Team:Brown/Modeling/Parameters

From 2010.igem.org

(Difference between revisions)
Line 15: Line 15:
<html>
<html>
-
<h1 class="title">Deterministic Modeling of a Bacterial Light Recognition Circuit</h1>
+
{{http://www.brownigem.com/latexconverted.html}}
-
<h1 id="players"
+
-
>Players</h1
+
-
><p
+
-
>The following are the players that are used in the modeling of our circuit:</p
+
-
><h2 id="transcription-factors"
+
-
>Transcription factors</h2
+
-
><ol
+
-
><li
+
-
  ><p
+
-
    >LovTAP</p
+
-
    ></li
+
-
  ><li
+
-
  ><p
+
-
    >LovTAP* (After light-induced conformational change)</p
+
-
    ></li
+
-
  ><li
+
-
  ><p
+
-
    >tetR</p
+
-
    ></li
+
-
  ><li
+
-
  ><p
+
-
    >Mnt</p
+
-
    ></li
+
-
  ><li
+
-
  ><p
+
-
    >AraC</p
+
-
    ></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="LaTeX"
+
-
      >$\delta = \left\{
+
-
    \begin{array}{ll}
+
-
        0 & \mbox{without light}\\
+
-
        1 & \mbox{with light}
+
-
    \end{array}
+
-
\right.$</span
+
-
      ></p
+
-
    ></li
+
-
  ><li
+
-
  ><p
+
-
    ><span class="LaTeX"
+
-
      >$c$</span
+
-
      > represents the rate of conformation change from LovTAP to LovTAP* under 470nm light.</p
+
-
    ></li
+
-
  ></ol
+
-
><h2 id="parameters"
+
-
>Parameters</h2
+
-
><ol
+
-
><li
+
-
  ><p
+
-
    ><span class="LaTeX"
+
-
      >$\alpha_x$</span
+
-
      > represents the <span class="LaTeX"
+
-
      >$x$</span
+
-
      >th synthesis rate <span class="LaTeX"
+
-
      >$\left(\dfrac{\text{nanomoles}}{\text{min}}\right)$</span
+
-
      >.<br
+
-
      /> <span class="LaTeX"
+
-
      >$\alpha=\left(\text{rate of transcription}\right)\times\left(\text{rate of translation}\right)$</span
+
-
      ><br
+
-
      /> For promoters for which reliable data is not available, we assume an average <em
+
-
      >E. coli</em
+
-
      > 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]: <span class="LaTeX"
+
-
      >$$\alpha = \left(\frac{4200}{\text{gene length}}\right)\times\left(\frac{2400\times\text{RBS Strength}}{\text{protein length}}\right) $$</span
+
-
      ></p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$\alpha_1$</span
+
-
      > LovTAP synthesis rate constant <span class="LaTeX"
+
-
      >$= 1.06432\times10^{-13}$</span
+
-
      > nanomoles. <span class="LaTeX"
+
-
      >$\alpha_2$</span
+
-
      > tetR synthesis rate constant <span class="LaTeX"
+
-
      >$= 1.15318\times10^{-13}$</span
+
-
      > nanomoles. <span class="LaTeX"
+
-
      >$\alpha_3$</span
+
-
      > Mnt synthesis rate constant <span class="LaTeX"
+
-
      >$= 6.0562\times*10^{-13}$</span
+
-
      > nanomoles. <span class="LaTeX"
+
-
      >$\alpha_4$</span
+
-
      > AraC synthesis rate constant <span class="LaTeX"
+
-
      >$= 5.99989\times10^{-14}$</span
+
-
      > nanomoles. <span class="LaTeX"
+
-
      >$\alpha_5$</span
+
-
      > LacI synthesis rate constant <span class="LaTeX"
+
-
      >$= 3.94791\times10^{-14}$</span
+
-
      > nanomoles. <span class="LaTeX"
+
-
      >$\alpha_6$</span
+
-
      > CI synthesis rate constant <span class="LaTeX"
+
-
      >$= 8.93023\times10^{-14}$</span
+
-
      > nanomoles. <span class="LaTeX"
+
-
      >$\alpha_7$</span
+
-
      > CI434 synthesis rate constant <span class="LaTeX"
+
-
      >$= 1.2236\times10^{-13}$</span
+
-
      > nanomoles. <span class="LaTeX"
+
-
      >$\alpha_8$</span
+
-
      > [check]SupD synthesis rate constant <span class="LaTeX"
+
-
      >$= 1.2236\times10^{-13}$</span
+
-
      > nanomoles. <span class="LaTeX"
+
-
      >$\alpha_9$</span
+
-
      > [check]T7ptag synthesis rate constant <span class="LaTeX"
+
-
      >$= 1.2236\times10^{-13}$</span
+
-
      > nanomoles. <span class="LaTeX"
+
-
      >$\alpha_{10}$</span
+
-
      > [check]GAL4 synthesis rate constant <span class="LaTeX"
+
-
      >$= 1.06432\times10^{-13}$</span
+
-
      > nanomoles.</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$\alpha_{11}$</span
+
-
      > S1 synthesis rate constant <span class="LaTeX"
+
-
      >$= 9.68992\times10^{-14}$</span
+
-
      > nanomoles. <span class="LaTeX"
+
-
      >$\alpha_{12}$</span
+
-
      > S2 synthesis rate constant <span class="LaTeX"
+
-
      >$= 9.68992\times10^{-14}$</span
+
-
      > nanomoles. <span class="LaTeX"
+
-
      >$\alpha_{13}$</span
+
-
      > S3 synthesis rate constant <span class="LaTeX"
+
-
      >$= 9.68992\times10^{-14}$</span
+
-
      > nanomoles. <span class="LaTeX"
+
-
      >$\alpha_{14}$</span
+
-
      > S4 synthesis rate constant <span class="LaTeX"
+
-
      >$= 9.68992\times10^{-14}$</span
+
-
      > nanomoles.</p
+
-
    ></li
+
-
  ><li
+
-
  ><p
+
-
    ><span class="LaTeX"
+
-
      >$\beta_x $</span
+
-
      > represents <span class="LaTeX"
+
-
      >$x$</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. <span class="LaTeX"
+
-
      >$$\forall x \ \beta_x = 0.1\alpha_x$$</span
+
-
      ></p
+
-
    ></li
+
-
  ><li
+
-
  ><p
+
-
    ><span class="LaTeX"
+
-
      >$\mu_x$</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="LaTeX"
+
-
      >$\mu_1= 0.0453$</span
+
-
      > Rate of LovTAP degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_2= 0.0453$</span
+
-
      > Rate of LovTAP* degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_3 = 0.0453$</span
+
-
      > tetR degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_4= 0.0453$</span
+
-
      > Rate of Mnt degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_5= 0.0453$</span
+
-
      > Rate of AraC degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_6= 0.0453$</span
+
-
      > Rate of LacI degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_7= 0.0453$</span
+
-
      > Rate of CI degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_8= 0.0453$</span
+
-
      > Rate of CI434 degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_9= 00453$</span
+
-
      > Rate of SupD degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_{10}= 0.0453$</span
+
-
      > Rate of T7ptag degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_{11}= 0.012$</span
+
-
      > Rate of T7 polymerase degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_{12}= 0.012$</span
+
-
      > Rate of GAL4 degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_{13}= 0.012$</span
+
-
      > Rate of S1 degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_{14}= 0.012$</span
+
-
      > Rate of S2 degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_{15}= 0.012$</span
+
-
      > Rate of S3 degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ><span class="LaTeX"
+
-
      >$\mu_{16}= 0.012$</span
+
-
      > Rate of S4 degredation <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      ></p
+
-
    ></li
+
-
  ><li
+
-
  ><p
+
-
    ><span class="LaTeX"
+
-
      >$n_x$</span
+
-
      > represents the hill coefficient for a given protein. <span class="LaTeX"
+
-
      >$n_1 = 1$</span
+
-
      > for LovTAP*</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$n_2 = 3$</span
+
-
      > for tetR)</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$n_3 = 2$</span
+
-
      > for CI</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$n_4 = 2$</span
+
-
      > for CI434</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$n_5 = 2$</span
+
-
      > Hill coefficient of GAL4</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$n_6 = 2$</span
+
-
      > Hill coefficient of AraC</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$n_7 = 2$</span
+
-
      > Hill coefficient of T7</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$n_8 = 2$</span
+
-
      > Hill coefficient of LacI</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$n_9 = 1$</span
+
-
      > Hill coefficient of Mnt</p
+
-
    ></li
+
-
  ><li
+
-
  ><p
+
-
    ><span class="LaTeX"
+
-
      >$K_x$</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="LaTeX"
+
-
      >$K_{d1} = 142$</span
+
-
      > for LovTAP*</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$K_{d2} = 0.179$</span
+
-
      > for tetR</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$K_{d3} = 50$</span
+
-
      > for CI</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$K_{d4} = 40$</span
+
-
      > for CI434</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$K_{d5} = 0.5$</span
+
-
      > for GAL4</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$K_{d6} = 14$</span
+
-
      > for AraC</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$K_{d7} = 2$</span
+
-
      > for T7</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$K_{d8} = 800$</span
+
-
      >for LacI</p
+
-
    ><p
+
-
    ><span class="LaTeX"
+
-
      >$K_{d9} = 50$</span
+
-
      > for Mnt</p
+
-
    ></li
+
-
  ><li
+
-
  ><p
+
-
    ><span class="LaTeX"
+
-
      >$c$</span
+
-
      > <span class="LaTeX"
+
-
      >$c_1 = 20.20$</span
+
-
      >, which represents the rate of light-induced LovTAP to LovTAP* conformation change <span class="LaTeX"
+
-
      >$(1/sec)$</span
+
-
      > <span class="LaTeX"
+
-
      >$c_2 = 20.20$</span
+
-
      > which represents the rate of the reaction SupD + T7ptag <span class="LaTeX"
+
-
      >$\rightarrow$</span
+
-
      > T7</p
+
-
    ></li
+
-
  ><li
+
-
  ><p
+
-
    ><span class="LaTeX"
+
-
      >$\delta = \left\{
+
-
    \begin{array}{ll}
+
-
        0 & \mbox{without light}\\
+
-
        1 & \mbox{with light}
+
-
    \end{array}\right.$</span
+
-
      ></p
+
-
    ></li
+
-
  ></ol
+
-
>
+
</html>
</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 soon-to-be updated [http://brownigem.com/parameters_2010.ods spreadsheet of parameters and sensitivities].

Revision as of 04:07, 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

{{http://www.brownigem.com/latexconverted.html}}


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

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