Team:Newcastle/Modelling/SporulationTuning

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==Sporulation Tuning==
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==Sporulation Tuning Model==
 +
The expression of KinA has been modelled as seen above, therefore we can now proceed further into the Sporulation Tuning Model, which is built from the KinA Expression Model with COPASI.
-
===KinA Expression Model===
+
To proceed with the modelling of our Sporulation Tuning Model, we have decided that in response to an unidentified stimuli, where KinA  autophosphorylates and then donates its phosphate groups to the response regulator Spo0F, the unidentified stimuli will be termed as 'sporulation signal'.<sup>[5]</sup>
-
Under normal conditions, LacI represses KinA.
+
Also, to simplify the modelling, the phosphatases that provide access for negative signals to influence the cell’s decision whether to sporulate or to continue vegetative growth,<sup>[4]</sup> such as Spo0E<sup>[1]</sup>, YisI, and YnzD,<sup>[5]</sup> are not taken into consideration while building this model.
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[[Image:TeamNewcastleKinAExpLacIKinA.png|110px|center]]
+
The following equations describe the model:
 +
[[Image:TeamNewcastleSporeTuneEqn1.png|170px|center]]
 +
<center>''Equation 1''</center>
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However, in the presence of IPTG, KinA can be expressed, as IPTG binds to LacI, deactivating it. Equations (a) and (b) describes how IPTG binds to LacI, forming LacI*, which is the deactivated form of LacI
+
[[Image:TeamNewcastleSporeTuneEqn2.png|130px|center]]
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[[Image:TeamNewcastleKinAExpLacIIPTG1.png|220px|center]]
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<center>''Equation 2''</center>
 +
[[Image:TeamNewcastleSporeTuneEqn3.png|100px|center]]
 +
<center>''Equation 3''</center>
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Over time, the deactivated form of LacI, LacI* may degrade. This is also taken into consideration while building the model.
 
-
[[Image:TeamNewcastleKinAExpDeactivatedLacIDegradation.png|80px|center]]
 
 +
As Spo0F lacks an output domain and is incapable of activating transcription; it serves only as an intermediary in the phosphorelay. The phosphotransferase Spo0B transfers the phosphate from Spo0F~P to Spo0A.<sup>[4]</sup>
 +
[[Image:TeamNewcastleSporeTuneEqn4.png|230px|center]]
 +
<center>''Equation 4''</center>
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Protein synthesis requires two steps, transcription and translation, and is further illustrated in Figure 1, below.
 
-
[[Image:TeamNewcastleKinAExpTranscriptiontranslation.png|300px|center]]
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[[Image:TeamNewcastleSporeTuneEqn5.png|160px|center]]
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<center>''Figure 1: Transcription and Translation''</center>
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<center>''Equation 5''</center>
 +
[[Image:TeamNewcastleSporeTuneEqn6.png|280px|center]]
 +
<center>''Equation 6''</center>
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Referring to Figure 1, the following equations can be written:
 
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;<u>Transcription of LacI,</u>
+
[[Image:TeamNewcastleSporeTuneEqn7.png|160px|center]]
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[[Image:TeamNewcastleKinAExpLacITranscription.png|120px|center]]
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<center>''Equation 7''</center>
 +
[[Image:TeamNewcastleSporeTuneEqn8.png|280px|center]]
 +
<center>''Equation 8''</center>
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;<u>Translation of LacI,</u>
 
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[[Image:TeamNewcastleKinAExpLacITranslation.png|80px|center]]
 
 +
[[Image:TeamNewcastleSporeTuneEqn9.png|160px|center]]
 +
<center>''Equation 9''</center>
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where mRNA_LacI is inducing the formation of LacI.
 
 +
With respect to Equations 1 to 9, as seen above, the corresponding fluxes are as follows:
 +
[[Image:TeamNewcastleSporeTuneFluxes2.png|200px|center]]
 +
<center>''Fluxes''</center>
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;<u>Transcription of KinA,</u>
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The phophorylated proteins Spo0FP, Spo0BP and Spo0AP will go through degradation, and the following equations, Equation 10, 11 and 12 describes degradation.
-
[[Image:TeamNewcastleKinAExpKinATranscription.png|130px|center]]
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 +
[[Image:TeamNewcastleSporeTuneEqn10.png|80px|center]]
 +
<center>''Equation 10''</center>
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where LacI is repressing mRNA_KinA, therefore a lower concentration of LacI would result in a higher concentration of mRNA_KinA.
 
 +
[[Image:TeamNewcastleSporeTuneEqn11.png|80px|center]]
 +
<center>''Equation 11''</center>
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;<u>Translation of KinA,</u>
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[[Image:TeamNewcastleSporeTuneEqn12.png|80px|center]]
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[[Image:TeamNewcastleKinAExpKinATranslation.png|80px|center]]
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<center>''Equation 12''</center>
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where mRNA_KinA is inducing the formation of KinA.
+
As parameters such as transcription and translation rates could not be found in literature, the following equations were used to calculate the transcription and translation rates whenever possible.
-
====Results====
+
[[Image:TeamNewcastleSporeTuneTranscriptionRate.png|270px|center]]
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The above equations were modelled in COPASI, and the following graphs show the behaviour of the system over time at different IPTG concentrations.
 
 +
[[Image:TeamNewcastleSporeTuneTranslationRate.png|220px|center]]
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;<u>IPTG concentration = 1000 nmol/fl</u>
 
-
[[Image:TeamNewcastleKinAExpPic1.png|center|500px]]
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Using the transcription and translation rate equations as seen above, the rates were calculated for the components Spo0A, Spo0B, Spo0F and KinA, and the results are reported in the table below.
 +
 
 +
[[Image:TeamNewcastleSporeTuneTranscriptionTranslateRate.png|330px|center]]
 +
<center>''Table 1: Transcription and Translation Rates''</center>
 +
 
 +
 
 +
For components where information on the CDS length could not be found, we used the value 0.1 for both the translation and transcription rate.
 +
 
 +
Also, the values for the various rate constants could not be found in literature either. Therefore, the following values were used:
 +
 
 +
k<sub>forward</sub> = 0.001
 +
 
 +
k<sub>reverse</sub> = 0.05
 +
 
 +
Other parameters and formulas which were used in this model are as follows:
 +
 
 +
Protein Degradation Rate = 0.0012
 +
 
 +
mRNA Degradation Rate = 0.0058
 +
 
 +
 
 +
[[Image:TeamNewcastleSporeTuneFunctions.png|600px|center]]
 +
<center>''Table 2: Functions used in the KinA Expression and Sporulation Tuning Models''</center>
 +
 
 +
 
 +
The CDS lengths was found on the [http://www.ncbi.nlm.nih.gov/Genbank/ GenBank] using the accession number, AL009126.
 +
 
 +
These parameters and functions were also used in the KinA Expression Model.
 +
 
 +
The Sporulation Tuning Model is available for download as follows:
 +
* [[:Image:SporeTuneModel (SBML and Copasi).zip|Sporulation Tuning Model (SBML and COPASI)]]
 +
 
 +
===Results===
 +
 
 +
At a constant IPTG concentration of 5000nmol/fl, we vary the concentration of the sporulation signal, [SS] and the following graphs show the results.
 +
 
 +
<u>'''At [SS] = 1000nmol/fl'''</u>
 +
 
 +
[[Image:TeamNewcastleSporeTunePic1.png|500px|center]]
<center>''Figure 1.1''</center>
<center>''Figure 1.1''</center>
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In Figure 1.1, at a IPTG concentration of 1000nmol/fl, due to the high concentration of LacI*, it is difficult to view the results for the other species, such as, KinA, LacI, mRNA_KinA, and mRNA_LacI as they are all concentrated at the bottom.
+
Figure 1.1 shows that at an IPTG concentration of 5000nmol/fl and sporulation signal concentration of 1000nmol/fl, the Spo0F concentration gets significantly higher than the other components.
 +
In order to take a better look at the behaviour of the rest of the components, the following graphs were produced.
-
[[Image:TeamNewcastleKinAExpPic2.png|center|500px]]
+
 
 +
[[Image:TeamNewcastleSporeTunePic2.png|500px|center]]
<center>''Figure 1.2''</center>
<center>''Figure 1.2''</center>
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Figure 1.2 shows the behaviour of KinA, LacI, mRNA_KinA and mRNA_LacI more clearly, at the IPTG concentration of 1000nmol/flu.
+
From Figure 1.2, the concentration of Spo0AP seems to be at a healthy concentration.
-
From Figure 1.1 and 1.2, it is observed that the concentration of LacI* is significantly higher than the other species when the IPTG concentration is set at 1000nmol/fl. Looking at Figure 1.2, while the concentration of KinA is increasing, it is still lower than that of LacI.
 
 +
[[Image:TeamNewcastleSporeTunePic3.png|500px|center]]
 +
<center>''Figure 1.3''</center>
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;<u>IPTG concentration = 3000 nmol/fl</u>
 
-
[[Image:TeamNewcastleKinAExpPic3.png|center|500px]]
+
[[Image:TeamNewcastleSporeTunePic4.png|500px|center]]
 +
<center>''Figure 1.4''</center>
 +
 
 +
 
 +
<u>'''At [SS] = 3000nmol/fl'''</u>
 +
 
 +
The concentration of the sporulation signal, [SS] is increased to 3000nmol/fl in the following graphs, and the results were investigated.
 +
 
 +
[[Image:TeamNewcastleSporeTunePic5.png|center|500px]]
<center>''Figure 2.1''</center>
<center>''Figure 2.1''</center>
-
Comparing Figure 1.1 and 2.1, though the IPTG concentration in Figure 2.1 is 3000nmol/fl, the LacI* concentration is not particularly different.
+
With a stronger sporulation signal, the concentration of Spo0FP and Spo0BP increased significantly, while the concentration of Spo0F dropped significantly from approximately 9000nmol/fl to 2300nmol/fl, comparing Figure 1.1 to 2.1.
-
[[Image:TeamNewcastleKinAExpPic4.png|center|500px]]
+
[[Image:TeamNewcastleSporeTunePic6.png|500px|center]]
<center>''Figure 2.2''</center>
<center>''Figure 2.2''</center>
-
As the IPTG concentration increases from 1000 to 3000nmol/fl, the KinA concentration is greater than the LacI concentration. However, upon a closer look, the KinA concentration did not increase due to the higher IPTG concentration. The KinA concentration is now higher than the LacI concentration because the LacI concentration decreased.
+
The concentration of LacI* remained approximately the same, so as Spo0AP.
 +
 
 +
 
 +
[[Image:TeamNewcastleSporeTunePic7.png|center|500px]]
 +
 
 +
 
 +
<center>''Figure 2.3''</center>
 +
 
 +
 
 +
[[Image:TeamNewcastleSporeTunePic8.png|center|500px]]
 +
<center>''Figure 2.4''</center>
 +
 
-
;<u>IPTG concentration = 5000 nmol/fl</u>
+
Comparing Figure 1.3 and 2.4, the concentration of Spo0A falls from approximately 100nmol/fl to 50nmol/fl when [SS] is increased.
-
[[Image:TeamNewcastleKinAExpPic5.png|center|500px]]
 
-
<center>''Figure 3.1''</center>
 
 +
Referring to the graphs obtained from the model, it seems like increasing the sporulation signal concentration, does not increase the Spo0AP concentration. However, the concentrations of Spo0BP and SpoFP did increase as the sporulation signal concentration increased.
-
Once again, as obsered in Figure 1.1 and 2.1, the concentration of LacI* in Figure 3.1 seems to reach the similar concentrations although the concentration of IPTG has been increased in each case. This seems to say that the concentration of LacI* has reached a threshold concentration.
 
 +
===Other Models===
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[[Image:TeamNewcastleKinAExpPic6.png|500px|center]]
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: '' See [[Team:Newcastle/Modelling/KinAExpression|KinA Expression Model]]''
-
<center>''Figure 3.2''</center>
+
 +
: '' See [[Team:Newcastle/Modelling/SinOperon|Sin Operon Model]]''
-
The KinA concentration in Figure 3.2 is greater than that of LacI once again. However, KinA concentration seems to be stagnant at approximately 90nmol/fl, while the LacI concentration constantly decreases with increased IPTG concentration. There, the IPTG concentration only seems to affect the LacI concentration.
 
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Latest revision as of 22:07, 21 October 2009


Sporulation Tuning Model

The expression of KinA has been modelled as seen above, therefore we can now proceed further into the Sporulation Tuning Model, which is built from the KinA Expression Model with COPASI.

To proceed with the modelling of our Sporulation Tuning Model, we have decided that in response to an unidentified stimuli, where KinA autophosphorylates and then donates its phosphate groups to the response regulator Spo0F, the unidentified stimuli will be termed as 'sporulation signal'.[5]

Also, to simplify the modelling, the phosphatases that provide access for negative signals to influence the cell’s decision whether to sporulate or to continue vegetative growth,[4] such as Spo0E[1], YisI, and YnzD,[5] are not taken into consideration while building this model.

The following equations describe the model:

TeamNewcastleSporeTuneEqn1.png
Equation 1


TeamNewcastleSporeTuneEqn2.png
Equation 2


TeamNewcastleSporeTuneEqn3.png
Equation 3


As Spo0F lacks an output domain and is incapable of activating transcription; it serves only as an intermediary in the phosphorelay. The phosphotransferase Spo0B transfers the phosphate from Spo0F~P to Spo0A.[4]

TeamNewcastleSporeTuneEqn4.png
Equation 4


TeamNewcastleSporeTuneEqn5.png
Equation 5


TeamNewcastleSporeTuneEqn6.png
Equation 6


TeamNewcastleSporeTuneEqn7.png
Equation 7


TeamNewcastleSporeTuneEqn8.png
Equation 8


TeamNewcastleSporeTuneEqn9.png
Equation 9


With respect to Equations 1 to 9, as seen above, the corresponding fluxes are as follows:

TeamNewcastleSporeTuneFluxes2.png
Fluxes


The phophorylated proteins Spo0FP, Spo0BP and Spo0AP will go through degradation, and the following equations, Equation 10, 11 and 12 describes degradation.

TeamNewcastleSporeTuneEqn10.png
Equation 10


TeamNewcastleSporeTuneEqn11.png
Equation 11


TeamNewcastleSporeTuneEqn12.png
Equation 12


As parameters such as transcription and translation rates could not be found in literature, the following equations were used to calculate the transcription and translation rates whenever possible.

TeamNewcastleSporeTuneTranscriptionRate.png


TeamNewcastleSporeTuneTranslationRate.png


Using the transcription and translation rate equations as seen above, the rates were calculated for the components Spo0A, Spo0B, Spo0F and KinA, and the results are reported in the table below.

TeamNewcastleSporeTuneTranscriptionTranslateRate.png
Table 1: Transcription and Translation Rates


For components where information on the CDS length could not be found, we used the value 0.1 for both the translation and transcription rate.

Also, the values for the various rate constants could not be found in literature either. Therefore, the following values were used:

kforward = 0.001

kreverse = 0.05

Other parameters and formulas which were used in this model are as follows:

Protein Degradation Rate = 0.0012

mRNA Degradation Rate = 0.0058


TeamNewcastleSporeTuneFunctions.png
Table 2: Functions used in the KinA Expression and Sporulation Tuning Models


The CDS lengths was found on the [http://www.ncbi.nlm.nih.gov/Genbank/ GenBank] using the accession number, AL009126.

These parameters and functions were also used in the KinA Expression Model.

The Sporulation Tuning Model is available for download as follows:

Results

At a constant IPTG concentration of 5000nmol/fl, we vary the concentration of the sporulation signal, [SS] and the following graphs show the results.

At [SS] = 1000nmol/fl

TeamNewcastleSporeTunePic1.png
Figure 1.1


Figure 1.1 shows that at an IPTG concentration of 5000nmol/fl and sporulation signal concentration of 1000nmol/fl, the Spo0F concentration gets significantly higher than the other components.

In order to take a better look at the behaviour of the rest of the components, the following graphs were produced.


TeamNewcastleSporeTunePic2.png
Figure 1.2


From Figure 1.2, the concentration of Spo0AP seems to be at a healthy concentration.


TeamNewcastleSporeTunePic3.png
Figure 1.3


TeamNewcastleSporeTunePic4.png
Figure 1.4


At [SS] = 3000nmol/fl

The concentration of the sporulation signal, [SS] is increased to 3000nmol/fl in the following graphs, and the results were investigated.

TeamNewcastleSporeTunePic5.png
Figure 2.1


With a stronger sporulation signal, the concentration of Spo0FP and Spo0BP increased significantly, while the concentration of Spo0F dropped significantly from approximately 9000nmol/fl to 2300nmol/fl, comparing Figure 1.1 to 2.1.


TeamNewcastleSporeTunePic6.png
Figure 2.2


The concentration of LacI* remained approximately the same, so as Spo0AP.


TeamNewcastleSporeTunePic7.png


Figure 2.3


TeamNewcastleSporeTunePic8.png
Figure 2.4


Comparing Figure 1.3 and 2.4, the concentration of Spo0A falls from approximately 100nmol/fl to 50nmol/fl when [SS] is increased.


Referring to the graphs obtained from the model, it seems like increasing the sporulation signal concentration, does not increase the Spo0AP concentration. However, the concentrations of Spo0BP and SpoFP did increase as the sporulation signal concentration increased.


Other Models

See KinA Expression Model
See Sin Operon Model





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