sub
 +
> = 0. 0453</span
 +
      > Rate of CI degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>8</sub
 +
> = 0. 0453</span
 +
      > Rate of CI434 degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>9</sub
 +
> = 00453</span
 +
      > Rate of SupD degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>10</sub
 +
> = 0. 0453</span
 +
      > Rate of T7ptag degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>11</sub
 +
> = 0. 012</span
 +
      > Rate of T7 polymerase degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>12</sub
 +
> = 0. 012</span
 +
      > Rate of GAL4 degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>13</sub
 +
> = 0. 012</span
 +
      > Rate of S1 degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>14</sub
 +
> = 0. 012</span
 +
      > Rate of S2 degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>15</sub
 +
> = 0. 012</span
 +
      > Rate of S3 degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ><span class="math"
 +
      >μ<sub
 +
>16</sub
 +
> = 0. 012</span
 +
      > Rate of S4 degredation <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      ></p
 +
    ></li
 +
  ><li
 +
  ><p
 +
    ><span class="math"
 +
      ><em
 +
>n</em
 +
><sub
 +
><em
 +
  >x</em
 +
  ></sub
 +
></span
 +
      > represents the hill coefficient for a given protein. <span class="math"
 +
      ><em
 +
>n</em
 +
><sub
 +
>1</sub
 +
> = 1</span
 +
      > for LovTAP*</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>n</em
 +
><sub
 +
>2</sub
 +
> = 3</span
 +
      > for tetR)</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>n</em
 +
><sub
 +
>3</sub
 +
> = 2</span
 +
      > for CI</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>n</em
 +
><sub
 +
>4</sub
 +
> = 2</span
 +
      > for CI434</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>n</em
 +
><sub
 +
>5</sub
 +
> = 2</span
 +
      > Hill coefficient of GAL4</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>n</em
 +
><sub
 +
>6</sub
 +
> = 2</span
 +
      > Hill coefficient of AraC</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>n</em
 +
><sub
 +
>7</sub
 +
> = 2</span
 +
      > Hill coefficient of T7</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>n</em
 +
><sub
 +
>8</sub
 +
> = 2</span
 +
      > Hill coefficient of LacI</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>n</em
 +
><sub
 +
>9</sub
 +
> = 1</span
 +
      > Hill coefficient of Mnt</p
 +
    ></li
 +
  ><li
 +
  ><p
 +
    ><span class="math"
 +
      ><em
 +
>K</em
 +
><sub
 +
><em
 +
  >x</em
 +
  ></sub
 +
></span
 +
      > represents, for a given protein, the ligand concentration producing half occupation (ligand concentration occupying half of the binding sites) in nanomoles. This is also the infamous &quot;microscopic dissociation constant&quot;. <span class="math"
 +
      ><em
 +
>K</em
 +
><sub
 +
><em
 +
  >d</em
 +
  >1</sub
 +
> = 142</span
 +
      > for LovTAP*</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>K</em
 +
><sub
 +
><em
 +
  >d</em
 +
  >2</sub
 +
> = 0. 179</span
 +
      > for tetR</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>K</em
 +
><sub
 +
><em
 +
  >d</em
 +
  >3</sub
 +
> = 50</span
 +
      > for CI</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>K</em
 +
><sub
 +
><em
 +
  >d</em
 +
  >4</sub
 +
> = 40</span
 +
      > for CI434</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>K</em
 +
><sub
 +
><em
 +
  >d</em
 +
  >5</sub
 +
> = 0. 5</span
 +
      > for GAL4</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>K</em
 +
><sub
 +
><em
 +
  >d</em
 +
  >6</sub
 +
> = 14</span
 +
      > for AraC</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>K</em
 +
><sub
 +
><em
 +
  >d</em
 +
  >7</sub
 +
> = 2</span
 +
      > for T7</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>K</em
 +
><sub
 +
><em
 +
  >d</em
 +
  >8</sub
 +
> = 800</span
 +
      >for LacI</p
 +
    ><p
 +
    ><span class="math"
 +
      ><em
 +
>K</em
 +
><sub
 +
><em
 +
  >d</em
 +
  >9</sub
 +
> = 50</span
 +
      > for Mnt</p
 +
    ></li
 +
  ><li
 +
  ><p
 +
    ><span class="math"
 +
      ><em
 +
>c</em
 +
></span
 +
      > <span class="math"
 +
      ><em
 +
>c</em
 +
><sub
 +
>1</sub
 +
> = 20. 20</span
 +
      >, which represents the rate of light-induced LovTAP to LovTAP* conformation change <span class="math"
 +
      >(1 / <em
 +
>s</em
 +
><em
 +
>e</em
 +
><em
 +
>c</em
 +
>)</span
 +
      > <span class="math"
 +
      ><em
 +
>c</em
 +
><sub
 +
>2</sub
 +
> = 20. 20</span
 +
      > which represents the rate of the reaction SupD + T7ptag <span class="math"
 +
      > → </span
 +
      > T7</p
 +
    ></li
 +
  ><li
 +
  ><p
 +
    ><span class="math"
 +
      >$\delta = \left\{
     \begin{array}{ll}
     \begin{array}{ll}
-
         0 & \mbox{without light}\\
+
         0 &amp; \mbox{without light}\\
-
         1 & \mbox{with light}
+
         1 &amp; \mbox{with light}
-
     \end{array}\right.</math></p></li></ol>
+
     \end{array}\right.$</span
 +
      ></p
 +
    ></li
 +
  ></ol
 +
>
 +
</html>
For a complete list of values and sensitivities, please see our [http://brownigem.com/parameters_2010.ods spreadsheet of parameters and sensitivities].
For a complete list of values and sensitivities, please see our [http://brownigem.com/parameters_2010.ods spreadsheet of parameters and sensitivities].

Revision as of 03:52, 27 October 2010

Parameters

As our circuit is relatively complex, we have many factors and thus many parameters with which to describe the function of these factors mathematically.

These parameters are as follows:

  1. δ is a function designed to represent the presence/absence of light in a Boolean fashion. δ=0 without light and 1 with light.
  2. c_1 represents the rate of conformational change from LovTAP to LovTAP* when irradiated with 470nm light.
  3. c_2 represents the rate of SupD + T7ptag --> T7 polymerase
  4. α represents the maximum protein synthesis rate in nanomoles/sec.
  5. β represents the basal synthesis rate. We assume ∀x β_x= .01α_x
  6. μ represents the protein degradation rate.
  7. n represents a ligand’s hill coefficient.
  8. K_m represents the ligand’s dissociation constant

Players

The following are the players that are used in the modeling of our circuit:

Transcription factors

  1. LovTAP

  2. LovTAP* (After light-induced conformational change)

  3. tetR

  4. Mnt

  5. AraC

  6. LacI

  7. CI

  8. CI434

  9. GAL4

Reporters

  1. S1

  2. S2

  3. S3

  4. S4

Constants

The following are the constants for which we need to find online or determine experimentally:

  1. $\delta = \left\{ \begin{array}{ll} 0 & \mbox{without light}\\ 1 & \mbox{with light} \end{array} \right.$

  2. c represents the rate of conformation change from LovTAP to LovTAP* under 470nm light.

Parameters

  1. αx represents the xth synthesis rate $\left(\dfrac{\text{nanomoles}}{\text{min}}\right)$.
    α = (rate of transcription) × (rate of translation)
    For promoters for which reliable data is not available, we assume an average E. coli transcription speed to be 70 nucleotides/second = 4,200 nucleotides/min, and an average translation speed of 40 amino acids/second = 2400, which is then further regulated by the appropriate ribosome binding site, represented as a normalized constant. Thus, we use the following equation to calculate unknown synthesis rates[0]:
    $\alpha = \left(\frac{4200}{\text{gene length}}\right)\times\left(\frac{2400\times\text{RBS Strength}}{\text{protein length}}\right) $

    α1 LovTAP synthesis rate constant  = 1. 06432 × 10 - 13 nanomoles. α2 tetR synthesis rate constant  = 1. 15318 × 10 - 13 nanomoles. α3 Mnt synthesis rate constant  = 6. 0562 ×  * 10 - 13 nanomoles. α4 AraC synthesis rate constant  = 5. 99989 × 10 - 14 nanomoles. α5 LacI synthesis rate constant  = 3. 94791 × 10 - 14 nanomoles. α6 CI synthesis rate constant  = 8. 93023 × 10 - 14 nanomoles. α7 CI434 synthesis rate constant  = 1. 2236 × 10 - 13 nanomoles. α8 [check]SupD synthesis rate constant  = 1. 2236 × 10 - 13 nanomoles. α9 [check]T7ptag synthesis rate constant  = 1. 2236 × 10 - 13 nanomoles. α10 [check]GAL4 synthesis rate constant  = 1. 06432 × 10 - 13 nanomoles.

    α11 S1 synthesis rate constant  = 9. 68992 × 10 - 14 nanomoles. α12 S2 synthesis rate constant  = 9. 68992 × 10 - 14 nanomoles. α13 S3 synthesis rate constant  = 9. 68992 × 10 - 14 nanomoles. α14 S4 synthesis rate constant  = 9. 68992 × 10 - 14 nanomoles.

  2. βx represents xth basal (un-induced or un-repressed) synthesis rate of a given promoter. We assume that, for all promoters, this is equal to 1% of the synthesis rate constant.
    ∀ x βx = 0. 1αx

  3. μx represents the degradation rate of a given protein. When the degredation rate is unknown, we assume a decay of 0.012 proteins/min (half-life of one hour) μ1 = 0. 0453 Rate of LovTAP degredation (1 / sec)μ2 = 0. 0453 Rate of LovTAP* degredation (1 / sec)μ3 = 0. 0453 tetR degredation (1 / sec)μ4 = 0. 0453 Rate of Mnt degredation (1 / sec)μ5 = 0. 0453 Rate of AraC degredation (1 / sec)μ6 = 0. 0453 Rate of LacI degredation (1 / sec)μ7 = 0. 0453 Rate of CI degredation (1 / sec)μ8 = 0. 0453 Rate of CI434 degredation (1 / sec)μ9 = 00453 Rate of SupD degredation (1 / sec)μ10 = 0. 0453 Rate of T7ptag degredation (1 / sec)μ11 = 0. 012 Rate of T7 polymerase degredation (1 / sec)μ12 = 0. 012 Rate of GAL4 degredation (1 / sec)μ13 = 0. 012 Rate of S1 degredation (1 / sec)μ14 = 0. 012 Rate of S2 degredation (1 / sec)μ15 = 0. 012 Rate of S3 degredation (1 / sec)μ16 = 0. 012 Rate of S4 degredation (1 / sec)

  4. nx represents the hill coefficient for a given protein. n1 = 1 for LovTAP*

    n2 = 3 for tetR)

    n3 = 2 for CI

    n4 = 2 for CI434

    n5 = 2 Hill coefficient of GAL4

    n6 = 2 Hill coefficient of AraC

    n7 = 2 Hill coefficient of T7

    n8 = 2 Hill coefficient of LacI

    n9 = 1 Hill coefficient of Mnt

  5. Kx represents, for a given protein, the ligand concentration producing half occupation (ligand concentration occupying half of the binding sites) in nanomoles. This is also the infamous "microscopic dissociation constant". Kd1 = 142 for LovTAP*

    Kd2 = 0. 179 for tetR

    Kd3 = 50 for CI

    Kd4 = 40 for CI434

    Kd5 = 0. 5 for GAL4

    Kd6 = 14 for AraC

    Kd7 = 2 for T7

    Kd8 = 800for LacI

    Kd9 = 50 for Mnt

  6. c c1 = 20. 20, which represents the rate of light-induced LovTAP to LovTAP* conformation change (1 / sec) c2 = 20. 20 which represents the rate of the reaction SupD + T7ptag  →  T7

  7. $\delta = \left\{ \begin{array}{ll} 0 & \mbox{without light}\\ 1 & \mbox{with light} \end{array}\right.$


For a complete list of values and sensitivities, please see our [http://brownigem.com/parameters_2010.ods spreadsheet of parameters and sensitivities].

Retrieved from "http://2010.igem.org/Team:Brown/Modeling/Parameters"