Presentation on theme: "Repressilator Presentation contents: The idea Experimental overview. The first attemp. The mathematical model. Determination of the appropiate parameters."— Presentation transcript:
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.
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”
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 mRNA production Protein production transcriptiontranslation 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 mRNA degradation rate (the same for all mRNA´s) =LacITetR l CI = Protein translation: protein degradation + modulated translation LacITetR l CI protein degradation rate (the same for all proteins) Symmetry is needed for periodic behaviour!!
To characterize translation and transcription modulated rates, we look for experimental results: May not be Zero!! Constant rate production Always linear production 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 Hill coefficient, cooperative binding dependent. ~ ~
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.
Tag proteins t 1/2 prot Kdeg prot Kdeg mRNA
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 (!!)