User:Daniela A. Garcia S./Notebook/Modeling UNAM-Genomics Mexico/2010/08/21

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Modeling: PoPS mathematical protocol

1) Raw data was processed by first subtracting the appropriate backgrounds.

Acorrected = Araw - Amedia
Gcorrected = Graw - Gmedia

2) The data was then converted to absolute units (CFU/well and GFP molecules/well) using the calibration method.

CFU = 3.1E8Acorrected - 1.6E6  
GFP = 7.0E8Gcorrected + 6.0E11

3) 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.

Stotal = dGFP/dt
Scell = Stotal/CFU

4) To interpret the behavior: the input is defined as the time dependent rate of mRNA synthesis, PoPS(t) (mRNA per cell per sec). The output is the synthesis rate of mature GFP, Scell (GFP molecules per cell per sec).

[M] = PoPS(t) - γM[M], concentration of mRNA per cell 
[I] = ρ[M] - (α + γI[I]), the level of immature GFP
Scell = α[I]
  • γM = 4.8E-3sec-1
  • Dilution of mRNA due to cell growth was negligible relative to degradation
  • ρ = 0.4 proteins per sec per mRNA
  • GFP maturation rate = 1.8E-3sec-1
  • The immature GFP is stable so that degradation was negligible
  • Dilution rate = 2E-4sec-1

5) Steady state relationship to calculate the specific output.


Transient output in the response time experiments. It relates the time dependent PoPS output to measured values of Scell.