SC462 Elements of Synthetic Biology: Life 2.0
Prof. Manish K Gupta Spring 2017
DA-IICT
Repressilator
Shreyas bhanderi
ID :- 201401049
Abstract
A cell is composed of many intertwined regulatory and signaling networks. This networks carry
out many essential functions in living cells. The repressilator is a synthetic genetic regulatory
network consisting of a ring-oscillator with three genes, each expressing a protein that represses
the next gene in the loop. The resulting oscillations of repressilator, 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. This arti cial clock displays noisy behavior, possibly because of stochastic
uctuations of its components. By incorporating more speci c control elements, a redesign of the
repressilator might reach (or more optimistically, surpass) the delity of the biological clocks that
natural selection has produced.
Introduction
Organisms are biochemically dynamic. They are continuously subjected to time-varying conditions
in the form of both extrinsic driving from the environment and intrinsic rhythms generated by
specialized cellular clocks within the organism itself. Relevant examples of the latter are the cardiac
pacemaker located at the sinoatrial node in mammalian hearts. and the circadian clock residing
at the suprachiasmatic nuclei in mammalian brains. These rhythm generators are composed of
thousands of clock cells that are intrinsically diverse but nevertheless manage to function in a
coherent oscillatory state. This is the case, for instance, of the circadian oscillations exhibited by
the suprachiasmatic nuclei, the period of which is known to be determined by the mean period of
the individual neurons making up the circadian clock. The mechanisms by which this collective
behavior arises remain to be understood.
Individual clock cells are known to operate through biochemical networks comprising multiple
regulatory feedback loops. The complexity of these systems has hindered a complete understanding
of natural genetic oscillators. Synthetic genetic networks, on the other hand, o
er an alternative
approach aimed at providing a relatively well controlled test bed in which the functions of natural
gene networks can be isolated and characterized in detail. In this direction, a synthetic biological
oscillator, termed the repressilator, was developed recently in Escherichia coli from a network of
three transcriptional repressors that inhibit one another in a cyclic way. Spontaneous oscillations
were observed in individual cells within a growing culture, although substantial variability and
noise was present among the di
erent cells.
Repressilators were rst reported in a paper by Michael Elowitz and Stanislas Leibler in 2000 [6].
This network was designed from scratch to exhibit a stable oscillation which is reported via the
expression of green
uorescent protein, and hence acts like an electrical oscillator system with xed
time periods. The network was implemented in Escherichia coli using standard molecular biology
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methods and observations were performed that verify that the engineered colonies do indeed exhibit
the desired oscillatory behavior.
Figure 1: The repressilator genetic regulatory network.
Michael Elowitz and Stanislas Leibler created a simple mathematical model of transcription regula-
tion. The mathematical model was composed of six molecular species: three mRNA concentrations
and three corresponding repressor protein concentrations. Each species was involved in transcrip-
tion, translation and degradation reactions. Six coupled rst-order di
erential equations described
the dynamic behaviour of the system. Using the model, the authors predicted what parameters
the stability of the steady state would be dependent on. In particular, the authors used the model
to determine how to induce stable oscillations. Parameters that would favour oscillations were
strong promoters, strong repression of transcription, cooperativity of repressor binding and similar
lifetimes of mRNA and Proteins. The actual synthetic biological system was constructed from nat-
ural components using molecular biological techniques. Two alterations to the natural components
were made to bring the system in line with the parameter space which favours oscillations: strong
but tightly repressable hybrid promoters, and carboxy-terminal tags for the repressor proteins thus
targetting them for protease degradation. A compatible reporter plasmid expressing GFP was also
inserted into the system.
Figure 2: The repressilator circuit with detailed regulation of the promoters. Gi;Mi; Pi and Di
are promoters, mRNA, protein and protein dimer for the gene i, respectively. Index i represents
the target gene (i = 1, 2, 3), whereas k is its repressor (k = 3, 1, 2). Blunt end arrows denote
repression, normal arrows denote activation/production and wavy arrows denote degradation[3].
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The repressilator consists of three genes connected in a feedback loop, such that each gene represses
the next gene in the loop, and is repressed by the previous gene. Thus, gene G1 is a source of mRNA
M1 (transcription) that codes for the monomer protein P1 produced in the translation process. The
proteins P1 participate in reversible homo-dimerization producing dimers D1, which are repressing
transcription factors (TFs) for the next gene G2. Similarly, gene G2 produces (via transcription,
translation and dimerization) dimer molecules D2, repressing transcription from G3. Finally, TF
molecules D3, produced from gene G3, repress production from G3, completing the cycle ( gure
2). In addition, green
uorescent protein is used as a reporter so that the behavior of the network
can be observed using
uorescence microscopy.
The temporal oscillations of
uorescence occured with a period of approximately 150 minutes,
three times as long as the average cell-division time. Additionally, although sibling cells displayed
correlated GFP levels for a long period of time after septation, there were variations in both period
and amplitude.
Detail description of the topic
The design of the repressilator was guided by two simple mathematical models, one continuous and
deterministic and the other discrete and stochastic.
These models were analyzed to determine the values for the various rates which would yield a
sustained oscillation. It was found that these oscillations were favoured by strong promoters coupled
to e cient ribosome binding sites, tight transcriptional repression (low `leakiness’), cooperative
repression characteristics, and comparable protein and mRNA decay rates.
Figure 3: A continuous simulation of the repressilator.
This analysis motivated two design features which were engineered into the genes: First, to decrease
leakiness the promoter regions were replaced with a tighter hybrid promoter which combined the
PL promoter with LacL and TetR operator sequences. Second, to reduce the disparity between
the lifetimes of the repressor proteins and the mRNAs, a carboxy terminal tag based on the ssRA
RNA sequence was added at the 3′ end of each repressor gene. This tag is recognized by proteases
which target the protein for degradation. The design was implemented using a low copy plasmid
encoding the repressilator, and the higher copy reporter, which were used to transform a culture
of Escherichia coli.
3
Figure 4: A discrete and stochastic simulation of the repressilator.
Figure 5 describes the repressilator schematically. A repressilator has three genes a, b and c
along with the corresponding proteins they express: A, B and C. These proteins act as repressors,
i.e. they repress or inhibit the rate of expression of the gene next in line. For example, protein
A represses gene b, slowing down the production of protein B. This inhibitory e
ect increases as
the concentration of the protein increases. Similar to A repressing b, B represses c and nally
C represses a to complete the cycle. Hence it is a negative feedback loop. For example, if we
were to start out with a bit of A and no B or C, and if these genes were not connected, then
the concentrations of each of A, B and C would keep on increasing since the rate of expression is
constant. The only check to this would then be the natural degradation of the proteins (maybe
into their constituent amino acids), which is also always present at a constant rate. However, once
they are connected, a high concentration of A would decrease the expression rate of b, which would
decrease the concentration of B. This would then let c express at a faster rate, which would increase
the concentration of C. This would ultimately result in a checking e
ect on the production of A,
which would have to decrease. Then b would be freer and B would increase, decreasing C and
increasing A again. Hence, the cycle would start once again. Oscillations can be expected, and are
found, in the concentrations of the proteins in the steady state (i.e. after a transient state).
Figure 5: Schematic description of a repressilator.
The repressilator created by Elowitz and Leibler is described thus (see gure 6). TetR, cl and
LacI are the three proteins that are expressed by their parent genes tetR, cI and lacI. The gene
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lacI is obtained from E. coli, tetR from the tetracycline-resistance transposon( A transposon is a
discrete piece of DNA that can insert itself into other DNA sequence within the cell. ) Tn10 and
cI from phage. The protein LacI inhibits the expression of the gene tetR. The protein TetR in
turn inhibits the expression of the gene cI while protein cl inhibits the expression of lacI, thus
completing the cycle. So it is a negative feedback circuit, which could lead to oscillations. A green
uorescent protein (GFP) is used to detect the concentration levels of the repressilator components.
In the left part of the gure 6 it can be seen that TetR inhibits GFP, so that decrease in intensity
of the GFP as seen by an optical microscope indicates high concentration of TetR. The experiment
performed by Elowitz and Leibler showed oscillations in the concentrations of the proteins with
time periods greater than cell-division time, implying that the state of the oscillator is transmitted
through generations.
Figure 6: Diagram of the repressilator showing the genes and the proteins that make up the
repressilator ( gure from [6] )
Elowitz and Leibler’s mathematical model :
Deterministic: Michaelis-Menten Kinetics The dynamic variables in this model are the
repressor proteins and the mRNA molecules. Gene expression is a combination of two processes:
transcription, in which a gene produces messenger RNA, and translation, in which proteins are pro-
duced from mRNA. Each of the three proteins/mRNA molecules were considered to be identically
behaved. There are six coupled rst-order di
erential equations.
dmi
dt
= ô€€€mi +
1 + pnj
+
0 (1)
dmi
dt
= ô€€€ (pi ô€€€ mi) (2)
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The indices i and j run from 1 to 3. Here i =lacI, tetR, cI, while j =cI,lacI,tetR. The quantities pi
and mi are the concentrations of the repressing protein and the mRNA respectively and suitably
normalized (‘concentration’ here means the average copy number per cell).(Copy number means
the average number of molecules of a gene per genome contained in a cell. ) The parameter
+
0
is the rate of production of the protein in absence of the repressing protein. In the presence of a
repressor the rate drops to
1+pnj
+
0 , where the rst term gives the e
ect of the concentration
of the repressor protein modi ed by the Hill coe cient n, and
0 is the ‘leakiness quotient’ that
describes translation rate independent of the repressor. So the process of gene expression in the
repressilator circuit is divided into two parts: the rate part that is modi ed by the concentration of
the repressor and the other part that is not. The parameter is the ratio of the decay rates of the
protein and the mRNA. The normalization of the protein and mRNA concentration are thus: mi
is normalized by the translation e ciency which is the average number of proteins produced per
mRNA molecule, while pi is normalized by the quantity Km (called the Michaelis constant) which
is the number of repressor necessary to half-maximally repress a promoter (i:e: an mRNA molecule
which performs translation). The Hill coe cient is a measure of the degree of cooperativity of the
attaching molecules (here the repressors). A Hill coe cient of 1 indicates that the e
ect of binding
a repressor does not depend on the number of repressors already present. A Hill coe cient greater
than one indicates positive cooperativity so that the e
ect of the binding of each new repressor is
enhanced by the number of repressors already bound. A Hill coe cient less than one indicates the
the e
ect of existing repressors decreases the e
ect of each new binding.
Figure 7: Oscillation in the levels of the three repressor proteins in the deterministic case. The inset
shows the normalized autocorrelation function of the rst protein. The parameter values used by
Elowitz and Leibler were as follows : average translation e ciency= 20 proteins per transcript, Hill
coe cient n = 2, protein half-life= 10 minutes, mRNA half-life= 2 minutes, Km = 40 repressors
per cell ( gure from [6]).
The shaded region in gure 8 shows the region of parameter space for which oscillations take place.
Stochastic: Gillespie Algorithm Elowitz and Leibler used the Gillespie SSA algorithm to
solve for the stochastic case ( following the Gillespie prescription ). Parameter values used were
chosen keeping in mind that they approximately be similar to those chosen in the deterministic
case. The output was the following gure.
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Figure 8: Analysis of the stability of the steady state against parameters and
x Km. Stable
and unstable regions in the ô€€€
parameter space with respect to the steady state are shown. The
cross mark in the unstable region of the graph corresponds to the parameter values of gure 7. It
is in the unstable steady state that oscillations occur ( gure from [6]).
It can clearly be seen ( gure 9 ) that there are oscillations which persist, but there is large vari-
ability. As a result, the autocorrelation time is nite (approximately two periods). So stochasticity
seems to be a nuisance for regular oscillations in the single repressilator both experimentally and
in simulations.
In this model, oscillations are not seen if the Hill coe cient is taken as 1. this means that a single
repressor attached to each transcript carries out the job of repression. This is called non-cooperative
binding. As the Hill coe cient is increased to 2, oscillations are observed for suitable values of
the parameters only if the mRNA level is included. For Hill coe cient 3 or larger, oscillations
take place even if the mRNA level is not included in he analysis. This seems to show that there is
positive cooperativity in the system.
There are several interesting side notes about this elegant yet simple experiment of Elowitz and
Leibler. First, the period of the GFP oscillations was roughly 150 minutes, which is about three
times as long as the length of one E. coli generation under the conditions of the experiment.
However, the two o
spring cells (E. coli reproduces by splitting in two) lost their synchronization
after a little over one generation time. So it can be said that Elowitz and Leibler observed a lot
of noise in their system. Random variation in the levels of repressors and mRNA, as well as other
factors, caused the repressilator to behave somewhat unpredictably.
All in all, these authors were able to produce an oscillating biological clock using the tools of
synthetic biology. The clock wasn’t perfect as it lost synchronization with each new generation,
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Figure 9: Figure 3.3: Oscillation in the levels of the three repressor proteins in the stochas tic case
(y-axis is proteins per cell). The inset shows the normalized autocor relation function of the rst
protein. A similar set of values of parameters to those of gure 3.1 were used ( gure from [6]).
and it doesn’t allow for an entire culture of bacteria to blink in sync with one another. However it
is remarkable that this novel system worked as well as it did. The promoters and repressor genes
are parts, each promoter-repressor pair is a device, and the entire clock/reporter can be thought of
as a system.
Examples of simulation experiments of original model
To run a time course simulation on the model as it is available from the BioModels Database [4],
the following steps have to be followed (the execution will lead to Figure 7 and 9 of the original
publication[6]):
1. Import the model identi ed by the Uni ed Resource Identi er [1] urn:miriam:biomodels.db:BIOMD0000000012
(NB: this is the reference for the model encoded in SBML and stored in BioModels Database.
An equivalent reference for the model encoded in CellML and stored in the CellML repository
would be [5] http://models.cellml.org/exposure/6ad4f33a31aa0b9aa81b6558979d72f5.)
2. Select a deterministic method KISAO:0000035 (NB: this is the reference for a term of the
Kinetic Simulation Algorithm Ontology) to run a simulation on that model.
3. Run a uniform time course for the duration of 1000 minutes with an output interval of 1 min.
4. Report the amount of Lactose Operon Repressor, Tetracycline Repressor and Repressor pro-
tein CI against time in a 2D Plot. The result of the simulation is shown in Figure 10.
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Figure 10: Time-course of the Repressilator model, imported from BioModels
Database (BIOMD0000000012), simulated in COPASI [2], and plotted with Gnuplot
(http://www.gnuplot.info/). The number of repressor proteins lacI, tetR and cI is shown
as a function of the simulated time.
Tools and database
SynBioSS Designer
SynBioSS Designer is a web service to create automatically kinetic model from a Biobricks construc-
tion [Michal Galdzicki et al., 2009], using a set of universal biological rules to get a biomolecular
interactions network.SynBioSS uses the registry of standard biological parts, a database of kinetic
parameters, and both graphical and command-line interfaces to multiscale simulation algorithms.
The International Genetically Engineered Machine (iGEM) Foundation is dedicated to education
and competition, progress of synthetic biology, and the development of an open community and col-
laboration. This organization promotes and fosters scienti c research and education by establishing
and operating the Registry of Standard Biological Parts, a community collection of biological com-
ponents which are used by SynBioSS to obtain the transcriptional units from the Biobricks system.
SynBioSS Designer has the advantage that allows designs and builds distinct genetic circuits from
these Biobricks, obtaining even biochemical and genetic complex buildings upon which could be
able modify some of their characteristics to get the desire reaction network that will describe the
created model, considering the biological rules and laws from which the software is based. SynBioSS
Designer considers the behavior of the individual parts as well as the behavior of the connectivity
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spatial and temporal of each part, including the biochemical interactions resulting of the system,
so it is accurately, then the biochemical reactions network resulting will become very likely respect
to the reaction generation network that should occurs in vivo underneath biochemical approach.
The types of reactions network generated through the Repressilator corresponding to transcription,
translation, regulation, and induction are stored in the SynBioSS Wiki, so assigns for each reaction
a rate law, according to the number of reactants or the nature of the reaction, and a default kinetic
constant of an appropriate order of magnitude in relation to the nature of the reaction. However,
must pay attention to these values having to seek in di
erent sources as SynBioSS Wiki or relevant
literature to get suitable information pertinent to the system, seeing the dynamic behavior based
on these parameter values. De nitively the reaction network generation will depends on the circuit
design provided through inputs and their properties where several of these can be changed[7].
Figure 11: Table1. The table shows a summary of indputs and their properties which can be
introduced and changed into SynBioss Designer. [7]
Given this information, the Designer begins by extracting all of the transcriptional units from the
sequence of BioBricks. In the Designer approach, a transcriptional unit is de ned as a promoter
followed by an RBS, coding DNA, and one or more terminators. In this case, is developed the
Repressilator, whose shows as far as Designer, a sequence consist of three transcriptional units that
generate a reaction network in accordance with the following reactions. Finally the output is a
reaction network representing all the steps in gene expression and regulation. SynBioss Designer
outputs either a NetCDF or SBML le [M. Hucka et al., 2003], which can then be loaded in
simulation software such as SynBioSS Desktop Simulator[7].
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BioModels Database
Original Model: BIOMD0000000012.origin
Submitter: Nicolas Le Novre
Submission ID: MODEL6615351360
Submission Date: 13 Sep 2005 12:43:31 UTC
This model describes the deterministic version of the repressilator system. The model is based upon
the equations in Box 1 of the paper [6]; however, these equations as printed are dimensionless, and
the correct dimensions have been returned to the equations, and the parameters set to reproduce
Figure 7 and Figure 9.
Figure 12: Parameters used in BioModels.
Discussion
Elowitz and Leibler built their repressilator in the bacteria E:coli, and used GFP to observe the
presence (or absence) of oscillations. Since single cells had no apparent means to achieve or maintain
synchrony, individual cells were isolated under the microscope and the their
uorescent intensity
was studied as these cells grew into small two-dimensional micro-colonies consisting of hundreds of
progeny cells. The graph shows temporal oscillations in GFP
uorescence intensity with a time-
period of roughly 150 minutes, which happened to be almost three times as large as cell-division
time-scales. Snapshots of a microcolony of bacteria are given in gure 14, while the
uorescence
intensity of the marked cell against time is given in gure 13.
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Figure 13: Oscillations in GFP
uorescence intensity (bars at the bottom indicate septation events)
( gure from [6])
Figure 14: Snapshots of a microcolony of E. coli taken in (a)
uorescence and (b) bright- eld. The
arrows indicate the cell under observation. ( gure from [6])
Looking at the graph ( gure 13), one can see that the time-period of oscillations is around 150
mins (peak-to-peak). The bars at the bottom of the graph show that septation (cell-division) occurs
about three times per oscillation cycle on average, that is, with a time period of about 50 mins. This
conforms to standard cell-division time-periods. Therefore it is seen that the state of the network
is transmitted to its o
springs despite there being noise in the form of stochastic
uctuations in
the dynamics of the cellular clock. However, signi cant di
erences in period and amplitude of
the oscillator were observed in the oscillator output. These di
erences were seen among cells in
di
erent lineages ( descended from di
erent ancestors) or among the cells in one lineage, which are
called siblings (see gure 15 ).
Elowitz and Leibler conclude that it is possible to design and construct a new arti cial genetic
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oscillator with new functional properties from generic components. It might then be possible to
attempt to understand the design principles of more complex oscillators such as the circadian
oscillator using the simple repressilator model. However, as opposed to the robust behaviour of
the circadian clock, the behaviour of the repressilator (according to the these experimental results)
seemed to be noisy and variable.
Figure 15: Top left gure shows phase delays after septation among sibling cells (blue and green)
relative to the reference cell(red). Top right gure shows that phase is maintained but amplitude
varies greatly after septation. Bottom left gure is for reduced period (green) and long delay(blue).
Bottom right gure shows large variations in period and amplitude. The top two gures and the
bottom left gure show the variation of oscillation among cells of the same lineage. The bottom
right one shows the variations between cells of di
erent lineages. ( gures from [6])
The repressilator is a milestone of synthetic biology which shows that genetic regulatory networks
which perform a novel desired function can be designed and implemented. Further, the initial ex-
periment gives new appreciation to the circadian clock found in many organisms, as they perform
much more robustly than the repressilator. More recent investigations at the RIKEN Quantitative
Biology Center have found that a single protein molecule could form a temperature independent,
self-sustainable oscillator when it takes chemical modi cations. Repressilators in adapted math-
ematical could potentially aid research in elds ranging from circadian biology to endocrinology.
They are increasingly able to demonstrate the synchronization inherent in natural biological systems
and the factors that a
ect them.
Elowitz and Leibler are an excellent example of the use of mathematical models to design arti cial
control circuits. These can be either used as components for biotechnology and synthetic biology,
or used to further study and understand properties of naturally evolved control elements.
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free, centralized database of curated, published, quantitative kinetic models of biochemical and
cellular systems, 2006.
[5] Hunter PJ Nielsen PF Lloyd CM, Lawson JR. The cellml model repository, 2008.
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