Quantitative dissection of the simple repression
Hernan G. Garciaaand Rob Phillipsb,1
Departments ofaPhysics andbApplied Physics, California Institute of Technology, Pasadena, CA 91125
Edited* by Curtis G. Callan, Princeton University, Princeton, NJ, and approved May 26, 2011 (received for review October 18, 2010)
We present a quantitative case study of transcriptional regulation in
which we carry out a systematic dialogue between theory and mea-
surement for an important and ubiquitous regulatory motif in bacte-
ria, namely, that of simple repression. This architecture is realized by
a single repressor binding site overlapping the promoter. From the
theory point of view, this motif is described by a single gene regula-
tion function based upon only a few parameters that are convenient
theoretically and accessible experimentally. The usual approach
is turned on its side by using the mathematical description of these
regulatory motifs as a predictive tool to determine the number of
repressors in a collection of strains with a large variation in repressor
copy number. The predictions and corresponding measurements
are carried out over a large dynamic range in both expression fold
change (spanning nearly four orders of magnitude) and repressor
copy number (spanning about two orders ofmagnitude). The predic-
tions are tested by measuring the resulting level of gene expression
and are then validated by using quantitative immunoblots. The key
outcomes of this study include a systematic quantitative analysis of
the limits and validity of the input–output relation for simple repres-
repressorinteractions for several distinct repressor binding sites, and
a repressor census for Lac repressor in Escherichia coli.
architectures de novo. These successes have engendered hopeful
analogies between the circuits found in cells and those that are the
basis of many familiar electronic devices (1, 2). However, in many
cases, unlike the situation with the electronic circuit analogy, our
understanding of these circuits is based upon enlightened empir-
icism rather than systematic, quantitative knowledge of the input–
output relations of the underlying genetic circuits.
Regulatorybiology has shed lightonthespace–time responseof
a wide variety of these genetic circuits. Examples range from the
complex regulatory networks that govern processes such as em-
bryonic development (3, 4) to the synthetic biology setting of
building completely new regulatory circuits in living cells (5).
In particular, the dissection of genetic regulatory networks is
resulting in the elucidation of ever more complex wiring diagrams
(see, as an example, ref. 6). With these advances it is becoming
increasingly difficult to develop intuition for the behavior of these
networks in space and time. In addition, often, the diagrams used
to depict these regulatory architectures make no reference to the
census of the various molecular actors (the intracellular number
of polymerases, activators, repressors, inducers, etc.) or to the
quantitative details of their interactions that dictate their re-
sponse. As a result, there is a growing need to put the description
of these networks on a firm quantitative footing.
Often, the default description of regulatory response is offered
by phenomenological Hill functions (7–12), which in the case of
repression have the form
gene expression level ¼
t is now possible not only to make quantitative, precise, and
reproducible measurements on the response of a variety of dif-
1 þ ð½R?=KdÞnþ β;
are constants that determine the maximum and basal levels of
expression, respectively. Although such descriptions might pro-
vide a satisfactory fit of the data, they can deprive us of insights
into the mechanistic underpinnings of a given regulatory response
or, worse, can force us into thinking about the behavior of a given
circuit in a way that is not faithful to the known architecture.
Alternatively, using thermodynamic models, it has been shown
for a wide class of regulatory architectures that for each and every
circuit, one can derive a corresponding “governing equation” that
provides the fold change in gene expression as a function of the
relevant regulatory tuning variables (13–15). The goal of our
work is to carry out a detailed experimental characterization of
the predictions posed by one such governing equation for the
regulatory motif describing simple repression (Fig. 1A) in which
a repressor can bind to a site overlapping the promoter, resulting
in the shutting down of expression of the associated gene. This
alone, there are >400 circuits that are regulated by different
transcription factors that repress by binding to a single site in the
vicinity of the promoter (16). Indeed, simple repression and ac-
tivation are often thought of as the elementary ingredients of
a much more diverse range of real regulatory circuits (17, 18).
As seen in Fig. 1, the level of expression in circuits governed by
simple repression can be tuned by several different parameters.
One of the key tuning variables in nearly all regulatory and sig-
naling networks is the numbers (or concentrations) of the rele-
vant molecular players in the process of interest. We use the
repressor number as one of the main tunable parameters in the
experiments described below, with a 100-fold range of different
repressor counts considered. To explore our understanding of
how this parameter dictates regulatory response, we need to
know how many repressors our strains of interest harbor. A se-
ries of beautiful recent experiments has made important progress
in carrying out the molecular census, using a variety of clever
methods. These molecular counts include the census of all actin-
related proteins in Schizosaccharomyces pombe cells (19), a count
of essentially all the proteins in Saccharomyces cerevisiae cells
(20), a determination of the distribution of both lipids and pro-
teins in synaptic vesicles (21), and several counts of the proteins
in E. coli (22, 23) and other cell types as well (24). Most relevant
to the current work is a recent experiment using a fluctuation-
based counting method to determine the number of transcription
factors in E. coli that control a synthetic circuit of interest (10).
Our work adds a twist to protein census taking by using ther-
modynamic models as a way to count the number of repressors in
a simple regulatory motif.
Quantitative control of the absolute number of transcription
factors is seldom used in experiments that aim to dissect regu-
latory architectures even though it is one of the main strategies
to verify the predictions from thermodynamic models (13–15).
Previous work has usually relied on the control of an external
Author contributions: H.G.G. and R.P. designed research; H.G.G. performed research; H.G.G.
and R.P. analyzed data; and H.G.G. and R.P. wrote the paper.
The authors declare no conflict of interest.
*This Direct Submission article had a prearranged editor.
1To whom correspondence should be addressed. E-mail: email@example.com.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
| July 19, 2011
| vol. 108
| no. 29
inducer to vary the regulatory response of a genetic circuit (5, 9,
11, 12, 25, 26). However, the use of inducer molecules, although
experimentally convenient, adds another layer of complexity to
the modeling approach and has been systematically character-
ized in only a few cases (11).
Recent measurements (10, 23, 27–31,) have also often focused
on the variability or “noise” associated with transcriptional reg-
ulation. Although there has been great recent interest in this
gene expression variability, we argue that a crucial quantitative
prerequisite to fully dissecting the properties of genetic networks
is a viable description of their mean response, and any concep-
tual frameworks used to describe the noise must first be consis-
tent with these mean responses.
In this work we test these thermodynamic models of transcrip-
tional regulation by generating parameter-free predictions for the
level of gene expression as a function of the regulatory tuning
variables of the simple repression architecture. We show signifi-
cant agreement between the theoretical description and the
measurements over multiple orders of magnitudes of the inputs
and outputs of the system. We conclude that through thermody-
namic models wecanaccurately predict thelevelofregulation due
to simple repression, opening the door to the design of synthetic
genetic circuits where the level of gene expression can be tuned
theoretically and to the better interpretation of the transcriptional
response of naturally occurring circuits.
Theory and Experimental Design
Although our analysis should be relevant generically for simple
repression, the reasoning behind our experiments is based upon a
series of earlier measurements and calculations on the level of
repression in the specific case of the lac operon (32, 33). In par-
ticular, we consider the case where there is only a single specific
in turn, different strains were constructed in which the strength of
that main operator was systematically weakened according to the
progression Oid to O1 to O2 to O3 shown in Fig. S1.
Thermodynamic models assume that the processes leading to
transcription initiation by RNA polymerase (RNAP) are in quasi-
equilibrium. This assumption means that we can use the tools of
statistical mechanics to describe the binding of RNA polymerase
and transcription factors (TFs) to DNA. Further, the level of gene
expression is assumed to be proportional to the probability that
RNA polymerase is bound to the promoter of interest (13, 34).
polymerase and the promoter and competition for those binding
sites by repressors. In Fig. 1A we show the thermodynamic states
and weights corresponding to a minimal model of the simple re-
pression regulatory motif. In this simplified model the promoter
can befound in only one ofthreestates: (i) empty, (ii) occupiedby
RNA polymerase, and (iii) occupied by Lac repressor. The par-
tition function for this system is obtained by summing over the
statistical weights of each of these states and is given by
RNA polymerase bound
where P is the number of RNA polymerase molecules, R is the
number of Lac repressor tetramers, and NNS∼ 5 × 106is the
number of nonspecific DNA sites (the length of the genome),
corresponding to the reservoir for both molecules. β = (kBT)−1
with kBbeing the Boltzmann constant and T the absolute tem-
perature. The energies Δεpd(RNA polymerase–DNA) and Δεrd
(repressor–DNA) correspond to the difference between specific
and nonspecific binding for RNA polymerase and Lac repressor,
respectively, where we make the simplifying assumption of a
homogeneous nonspecific background. The factor of 2 in front
of the number of Lac repressors stems from the fact that this
molecule is a tetramer, a dimer of dimers, with two binding
heads. Therefore, 2R corresponds to the number of binding
heads inside the cell. For a complete derivation of these terms,
please refer to refs. 14 and 35, SI Text and Fig. S2.
The probability of finding RNA polymerase bound to the
promoter is then given by
where Z is the partition function defined in Eq. 2. A much more
convenient quantity to measure is the fold change or relative
change in gene expression due to the presence of the transcrip-
tion factor; namely,
fold change ¼pboundðR ≠ 0Þ
pboundðR ¼ 0Þ¼
The great advantage of this quantity is that it is easily accessible
both theoretically and experimentally. It is unitless and can be
measured by comparing the levels of gene expression (in any ar-
bitrary or absolute units) when Lac repressor is present and
absent. We define this fold change in gene expression with respect
to the absence of transcription factor and not with respect to
a state where the transcription factor is fully induced such as in
the presence of saturating concentrations of Isopropyl β-D-1-
thiogalactopyranoside (IPTG).Usinginducerswouldrequire usto
consider theinductionprocess explicitly (11).Inthecase ofa weak
promoter such as lacUV5 used in this work (ref. 15 and SI Text)
the term ðP = NNSÞe−βΔεpd<< 1. This outcome results in the fold
change collapsing to the simpler form,
R (number of repressors)
Repressor copy number
the thermodynamic model describing this regulatory motif. We
assume that Lac repressor sterically excludes RNA polymerase
from the promoter, although that assumption is not critical to
our analysis. P and R are the numbers of RNA polymerase and
Lac repressor molecules inside the cell, respectively. NNSis the
number of nonspecific sites, which we assume to be the size of
the genome. Δεpdand Δεrdare the difference in energy be-
tween being specifically and nonspecifically bound for RNA
polymerase and Lac repressor, respectively. The difference in
color in the repressor binding site denotes an overlap of the
binding site with the promoter. (B) The tuning variables that
can be varied in the model and controlled experimentally are
the binding strength (by changing the Lac repressor operator
sequence) and the number of Lac repressors (by changing its mRNA ribosomal binding site). The effect of tuning these parameters on the fold change in gene
expression is shown in the graphs. Note that stronger repressor binding corresponds to a larger fold change. For a detailed derivation of the expression and
discussion of the assumptions used see SI Text and Fig. S2.
The simple repression motif. (A) States and weights of
| www.pnas.org/cgi/doi/10.1073/pnas.1015616108Garcia and Phillips
fold change ¼
This last expression serves as the basis of our experimental de-
sign where we identify two tuning variables that can be controlled
experimentally in a systematic fashion: the binding energy and
the number of Lac repressors. In Fig. 1B we show the predicted
fold change as a function of these two experimentally accessible
parameters. Alternatively, the binding of Lac repressor can be
described by a dissociation constant, the concentration of Lac
repressor for which the fold change in gene expression is 1/2.
This approach is explained in SI Text. Throughout the text we
report both binding energies and approximate dissociation con-
stants, although all of our measurements and analysis are built
around binding energies and repressor numbers. Approximate
concentrations and dissociation constants are provided merely as
rough estimates for the purposes of comparison with literature
values in which sometimes these quantities are favored. For
details of the estimation of the concentrations and dissociation
constants, see SI Text, Connecting Δεrdto Kd.
Earlier hints as to how simple repression plays out quantitatively
in gene expression for constructs bearing each one of the four
operators and for two different numbers of Lac repressor per cell.
be noted, though, that these original measurements were not per-
formed with the intention of the kind of quantitative dissection
advocated here and that therefore the uncertainties in the pa-
consistent with our own data. Additionally, in SI Text and Fig. S5
we show that our results do not depend on the particular choice
of quantification protocol for our enzymatic reporter. Finally, as
shown in SI Text and Table S2, even if we replace our reporter with
a fluorescent protein the results are essentially unaltered.
For the measurements reported here, we created ∼30 strains of
bacteria where we systematically tuned the number of repressors,
using a recently developed scheme for controlling ribosomal bind-
ing strength (37). Although this scheme provides a rough expec-
had no precise or accurate a priori knowledge of the actual in-
tracellular numbers of Lac repressors. These strains bear reporter
constructs regulated by simple repression such as those shown in
Fig. S1, for which we measure the fold change in gene expression.
If we are to believe the input–output function from Eq. 5, once
we know the binding energy of the operator in question there is a
direct and unequivocal relation between the fold change in gene
expression and the number of repressor molecules. Testing these
predictions requires an accurate and precise quantification of the
absolute levels of repressor inside the cell. In fact, we view this
approach as a way to count molecules by inference by looking at
levels of gene expression and passing these levels of expression
through the theoretical filter of Eq. 5.
In the following sections we test these parameter-free pre-
dictions over a wide range of both expression and repressor
numbers and show that they largely jibe with our experimental
observations. The logic advocated here is that if Eq. 5 is shown to
be predictive, it will open the door to creating synthetic gene
regulatory circuits whose level of gene expression can be pre-
cisely tuned a priori and to being able to predict the regulation of
a particular promoter by just looking at its regulatory sequence.
In addition, a predictive understanding of the input–output re-
lation of these architectures will serve as a jumping-off point for
the design and understanding of more complex circuits such as
those involving DNA looping, cooperative repression, etc. (15).
Eq. 5 represents a provocatively simple expression purporting
to describe the response of a bacterial cell to a wide variety of
perturbations such as altering the DNA target sites (with the Kds
changing by three orders of magnitude or, equivalently, Δεrd
changing by 7 KBT) (15, 36, 38, 39) and repressor copy numbers
(with the copy numbers changing by several orders of magni-
tude). If we take this equation seriously, it implies that once we
have determined the parameter Δεrd, there is a quantitative re-
lation between the fold change in gene expression and the cor-
responding number of Lac repressors. Namely, once we know
one quantity we can predict the other.
To exploit Eq. 5 we designed lacUV5 promoters with a single
binding site for Lac repressor at the wild-type position of O1.
These promoters bore Oid, O1, O2, or O3 and controlled the
expression of the enzymatic reporter gene lacZ (Materials and
Methods and Fig. S1), although as reported in SI Text, we also
examined many of the same constructs using fluorescence as well,
resulting in nearly identical results. We integrated each one of
these simple repression constructs such as the one shown in in Fig.
1A in the chromosome of a strain bearing no Lac repressor and in
six different strains that we systematically designed to express
different constitutivelevels of Lacrepressor. Asmentioned above,
although we had a qualitative expectation about the number of
Lac repressors present in each strain, we had no previous quan-
titative information about that magnitude.
Taking the Repressor Census Through Thermodynamic Models. We
measured the fold change in gene expression of our simple re-
six different strain backgrounds we created. There are several
different ways to explore the results in conjunction with Eq. 5. As
noted above, one scheme is to determine the absolute number of
repressor molecules within one strain and to combine this with the
measured fold change to obtain the in vivo binding energy for each
of the different operators through Eq. 5. With these binding en-
model on the stand is to predict the number of repressors in the
other strains.An alternative concept is simply to use all of the fold-
change and repressor count measurements and to see how well
they agree with the functional form provided by Eq. 5 by making
one global fit to the in vivo binding energy for each operator.
Regardless of the scheme chosen it is necessary to possess an
absolute count of the repressor number in each one of our strain
backgrounds. Details of this determination are given below. To
carry out the first scheme presented above we used strain
RBS1027 as the basis of the calculation of the binding energies.
The resulting fold change in gene expression for each operator in
this strain background and the calculated binding energies are
shown in Fig. 2A. Using these binding energies we plot the fold
change in gene expression as a function of binding energy for all
strains and choices of operators in Fig. 2B (the corresponding
absolute values of gene expression measured for each strain are
shown in Fig. S6). The data in Fig. 2B are fitted to Eq. 5 to gen-
erate a prediction for the number of repressors within each one of
the five remaining strains. These predictions are shown in Fig. 2C.
Because the majority of our strains were created for this
particular work, the resulting predicted cellular numbers cannot
be compared with any external standard. However, strain HG104
expresses wild-type levels of repressor from the native lacI gene.
Indeed, for this strain we predict 8.8 ± 0.8 repressor tetramers
per cell, comparable to the previous and, to our knowledge, only
available absolute measurement (40).
To bring the predictions of the model for simple repression to
fruition we need to directly measure the number of repressors in
each one of our six strains. We measured the in vivo number of
Lac repressors in these six strains by performing quantitative
immunoblots (19, 41, 42) from cell lysates such as those shown in
Fig. 3A. To get an absolute count of the amount of Lac repressor
in each strain a series of dilutions of a purified Lac repressor
standard of a known concentration was used (Fig. 3B). Quantifi-
cation of the luminescence of the immunoblots was performed
using a cooled CCD camera. Care was taken to account for spatial
nonuniformities in the light collection as depicted in Fig. 3C. We
can reliably detect a wide range of purified Lac repressor stand-
Garcia and PhillipsPNAS
| July 19, 2011
| vol. 108
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ards using our immunoblots (as low as 50 pg, corresponding to
around five repressors per cell). This result increases our confi-
dence in the method as a way of precisely quantifying protein
counts in bulk even at very low levels (Materials and Methods and
Fig. 3D). It is important to note, however, that counting methods
based on purification, such as immunoblots, have the inherent
caveat that some proteins might have stayed behind in the dif-
ferent fractions. Although we took action to reduce this effect, the
results from immunoblots should be viewed as a lower bound on
the actual number of proteins in vivo.
Our predictions for the number of Lac repressors in each
strain can now be compared with the direct measurements of this
quantity, which are shown in Fig. 4A. In Fig. 4B we compare the
predictions and direct measurements explicitly. The direct mea-
surements are comparable to the predictions within experimen-
tal error, giving us confidence that the proposed input–output
function from Eq. 5 appropriately describes the input–output
properties of the simple repression regulatory motif. This result
suggests in turn that once we know the binding energy for an
operator, we have predictive power. Although this analysis yiel-
ded results that are largely consistent between theory and ex-
periment, it appears that we systematically underestimate the
number of repressors in the two strains with the highest repressor
number. The reader is referred to SI Text for a further discussion
of these two strains.
Direct Determination of the in Vivo Lac Repressor Binding Energies.
The scheme for exploring the limits and validity of the thermo-
one strain to determine the binding energy of Lac repressor to its
operator DNA. However, as noted earlier, an alternative ap-
proach is to simply use the entirety of our data to evaluate global
fits of Eq. 5 to the data corresponding to a given operator.
Implementation of this concept is shown in Fig. S7B, where we
combine all of our measurements to determine the best values of
the different in vivo binding energies. On the other hand, one
might choose to use the information about fold change and re-
pressor copy number for one particular strain to derive the dif-
ferent binding energies. This analysis can be done, in turn, for all
strains created for this work in an analogous way to what we did
with strain RBS1027 in the previous section. In Fig. 5 we compare
such fits with the binding energies that can be obtained from an-
alyzing a single strain. Additionally, we show the energies
obtained from the Oehler et al. data (33)(SI Text and Fig. S8) and
from Fig. S7B for comparison. These multiple approaches for
obtaining the binding energies, all leading to essentially compa-
rable results (for example, Fig. S7A), increase our confidence in
the simple model of Eq. 5 and in the minimalist modeling phi-
losophy used to obtain it as a quantitative and predictive tool.
Finally, it is common in the theoretical treatment of experi-
ments on transcriptional regulation to include a constant level of
expression dubbed the “leakiness”. Such leakiness is usually un-
8.8 ± 0.8
40 ± 4
75 ± 2
270 ± 20
400 ± 50
-17.3 ± 0.2
-15.8 ± 0.2
-14.3 ± 0.2
-10.0 ± 0.3
(0.6 ± 0.1) x 10-3
(2.8 ± 0.5) x 10-3
(12 ± 1) x 10-3
0.48 ± 0.05
Fold-change and binding energies
obtained from strain RBS1027
Binding site energy (k
Approximate dissociation constant (M)
−18 −17 −16 −15 −14 −13 −12 −11 −10 −9
repressors for different strains. (A) The operator binding energies and ap-
proximate dissociation constants are deduced from the measurement of the
fold change for the different operators in strain RBS1027 combined with our
knowledge of its intracellular number of repressors, using Eq. 5. (B) The fold
change in gene expression is measured for all four operators in six different
strain backgrounds (including RBS1027). Using the binding energies from A,
we fit the data to Eq. 5 to make a parameter-free prediction of the number
of repressors present in each strain shown in C. Errors in the predictions
represent the SE of the corresponding fit. The errors in the binding energies
are here denoted as gray shaded regions. Estimated dissociation constants
are shown for convenience for comparison with literature values. The basis
for these estimates is explained in SI Text.
Single-site binding energies and prediction of the number of
Purified LacI standard
of the in vivo number of Lac repressors. (A)
immunoblot. (B) Map of the samples loaded
on the membrane shown in A. The blank
(HG105) and 1I samples are used to create
a normalizationmapbysubtracting theblank
1I. White spots correspond to the cell lysates
measured and the blue spots correspond to
the different concentrations of purified Lac
repressor standard. (C) Normalization map
generated by fitting a 2D polynomial to 1I
samples scattered around the membrane
(black dots) after removing the blank. This
map was used to account for nonuniformities
in the collection of luminescence from the
membrane. (D) Luminescence vs. quantity of
LacI loaded. The calibration samples are used
unknown amounts of repressor loaded are
determined by using the calibration curve.
Samples 1I and RBS1 have been diluted 1:8
to match them to the dynamic range of the
within a spot (SI Text).
Immunoblots for the measurement
| www.pnas.org/cgi/doi/10.1073/pnas.1015616108Garcia and Phillips
derstood as a low level of activity that is independent of any
regulation. The reader is referred to SI Text and Fig. S9 for
a more detailed description of leakiness where we show that the
values obtained for the binding energies do not change signifi-
cantly for reasonable values of the leakiness.
Theoretical models of gene expression, especially in bacteria, have
reached a very high level of sophistication. Similarly, measure-
ments of gene expression have come to the point where they are
both reproducible and quantitative enough to serve as the basis for
explicit attempts at confronting theory and experiment and to
explore themeritsofthesetheoreticalperspectivesasa conceptual
framework for describing regulatory response. Indeed, such
measurements have now reached the point where in our view it is
for a theoretical response that is commensurate with the level of
quantitative detail in the experiments themselves. To that end, we
haveundertakena detailedstudy ofone ofthemostimportant and
fundamental regulatory building blocks found in living organisms
from all three domains of life, namely, simple repression. Simple
repression and its positive regulation counterpart, namely simple
activation, serve as the paradigmatic building blocks of the much
richer regulatory strategies that are used in the growing list of both
natural and synthetic networks now being explored.
In recent years, the governing equations characterizing the
transcriptional response of these elementary regulatory building
blocks and much more complicated assemblies of them have been
worked out in detail using the ideas of statistical mechanics. The
work described here provides a template for the kind of rich in-
terplay between theory and experiment that should be demanded
of these other networks as well. In particular, the governing equa-
tions describing regulatory architectures feature certain key tuning
variables that serve to elicit different biological responses. In the
experiments described here, we have explored two of the elemen-
tary tuning parameters that govern the simple repression motif,
namely, the strength of the transcription factor binding sites and
the molecular counts of the repressors themselves. We have shown
that an input–output function for simple repression obtained from
thermodynamic assumptions, which depends on those two tuning
parameters, can indeed predict in a parameter-free manner the
regulatory outcome over roughly four orders of magnitude in the
Using the thermodynamic model approach coupled tightly with
precise measurements we have been able to perform a systematic
quantitative dissection of the input–output relation for simple
repression and believe that similar analyses should be carried out
for each of the other governing equations describing key regula-
tory motifs. As a by-product of these measurements, we have
been able to make a precise determination of the in vivo binding
energies for DNA–repressor interactions. In addition, these
results provide a census of the repressor content for Lac repressor
in E. coli over a large dynamic range (roughly two orders of
magnitude in repressor counts). The predictive power revealed by
this model on the basis of a few parameters is one of the first steps
toward having a standardized description of a regulatory archi-
tecture on the basis of its microscopic parameters (1, 2). Hark-
ening back to the electronic circuit analogy, the results presented
here are analogous to illustrating that for a resistor there is
a value for the resistance that is necessary and sufficient to predict
the current given the voltage. In our case specification of the
binding energy Δεrdis necessary and sufficient to predict the fold
change in gene expression given the number of repressors.
Further characterization of this architecture should explore the
role of promoter copy number and operator position as these ar-
chitectural features are known to alter the expression profile as
simple repressionin thelacoperon, itisnow important toexamine
idea being to explore the extent to which the successes found in
this case can be expected to apply to other genes.
Materials and Methods
DNA Constructs and Strains. The construction of all plasmids and strains is
described in detail in SI Text.
In short, plasmids pZS25O1+11, pZS25O2+11, pZS25O3+11, and pZS25Oid
+11 have a lacUV5 promoter controlling the expression of a LacZ reporter as
shown schematically in Fig. S1.
Plasmid pZS3*1-lacI expresses Lac repressor off of a pLtetO-1promoter (46).
The ribosomal binding site of this construct was weakened following ref. 37,
using site-directed mutagenesis (Quikchange II; Stratagene) in order to
generate constructs expressing LacI at different levels as described in SI Text
and Table S3.
The E. coli strains used in this experiment are shown in Table S4. HG105 is
wild-type E. coli (MG1655) with a complete deletion of the lacIZYA genes.
HG104 is also wild-type E. coli with a deletion of the lacZYA genes. We
therefore expect strain HG104 to express wild-type levels of Lac repressor.
Reporter constructs and Lac repressor constructs were integrated into
the galK and ybcN regions, respectively, using recombineering (47) and
combined using P1 transduction. Please refer to SI Text for details.
Growth Conditions and Gene Expression Measurements. Strains to be assayed
were grown in M9 minimal medium plus 0.5% glucose and harvested during
Number of repressors
11 ± 2
30 ± 10
62 ± 15
130 ± 20
610 ± 80
870 ± 170
number. (A) Immunoblots were used to measure the number of Lac re-
pressors in six strains with different constitutive levels of Lac repressor. Each
value corresponds to an average of cultures grown on at least 3 different
days. The error bars are the SD of these measurements. (B) The fold-change
measurements in Fig. 2B were combined with the binding energies obtained
from Fig. 2A (derived from strain RBS1027) to predict the number of Lac
repressors per cell in each one of the six strains used in this work. These
predictions were examined experimentally by counting the number of Lac
repressors using quantitative immunoblots.
Experimental and theoretical characterization of repressor copy
Oehler et al.
Binding energy (k
combine the measurements of the fold change in gene expression with the
corresponding number of repressors and solve Eq. 5 to obtain an estimate of
the binding energies (dots). The energies obtained from the Oehler et al.
data (33) are also shown. The lines correspond to using all measurements of
the fold change in gene expression with their corresponding repressor
numbers to fit Eq. 5 to obtain the best possible estimate for the binding
energies. This fit is shown in Fig. S7B. The results of this approach are shown
as horizontal lines and the shaded region captures the uncertainty.
Determination of the in vivo binding energies. For each strain we
Garcia and PhillipsPNAS
| July 19, 2011
| vol. 108
| no. 29
exponential growth. Our protocol for measuring LacZ activity is basically
a slightly modified version of the one described in refs. 48 and 49. Details are
given in SI Text.
Measuring in Vivo Lac Repressor Number. Cell lysates of our different strains
bearing Lac repressor were obtained as described in SI Text. Calibration
samples using a known concentration of purified Lac repressor (courtesy of
Stephanie Johnson, California Institute of Technology, Pasadena, CA) diluted
in a lysate of HG105 strain (strain without Lac repressor) were used.
A nitrocellulose membrane was prepared for sample loading and after-
ward blocked and treated with anti-LacI primary monoclonal antibody and
HRP-linked secondary antibody as discussed in SI Text. Two microliters of
each sample was spotted on the membrane in a pattern similar to that of
a 96-well plate. The resulting drops had a typical size of 3 mm. All samples
were loaded in triplicate with the exception of samples 1I and HG105. Both
of them were loaded on the order of 20 times on different positions of the
membrane to obtain a spatial standard that would allow for corrections of
nonuniformities in the light collection (see below).
The membrane was dried and developed with Thermo Scientific Super-
Signal West Femto Substrate and imaged in a Bio-Rad VersaDoc 3000 system
with an exposure of 5 min. A typical raw image of one of the membranes is
shown in Fig. 3A and the corresponding loading map can be seen in Fig. 3B.
Custom Matlab code was written to detect the spots and calculate their total
luminescence. The luminescence coming from the HG105 blank samples was
fitted to a second-degree polynomial, which was in turn subtracted from all
other luminescence values. After this procedure another second-degree
polynomial was fitted to the 1I samples, resulting in a typical surface such as
the one shown in Fig. 3C. Note that differences of up to 25% could be ob-
served between different positions on the membrane. This last polynomial
was used to normalize the intensity of all other samples.
The luminescence corresponding to the calibration samples was overlaid
apower law using only thecalibration datapoints inthe rangeof thesamples
that were to be measured. An example of this calibration is shown in Fig. 3C.
For additional details please refer to SI Text.
Finally, the amount of Lac repressor found in a spot was related to the
number of Lac repressor molecules per cell by calibration of the OD readings
of the original cultures to cell density as described in SI Text.
ACKNOWLEDGMENTS. We thank Rob Brewster, Stephanie Johnson, Jane
Kondev, Tom Kuhlman, Kathy Matthews, Ron Milo, Alvaro Sanchez, Paul
Wiggins, andBob Schleif for enlighteningdiscussions overthe course ofmany
years and comments on the manuscript, and to Thomas Gregor and Ted Cox
for lending their respective laboratory spaces for further experiments. We
thank Franz Weinert, James Boedicker, Heun Jin Lee, and Maja Bialecka for
help with the cell counts calibration. We thank the National Institutes of
Health for support through Grant DP1 OD000217 (Director’s Pioneer Award)
and Grant R01 GM085286, and La Fondation Pierre Gilles de Gennes (R.P.).
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| www.pnas.org/cgi/doi/10.1073/pnas.1015616108Garcia and Phillips