View source for Part:BBa R0011:Experience/iGEM10 Kyoto

==iGEM Kyoto 2010: RPUs of R0011 in low number copy plasmid with various concentrations of IPTG==
===Introduction===
RPUs (Relative Promoter Activity) of R0011 were measured in pSB4K5, a low copy number plasmid, and E.coli KRX, the strain overexpressing lacI in order to repress activity of R0011 at low concentration of IPTG.

===Results===
{| class="metadata center"
|+  Table1. RPU of R0011 at various concnetaraitons of IPTG
!rowspan="2"|IPTG (mM)||colspan="6"|RPU
|-
!A||B||C||Average||s.d.||CV
|-
|0||*||0.0122||0.0147||0.0134||0.00821||0.611
|-
|0.01||0.0191||0.00963||0.00244||0.0104||0.0084||0.806
|-
|0.03||0.177||0.155||0.198||0.174||0.0173||0.0997
|-
|0.1||0.205||0.191||0.269||0.221||0.0416||0.188
|-
|0.3||0.938||0.955||0.955||0.949||0.00981||0.0103
|-
|0.8||1.44||*||1.21||1.37||0.161||0.122
|-
|1.0||1.60||1.58||1.65||1.65||0.106||0.0640
|-
|2.0||1.49||1.83||1.39||1.57||0.233||0.148
|}
* *One of RPU in IPTG 0mM couldn’t be measured. One of RPU in IPTG 0.8mM couldn't also be measured.
* *In this table, RPU in 0, 0.01, 0.1, 1.0 mM IPTG is measured after cell lysed by the cell lysis reagent and RPU in 0.05, 0.3, 0.8, 2.0 mM IPTG is measured without cell lysis.

[[Image:KyotoGrpA001.png|900px|center|thumb|Fig.1: The growth curves of the cells at various concentrations of IPTG between 2h and 4h. The vertical axis is linear.]]
 
[[Image:KyotoGrpA002.png|900px|center|thumb|Fig.2: The growth curves of the cells at various concentrations of IPTG between 2h and 4h. The vertical axis is logarithm.]]

[[Image:KyotoGrpA003.png|900px|center|thumb|Fig.3: The RPUs at various concentrations of IPTG. The blue line indicates the fit/calculated curve predicted by our model. The data represent the mean +/- s.d. obtained by triplicate experiments, ]]

RPUs of R0011 with various IPTG concentrations were measured by using BBa_K358000. In this experiment, we used pSB4K5 and E.coli KRX in order to repress activity of R0011 at low concentration of IPTG. The results were listed in table1. RPU of R0011 with much IPTG equals to the value of R0011 not repressed and this value is higher than RPU of R0011 without IPTG by about 160.
In order to measure and calculate RPU, we made some assumptions. The growth curve of E.coli was measured to confirm our assumptions
In graph3, the simulation we made was fitted to our experimental data.

====Discussion====
The result indicates that the maximum activity of R0011 is about 1.6 RPU and the minimum is less than 0.01 RPU and that R0011 has wide range of activity (the maximum activity of R0011 is at least about 160 fold greater than the minimum activity at least). The maximum activity of R0011, 1.6 RPU agrees with the previous data.

By the way, we found that supplemented M9 medium was contaminated by approximately 0.01mM lactose.
[[Image:KyotoGrp100915-1.png|450px|center]]

We thought that lactose in the supplemented M9 medium comes from casamino acids because casamino acids is made from milk which contains lactose. Therefore, we tried to culture E.coli and measure RPU without the casamino acids because lactose in the supplemented M9 medium can induce R0011. However, without casamino acids, the growth rate of E.coli declined and we could not measure RPU. All RPU data was measured with casamino acids. Accordingly, the real value for RPU of R0011 at low IPTG concentration may be lower than the value gained from this experiment. CV in 0mM IPTG is so high, 0.611, and CV in 0.01mM IPTG is also high, 0.806.

We cannot trust RPU in 0mM and 0.01mM ITPG so much. 

we could characterize R0011 at high IPTG concentration correctly. However, characterization of R0011 at low IPTG concentration may be required additional measurements.

====Materials====
=====The parts construction for the measurement=====
<partinfo>BBa_K358000</partinfo> to measure GFP fluorescence expressed by R0011, the test promoter

<partinfo>BBa_K358001</partinfo> to measure GFP fluorescence expressed by J23101, the standard promoter

=====The plasmid=====
<partinfo>pSB4K5</partinfo>

=====The E.coli strain=====
KRX purchased by Promega

=====The medium=====
The supplemented M9 medium
which contains,
{|
| Na2HPO4 || 6.0g
|-
| KH2PO4 || 3.0g
|-
| NaCl || 0.5g
|-
| NH4Cl || 1.0g
|-
| MgSO4 || 0.1M
|-
| CaCl2 || 0.5M
|-
| Thiamine Hydrochloride || 1mM
|-
| Casamino Acids || 0.2%
|-
| Glucose || 0.4%
|-
| Antibiotics (Kanamycin 50mg)
|colspan="2"| for 1L
|}

=====The cell lysis reagent=====
CelLytic&trademark; B Cell Lysis Reagent purchased by SIGMA-ALDRICH

====Methods====
We measured GFP fluorescence after cells are lysed by the cell lysis reagent.

Unfortunately, however, we run short of the cell lysis reagent and some samples were measured without cell lysed. Though we used two ways to measure GFP fluorescence, we think both ways are valid because RPU of fully activated R0011 which was measured after cell lyzed agree with RPU of non-repressed R0011 measured previously without cell lyzed and because the way of measurement of RPU is recommended by previous iGEM team.

=====Method1. The measurement of RPU after cell lysis=====
# Pour 5mL the supplemented M9 medium to each falcon tube. 
# Add proper amount of 0.025M IPTG aq to each test tube and mix well to make the medium including IPTG concentration which you hope. 
# Pick out a colony on the plate of E.coli and put into three falcon tubes. 
# Incubate the culture at 37℃ for 16h. 
# Measure OD600 of the overnight culture. 
# Pour 5mL the supplemented M9 medium to each new falcon tube. Pre-warm these tubes at 37℃. 
# Pour 50µL the overnight culture to 5mL the fresh medium. 
# Incubate the diluted culture at 37℃. 
# Measure OD600 of the culture after 2h, 2.5h, 3h, 3.5h and 4h. 
# Pour 1mL of the culture to 1.5mL tube after 3h and 3.5h. 
# Centrifuge the 1.5mL tube at 14,000rpm and at 4℃ for 2min. 
# Discard the supernatant. 
# Freeze the pellets and store it in a fridge as samples for measurement of GFP fluorescence. 
# Measure GFP fluorescence.
# Add 75µL the cell lysis reagent to the pellet in the 1.5mL tube and mix well and dissolve it. 
# Centrifuge the tube at 15,000rpm and at 4℃ for 1min. 
# Take out 50µL supernatant and add to each well of a plate. 
# Add 50µL the cell lysis reagent to a well to correct the back. 
# Set the plate in the plate reader, Wallac 1420 Multilabel Counter, and measure GFP fluorescence of the samples (Ex/Em = 485/535nm, 1sec).
===== Method2. The measurement of RPU after cell lysis=====
# Pour 5mL the supplemented M9 medium to each falcon tube. 
# Add proper amount of 0.025M IPTG aq to each test tube and mix well to make the medium including IPTG concentration which you hope. 
# Pick out a colony on the plate of E.coli and put into three falcon tubes. 
# Incubate the culture at 37℃ for 16h. 
# Measure OD600 of the overnight culture. 
# Pour 5mL the supplemented M9 medium to each new falcon tube. Pre-warm these tubes at 37℃. 
# Pour 50µL the overnight culture to 5mL the fresh medium. 
# Incubate the diluted culture at 37℃. 
# Measure OD600 of the culture after 2h, 2.5h, 3h, 3.5h and 4h. 
# Pour 300µL of the culture to 1.5mL tube after 3h and 3.5h and cool it on ice. 
# Add 200µL the culture to each well of a plate. 
# Add 200µL the supplemented M9 medium to a well to correct tha back. 
# Set the plate in the plate reader, Wallac 1420 Multilabel Counter, and measure GFP fluorescence of the samples (Ex/Em = 485/535nm, 1sec).

====Analysis of data====
RPU is calculated as follows. 
[[Image:KyotoGoalA001.png|600px|center]]

We also use these rough calculations;
[[Image:KyotoGoalA002.png|600px|center]]
[[Image:KyotoGoalA003.png|600px|center]]

Here, F<sub>3h</sub> and F<sub>3.5h</sub> are the GFP fluorescence measured at 3h and 3.5h, respectively,

ABS<sub>3h</sub> and ABS<sub>3.5h</sub> are OD600 of the culture at 3h and 3.5h, respectively.

From the experimental data of cell growth from 2h to 4h after dilution (Figure1 and Figure2), we assumed cell growth from 3h to 3.5h after dilution can be approximated as linear. Thus, the mean ABS can be calculated as described in (3). If GFP concentration in cell is in steady states, the increase of GFP fluorescence depends only on cell growth. We used the first approximation based on these assumptions to calculate RPU.

====Modeling====
[[Image:KyotoFigM001.png|600px|center]]
LacI, the repressor of lactose promoter, binds to DNA sequence of lactose promoter and represses it. R0011, a lactose promoter, has two operator regions where LacI binds <sup>[[#RefM1-1|[1]]]</sup>. The equilibrium reaction of binding and dissociation of LacI and the lactose promoter can be described as equation1.

[[Image:KyotoModeling1-1.png|600px|center]]

Here, 
* [X] means the concentration of LacI, 
* [D] means the concentration of the lactose promoter not binding LacI, 
* [DX] means the concentration of the lactose promoter binding a lacI,
* [DX<sub>2</sub>] means the concentration of the lactose promoter binding two LacI,
* K<sub>1</sub> means the equilibrium constant for the reaction between [D] and [X],
* K<sub>2</sub> means the equilibrium constant for the reaction between [DX] and [X].
* The equilibrium constants K<sub>1</sub> and K<sub>2</sub> are described as equation2 and equation3 respectively.

[[Image:KyotoModeling1-2.png|600px|center]]
[[Image:KyotoModeling1-3.png|600px|center]]

From equation2 and equation3, equation4 is established.

[[Image:KyotoModeling1-4.png|600px|center]]

Here,
* &alpha; is the promoter activity when all the lactose promoter are bound by two LacIs,
* &beta; is the promoter activity when all the lactose promoter are bound by a LacI,
* [[Image:KyotoModeling1-a.png|100px]] is the ratio of [D] to the total concentration of lactose promoter,
* [[Image:KyotoModeling1-b.png|100px]] is the ratio of [DX] to the total concentration of lactose promoter.
In this model, we assumed that the promoter activity is completely repressed when two lacI bind to the operator regions on lactose promoter.
The inducer of lactose promoter, Lactose and IPTG, binds to LacI, and changes LacI conformation so that LacI dissociates from lactose promoter. The equilibrium reaction of the inducer and LacI is described as follows.

[[Image:KyotoModeling1-5.png|600px|center]]

Here,
* [S<sub>X</sub>] is the inducer concentration, 
* [X] is the concentration of LacI not binding with the inducer, 
* n is the number of the inducer molecule binds to one LacI molecule.
The equbilium constant, K<sub>X<sup>n</sup></sub>, is described as equation6.

[[Image:KyotoModeling1-6.png|600px|center]]

We assumed that the total concentration of LacI in a cell did not change in the log phase growth in which the cell growth does not change because the rate of the cell growth was constant and it compensated the increasing of traslated lacI.
Therefore, let X<sub>T</sub> as the concentration of total LacI, and equation7 is applied.

[[Image:KyotoModeling1-7.png|600px|center]]

From equation6 and equation7, equation8 is established .

[[Image:KyotoModeling1-8.png|600px|center]]
From equation4 and equation8, the relationship between IPTG and lactose promoter activity is described as follows.

[[Image:KyotoModeling1-9.png|600px|center]]
We apply equation9 to the result of characterization of R0011 and parameters are decided by using 
MATLAB 7.10.0 (MathWorks).

The results is shown in Figure3.
The orange markers and error bars are experimental data and blue line is the expectation from this model.
The data of 0.5mM IPTG does not be used in fitting the model. 

Parameters are shown in table below.

{| class="metadata center"
!symbol||description||value||unit||note
|-
|&alpha;||the transcription constant for [D]||1.667||RPU||calculated from the experimental result
|-
|&beta;||the transcription constant for [DX]||0.0000149||RPU||calculated from the experimental result
|-
|K<sub>1</sub>||the equilibrium constant for between [D] and [X]||1.607||mM||calculated from the experimental result
|-
|K<sub>2</sub>||the equilibrium constant for between [DX] and [X]||0.339||mM||calculated from the experimental result
|-
|X<sub>T</sub>||total concentration of lacI||5.131||mM||calculated from the experimental result
|-
|K<sub>X</sub>||the equilibrium constant for between [S<sub>X</sub>] and [X]||0.05321||mM||calculated from the experimental result
|-
|n||the number of IPTG molecules binding to a lacI||1.285||-||calculated from the experimental result
|}