Tokyo/Hill function fitting

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<br>[[Tokyo/Works|Works top]]　　0.[[Tokyo/Works/Hybrid promoter|Hybrid promoter]]　　1.[[Tokyo/Works/Formulation |Formulation]]　　'''2.[[Tokyo/Works/Assay |Assay1]]'''　　3.[[Tokyo/Works/Simulation |Simulation]]　　4.[[Tokyo/Works/Assay2 |Assay2]]　　5.[[Tokyo/Works/Future works |Future works]]
<br>[[Tokyo/Works|Works top]]　　0.[[Tokyo/Works/Hybrid promoter|Hybrid promoter]]　　1.[[Tokyo/Works/Formulation |Formulation]]　　'''2.[[Tokyo/Works/Assay |Assay1]]'''　　3.[[Tokyo/Works/Simulation |Simulation]]　　4.[[Tokyo/Works/Assay2 |Assay2]]　　5.[[Tokyo/Works/Future works |Future works]]
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<br><br>
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[[Tokyo/Hill function fitting |Purpose of this assay]]　　[[Tokyo/AHL assay|1.AHL assay]]　　[[Tokyo/IPTG assay|2.IPTG assay]]　　[[Tokyo/Preliminary assays |Preliminary assays]]
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[[Tokyo/Hill function fitting |Purpose of this assay]]　　[[Tokyo/AHL assay|1.AHL assay]]　　[[Tokyo/IPTG assay|2.LacI-IPTG assay]]　　[[Tokyo/Preliminary assays |Preliminary assays]]
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<ヒル関数の導出>
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==Objective==
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<br>  
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== We have conducted the assays to obtain parameters in the Hill function expressing our model. ==
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How the hill function is deviated is described below.
== Deviation of Hill function ==
== Deviation of Hill function ==
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<br>
 
<br>[[Image:expression6-3.JPG|400px|none|thumb|Ex.6.1]]
<br>[[Image:expression6-3.JPG|400px|none|thumb|Ex.6.1]]
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'''1.Hill function for the activator AHL'''  
'''1.Hill function for the activator AHL'''  
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[[Image:hill-fitting-1.jpg|200px|right|thumb|Figure 1]]
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[[Image:hill-fitting-1.jpg|200px|right|thumb|'''Fig. 1''' AHL absorbed in a cell binds to LuxR to make a complex, which activates the lax lac hybrid promoter and expression of GFP downstream of it. In this way, a cell receives AHL as an input and gives off green fluorescence as its output. ]]
Without the repression by LacI( [LacI]=0 ), Ex.6.1 was described as  
Without the repression by LacI( [LacI]=0 ), Ex.6.1 was described as  
<br>[[Image:expression6-4.JPG|300px|none|thumb|Ex.6.2]]
<br>[[Image:expression6-4.JPG|300px|none|thumb|Ex.6.2]]
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'''2.Hill function for the repressor LacI'''  
'''2.Hill function for the repressor LacI'''  
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[[Image:hill-fitting-2.jpg|200px|right|thumb|Figure 2]]
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[[Image:hill-fitting-2.jpg|200px|right|thumb|'''Fig. 2''' In a lacI producing cell, the lux lac hybrid promoter is repressed by lacI, which can be repressed by externally added IPTG. In this case, the output is fluorescence of GFP but the input is IPTG. ]]
When the concentration of AHL was assumed to be infinity, Ex.6.1 was described as
When the concentration of AHL was assumed to be infinity, Ex.6.1 was described as
<br>[[Image:expression6-6.JPG|300px|none|thumb|Ex.6.5]]
<br>[[Image:expression6-6.JPG|300px|none|thumb|Ex.6.5]]
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Therefore,the equilibrium constant k0 was obtained as
Therefore,the equilibrium constant k0 was obtained as
<br>[[Image:expression6-13.JPG|500px|none|thumb|Ex.6.8]]
<br>[[Image:expression6-13.JPG|500px|none|thumb|Ex.6.8]]
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Moreover, assume that [IPTG]total was more than [LacI=IPTG] predominantly,
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Moreover, assume that [IPTG]_total was more than [LacI=IPTG] predominantly,
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<br>[[Image:expression6-14.JPG|400px|none|thumb|Ex.6.9]]
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<br>[[Image:expression6-14.JPG|300px|none|thumb|Ex.6.9]]
By substituting　Ex.6.9 into Ex.6.8, [LacI] was obtained as
By substituting　Ex.6.9 into Ex.6.8, [LacI] was obtained as
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<br>[[Image:expression6-15.JPG|400px|none|thumb|Ex.6.10]]
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<br>[[Image:expression6-15.JPG|270px|none|thumb|Ex.6.10]]
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As a result, by substituting　Ex.6.10 into Ex.6.7,the Hill function for LacI was obtained as
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the function of [IPTG]total,
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<br>[[Image:expression6-16.JPG|400px|none|thumb|Ex.6.11]]
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Here k0=0.0337(/μM),[LacI]total=140(μM).
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<br>[[Image:expression6-2.JPG|300px|]]
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Latest revision as of 05:05, 27 October 2007


Works top　　0.Hybrid promoter　　1.Formulation　　2.Assay1　　3.Simulation　　4.Assay2　　5.Future works

Purpose of this assay　　1.AHL assay　　2.LacI-IPTG assay　　Preliminary assays


Objective


We have conducted the assays to obtain parameters in the Hill function expressing our model.

How the hill function is deviated is described below.

Deviation of Hill function


Ex.6.1


1.Hill function for the activator AHL

Fig. 1 AHL absorbed in a cell binds to LuxR to make a complex, which activates the lax lac hybrid promoter and expression of GFP downstream of it. In this way, a cell receives AHL as an input and gives off green fluorescence as its output.

Without the repression by LacI( [LacI]=0 ), Ex.6.1 was described as


Ex.6.2

Therefore, in the steady state the Hill function for the activator AHL was given as

Ex.6.3
Ex.6.4

2.Hill function for the repressor LacI

Fig. 2 In a lacI producing cell, the lux lac hybrid promoter is repressed by lacI, which can be repressed by externally added IPTG. In this case, the output is fluorescence of GFP but the input is IPTG.

When the concentration of AHL was assumed to be infinity, Ex.6.1 was described as


Ex.6.5

Therefore, in the steady state the Hill function for the repressor LacI was given as


Ex.6.6

Ex.6.7


However, the amount of LacI cannot be actually measured.So,we used the inducer IPTG to calculate the Hill function for LacI.
Assume that the reaction between [LacI] and [IPTG] is the equilibrium reaction,these concentration in equilibrium state were shown in Fig.3.


Figure 3

Therefore,the equilibrium constant k0 was obtained as


Ex.6.8

Moreover, assume that [IPTG]_total was more than [LacI=IPTG] predominantly,


Ex.6.9

By substituting　Ex.6.9 into Ex.6.8, [LacI] was obtained as


Ex.6.10

As a result, by substituting　Ex.6.10 into Ex.6.7,the Hill function for LacI was obtained as the function of [IPTG]total,


Ex.6.11

Here k0=0.0337(/μM),[LacI]total=140(μM).

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