Team:Brown/Modeling/Parameters

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{{:Team:Brown/templates/header}}
{{:Team:Brown/templates/header}}
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==Parameters==
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=Modeling 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.  
As our circuit is relatively complex, we have many factors and thus many parameters with which to describe the function of these factors mathematically.  
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# K_m represents the ligand’s dissociation constant
# K_m represents the ligand’s dissociation constant
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= Players =
 
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The following are the players that are used in the modeling of our circuit:
 
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== Transcription factors ==
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For a complete, up-to-date list of values and sensitivities, please see our current [http://www.brownigem.com/2010_parameters.ods spreadsheet of parameters and sensitivities] (or [http://www.brownigem.com/2010_parameters.xls here] for closed source Microsoft Excel format).
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# LovTAP
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Alternatively, please see our prettier [http://www.brownigem.com/2010_parameters.pdf typeset PDF file].
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# LovTAP* (After light-induced conformational change)
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# tetR
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# Mnt
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# AraC
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# LacI
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# CI
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# CI434
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# GAL4
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== Reporters ==
 
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# S1
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{| {{table}}
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# S2
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| align="center" style="background:#f0f0f0;"|'''Brown iGEM 2010 – Modeling Parameters'''
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# S3
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| align="center" style="background:#f0f0f0;"|''''''
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# S4
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| align="center" style="background:#f0f0f0;"|''''''
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| align="center" style="background:#f0f0f0;"|''''''
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== Constants ==
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|-
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| ||||||
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The following are the constants for which we need to find online or determine experimentally:
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|-
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| Parameter Name||Value||Units||Source
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# <math>\delta = \left\{
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|-
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    \begin{array}{ll}
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| ||||||
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        0 & \mbox{without light}\\
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|-
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        1 & \mbox{with light}
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| LovTAP rate of maximum synthesis||1.0643E-013||nanomoles/min||Determined as explained in Brown 2010 wiki
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    \end{array}
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|-
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\right.</math>
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| tatR rate of maximum synthesis||1.1532E-013||nanomoles/min||Determined as explained in Brown 2010 wiki
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# <math>c</math> represents the rate of conformation change from LovTAP to LovTAP* under 470nm light.
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|-
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| Mnt rate of maximum synthesis||6.0562E-013||nanomoles/min||Determined as explained in Brown 2010 wiki
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== Parameters ==
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|-
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| AraC rate of maximum synthesis||5.9999E-014||nanomoles/min||Determined as explained in Brown 2010 wiki
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<ol>
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|-
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<li><p><math>\alpha_x</math> represents the <math>x</math>th synthesis rate <math>\left(\dfrac{\text{nanomoles}}{\text{min}}\right)</math>.<br />
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| LacI rate of maximum synthesis||3.9479E-014||nanomoles/min||Determined as explained in Brown 2010 wiki
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<math>\alpha=\left(\text{rate of transcription}\right)\times\left(\text{rate of translation}\right)</math><br />
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|-
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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>
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| CI rate of maximum synthesis||8.9302E-014||nanomoles/min||Determined as explained in Brown 2010 wiki
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|-
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<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>
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| CI434 rate of maximum synthesis||1.2236E-013||nanomoles/min||Determined as explained in Brown 2010 wiki
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|-
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<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>
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| SupD rate of maximum synthesis||2.7149E-012||nanomoles/min||Determined as explained in Brown 2010 wiki
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<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>
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|-
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<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>
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| T7ptag rate of maximum synthesis||7.0208E-015||nanomoles/min||Determined as explained in Brown 2010 wiki
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<li><p><math>n_x</math> represents the hill coefficient for a given protein. <math>n_1 = 1</math> for LovTAP*</p>
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|-
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| GAL4 rate of maximum synthesis||2.9175E-013||nanomoles/min||Determined as explained in Brown 2010 wiki
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<p><math>n_2 = 3</math> for tetR)</p>
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|-
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| S1 rate of maximum synthesis||9.6899E-014||nanomoles/min||Determined as explained in Brown 2010 wiki
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<p><math>n_3 = 2</math> for CI</p>
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|-
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| ||||||
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<p><math>n_4 = 2</math> for CI434</p>
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|-
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| LovTAP rate of basal synthesis||1.0643E-015||nanomoles/min||Determined as explained in Brown 2010 wiki
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<p><math>n_5 = 2</math> Hill coefficient of GAL4</p>
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|-
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| tatR rate of basal synthesis||1.1532E-015||nanomoles/min||Determined as explained in Brown 2010 wiki
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<p><math>n_6 = 2</math> Hill coefficient of AraC</p>
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|-
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| Mnt rate of basal synthesis||6.0562E-015||nanomoles/min||Determined as explained in Brown 2010 wiki
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<p><math>n_7 = 2</math> Hill coefficient of T7</p>
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|-
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| AraC rate of basal synthesis||5.9999E-016||nanomoles/min||Determined as explained in Brown 2010 wiki
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<p><math>n_8 = 2</math> Hill coefficient of LacI</p>
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|-
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| LacI rate of basal synthesis||3.9479E-016||nanomoles/min||Determined as explained in Brown 2010 wiki
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<p><math>n_9 = 1</math> Hill coefficient of Mnt</p>
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|-
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</li>
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| CI rate of basal synthesis||8.9302E-016||nanomoles/min||Determined as explained in Brown 2010 wiki
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<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>
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|-
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| CI434 rate of basal synthesis||1.2236E-015||nanomoles/min||Determined as explained in Brown 2010 wiki
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<p><math>K_{d2} = 0.179</math> for tetR</p>
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|-
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| SupD rate of basal synthesis||2.7149E-014||nanomoles/min||Determined as explained in Brown 2010 wiki
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<p><math>K_{d3} = 50</math> for CI</p>
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|-
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| T7ptag rate of basal synthesis||7.0208E-017||nanomoles/min||Determined as explained in Brown 2010 wiki
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<p><math>K_{d4} = 40</math> for CI434</p>
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|-
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| GAL4 rate of basal synthesis||2.9175E-015||nanomoles/min||Determined as explained in Brown 2010 wiki
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<p><math>K_{d5} = 0.5</math> for GAL4</p>
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|-
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| S1 rate of basal synthesis||9.6899E-016||nanomoles/min||Determined as explained in Brown 2010 wiki
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<p><math>K_{d6} = 14</math> for AraC</p>
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|-
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| ||||||
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<p><math>K_{d7} = 2</math> for T7</p>
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|-
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| LovTAP degradation rate||6.6667E-002||1/sec||Determined as explained in Brown 2010 wiki
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<p><math>K_{d8} = 800</math>for LacI</p>
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|-
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| LovTAP* degradation rate||6.6667E-002||1/sec||Determined as explained in Brown 2010 wiki
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<p><math>K_{d9} = 50</math> for Mnt</p>
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|-
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</li>
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| tetR degradation rate||6.6667E-002||1/sec||Determined as explained in Brown 2010 wiki
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<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>
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|-
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<li><p><math>\delta = \left\{
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| Mnt degradation rate||6.6667E-002||1/sec||Determined as explained in Brown 2010 wiki
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    \begin{array}{ll}
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|-
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        0 & \mbox{without light}\\
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| AraC degradation rate||6.6667E-002||1/sec||Determined as explained in Brown 2010 wiki
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        1 & \mbox{with light}
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|-
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    \end{array}\right.</math></p></li></ol>
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| LacI degradation rate||6.6667E-002||1/sec||Determined as explained in Brown 2010 wiki
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|-
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| CI degradation rate||5.6061E-002||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
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For a complete list of values and sensitivities, please see our [http://brownigem.com/parameters_2010.ods spreadsheet of parameters and sensitivities].
+
|-
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| CI434 degradation rate||1.2424E-001||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
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|-
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| SupD degradation rate||6.6667E-002||1/sec||As explained in wiki
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|-
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| T7ptag degradation rate||6.6667E-002||1/sec||As explained in wiki
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|-
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| T7 polymerase degradation rate||5.8333E-002||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
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|-
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| GAL4 degradation rate||6.6667E-002||1/sec||As explained in wiki
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|-
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| S1 degradation rate||5.0000E-002||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
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|-
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| S2 degradation rate||5.0000E-002||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
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|-
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| S3 degradation rate||5.0000E-002||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
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|-
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| S4 degradation rate||5.0000E-002||1/sec||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
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|-
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| ||||||
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|-
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| LovTAP* hill coefficient||1||||Estimate
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|-
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| tetR hill coefficient||3||||https://2007.igem.org/ETHZ/Parameters
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|-
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| CI hill coefficient||2||||https://2007.igem.org/ETHZ/Parameters
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|-
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| CI434 hill coefficient||2||||PKU 2009 wiki
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|-
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| GAL4 hill coefficient||2||||PKU 2009 wiki
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|-
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| AraC hill coefficient||2||||PKU 2009 wiki
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|-
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| T7 hill coefficient||2||||PKU 2009 wiki
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|-
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| LacI hill coefficient||2||||PKU 2009 wiki
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|-
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| Mnt hill coefficient||1||||PKU 2009 wiki
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|-
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| ||||||
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|-
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| LovTAP* dissociation constant||142.000||nanomoles||Light-activated DNA binding in a designed allosteric protein,Devin Strickland, Keith Moffat, and Tobin R. Sosnick
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|-
 +
| tetR dissociation constant||0.179||nanomoles||https://2007.igem.org/ETHZ/Parameters
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|-
 +
| CI dissociation constant||50.000||nanomoles||https://2007.igem.org/ETHZ/Parameters
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|-
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| CI434 dissociation constant||40.000||nanomoles||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
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|-
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| GAL4 dissociation constant||0.500||nanomoles||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
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|-
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| AraC dissociation constant||14.000||nanomoles||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
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|-
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| T7 dissociation constant||2.000||nanomoles||https://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
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|-
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| LacI dissociation constant||800.000||nanomoles||https://2007.igem.org/ETHZ/Parameters
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|-
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| Mnt dissociation constant||50.000||nanomoles||Estimate
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|-
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| ||||||
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|-
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| LovTAP → LovTAP* reaction rate||0.100||1/sec||Estimate
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|-
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| SupD + T7ptag → T7 reaction rate||0.100||1/sec||Estimate
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|-
 +
|
 +
|}

Latest revision as of 22:14, 27 October 2010

Modeling 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


For a complete, up-to-date list of values and sensitivities, please see our current [http://www.brownigem.com/2010_parameters.ods spreadsheet of parameters and sensitivities] (or [http://www.brownigem.com/2010_parameters.xls here] for closed source Microsoft Excel format).

Alternatively, please see our prettier [http://www.brownigem.com/2010_parameters.pdf typeset PDF file].


Brown iGEM 2010 – Modeling Parameters ' ' '
Parameter NameValueUnitsSource
LovTAP rate of maximum synthesis1.0643E-013nanomoles/minDetermined as explained in Brown 2010 wiki
tatR rate of maximum synthesis1.1532E-013nanomoles/minDetermined as explained in Brown 2010 wiki
Mnt rate of maximum synthesis6.0562E-013nanomoles/minDetermined as explained in Brown 2010 wiki
AraC rate of maximum synthesis5.9999E-014nanomoles/minDetermined as explained in Brown 2010 wiki
LacI rate of maximum synthesis3.9479E-014nanomoles/minDetermined as explained in Brown 2010 wiki
CI rate of maximum synthesis8.9302E-014nanomoles/minDetermined as explained in Brown 2010 wiki
CI434 rate of maximum synthesis1.2236E-013nanomoles/minDetermined as explained in Brown 2010 wiki
SupD rate of maximum synthesis2.7149E-012nanomoles/minDetermined as explained in Brown 2010 wiki
T7ptag rate of maximum synthesis7.0208E-015nanomoles/minDetermined as explained in Brown 2010 wiki
GAL4 rate of maximum synthesis2.9175E-013nanomoles/minDetermined as explained in Brown 2010 wiki
S1 rate of maximum synthesis9.6899E-014nanomoles/minDetermined as explained in Brown 2010 wiki
LovTAP rate of basal synthesis1.0643E-015nanomoles/minDetermined as explained in Brown 2010 wiki
tatR rate of basal synthesis1.1532E-015nanomoles/minDetermined as explained in Brown 2010 wiki
Mnt rate of basal synthesis6.0562E-015nanomoles/minDetermined as explained in Brown 2010 wiki
AraC rate of basal synthesis5.9999E-016nanomoles/minDetermined as explained in Brown 2010 wiki
LacI rate of basal synthesis3.9479E-016nanomoles/minDetermined as explained in Brown 2010 wiki
CI rate of basal synthesis8.9302E-016nanomoles/minDetermined as explained in Brown 2010 wiki
CI434 rate of basal synthesis1.2236E-015nanomoles/minDetermined as explained in Brown 2010 wiki
SupD rate of basal synthesis2.7149E-014nanomoles/minDetermined as explained in Brown 2010 wiki
T7ptag rate of basal synthesis7.0208E-017nanomoles/minDetermined as explained in Brown 2010 wiki
GAL4 rate of basal synthesis2.9175E-015nanomoles/minDetermined as explained in Brown 2010 wiki
S1 rate of basal synthesis9.6899E-016nanomoles/minDetermined as explained in Brown 2010 wiki
LovTAP degradation rate6.6667E-0021/secDetermined as explained in Brown 2010 wiki
LovTAP* degradation rate6.6667E-0021/secDetermined as explained in Brown 2010 wiki
tetR degradation rate6.6667E-0021/secDetermined as explained in Brown 2010 wiki
Mnt degradation rate6.6667E-0021/secDetermined as explained in Brown 2010 wiki
AraC degradation rate6.6667E-0021/secDetermined as explained in Brown 2010 wiki
LacI degradation rate6.6667E-0021/secDetermined as explained in Brown 2010 wiki
CI degradation rate5.6061E-0021/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
CI434 degradation rate1.2424E-0011/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
SupD degradation rate6.6667E-0021/secAs explained in wiki
T7ptag degradation rate6.6667E-0021/secAs explained in wiki
T7 polymerase degradation rate5.8333E-0021/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
GAL4 degradation rate6.6667E-0021/secAs explained in wiki
S1 degradation rate5.0000E-0021/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
S2 degradation rate5.0000E-0021/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
S3 degradation rate5.0000E-0021/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
S4 degradation rate5.0000E-0021/sechttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
LovTAP* hill coefficient1Estimate
tetR hill coefficient3https://2007.igem.org/ETHZ/Parameters
CI hill coefficient2https://2007.igem.org/ETHZ/Parameters
CI434 hill coefficient2PKU 2009 wiki
GAL4 hill coefficient2PKU 2009 wiki
AraC hill coefficient2PKU 2009 wiki
T7 hill coefficient2PKU 2009 wiki
LacI hill coefficient2PKU 2009 wiki
Mnt hill coefficient1PKU 2009 wiki
LovTAP* dissociation constant142.000nanomolesLight-activated DNA binding in a designed allosteric protein,Devin Strickland, Keith Moffat, and Tobin R. Sosnick
tetR dissociation constant0.179nanomoleshttps://2007.igem.org/ETHZ/Parameters
CI dissociation constant50.000nanomoleshttps://2007.igem.org/ETHZ/Parameters
CI434 dissociation constant40.000nanomoleshttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
GAL4 dissociation constant0.500nanomoleshttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
AraC dissociation constant14.000nanomoleshttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
T7 dissociation constant2.000nanomoleshttps://2009.igem.org/Team:PKU_Beijing/Modeling/Parameters
LacI dissociation constant800.000nanomoleshttps://2007.igem.org/ETHZ/Parameters
Mnt dissociation constant50.000nanomolesEstimate
LovTAP → LovTAP* reaction rate0.1001/secEstimate
SupD + T7ptag → T7 reaction rate0.1001/secEstimate
Retrieved from "http://2010.igem.org/Team:Brown/Modeling/Parameters"