Team:Carnegie Mellon/SensorModel

From 2014.igem.org

(Difference between revisions)
Line 110: Line 110:
<hr>
<hr>
<h2> <center>The Outline</center></h2>
<h2> <center>The Outline</center></h2>
-
<p align="left">  The model captures a total of 17 different interactions.</br></br>  
+
<p align="left">  T7-Intein is the N terminal T7 RNAP – N terminal intein – Estrogen Ligand Binding Domain – C terminal
-
1. The rate at which mRNA T7-Intein is transcribed.</br>
+
 
 +
intein – C terminal T7 RNAP</br></br>
 +
The model captures a total of 17 different interactions.</br>
 +
1. The rate at which mRNA T7-Intein and YFP is transcribed.</br>
2. The rate at which mRNA T7-Intein is degraded.</br>
2. The rate at which mRNA T7-Intein is degraded.</br>
3. The rate at which T7-Intein is translated.</br>
3. The rate at which T7-Intein is translated.</br>
4. The rate at which T7-Intein is degraded.</br>
4. The rate at which T7-Intein is degraded.</br>
-
5. The rate at which T7 polymerase is degraded.</br>
+
5. The rate at which T7 RNAP polymerase is degraded.</br>
6. The rate at which estrogen enters the cell.</br>
6. The rate at which estrogen enters the cell.</br>
7. The rate at which estrogen leaves the cell.</br>
7. The rate at which estrogen leaves the cell.</br>
-
8. The rate at which estrogen binds to the intein.</br>
+
8. The rate at which estrogen binds to the intein-LBD.</br>
-
9. The rate at which estrogen disassociates from the intein.</br>
+
9. The rate at which estrogen disassociates from the intein-LBD.</br>
-
10. The rate at which the intein is spliced out and T7 is formed.</br>
+
10. The rate at which the intein is spliced out and T7 RNAP is formed.</br>
-
11. The rate at which T7 binds to the promoter of plasmid 2.</br>
+
11. The rate at which T7 RNAP binds to the T7 promoter of plasmid 2.</br>
12. The rate at which mRNA RFP is transcribed.</br>
12. The rate at which mRNA RFP is transcribed.</br>
13. The rate at which mRNA RFP is degraded.</br>
13. The rate at which mRNA RFP is degraded.</br>
Line 127: Line 130:
15. The rate at which RFP is degraded.</br>
15. The rate at which RFP is degraded.</br>
16. The rate at which YFP is translated.</br>
16. The rate at which YFP is translated.</br>
-
17. The rate at which YFP is degraded.</br></br></p>
+
17. The rate at which YFP is degraded.
 +
</br></br></p>
<p> <center>To run the model simply open the latest version of Rulebender, go to the simulation tab, provide the file path for the file you wish to run, and hit run.</center>
<p> <center>To run the model simply open the latest version of Rulebender, go to the simulation tab, provide the file path for the file you wish to run, and hit run.</center>
</p>
</p>
Line 164: Line 168:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     The experiment can be carried out under various temperatures. Temperature affects the rate of intein splicing.
+
                     The experiment can be carried out under various temperatures. Temperature affects the rate of intein splicing and RFP levels of
 +
                    fluorescence.
                 </p>
                 </p>
             </td>
             </td>
Line 198: Line 203:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Number of rfp containing plasmids per cell.
+
                     Number of RFP containing plasmids per cell (pSB3K3).
                 </p>
                 </p>
             </td>
             </td>
Line 210: Line 215:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     2984 copies/cell
+
                     298 copies/cell
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Number of intein containing plasmids per cell.
+
                     Number of intein containing plasmids per cell (pSB1C3).
                 </p>
                 </p>
             </td>
             </td>
Line 227: Line 232:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     ppt * 5.6e-02 nM
+
                     ppt * 5.6*10<sup>-2</sup> nM
                 </p>
                 </p>
             </td>
             </td>
Line 329: Line 334:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     int_copies * 1.0e-03 nM
+
                     int_copies * 1.0*10<sup>-3</sup> nM
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Concentration of T7-Intein plasmids.
+
                     Concentration of T7-Intein plasmids (pSB1C3).
                 </p>
                 </p>
             </td>
             </td>
Line 346: Line 351:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     rfp_copies * 1.0e-03 nM
+
                     rfp_copies * 1.0*10<sup>-3</sup> nM
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Concentration of T7-RFP plasmids.
+
                     Concentration of T7-RFP plasmids (pSB3K3).
                 </p>
                 </p>
             </td>
             </td>
Line 368: Line 373:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Assume initial concentration of T7 bound to plasmid 2 is 0 nM.
+
                     Assume initial concentration of T7 RNAP bound to plasmid 2 is 0 nM.
                 </p>
                 </p>
             </td>
             </td>
Line 448: Line 453:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     1.7e-02 s<sup>-1</sup>
+
                     1.7*10<sup>-2</sup> s<sup>-1</sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
Rate at which estrogen diffuses through membrane. The diffusion coefficient of a steroid hormone in an aqueous phase = 10<sup>-13</sup> m<sup>2</sup>/s and the surface area of a bacteria is 6 * 10<sup>-12 </sup>m<sup>2</sup>. Thus (10<sup>-13</sup> m<sup>2</sup>/s) / (6 * 10                   <sup>-12 </sup>m<sup>2</sup>) = 1.7e-02 s<sup>-1</sup>
+
Rate at which estrogen diffuses through membrane. The diffusion coefficient of a steroid hormone in an aqueous phase = 10<sup>-13</sup> m                   <sup>2</sup>/s [1] and the surface area of a bacteria is 6 * 10<sup>-12 </sup>m<sup>2 </sup>[2]. Thus (10<sup>-13</sup> m<sup>2</sup>/s) /
 +
                    (6 * 10<sup>-12 </sup>m<sup>2</sup>) = 1.7*10<sup>-2</sup> s<sup>-1</sup>
                 </p>
                 </p>
             </td>
             </td>
Line 465: Line 471:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     1.3e-03 nM<sup>-1</sup>s<sup>-1</sup>
+
                     1.3*10<sup>-3</sup> nM<sup>-1</sup>s<sup>-1</sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which estrogen binds to the intein. The intein is the human estrogen receptor, so the value is from the literature.
+
                     Rate at which estrogen binds to the intein. The intein contains the ligand binding domain of the human estrogen receptor, so the value is
 +
                    from the literature [3].
                 </p>
                 </p>
             </td>
             </td>
Line 482: Line 489:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     1.2e-03 s<sup>-1</sup>
+
                     1.2*10<sup>-3</sup> s<sup>-1</sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which estrogen dissociates from the intein. Based on literature value of human estrogen receptor.
+
                     Rate at which estrogen dissociates from the intein. Based on literature value of human estrogen receptor [3].
                 </p>
                 </p>
             </td>
             </td>
Line 499: Line 506:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     7.1e-04 s<sup>-1</sup>
+
                     7.1*10<sup>-4</sup> s<sup>-1</sup><sup></sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which intein splices out. Based on literature values of other inteins’ splicing kinetics.
+
                     Rate at which intein splices out. Based on literature values of other inteins’ splicing kinetics [4].
                 </p>
                 </p>
             </td>
             </td>
Line 516: Line 523:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     3.3e-01 nM<sup>-1</sup>s<sup>-1</sup>
+
                     3.3*10<sup>-1</sup> nM<sup>-1</sup>s<sup>-1</sup><sup></sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which T7 binds to the RFP plasmid. Value obtained from literature.
+
                     Rate at which T7 RNAP binds to the T7 promoter of the RFP plasmid. Value obtained from literature [5].
                 </p>
                 </p>
             </td>
             </td>
Line 533: Line 540:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     1.0e-01 s<sup>-1</sup>
+
                     1.0*10<sup>-1</sup> s<sup>-1</sup><sup></sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which T7 dissociates from the RFP plasmid. Value obtained from literature.
+
                     Rate at which T7 RNAP dissociates from the T7 promoter of the RFP plasmid. Value obtained from literature [5].
                 </p>
                 </p>
             </td>
             </td>
Line 550: Line 557:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     8.8e-01 nM s<sup>-1</sup>
+
                     8.8*10<sup>-1</sup> nM s<sup>-1</sup><sup></sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which mRNA is synthesized from RFP plasmid. From iGEM team PKU ’09.
+
                     Rate at which mRNA is synthesized from RFP plasmid. From iGEM team PKU ’09 [6].
                 </p>
                 </p>
             </td>
             </td>
Line 567: Line 574:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     4.3e-03 s<sup>-1</sup>
+
                     4.3*10<sup>-3</sup> s<sup>-1</sup><sup></sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which mRNA RFP degrades. From iGEM team PKU ’09.
+
                     Rate at which mRNA RFP degrades. From iGEM team PKU ’09 [6].
                 </p>
                 </p>
             </td>
             </td>
Line 584: Line 591:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     9.0e03 s<sup>-1</sup>
+
                     9.0*10<sup>-3</sup> s<sup>-1</sup><sup></sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which RFP protein is made. From iGEM team PKU ’09.
+
                     Rate at which RFP protein is made. From iGEM team PKU ’09 [6].
                 </p>
                 </p>
             </td>
             </td>
Line 601: Line 608:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     8.3e-04 s<sup>-1</sup>
+
                     8.3*10<sup>-4</sup> s<sup>-1</sup><sup></sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which RFP protein degrades. From iGEM team PKU ’09.
+
                     Rate at which RFP protein degrades. From iGEM team PKU ’09 [6].
                 </p>
                 </p>
             </td>
             </td>
Line 618: Line 625:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     2.6e-02 nM s<sup>-1</sup>
+
                     2.6*10<sup>-2</sup> nM s<sup>-1</sup><sup></sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which mRNA is synthesized from T7-Intein plasmid. From iGEM team PKU ’09.
+
                     Rate at which mRNA is synthesized from T7-Intein plasmid. From iGEM team PKU ’09 [6].
                 </p>
                 </p>
             </td>
             </td>
Line 635: Line 642:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     4.3e-03 s<sup>-1</sup>
+
                     4.3*10<sup>-3</sup> s<sup>-1</sup><sup></sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which mRNA of T7-Intein degrades. From iGEM team PKU ’09.
+
                     Rate at which mRNA of T7-Intein degrades. From iGEM team PKU ’09 [6].
                 </p>
                 </p>
             </td>
             </td>
Line 652: Line 659:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     2.2e-03 s<sup>-1</sup>
+
                     2.2*10<sup>-3</sup> s<sup>-1</sup><sup></sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which T7-Intein is made from mRNA. From iGEM team PKU ’09.
+
                     Rate at which T7-Intein is made from mRNA. From iGEM team PKU ’09 [6].
                 </p>
                 </p>
             </td>
             </td>
Line 669: Line 676:
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     9.7e-04
+
                     9.7*10<sup>-4</sup> s<sup>-1</sup>
                 </p>
                 </p>
             </td>
             </td>
             <td width="180" valign="top">
             <td width="180" valign="top">
                 <p align="center">
                 <p align="center">
-
                     Rate at which T7 polymerase is degraded. From iGEM team PKU ’09.
+
                     Rate at which T7 polymerase is degraded. From iGEM team PKU ’09 [6].
                 </p>
                 </p>
             </td>
             </td>
Line 709: Line 716:
The rate at which the intein splices out is dependent on the temperature of environment surrounding the cell. Since the cell is an E. coli cell, the optimal temperature for the surrounding environment is 37 degrees Celsius. This was confirmed in the wet-lab. Thus:</br></br>
The rate at which the intein splices out is dependent on the temperature of environment surrounding the cell. Since the cell is an E. coli cell, the optimal temperature for the surrounding environment is 37 degrees Celsius. This was confirmed in the wet-lab. Thus:</br></br>
-
int_Splice() = k_splice * (1/(1 + sqrt(abs(37 – Temp)))</br>
+
int_Splice() = k_splice * (1/(1 + sqrt(abs(37 – Temp)))
-
</p>
+
-
<p> The units of concentration in all of the graphs are in nM. The units of time in all of the graphs are in seconds. According to the literature enhanced GFP can be detected fairly reasonably at concentrations greater than 1 µm. Thus we can assume that regular RFP will be detected at concentrations of around 100 µm. All of the simulations were carried out at 37 degrees Celsius for the optimal results. The sensor should detect estrogen within a couple of hours, thus the simulation ends in a couple of hours.</p></br>
+
-
 
+
-
 
+
-
 
+
-
<p>protein_INT_synth() = k_prot_int * mRNA_INT * sqrt(1/(1 + T7_unbound))</br></br>
+
-
 
+
-
The rate at which YFP is produced increases proportionally with the concentration of mRNA T7-Intein present (as the YFP sequence is located on the same mRNA) and decreases proportionally with the square root of the concentration of YFP currently present in the cell. Essentially the cell will make less YFP if there is already a lot of YFP currently present. Thus:</br></br>
+
-
 
+
-
protein_INT_synth() = k_prot_int * mRNA_INT * sqrt(1/(1 + T7_unbound))</br></br>
+
-
 
+
-
The rate at which the intein splices out is dependent on the temperature of environment surrounding the cell. Since the cell is an E. coli cell, the optimal temperature for the surrounding environment is 37 degrees Celsius. This was confirmed in the wet-lab. Thus:</br></br>
+
-
int_Splice() = k_splice * (1/(1 + sqrt(abs(37 – Temp)))</br>
 
</p>
</p>
<hr>
<hr>
<h2><p>Results</p></h2>
<h2><p>Results</p></h2>
-
<p>The units of concentration in all of the graphs are in nM. The units of time in all of the graphs are in seconds. According to the literature enhanced GFP can be detected fairly reasonably at concentrations greater than 1 µm. Thus we can assume that regular RFP will be detected at concentrations of around 100 µm. All of the simulations were carried out at 37 degrees Celsius for the optimal results. The sensor should detect estrogen within a couple of hours, thus the simulation ends in a couple of hours.</br></br>INSERT GRAPHS</p>
+
<p>The units of concentration in all of the graphs are in nM. The units of time in all of the graphs are in seconds. According to the literature enhanced GFP can be detected fairly reasonably at concentrations greater than 1 µm [7]. Thus we can assume that regular RFP will be detected at concentrations of around 100 µm. All of the simulations were carried out at 37 degrees Celsius for the optimal results. The sensor should detect estrogen within a couple of hours, thus the simulation ends in a couple of hours.</br></br>INSERT GRAPHS</p>
<h2>Code</h2>
<h2>Code</h2>

Revision as of 05:47, 17 October 2014

Carousel Template · Bootstrap

Purpose

The bacterial cell model was written in the BioNetGen Language, a rule-based modeling language that is useful for generating differential equations from a description of how various biological components interact with one another. The model was constructed from both data found in the literature and experimental data from the lab. This allows the model to run various simulations of the experiment under different conditions in order to find the optimal conditions for running the experiment. Also if the experiments are not producing any measurable results, the model can be used to identify which component of the experiment could be the problem.


The Outline

T7-Intein is the N terminal T7 RNAP – N terminal intein – Estrogen Ligand Binding Domain – C terminal intein – C terminal T7 RNAP

The model captures a total of 17 different interactions.
1. The rate at which mRNA T7-Intein and YFP is transcribed.
2. The rate at which mRNA T7-Intein is degraded.
3. The rate at which T7-Intein is translated.
4. The rate at which T7-Intein is degraded.
5. The rate at which T7 RNAP polymerase is degraded.
6. The rate at which estrogen enters the cell.
7. The rate at which estrogen leaves the cell.
8. The rate at which estrogen binds to the intein-LBD.
9. The rate at which estrogen disassociates from the intein-LBD.
10. The rate at which the intein is spliced out and T7 RNAP is formed.
11. The rate at which T7 RNAP binds to the T7 promoter of plasmid 2.
12. The rate at which mRNA RFP is transcribed.
13. The rate at which mRNA RFP is degraded.
14. The rate at which RFP is translated.
15. The rate at which RFP is degraded.
16. The rate at which YFP is translated.
17. The rate at which YFP is degraded.

To run the model simply open the latest version of Rulebender, go to the simulation tab, provide the file path for the file you wish to run, and hit run.


The Parameters

Parameter

Value

Reasoning

Temp

Variable (default value of 37 Celsius)

The experiment can be carried out under various temperatures. Temperature affects the rate of intein splicing and RFP levels of fluorescence.

ppt

Variable (default value of 1000)

Parts per trillion of estrogen in the water you are testing.

rfp_copies

15 copies/cell

Number of RFP containing plasmids per cell (pSB3K3).

int_copies

298 copies/cell

Number of intein containing plasmids per cell (pSB1C3).

estrogen_out

ppt * 5.6*10-2 nM

Concentration of estrogen outside the cell.

estrogen_in

0 nM

Concentration of estrogen inside the cell. Since e. coli is a prokaryote assume it is 0 nM.

t7_intein

0 nM

Assume initial concentration of T7-Intein complex is 0 nM.

t7_estrogen_u

0 nM

Assume initial concentration of T7-Intein complex bound to estrogen is 0 nM.

t7_estrogen_s

0 nM

Assume initial concentration of spliced out Intein-Estrogen complex is 0 nM.

t7_nc

0 nM

Assume initial concentration of T7 polymerase is 0 nM.

plas_int

int_copies * 1.0*10-3 nM

Concentration of T7-Intein plasmids (pSB1C3).

plas_rfp

rfp_copies * 1.0*10-3 nM

Concentration of T7-RFP plasmids (pSB3K3).

t7_rfp

0 nM

Assume initial concentration of T7 RNAP bound to plasmid 2 is 0 nM.

mrna_rfp

0 nM

Assume initial concentration of mRNA RFP is 0 nM.

prot_rfp

0 nM

Assume initial concentration of protein RFP is 0 nM.

mrna_int

0 nM

Assume initial concentration of mRNA intein is 0 nM.

prot_yfp

0 nM

Assume initial concentration of protein YFP is 0 nM.

k_e

1.7*10-2 s-1

Rate at which estrogen diffuses through membrane. The diffusion coefficient of a steroid hormone in an aqueous phase = 10-13 m 2/s [1] and the surface area of a bacteria is 6 * 10-12 m2 [2]. Thus (10-13 m2/s) / (6 * 10-12 m2) = 1.7*10-2 s-1

k_e_t7_on

1.3*10-3 nM-1s-1

Rate at which estrogen binds to the intein. The intein contains the ligand binding domain of the human estrogen receptor, so the value is from the literature [3].

k_e_t7_off

1.2*10-3 s-1

Rate at which estrogen dissociates from the intein. Based on literature value of human estrogen receptor [3].

k_splice

7.1*10-4 s-1

Rate at which intein splices out. Based on literature values of other inteins’ splicing kinetics [4].

k_t7_rfp_on

3.3*10-1 nM-1s-1

Rate at which T7 RNAP binds to the T7 promoter of the RFP plasmid. Value obtained from literature [5].

k_t7_rfp_off

1.0*10-1 s-1

Rate at which T7 RNAP dissociates from the T7 promoter of the RFP plasmid. Value obtained from literature [5].

k_rna_rfp

8.8*10-1 nM s-1

Rate at which mRNA is synthesized from RFP plasmid. From iGEM team PKU ’09 [6].

k_rna_deg_rfp

4.3*10-3 s-1

Rate at which mRNA RFP degrades. From iGEM team PKU ’09 [6].

k_prot_rfp

9.0*10-3 s-1

Rate at which RFP protein is made. From iGEM team PKU ’09 [6].

k_prot_deg_rfp

8.3*10-4 s-1

Rate at which RFP protein degrades. From iGEM team PKU ’09 [6].

k_rna_int

2.6*10-2 nM s-1

Rate at which mRNA is synthesized from T7-Intein plasmid. From iGEM team PKU ’09 [6].

k_rna_deg_int

4.3*10-3 s-1

Rate at which mRNA of T7-Intein degrades. From iGEM team PKU ’09 [6].

k_prot_int

2.2*10-3 s-1

Rate at which T7-Intein is made from mRNA. From iGEM team PKU ’09 [6].

k_prot_deg_int

9.7*10-4 s-1

Rate at which T7 polymerase is degraded. From iGEM team PKU ’09 [6].


Insights

Insight: In order to accurately describe the behavior of certain interactions in the cell, it is necessary to use more than just simple rate constants. New functions which modify the rate constant based on cellular conditions must be introduced.
The rate at which mRNA RFP is synthesized is the product of the rate constant and the number of T7 polymerases bound to the RFP plasmid. Thus:

mRNA_RFP_synth() = k_rna_rfp * T7_RFP

The rate at which RFP protein is produced increases proportionally with the concentration of mRNA RFP present and decreases proportionally with the square root of the concentration of RFP currently present in the cell. Essentially the cell will make less RFP if there is already a lot of RFP currently present. Thus:

protein_RFP_synth() = k_prot_rfp * mRNA_RFP * sqrt(1/(1 + prot_RFP))

The rate at which estrogen enters and exits the cell also depends on the concentration gradient of estrogen. If the concentration of estrogen outside the cell is much greater than the concentration of estrogen inside the cell, then estrogen will enter the cell at a much faster rate than if the concentration gradient is not as large. Thus:

e_in() = k_e * (E_out)/(E_out + E_in)
e_out() = k_e * (E_in)/(E_out + E_in)

The rate at which the T7-Intein complex is produced increases proportionally with the concentration of mRNA T7-Intein present and decreases proportionally with the square root of the concentration of T7-Intein complex currently present in the cell. Essentially the cell will make less T7-Intein complex if there is already a lot of T7-Intein currently present. Thus:

protein_INT_synth() = k_prot_int * mRNA_INT * sqrt(1/(1 + T7_unbound))

The rate at which YFP is produced increases proportionally with the concentration of mRNA T7-Intein present (as the YFP sequence is located on the same mRNA) and decreases proportionally with the square root of the concentration of YFP currently present in the cell. Essentially the cell will make less YFP if there is already a lot of YFP currently present. Thus:

protein_INT_synth() = k_prot_int * mRNA_INT * sqrt(1/(1 + T7_unbound))

The rate at which the intein splices out is dependent on the temperature of environment surrounding the cell. Since the cell is an E. coli cell, the optimal temperature for the surrounding environment is 37 degrees Celsius. This was confirmed in the wet-lab. Thus:

int_Splice() = k_splice * (1/(1 + sqrt(abs(37 – Temp)))


Results

The units of concentration in all of the graphs are in nM. The units of time in all of the graphs are in seconds. According to the literature enhanced GFP can be detected fairly reasonably at concentrations greater than 1 µm [7]. Thus we can assume that regular RFP will be detected at concentrations of around 100 µm. All of the simulations were carried out at 37 degrees Celsius for the optimal results. The sensor should detect estrogen within a couple of hours, thus the simulation ends in a couple of hours.

INSERT GRAPHS

Code