Jeelean Lim
true
10000
0.1
true
bdf15
1000
This CellML version of this model is not able to reproduce the results shown in Fig1c of the original publication, as the initial conditions for protein concentrations were not provided. The original published equations were scaled and modified with reference to the same model on the Biomodels database BIOMD0000000012 - Elowitz2000_Repressilator). Once the model comes to equilibrium (t > 400 minutes,) its output is correct.
The University of Auckland
Auckland Bioengineering Institute
Lim
Jeelean
1000
5000
Lim
Jeelean
There was an error in rescaling previously:
m in the equations in box 1 is not rescaled to the mRNA divided by the translation efficiency, M/eff, but is just M*eff/K_m, with the efficiency taken in units of rescaled protein p = P/K_m.
The 2 forms of the differential equations are therefore:
dM_i/dt = K_m/(eff*tavg) * alpha * Km^n/(Km^n+P_j^n) + alpha0 - M_i/tavg
and
dPi/dt = beta*(Mi*eff/tavg - Pi/tavg)
Rescaled protein numbers were also used for the alphas:
beta = proteindecay/mRNAdecay = rnahalflife/proteinhalflife = 0.2
and
alpha0 = number of maximal rescaled proteins per cell in steady state under full repression:
with a0 = leaky promotor strength = 5*10^-4 mRNA per second
max. translation = eff*a0
protein decay = Pi/average_protein_lifetime
in steady state: max. translation = protein decay =>
P_max = eff*a0*average_protein_lifetime(in seconds) = 20*5*10^(-4)*10/ln(2)*60 = 8.656
alpha0 = p_max = P_max/K_m = 0.216
and for the completely repressor free state:
a = fully induced promotor strength = 0.5 mRNAs per second
P_max= 20*0.5*10/ln(2)*60 = 8656.2
p_max = 216.4 = alpha + alpha0
alpha = 216.2
These corrections seem to give more sensible results. The protein numbers are still the same, but the mRNA numbers are only about 1/15th of the proteins.
10659856
Jeelean Lim
403
A Synthetic Oscillatory Network of Transciptional Regulators
338
335
1000
2009-04-02T00:00:00+00:00
Corrected end value for session
keyword
Endler
Lukas
jlim063@aucklanduni.ac.nz
Stanislas
Leibler
2000-01-20 00:00
This is the CellML description of Elowitz and Leibler's mathematical model on the synthetic oscillatory network of transcriptional regulators
synthetic biology
gene regulation
Nature
Elowitz
Michael
2009-04-28T11:49:59+12:00
2009-04-30T12:38:21+12:00