1. science
2. mathematics
3. geometry

THE REPRESSILATOR
A synthetic oscillatory network
of transcriptional regulators
Michael B. Elowitz & Stanislas Leibler, 2000
Context
•  The « design principles » underlying networks of
interacting biomolecules are poorly understood
!  Comparing designed networks with their natural counterparts may
help to understand such « design principles »
Goals
•  Design and construction of a synthetic network to
implement a particular function
•  identify possible classes of dynamic behaviour and
determine which experimental parameters should be
adjusted to obtain sustained oscillations
•  Doing it with new functional properties from generic
components that naturally occur in other contexts.
General specificities
•  Used 3 transcriptional repressor systems, termed the
repressilator, in Escherichia coli.
•  The network periodically induces the synthesis of green
fluorescent protein
•  oscillations, with typical periods of hours, are slower than
the cell-division cycle, so the state of the oscillator has to
be transmitted from generation to generation.
Cyclic negative-feedback loop
•  REPRESSILATOR: 3 repressors genes and their corresponding
promoters
•  Reporter: expresses an intermediate-stability GFP variant
Network Design
simple mathematical model of transcriptional regulation
Deterministic, continuous approximation (= continuous
dynamical variables)
•  α0 is the number of protein copies per cell produced from a given promoter
type during continuous growth in the presence of saturating amounts of
repressor •  α+α0 is the number of protein copies in the absence of repressor •  β denote the ratio of the protein decay rate to the mRNA decay rate
•  n is a Hill coefficient Deterministic model: results
•  Depending on the values of the model’s parameters, the system may
converge toward a stable steady state, or the steady state may become
unstable, leading to a sustained limit-cycle oscillations.
Experimental approach
•  used standard molecular biology techniques to construct a
low-copy plasmid encoding the repressilator and a
compatible, higher-copy reporter plasmid containing the
tet-repressible promoter PLtetO1 fused to an intermediate
stability variant of gfp11
•  Because the inducer IPTG interferes with repression by
LacI, we expected that a transient pulse of IPTG might be
capable of synchronizing a population of repressilatorcontaining cells.
Increasing the chance to get an oscillatory regime
•  two alterations to natural components:
1. 
use strong, yet tightly repressible hybrid promoters
! address transcriptional strength and tightness
2. 
insert a carboxy-terminal tag at the end of each repressor protein
! Proteases in E. coli recognize this tag and target the
attached protein for destruction
! bring the effective repressor protein lifetimes closer to that of
mRNA
Experimental approach: results
•  Single damped oscillation of GFP fluorescence per cell
after transfer to media lacking IPTG.
•  no global synchronization (not expected)
! studied the repressilator by isolating single cells under
the microscope and monitoring their fluorescence intensity
as they grew
•  total observation time was limited about 10 hours of
growth at 30°C.
! colonies enter in a stationary phase
Experimental approach: results
•  period of around 150
minutes, 3 times longer
than the typical celldivision time.
Oscillatory behavior and negative controls
Red = fluorescence of
reference cell
Green and blue = two
references siblings cells
(cellules filles)
•  In some individuals, periods were omitted or phase delayed in one cell relative to
its sibling (a,b,c)
•  significant variations in the period and amplitude of the oscillator (d)
•  (e) includes deliberate disruption of the network (by adding sufficient IPTG to
interfere with LacI) and (f) observation of GFP expression in the absence of the
repressilator (only the reporter)
Stochastic, discrete approximation
•  stochastic effects may be responsible for noisy operation
in natural gene-expression networks.
! adapt equations to perform stochastic simulations.
!to obtain cooperativity in repression analogous to the
continuous case: assumed two operator sites on each
promoter and change several parameters.
•  In order to distinguish such stochastic effects from
possible intrinsically complex dynamics (such as
intermittence or chaotic behaviour), further studies are
needed.
Stochastic, discrete approximation
•  Oscillations persist with the
stochastic model and adapted
parameters values but with a large
variability, ?resulting in a finite
autocorrelation time?
Conclusion
•  By varying the host species and genetic background would
allow to reduce spurious interactions with endogenous cellular
sub-systems, and to investigate how the network is embedded
in the cell.
! In fact, the entry into the stationary phase stops the repressilator,
indicating that the network is coupled to the global regulation of cell
growth.
•  Instead of three repressors, it seems that circadian oscillators
use both positive and negative control elements. In the
presence of interactions between positive and negative control
elements that lead to bistable, hysteretic behavior, an
oscillating circuit shows high noise-resistance.