Tokyo/Hill function fitting

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Revision as of 07:03, 25 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.IPTG assay　　Preliminary assays

<ヒル関数の導出>

Deviation of Hill function

Ex.6.1

1.Hill function for the activator AHL

Figure 1

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

Figure 2

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

k0 was obtained as