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: firstname.lastname@example.org.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
| 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