# IGEM:IMPERIAL/2009/M3/Assays/F2620/dataprocess

## Contents

# Data processing

### Output calculation

We calculated the output of BBa_E0240 using the relative measurements of the plate reader.

1. Raw data from the Wallac Victor3 multi-well fluorimeter was processed by first
subtracting the appropriate backgrounds. The absorbance of wells containing
supplemented M9 medium, Amedia, was subtracted from the sample absorbance data, Araw.
The resulting data, Acorrected, was assumed to be directly proportional to the number of
cells in the well.

Acorrected = Araw - Amedia (Equation 1)

2. The fluorescence data for the GFP-free BBa_T9002 mutant, Gcells, was
subtracted from the sample fluorescence data, Graw, and the resulting data Gcorrected was
assumed proportional to the total number of GFP molecules in the well.

Gcorrectted = Graw - Gcells (Equation 2)

### Relating GFP expression to promoter output

3. The data was then converted to absolute units (CFU/well and GFP molecules/well) using
the calibration curves described in the calibration assays.

- their data

CFU = 3.1E8 * Acorrected - 1.6E6 (Equation 3)

GFP = 7.0E8 * Gcorrected + 6.0E11 (Equation 4)

4. Mean synthesis rates of GFP per cell, Scell, were calculated by assuming the total GFP
synthesis rate, Stotal, to be equal to the time differential of GFP. Scell was then calculated
via Equation 6. Note that since we have measured the total amount of GFP in the well
and since we have assumed that GFP is not degraded, we can calculate the total synthesis
rate of GFP and hence the per cell synthesis rate of GFP without considering dilution due
to cell growth.

Stotal =dGFP/dt(Equation 5)

Scell = Stotal/CFU (Equation 6)

5. From modelling, we can calculate PoPS(t)

PoPS(t) =S˙˙cell + (gamma2 + gamma1 + a)S˙cell + gamma1(gamma2 + a)Scell * a#(Equation 11)

where [M] is the concentration of mRNA per cell, [I] is the level of immature GFP,
PoPS(t) is the time dependent rate of mRNA synthesis, gamma1 is the degradation rate of
mRNA, rho is the constant rate of protein synthesis per mRNA, a is the maturation rate of
GFP, and gamma2 is the degradation rate of immature GFP (incorporating degradation and
dilution due to cell growth).

### Modelling

5. To interpret the behavior of BBa_F2620 from our observations of BBa_E0240, we
employed an ODE model relating the output of BBa_E0240 to its input (the output of
BBa_F2620). We defined the input to BBa_E0240 to be the time dependent rate of
mRNA synthesis, PoPS(t) (mRNA per cell per sec). We defined the output of
BBa_E0240 to be the synthesis rate of mature GFP, Scell (GFP molecules per cell per sec).
The model includes two species and four parameters. The differential equations
governing the levels of the two species are:

[M˙] = PoPS(t) -gamma1[M] (Equation 7)

[I˙] = rho[M] - (a + gamma2 )[I] (Equation 8)

Scell = a[I] (Equation 9)

where [M] is the concentration of mRNA per cell, [I] is the level of immature GFP, PoPS(t) is the time dependent rate of mRNA synthesis, gamma1 is the degradation rate of mRNA, rho is the constant rate of protein synthesis per mRNA, a is the maturation rate of GFP, and gamma2 is the degradation rate of immature GFP (incorporating degradation and dilution due to cell growth).

6. We parameterized the model using published and unpublished data and via experiments using BBa_T9002. We assumed a value of 4.8E-3 sec-1 for gamma1 based on unpublished measurements performed in our lab on an almost identical mRNA, produced by BBa_I7107 (the transcript in the current study has two extra A nucleotides on the 5' end but an unchanged secondary structure). This value is also consistent with published data on mRNA decay in E. coli 10. We assumed that dilution of mRNA due to cell growth was negligible relative to degradation.

We estimated a value for rho of 0.4 proteins per sec per mRNA based on unpublished measurements from the Endy Lab on BBa_I7107. Again, this value is consistent with published data11,12 for translation rates per mRNA.

We measured an average GFP maturation rate of 1.8E-3 sec-1 as described above. Finally, we assumed that immature GFP is stable so that degradation was negligible relative to dilution due to growth. An average dilution rate of 2E-4 sec-1 was calculated from the multi-well fluorimeter absorbance data (corresponding to a 55 min doubling time). At the 60 min timepoint used in the snapshot transfer functions, the above model for BBa_E0240 behavior is in steady state. Hence, we used the steady state relationship of Equation 10 to calculate the specific output of BBa_F2620 from the observed output of BBa_E0240.

PoPSss =Ma + rho I ( )Scellss a# (Equation 10) To calculate the transient output of BBa_F2620 in the response time experiments, we rearrange the model (Equations 7, 8, and 9) to relate the time dependent PoPS output to measured values of Scell.

PoPS(t) =S˙˙cell + (" I + "M + a)S˙cell + "M (" I + a)Scella#(Equation 11)