# Tokyo/Hill function fitting

### From 2007.igem.org

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

**1.Hill function for the activator AHL**

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

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

**2.Hill function for the repressor LacI**

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

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

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.

Therefore,the equilibrium constant k0 was obtained as

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

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

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,

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