Construction of a
genetic toggle switch in
E.Coli
PRESENTATION
Introduction
 Paper published in 2000
 What they know:
1) Observation: Multi-stability and
oscillations in natural, specialized gene
circuits
◦ E.g: Circadian clock in cyanobacteria
2) State of art: Gap between practical
theories of enzyme regulation network
(available) and gene regulation network
(unavailable)
Source: Ditty JL & al., A Cyanobacterial circadian timing mechanism.
(2003) Annu. Rev. Genet. 37:513–43.
Goals
 Create a practical scheme to verify mathematical prediction of gene expression dynamics
 Construction of a gene regulatory network :
◦ Synthetic (plasmid)
◦ Bistable
◦ With a nearly ideal switching threshold
◦ Constructed from any two repressible promoters
 Non-specialized one !
Toggle switch: The theoretical part
The genetic scheme:
The mathematical model:
𝑑𝑈
𝛼1
=
−𝑈
𝑑𝑡 1 + 𝑉𝛽
𝑑𝑉
𝛼2
=
−𝑉
𝑑𝑡 1 + 𝑈 𝛾
 Mutual inhibitory arrangement of R
 Switch = introduction of inducer 1 or 2
Variables & parameters
U,V: Concentration of repressor 1,2
 Robust
Wide range of parameters
=
No in vivo random flips
α1 ,α2: Net rate of synthesis of repressor 1,2
β,γ: cooperativity of repression of promoter 2,1
The mathematical model:
Getting deeper and deeper part 1
Cooperativity:
• Arise when multimeric repressor or
multiple repressors used for the same
locus
• Positive or negative value
Red : Cooperative repression of
promoters (constitutively transcribed)
• Quantified by the Hill equation:
Green : degradation/dilution of
repressors
Source: IGEM 2013,
Duke project
TOGGLE SWITCH: THE THEORETICAL PART
The mathematical model:
Getting deeper and deeper part 2
NULLCLINES
Three key features
1. β,γ<1  no sigmoïdal curves (hill)  only one steady state
2.
𝛼
(𝛼1)±1
2
>>> 1  unbalanced promoter strength  only one
steady state
3. Two bassins of attractions  Initial conditions above/below
separatrix  high/low steady state
TOGGLE SWITCH: THE THEORETICAL PART
Balanced promoter
strengths
Unbalanced
promoter strengths
See next slide
The mathematical model:
Getting deeper and deeper part 3
Two important parts:
1. β,γ>1  condition for bistability
2. Higher cooperativity  Higher
robustness for the bistable behavior
of the system
TOGGLE SWITCH: THE THEORETICAL PART
Toggle switch : The practical part
 A plasmid transfected in E.coli : The toggle switch plasmid…
Practically ?
 Same P2/R2/I2 (Ptrc-2/LacI/IPTG)
..which is used to reproduce this scheme
 α1 ,α2 = f(RBS)
 Reporter = GFP linked to Ptrc-2
“High” state: GFP on
“Low state”: GFP off
Note: AmpR, Rep origin,…
Result n°1 : demonstration of bistability
Q2: ARE THE TWO STEADY STATE STABLE IN
LONG TERM ?
Q1: TWO STEADY STATE ?
Yes !
Control:
-plasmid with
P2+R2+reporter only
(pTAK102)
-plasmid with
P1+R1+reporter only
Note:
-pTAK105 problem :
𝛼
(𝛼1)±1 << 1
2
(due to efficiency of
Tet rep)
Yes !
Result n°2: Description of the bifurcation
point.
Does it exist (theoretically and practically)?
Red circle: pTAK117
Blue triangle: pTAK102
Red line: separatrix (<XPP)
Yellow line: separatrix (<XPP)
Quasi-discontinuous jump for the practical
toggle switch plasmid
 Mean definition of 3A and 3B ???
Result n°2: Description of the bifurcation
point
Q: Is the bifurcation point
deterministic
Answer : NEARLY ;)
Bimodal
distribution due to
stochastic nature of
the expression of
the gene
(variability)
Results from the cytometer for
population grown in a [IPTG]
shown in the graph from previous
slide
Result n°2: Description of the bifurcation
point
How many time to switch from
one state to another ?