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Repressilator Presentation contents:
The idea
Experimental overview. The first attemp.
The mathematical model.
Determination of the appropiate parameters.
Experimental setting in more detail.
Tunning out to the correct parameters.
The repressilator in the language of BioBricks and
MIT´s abstraction hierarchy.
The idea
So, what is it?
• An oscillatory network
• A genetic construction with three genes, each one
regulates the next
• Repressor depending regulation  negative
feedback
• “a 3-element negative feedback
transcriptional loop”
• “tide producing machine”
how does it work?
don´t get lost products!!
synchronisation
Start!
...ad infinitum?
Experimental overview.
The first attemp.
Did you say plasmids?
Let’s zoom in...
promoter/operator cI dependent
complete gene:
RBS + coding sequence
terminator
One should expect that, if the 3 genes have equal
kinetic constants (i.e. if there is symmetry), we
will find E.Coli oscillating in fluorescence!
We go to the Lab, and make the experiment;
but... no oscillation is found!!
How can it be posible?
Can we find and solve the problem?
Sure! But we have to modelize!!
The mathematical model.
Determination of the appropiate
parameters.
We see expression of repressor proteins as a 2 step process:
Repressed
Gene
transcription
mRNA
production
translation
Protein
production
We have to modelize each step, i.e.,
our model needs the number of mRNA´s and Proteins as variables.
We make an approximation: instead of talking about the number of
proteins and mRNA´s, we treat them as continous variables, and talk
about concentrations.
We will use Initial Value Problems (ODEs) !!!
mRNA transcription:
mRNA degradation + modulated transcription
Protein translation:
protein degradation + modulated translation
=
LacI
= l CI
TetR
l CI
LacI
TetR
Symmetry is needed for
periodic behaviour!!
mRNA degradation rate (the same for all mRNA´s)
protein degradation rate (the same for all proteins)
To characterize translation and transcription modulated rates, we
look for experimental results:
May not be Zero!!
Constant rate
production
Always linear production
~
~
Hill coefficient, cooperative binding dependent.
Constant rate production of mRNA in the absence of repressor
Constant rate production of mRNA when promoter is maximally repressed
Production rate of proteins dependent of mRNA levels
Repressor levels to half maximally repress a promoter
And conclude:
Thus:
Typical or obligate constants:
}
Initial Values for integration
We begin on a induced stationary state:
1.- IPTG causes lacI death.
2.- Then stationary state forces tetR mRNA to maximally transcribe.
3.- Thus, tetR is maximally translate too.
4.- In this state, l CI and GFP mRNAs are maximally repressed.
5.- And l CI and GFP, minimally produced.
6.- Finally, lacI mRNA is maximally transcribed (neglecting repressor amounts!).
Then, we can simulate this equations in mathematica, and play with parameters.
We can modelized the GFP response (not doing in nature!!), and see if it
matches with experimental results!!
To this aim, we add this equations:
Now, the simulations are shown in the Mathematica file!!
We find a steady state, wich is stable for the parameters of the experiment.
We change the parameters until the steady state becomes unstable;
then we check our model with the experimental results.
Experimental period:
160±40 min.
Model period:
~130 min. !!
Can we improove the model?
If we add a basal transcription constant in GFP equations linear in time, we get the
increase behaviour in fluorescence.
Interpretation?
Another problem:
stochastic noise maybe
due to
the discreteness of
mRNA and proteins
Experimental setting in more detail.
Tuning our system to the correct
parameters.
• Hybrid promoters   Ktransc
• Good RBS   Keff
• Tag proteins   t1/2 prot 
Kdegprot  KdegmRNA
• Leakness  intrinsic ??
• Hybrid promoters   Ktransc
• Good RBS   Keff
[protein]
 [protein]
[mRNA]
• Tag proteins   t1/2 prot 
Kdegprot  KdegmRNA
• Leakness  intrinsic ??
• Any way of getting rid of the Kbasal ?
• Is it our particular ‘Heisenberg dilemma’ ?
 One possible solution:
weaker promoters ( < Ktransc )
+ strong repressors ( high promoter affinity )
maybe 0 now really means 0 !!
... now we go on the bench
(again)
• Beautiful oscillatory fluorescence in log
phase
• Life cycle < Fluorescence period
• Better ‘theorical’ results than Nature’s paper (!!)
let’s talk about siblings...
fluorescence (units)
time (min)
phase delays
amplitude variation
reduced period
phase delay
The repressilator
in the language of BioBricks
and MIT´s abstraction hierarchy
One can try with this scheme to talk about the plasmid as parts:
But this is not
MIT´s language!!
This is the right scheme, because
PoPS is universal, an we can see
how the parts are organized in
devices with PoPS as in/out
signal.
Check Parts on
the Registry!!
In device´s language:
Take care!! Inverters cannot be of the same type!!