Biochemical Engineering Journal Forward engineering of synthetic ...

Biochemical Engineering Journal 47 (2009) 38–47
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Biochemical Engineering Journal
journal homepage: www.elsevier.com/locate/bej
Forward engineering of synthetic bio-logical AND gates
Kavita Iyer Ramalingam 1 , Jonathan R. Tomshine 1 , Jennifer A. Maynard 2 , Yiannis N. Kaznessis ∗
Department of Chemical Engineering & Materials Science, University of Minnesota, 421 Washington Ave SE, Minneapolis, MN 55455, United States
article
info
abstract
Article history:
Received 7 April 2009
Received in revised form 22 June 2009
Accepted 25 June 2009
Keywords:
Logical AND gate
Multiscale models
Biocomputing
Stochastic simulations
Synthetic biology
Gene regulatory networks
Computer-aided design
The field of synthetic biology has produced genetic circuits capable of emulating functional paradigms
seen in digital electronic circuits. Examples are bistable switches, oscillators, and logic gates. The present
work combines detailed mechanistic-kinetic models and stochastic simulation techniques as well as the
techniques of in vivo molecular biology to study the potential of a synthetic, single promoter AND gate.
This device is composed of elements of the tet, lac, and -phage promoters and is responsive to the
commonly used inducers IPTG and aTc, producing GFP as an output signal. The quantitative behavior of
the AND gate phenotype is studied both in numero and in vivo as a function of promoter topology. The
model is constructed from kinetic data obtained from the literature and yields clearly defined ON/OFF
logical behavior at realistic inducer concentrations. These behaviors are matched with observed in vivo
data obtained through fluorescence-activated cell sorting. The effect of incomplete repression by weaker
LacI repressor is also investigated and quantified. The simulation results, coupled with in vivo data, not
only identify important design degrees of freedom, but also provide parameters that can be used to guide
future synthetic designs using these common regulatory elements.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
A plethora of synthetic gene regulatory networks has been
created by arranging naturally occurring regulatory proteins to
produce novel biological phenotypic functions [1–4]. To date, the
network paradigms that have been most thoroughly studied are
the bistable switch [5–8], the oscillator [7,9], and various logic gates
[10–17].
In this work we combine multiscale models with synthetic
bioengineering experiments to design, build, and characterize a
high-fidelity logical AND gate in bacteria. A reductionist modeling
approach is pursued. We adopt the molecular biology dogma
that there are universal molecular mechanisms underlying the
emergence of phenotypes. Consequently, we represent all gene
expression molecular level events with reactions, including all the
biomolecular interactions involved in transcription, translation,
regulation and induction. This way, we relate each model reaction
toarealin vivo reaction event and any biological system can be
modeled by a network of reactions.
Because biological interactions regularly occur away from the
thermodynamic limit, the simulations of reaction networks we con-
∗ Corresponding author. Tel.: +1 612 624 4197; fax: +1 612 626 7246.
E-mail address: yiannis@cems.umn.edu (Y.N. Kaznessis).
1 These authors contributed equally to this work.
2 Current address: Department of Chemical Engineering, University of Texas,
Austin, United States.
duct are stochastic, i.e., they generate probability distributions of
molecular concentration. These distributions are directly comparable
to experimentally observed variation. Detailed models then
provide the opportunity to gain molecular level insight [18–22].
Experimentally, we constructed an in vivo synthetic-hybrid system
consisting of multiple operators within a single promoter. The
operator sequences employed are derived from three unrelated natural
regulatory elements: the tetracycline (tet), lactose (lac) and
-phage operons arranged logically within a single transcriptional
unit. Specifically, we built six single promoter regulatory motifs by
shuffling tet and lac operator sites (T and L, respectively) in and
around the P L (-phage): LLT, LTL, TLL, TLT, TTL and LTT (Fig. 1;
detailed sequence information is available in supplement). The promoters
drive expression of green fluorescent protein (GFP). The
regulatory architecture is designed such that each operator’s position
efficiently interferes with RNA polymerase (RNAp) promoter
binding while causing the least perturbance to promoter function
[23]. To study the logical gate fidelity among the designed variants,
the synthetic promoter sequences were incorporated in the
reporter vector pGLOW to direct the transcription of GFP. We engineer
the system in an Escherichia Coli strain that constitutively
expresses lactose repressor (LacI) and tetracycline repressor (TetR)
proteins.
The output fluorescence is then dependent on the input of
two small molecule inducers, anhydrotetracycline (aTc) and isopropyl--thiogalactoside
(IPTG). IPTG and aTc interact with LacI and
TetR, respectively, which then free the operator sites for RNAp to
bind and initiate transcription. The simplicity of these designs is
1369-703X/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.bej.2009.06.014

K.I. Ramalingam et al. / Biochemical Engineering Journal 47 (2009) 38–47 39
Functional synthetic modules of six designed promoters were
constructed using standard molecular biology techniques. They
were designed using naturally existing, well-characterized genetic
elements from Tet, Lac and -phage operons differing in relative
positions within the transcriptional unit (Fig. 1; details in
Supplementary material). The architecture was based on the modular
system of Lutz and Bujard [24,26] however differing in the
individual elements used (sequences of lac and tet operators and -
phage promoter). All promoter/operator sequences, transcriptional
start site and the ribosome binding sites are obtained from published
sequences [24]. Two overlapping synthetic oligonucleotides
(∼110 bp each) corresponding to the sequence of each synthetichybrid
promoter were assembled using polymerase chain reaction
(PCR) amplification with outside primers corresponding to the terminal
20 bp of each larger oligonucleotide. After gel purification,
each promoter variant was introduced in the pGLOW-TOPO plasmid
(Invitrogen, Carlsbad, CA) upstream of Cycle 3 GFP for use in in
vivo promoter activity assays. Integrity of the promoter sequences
was confirmed by DNA sequencing and visual verification of constitutive
GFP expression in Top 10 cells (lacI − , tetR − ). Subsequently,
plasmids were transformed into DH5Pro (lacI + , tetR + ) to assess
promoter function in the presence of repressors.
2.2. In vivo promoter activity studies
E. coli strain DH5Pro was used for all in vivo promoter activity
assays in the presence of IPTG and aTc inducers. A promoter-less
pGLOW variant (containing a non-functional DNA fragment) served
as a negative control. Overnight cultures were inoculated 1:100 into
fresh LB medium containing 200 g/mL ampicillin and 50 g/mL
spectinomycin. Inducer concentrations varied from 0 to 2 mM of
IPTG and 0 to 200 ng/mL aTc, resulting in a matrix of 36 different
inducer pair combinations, each of which was monitored for GFP
output over a 24-h period. Specifically, cultures were maintained at
37 ◦ C with shaking (250 rpm). At 3, 6 and 9 h time points samples
were taken and the cells diluted 1:10 to restrict growth to logarithmic
phase and retain constant cellular parameters (e.g., 70 levels).
Samples were monitored for growth state by OD 600 .
2.3. GFP quantification using flow cytometry
Fig. 1. Schematic representation of the synthetic bio-logical AND gates. Promoter
sequence data is available in supplement.
highlighted by the minimal number of regulatory components
required to achieve high-fidelity, robust AND gate functionality.
Prior studies served as a prelude to the construction of “TLT”
first [24], in which a single lacO is inserted between −35 and −10
hexamers, reportedly the most effective operator position. More
recently, Cox et al. [25] presented a powerful, combinatorial method
for quickly generating single promoter motifs with a wide variety
of logical gate phenotypic behavior. The methods presented herein
represent a different design philosophy, though some of the same
promoter designs are ultimately reached. Rather than construct and
screen a large library of putative promoters, we are guided by models
to rationally construct a small number of promoters in a targeted
fashion. Importantly, the modeling approach is general enough that
it is in principle applicable to any gene regulatory network, and this
work serves to validate the approach.
2. Methods and models
2.1. Promoter and plasmid construction, strains
In vivo GFP fluorescence was measured using a Becton Dickinson
FACS Calibur flow cytometer equipped with a 488 nm argon
laser and a 515–545 nm emission filter (FL1) at low flow rate.
Samples were fixed with paraformaldehyde (PFA) to halt GFP production
and degradation after harvesting at each time point. One
milliliter of cell culture was centrifuged to collect the cells, fixed
for 15–30 min in 4% paraformaldehyde (PFA) and re-suspended in
phosphate buffered saline (PBS). For each sample, 100,000 gated
events were collected and analyzed using Cellquest software (BD
Biosciences). GFP fluorescence detected by the FL1 channel was
represented as the mean fluorescence versus the normalized population
distribution after subtraction of background fluorescence.
Background fluorescence was determined using two sets of controls.
First, from non-induced cells harboring functional pGLOW
plasmids and second, from induced cells maintaining a pGLOW
variant with a non-functional promoter sequence. Each of the six
synthetic-hybrid promoter variants was characterized under identical
experimental conditions for comparison of promoter activity
and AND logic gate behavior.
2.4. Kinetic models and parameters
The set of reactions modeling the LTT logical AND gate synthetic
circuit is presented as an example in Table 2. The novelty of the
approach lays with the detailed incorporation of all biomolecular
interactions describing all of the known interaction events in
the transcription, translation, repression, and induction processes.
This reductionist approach results in large, complex reaction networks
that are difficult to simulate. However, although the resulting

40 K.I. Ramalingam et al. / Biochemical Engineering Journal 47 (2009) 38–47
Table 1
Kinetic constants obtained for RNAp displacing
operator-bound LacI in each of the 3 promoters
containing 2 tetO sites (reactions 2 and 3 of Table 2).
System k (L mol −1 s −1 )
LTT 6.23 × 10 5
TLT 4.54 × 10 5
TTL 1.09 × 10 5
models are challenging to solve, the approach is general enough
to be applicable to a wide variety of synthetic gene network constructs,
such as oscillators, bistable switches, tetracycline-inducible
networks among others [19,21,27,28].
More than sixty reactions comprise the network of components
used to simulate the AND gates. Many reactions are reversible, and
these are represented as pairs of irreversible reactions. All reactions
are modeled as initially occurring in a well mixed volume of 10 −15 L
which represents a cell, and each cell is assumed to contain one copy
of the simulated plasmid. That is, the cell contains one “molecule”
of each DNA species. Cell growth is handled by allowing the reaction
volume to double over a period of time (60 min) followed by
an instantaneous halving of volume to represent cytokinesis, thus
matching the log phase growth maintained in the in vivo work.
Each of the 60–70 reactions demands at least one kinetic parameter,
and in some cases (particularly transcriptional or translational
elongation modeled as gamma-distributed random processes), two
parameters. These kinetic parameters can be obtained from literature
directly or reasonably inferred from published thermodynamic
data [29–35]. Indeed, one of the reasons the tetracycline and lactose
operon systems were chosen is that they are exceptionally
well studied, and the kinetic and thermodynamic data necessary
to populate Table 2 are available in the literature.
Initially, in the first round of modeling before we conducted any
experiments we did not account for the leakiness of the promoters.
The simulations revealed a high-fidelity AND gate for all six
promoters. Indeed, in the absence of leakiness all the promoters
with double-tetO (TTL, TLT, LLT) had the exact same behavior. So
did the three promoters with double-lacO. Insupplementary text
we present results of the simulations with the reaction network
without leakiness.
After we conducted the experiments it became clear that leakiness
of the promoters as a function of the position of the lactose
operator(s) relative to the −35 and −10 sequences of the promoter
(promoter topology) is a critical model parameter. It also became
quickly clear that it is unavailable in literature sources. Without
additional kinetic information, the behavior of the models would
depend only on the number of lacO or tetO sites present. That is, all
promoters containing two lacO sites and one tetO site would be considered
equivalent, regardless of topology, as the initial simulation
results suggested. Although the leakiness of promoters with lacO
has been discussed in the literature [24,26], there was no existing
information available to quantify the differences between designs
of equivalent composition (number and type of operator sites) but
differing topology.
To address this issue, two reactions were added in each model,
reactions 2 and 3 of Table 2, to capture the finite probability of
RNAp binding the promoter and initiating transcription by displacing
a bound LacI repressor protein from the promoter (“leakiness”).
As these two reactions essentially represent the same event, they
are constrained to have the same kinetic parameter. This parameter
was then used to fit the model results to the experimental measurements,
producing values for the kinetic constants of these reactions
as explained in supplement and listed in Table 1.
It should also be noted that, while the kinetic constants for reactions
2 and 3 (as well as the levels of LacI and TetR expressed
by the DH5Pro cells in use) were fit to experimental data afterthe-fact
and thus not available a priori, the rest of the model was
constructed before experimental work began. While the absence
of these parameters led to some quantitative error in this initial
round of modeling (see supplementary text), the general viability
of the proposed system was verified in advance of any lab work—a
significant benefit of “model-driven designs”.
Finally, we should note again that although the model is complex,
the approach to build it is not. Indeed we have pursued the
same modeling approach in all of our previous work and recently
we presented and made publicly available a software tool that codifies
this approach so that a user can generate complex reaction
networks of arbitrary synthetic gene network constructs by only
entering interacting components and defining regulatory relations
[36,37]. With the tool, we are also making available all the files for
the AND gate reaction network.
2.5. Algorithms and simulations
The numerical simulations are carried out using the multiscale
simulation algorithm developed in our group [18,20,28,37,38]
rather than by simply solving a system of ordinary differential equations.
This is necessitated by the inherently stochastic nature of
biomolecular interactions [39], the small size of a bacterium, and
the dilute nature of some of the reactants. Indeed, promoter and
operator sites may be present in quantities as small as one copy
per cell, rendering continuous-deterministic models distinctly false
(see Supplementary material for further discussion and a presentation
of the discrete nature of reactions used to model the AND
gates).
Furthermore, the kinetic constants span twenty orders of
magnitude, resulting in a model that is stiff to propagate in
time. Thus, while there is the need to simulate parts of the
network discretely and stochastically, simulating with a simple
kinetic Monte Carlo algorithm would be computationally
intractable. The algorithm developed in our group, dynamically
determines appropriate stochastic-discrete, stochastic-continuous
and deterministic-continuous modeling regimes for each molecular
species and each reaction and uses the appropriate modeling
formalism to numerically propagate the system forward in time.
While computationally efficient, it is also accurate—never generating
negative species populations.
A disadvantage of stochastic simulations is that an ensemble
of simulations must be conducted for meaningful results to be
obtained. In the present case, 1000 trajectories are generated for
each aTc/IPTG pair of concentrations (a grid of 36 pairs), resulting
in 36,000 simulations for each of the six reaction networks.
On the other hand, the time-dependent probability distribution of
species-numbers can only be adequately sampled with stochastic
simulations, providing phenotypic distributions (as in Figs. 2 and 4)
that are directly comparable to experimentally observed variability.
3. Results
We have simulated and experimentally constructed six different
promoters in E. coli combining tetracycline (T) and lactose (L)
operators in the three positions around the promoter −35 and −10
positions (TTL, TLT, LTT, LLT, LTL, TLL). We induced them, both in silico
and in vivo, with 36 different concentrations of IPTG and aTc inducers.
We tested their behavior and evaluated whether they behave
like an AND gate, turning on the expression of GFP downstream if
both IPTG and aTc are present in the culture.
In terms of simulation results, the stochasticity of all biomolecular
interactions comprising the synthetic bio-logical gate, as
detailed in Section 2, results in probability distributions of GFP

K.I. Ramalingam et al. / Biochemical Engineering Journal 47 (2009) 38–47 41
Fig. 2. The stochastic kinetic models pursued in this study generate not only mean steady-state values of GFP expression level, but ensembles of trials—“virtual cells” exhibiting
varied levels of GFP expression. Moreover, these evolve dynamically in time. Histograms for the LTT (a) and TTL (b) systems plot GFP levels versus time for the case of 100 ng/mL
aTc and 1 mM IPTG. The colors of the heat map are assigned based on the log (base-e) of the number of cells per bin (plus one, to avoid taking the log of zero). Lines showing
the mean value (white) and a one standard deviation interval (black dashed) are also included.
concentrations. Fig. 2 depicts the results of two simulated systems,
the LTT (a) and TTL (b) promoters, in the form of a histogram
of GFP levels at different time points for the case of the highest
inducer levels investigated (6 × 10 6 molecules/cell or 1 mM IPTG
and 259 molecules/cell or 200 ng/mL of aTc). The steady-state GFP
expression is at its highest at these inducer concentrations, compared
to all 36 different concentration pairs used. Superimposed on
the histograms are lines representing the mean and a one standard
deviation interval. This figure shows that the distribution of states
does not change significantly between 6 and 9 h, indicating that a
steady-state has been achieved. This is the case for all six systems
simulated, under all inducer concentrations.
Using flow cytometry, probability distributions are measured
experimentally for all six promoters in all 36 inducer pair concentrations
at 3, 6, and 9 h post-induction. A compilation of both
experimental and simulation results at 6 h post-induction are provided
in Fig. 3 in the form of mean GFP level. The color-coded,
two-dimensional surfaces are constructed from the 36 mean GFP
levels at the different IPTG and aTc inducer concentrations. For
example, Fig. 4 presents the model-generated distributions calculated
for the TTL system at a fixed time point (6 h post-induction) at
various inducer concentrations. Using the mean value of each distribution,
corresponding to different aTc–IPTG concentrations, we
construct the three-dimensional plots of GFP as a function of aTc
and IPTG.
More specifically, to compare the simulation with the experimental
results we determine the average number of GFP molecules
per cell at 6 h, averaging over 1000 simulation trajectories, and the
average fluorescence strength at 6 h, averaging over 100,000 cytometry
measurements. The third column of Fig. 3 depicts the square of
the difference between the experimental and simulation values of
mean GFP per cell as evaluated at each point in the aTc–IPTG plane.
Note that only one system containing one tetO site and two lacO
sites is displayed, since the behavior of all three (LLT, LTL, TLL) was
identical (more in Section 4).
As discussed in detail in Section 2, a first round of simulations,
which did not take into account promoter leakiness, showed that
we could expect an AND gate behavior from the promoters we
constructed. The results from these simulations, however, did not
differentiate between the different topologies. In other words, the
simulations of TTL, TLT, and LTT systems gave identical results. So
did the simulations of LLT, LTL, and TLL systems.
In order to ultimately obtain the observed match between simulations
and experiment for each promoter design, the operator
position dependent leakiness had to be taken into account in the
models. Two more reactions were added in the models and the lacO
leakiness reactions (reactions 2 and 3 of Table 2) were fit to experimental
data. The values of the kinetic constants for the leakiness
reactions are shown in Table 1.
Fig. 5 depicts detailed histograms of experimental flow cytometry
data for selected systems (TTL, LTT, and LTL) and induction
conditions, also 6 h post-induction. The simulation data are also
analyzed in terms of the fraction of cells in an ON or OFF state (where
“ON” is defined as greater than 50 molecules of GFP—that is, 5% of
the maximum GFP expression level observed under any conditions:
1015 molecules of GFP observed for an LTT promoter design with
2 mM IPTG and 100 ng/mL of aTc) in Fig. 6.
Since the model is detailed, with each simulated reaction step
corresponding to a real biochemical reaction, a sensitivity analysis
can be undertaken. While there has been no attempt made to
exhaustively analyze the response of the model to all 60–70 parameters,
selected analyses are presented in Fig. 7 (GFP expression
versus repressor generation rates in a fully induced state) and 8
(GFP expression versus leaky initiation rate in the presence of aTc,
both with and without IPTG).
4. Discussion
Let us first focus on the experimental results (first column of
Fig. 3). A high-fidelity bio-logical AND gate will have high GFP
expression levels only at high concentrations of both aTc and IPTG. It
is clear that none of the designed bio-logical gates is of perfect, digital
fidelity. In the double-tetO systems (promoters containing two
tetO sites and one lacO site: LTT, TLT, and TTL) there is always a GFP
signal for non-zero aTc concentrations, even without IPTG present.
This is clearly the result of leakiness of promoters containing the
lactose operator.
Nonetheless, despite the imperfect AND gate phenotype, the
double-tetO systems exhibit varying degrees of AND gate functionality
with no GFP expressed in the absence of inducers and high GFP
levels in response to high inducer concentrations. There is a monotonic
increase of output signal with inducer concentrations at low
aTc and IPTG levels. The output signal strength reaches a plateau
past low IPTG and aTC levels. Increasing the concentration beyond
0.1–1 mM IPTG does not result in significantly stronger fluorescence
signals. In prior reports, the lacO 1 location within a promoter
sequence has been found to significantly impact promoter repressibility,
with a centrally placed lacO 1 in the core promoter region

42 K.I. Ramalingam et al. / Biochemical Engineering Journal 47 (2009) 38–47
Fig. 3. The x and y axes form a grid of 36 pairs of inducer concentrations. The concentrations tested were 0, 1, 10, 50, 100, and 200 ng/mL for aTC and 0, 0.001, 0.002, 0.005,
0.010, 0.100, and 1.000 mM for IPTG (all experimental histograms in Supplementary material). The third column of heat maps shows the square of the difference between
the experiments and the simulations. These four pairs of profiles depict the modeled (left) and observed (center) behavior of four promoter designs: (a) LTT, (b) TLT, (c) TTL,
and (d) LTL. Only one representative promoter with 2-Lac operator elements is depicted, as none of the 2-Lac designs induces to a significant degree. In all cases, with both
experiment and simulation, behavior is depicted 6 h after induction. The plotted model values are the means of 1000 independent stochastic kinetic simulations, whereas
experimental values are the means of 100,000 FACS observations.

K.I. Ramalingam et al. / Biochemical Engineering Journal 47 (2009) 38–47 43
Fig. 4. Model histograms: Conditions are ±100 ng/mL aTc and ±1 mM IPTG, e.g., ± refers to 100 ng/mL aTc and 1 mM IPTG. Here, the profile of the TTL system (a) is examined
in detail at four points as marked by the colored rings. Each of the four points circled by a colored ring in (a) corresponds to the identically colored histogram plot as depicted
in panel (b). These histograms can be compared to the experimental FACS histograms obtained for the TTL system in Fig. 5a (the induction levels are identical). The histograms
produced by the models, however, are free from the noise (dust, dead cell debris, etc.) present in the experimental data at low fluorescence values. This type of comparison
would be impossible using simplified or differential equation models.
Table 2
The complete network of reactions in a synthetic logical AND gate model. As an example the reactions of the LTT system are shown. Source numbers correspond to the
following references: (1) [30], (2) [31], (3) [34], (4) [35], (5) [33], (6) [32], (7) [29].
Number General transcription and translation reactions k Source Number TetR repression, 2nd Tet operator k Source
1 RNAp + lacP + lacO 1 + tetO 1 + tetO 2 → RNAp:lacP 1.00E+07 3 33 tetR2 + tetO 2 → tetR2:tetO 2 10000000 2 a
2 (See below) 34 tetR2:tetO 2 → tetR2 + tetO 2 0.001 2 a
3 (See below) 35 tetR2:aTc + tetO 2 → tetR2:tetO 2:aTc 10000000 6 a
4 RNAp:lacP → RNAp:lacP a 0.01 4 36 tetR2:tetO 2:aTc → tetR2:aTc + tetO 2 1 6 a,b
5 RNAp:lacP → RNAp + lacP + lacO 1 + tetO 1 + tetO 2 1 3 37 tetR2:aTc2 + tetO 2 → tetR2:tetO 2:aTc2 10000000 6 a
6 RNAp:lacP a → lacP + lacO 1 + tetO 1 + tetO 2 + RNAp:DNAc 30 5 38 tetR2:tetO 2:aTc2 → tetR2:aTc2 + tetO 2 100000 6 a,b
7 RNAp:DNAgfp → RNAp + gfp mRNA 30 5 d 39 tetR2:tetO 2 +aTc→ tetR2:tetO 2:aTc 10000000 6 a
8 gfp mRNA + rib → rib:gfp mRNA 100000 e 40 tetR2:tetO 2:aTc → tetR2:tetO 2 + aTc 0.001 6 a
9 rib:gfp mRNA → rib:gfp mRNA 1 + gfp mRNA 33 5 41 tetR2:tetO 2:aTc + aTc → tetR2:tetO 2:aTc2 10000000 6 a
10 rib:gfp mRNA 1 → rib + gfp 33 5 d 42 tetR2:tetO 2:aTc2 → tetR2:tetO 2:aTc + aTc 0.001 6 a
Lad repression at lac operator
Nonspecific DNA interactions
11 lacl4 + lacO 1 → lacl4:lacO 1 2E + 09 1 43 Iacl4 + nsDNA → lacl4:nsDNA 1000 7 a
12 lacl4:lacO 1 → lacl4 + lacO 1 4.00E−04 1 44 lacl4:nsDNA → Iacl4 + nsDNA 0.0041667 7 a
13 Iacl4 + IPTG → lacl4:IPTG 4.60E+06 1 45 lacl4:IPTG + nsDNA → lad4:IPTG:nsDNA 1000 7 a
14 lacl4:IPTG → Iacl4 + IPTG 0.2 1 46 lacl4:IPTG:nsDNA → lacl4:IPTG + nsDNA 0.0041667 7 a
15 lacl4:lacO 1 + IPTG → lacl4:lacO 1:IPTG 1.00E+06 1 47 tetR2 + nsDNA → tetR2:nsDNA 1000 7 a
16 lacl4:lacO 1:IPTG → lacl4:lacO 1 + IPTG 0.8 1 48 tetR2:nsDNA → tetR2 + nsDNA 3.2409 7 a
17 lacl4:IPTG + lacO 1 → lacl4:lacO 1:IPTG 2E+09 1 49 tetR2:aTc + nsDNA → tetR2:aTc:nsDNA 1000 7 a
18 lacl4:lacO 1:IPTG → lacl4:IPTG + lacO 1 0.4 1 50 tetR2:aTc:nsDNA → tetR2:aTc + nsDNA 3.2409 7 a
TetR repression, 1st Tet operator
Degradation and dilution reactions
19 tetR2+aTc→ tetR2:aTc 100000000 6 a 51 →tetR2 1.00E−11 f
20 tetR2:aTc → tetR2 + aTc 0.001 6 a 52 tetR2→ 2.89E−04 f
21 tetR2:aTc + aTc → tetR2:aTc2 100000000 6 a 53 tetR2:aTc → aTc 2.89E−04 f
22 tetR2:aTc2 → tetR2:aTc + aTc 0.001 6 a 54 tetR2:aTc2 → 2aTc 2.89E−04 f
23 tetR2 + tetO 1 → tetR2:tetO 1 100000000 2 a 55 →Iacl4 1.00E−09 f
24 t6lR2:tetO 1 → tetR2 + tetO 1 0.001 2 a 56 Iacl4→ 2.89E−04 f
25 tetR2:aTc + tetO 1 → tetR2tetO 1:aTc 100000000 6 a 57 lacl4:IPTG → IPTG 2.89E−04 f
26 te1R2:tetO 1:aTc → tetR2:aTc + tetO 1 1 6 a,b 58 gfp mRNA → 1.16E−03 e
27 tetR2:aTc2 + tet01 → tetR2:tetO 1:aTc2 100000000 6 a 59 gfp→ 3.21E−05 c
28 tetR2:tetO 1:aTc2 → tetR2:aTc2 + tetO 1 100000 6 a,b 60 lacl4:nsDNA → nsDNA 1.93E−04 g
29 tetR2:tetO 1 +aTc→ tetR2tetO 1:aTc 100000000 6 a 61 lacl4:IPTG:nsDNA → nsDNA + IPTG 1.93E−04 g
30 tetR2:tetO 1:aTc → tetR2:tetO 1 + aTc 0.001 6 a 62 tetR2:aTc:nsDNA + nsDNA + aTc 1.93E−04 g
31 tetR2:tetO 1:aTc + aTc → tetR2:tetO 1:aTc2 100000000 6 a 63 tetR2:nsDNA → nsDNA 1.93E−04 g
32 tetR2:tetO 1:aTc2 → tetR2tetO 1:aTc + aTc 0.001 6 a
Lad/lacO leakiness reactions
2 RNAp + lacP + lacl4:lacO 1 + tetO 1 + tetO 2 → RNAp:
lacP + Iacl4
3 RNAp + lacP + lacl4:lacO 1:IPTG + tetO 1 + tetO 2 → RNAp:
lacP + lacl4:IPTG
6.23E+05
6.23E+05
f
f
a The indicated reference provides affinity data, so the forward rate is assumed and the reverse rate is calculated to match the data.
b The affinities at the two distinct levels of aTc induction (a single aTc molecule or two aTc molecules bound to TetR) are estimated, based on a single literature value.
c This value is based on a 6-h half-life. Effectively, this species does not degrade chemically—rather, the rate of dilution through cell growth is much greater than the
degradation rate.
d This reaction time is gamma-distributed, based on the indicated 1st order constant occurring at each step over a span of 600 nucleotides (200 amino acids).
e This value has been adjusted to give ∼20 polypeptides per mRNA transcript.
f These parameters are fit to experimental data obtained in this study—they are not obtained from previously published sources.
g This “degradation” rate matches the rate of dilution due to cell growth. It is intended to represent dilution of DNA-bound species during DNA replication and cell growth.

44 K.I. Ramalingam et al. / Biochemical Engineering Journal 47 (2009) 38–47
Fig. 5. Experimental histograms: Conditions are ±100 ng/mL aTc and ±1 mM IPTG, e.g., ± refers to 100 ng/mL aTc and 1 mM IPTG. Panel (a) depicts a TTL promoter design
which behaves as a true AND gate. With no inducer, or with aTc or IPTG alone (even at fairly high levels), a singe un-induced population is observed with minimal leakiness.
Only when aTc and IPTG are both present are the cells induced. Panel (b) depicts an LTT promoter design, where the single lac operator site has been moved upstream of the
−35 sequence. In this case, LacI is no longer able to entirely suppress transcription and an intermediate level of induction (leakiness) occurs at conditions of high aTc but no
IPTG. The addition of IPTG fully induces the system at a higher level than that of the TTL system. The promoter examined in panel (c) is of an LTL design, where lac operator
sites have been placed both upstream of the −35 sequence and downstream of the −10. In this case, even high levels of IPTG are unable to induce the system, regardless of
aTc concentration. Models suggest that this design may become feasible if the cells’ intrinsic rate of constitutive LacI synthesis (and hence steady-state LacI concentration)
were lowered. All data is obtained 6 h after induction.
offering the best repression [24]. This trend agrees with the LTT and
TLT systems under investigation, with the latter expressing tighter
control. However with TTL, lacO 1 positioned downstream of −10
hexamer provided greater repression than either the TLT or LTT systems,
an interesting deviation from the observations of Lanzer and
Bujard [24].
The promoters remained tightly repressed under the following
conditions: 0–1 mM IPTG and no aTc and 0–10 ng/mL aTc and no
IPTG, defining the off limit of the switch. Induction was observed
only above 10 ng/mL aTc concentrations, indicating the system’s
transition from an AND gate to single input switch.
Interestingly, the fidelity of the AND gate appears to improve
by moving lacO downstream in the promoter. Although the maximum
amount of GFP expressed under full induction (the plateau
regions) is lower as lacO is moved downstream in the promoter,
the leakiness effect on the fidelity of the AND gate appears to be
attenuated—a trend that is also observed in the model (Fig. 8). To
better understand this effect, the TTL and LTT promoters were investigated
under identical in vivo experimental conditions, producing
the qualitatively different histograms in panels (a) and (b) of Fig. 5.
Under conditions of increasing aTc concentration and IPTG absent,
downstream positioning of lacO in TTL conferred an order of magnitude
tighter control, yielding the best AND gate switch among
the systems investigated. Thus lacO–repressor complex seems to
be performing well at maintaining the regulatable gene circuit in a
repressed state under high aTc concentrations (up to 100 ng/mL),
a condition corresponding to free tetO 2 or increased probability
for recruitment of RNAp to initiate transcription. Consequently TTL
displayed an enhanced aTc induction threshold concentration comparedtoLTTorTLT.
The fuzziness of the AND gate can also be viewed in terms of
phenotypic diversity in response to inducers. Phenotypic variation
as a result of point mutation or altered connectivity in synthetic
circuits has been observed [10–12,16,40]. This study indicates that
variability in logic behavior can be attained through permutations
of operator position within a transcriptional unit.
The double-lacO systems, on the other hand, express almost no
appreciable GFP levels even at the highest inducer concentrations.
This can be explained by relatively high concentrations of LacI constitutively
expressed in the E. coli strain DH5Pro. Given the high
levels of LacI present, even under conditions of strong induction,
most lacO sites remain bound by repressor. For instance, the simulations
of the LTT system – the most active promoter – show that
under conditions of strong induction (6 h after the addition of 1 mM
IPTG), the single lacO site is only free in 6.8% of the cells in the 1000-
cell ensemble. In the rest of the cells it is occupied (0.1% of the cells
Fig. 6. The surfaces represent the fraction of simulated cells that are in an OFF state at 6 h post-induction. Panel (a) is an LTT system, while panel (b) is the TTL system. Here, a
cell is described as “ON” if it is expressing greater than 50 molecules of GFP per cell. This threshold is arbitrarily set at 5% of the absolute maximum GFP expression observed
under any conditions. The “OFF” state is defined as 1 − “ON”. While these panels bear a resemblance to their mean value counterparts in Fig. 3, it should be noted that even
with the more active LTT promoter, not all cells are predicted to induce. Indeed, the lower activity of the TTL design is manifested in a very significant fraction of cells that are
OFF, expressing very low levels of GFP, even in the fully induced plateau region.

K.I. Ramalingam et al. / Biochemical Engineering Journal 47 (2009) 38–47 45
Fig. 7. The heat map depicts the simulated effect of varying the constitutive expression
rates of LacI and TetR on GFP expression levels under conditions of full induction
(1 mM IPTG, 100 mg/mL aTc) in a hypothetical double-tetO system that is free of
leaky expression. At higher levels of repressor expression (upper-right), cellular
concentrations are high enough that even these “full” inducer concentrations are
insufficient to free the operator sites and allow transcription. The tighter binding
of TetR to its operator site, and the fact that there are two such sites, produces the
steeper gradient along the horizontal axis, as compared to the vertical axis. The red
circle at the top of the figure shows the rates employed in the rest of the simulations.
These parameters were chosen with the aid of similar plots evaluated for doublelacO
systems and zero induction conditions (not shown). (For interpretation of the
references to color in this figure legend, the reader is referred to the web version of
the article.)
by LacI alone, 88.3% by LacI:IPTG complex, 4.7% by RNAp closed
complex, and 0.1% by RNAp open complex). Nevertheless, these 6.8%
of cells are sufficient to produce the observed GFP output.
The addition of a second lacO site (in place of a tetO) might
be expected to yield a further 93.2% reduction in the number
of promoters with both lacO sitesfree–atotalof0.5% of cells
(0.0682 = 0.0046) – and this is precisely what is observed. The simulations
for the LTL system show that, under the same conditions
mentioned above, both lacO sites are simultaneously free in only 5
Fig. 8. A sensitivity analysis of the effect of increasing LacI/lacO “leakiness,” whereby
RNAp binds to the promoter, displacing lacO-bound LacI. At lower leakiness rates,
the fully induced (+aTc/+IPTG) level of GFP expression is lower, but leaky expression
(+aTc/−IPTG) is proportionally lower still. The system is evaluated at 6 h postinduction
with 100 mM aTc and (if present) 1 mM IPTG. The three vertical red lines
indicate the observed experimental values listed in Table 1, with the least active
(and least leaky) TTL design at left, the most active (and most leaky) LTT design at
right, and TLT in the center. (For interpretation of the references to color in this figure
legend, the reader is referred to the web version of the article.)
cells of the 1000-cell ensemble, or 0.5% of cells (one lacO site was
free in 10.9% of cells, and neither site was free in 88.6% of cells).
Furthermore, the leakiness reactions employed in the model
(reactions 2 and 3 of Table 2) allow RNAp to dislodge only one
lacO-bound LacI molecule. Therefore, in the case of the double-tetO
systems, all cells are subject to some form of transcription initiation
at all times—either normal initiation at a LacI-free promoter
or leaky initiation at a promoter containing its maximum of one
bound LacI. The double-lacO systems, on the other hand, possess
states at which initiation is strictly forbidden—namely the state in
which neither operator is free (which accounts for 88.6% of cells
in the LTL system, as discussed above). While these double-lacO
designs may still be induced by adding sufficient IPTG, the levels
required are beyond the range that can be employed in the in vivo
work.
Fig. 3 demonstrates that the model captures the experimentally
observed synthetic phenotypes. The fit of the simulated dynamic
behavior of a complex network with more than 60 reactions modeled
stochastically to experimental flow cytometry measurements
is remarkable. The agreement between experimental and simulation
results is quantified in the third column of Fig. 3, where the
square of the difference between mean observed and simulated
GFP expression is presented. The fit between experimental and simulation
results is worst at conditions of low but non-zero aTc and
non-zero IPTG. In this region, the simulations induce more slowly
with increasing aTc than do the experimental results, most likely
due to an inaccuracy in the parameters governing aTc induction.
This is not entirely unexpected, as the kinetic parameters governing
aTc induction are not as well documented as those governing
IPTG induction.
It should also be emphasized that aside from the variation in
the kinetic parameters of reactions 2 and 3 of Table 2, the models
depicted in Fig. 3 are identical in every other respect. This indicates
that, given a model of more than 60 individual reactions, the model
parameter that should depend on promoter configuration is indeed
sufficient to account for the observed variability among the promoter
designs. Since these rates were unavailable in the literature,
they were fit by minimizing the sum-of-squares of relative expression
levels at 3 conditions: no induction, high aTc/no IPTG, and high
aTc/high IPTG. Shifting lacO 1 location within the hybrid tet–lac promoter
changes the values of the kinetic constant for reactions 2 and
3, decreasing these k values with more favorable lacO 1 placement
and consequently improved repression under no IPTG and high aTc
conditions.
The data generated in this study, both simulated and experimentally
observed, ultimately consist of quantifications of the behavior
of individual cells. Although the most straightforward analysis
involves the computation of mean values of cell fluorescence or GFP
expression level, there is also considerable information contained
in the distributions of cell behavior—information that cannot be
obtained through an ordinary differential equation simulation.
For instance, of the 6 systems simulated, the highest GFP expression
level of any cell at 6 h post-induction was 1015 molecules of
GFP (for an LTT promoter design with 2 mM IPTG and 100 ng/mL of
aTc). At the other extreme, zero induction at 6 h, greater than 95%
of cells had exactly zero GFP expression for all 6 systems tested. If
one arbitrarily defines the minimum “ON” state to be ∼5% of the
absolute maximum GFP expression level – 50 molecules per cell,
with “OFF” = 1 − “ON” – then one can analyze the percentage of cells
falling on either side of that threshold. This can help determine the
noise-induced states of the AND gates.
Even with the most active promoter design, LTT, the model predicts
that only 85% of cells are “ON” (>50 molecules of GFP) at
conditions of 1 mM IPTG and 100 ng/mL of aTc at 6 h post-induction,
with 95% of cells expressing between 20 and 296 molecules of GFP.
On the other hand, the TTL design – the least active of the functional

46 K.I. Ramalingam et al. / Biochemical Engineering Journal 47 (2009) 38–47
AND gates – gave only 43% of cells in an “OFF” state (at identical conditions)
with 95% of cells expressing between 6 and 217 molecules
of GFP. Full plots for the simulated fraction of cells in an OFF state
at all induction conditions are provided in Fig. 6. One can further
understand the nature of the distributions with histograms, as is
done in Figs. 2 and 4 (simulation) or Fig. 5 (experiment).
As with the simulation data, the experimental data can also be
viewed as individual cellular measurements. When one applies the
same criterion for a cell being “ON” – i.e., reaching 5% of the absolute
maximum observed fluorescence level at 6 h post-induction – the
results are somewhat different. The real cells, unlike the simulated
ones, tend to induce more uniformly, with 97% of LTT systems “ON”
at conditions of 1 mM IPTG and 100 ng/mL of aTc. As with the simulation,
TTL is less active and fewer cells meet the “ON” criterion –
91% – though this is still a much higher value than the simulations
predict. Therefore, while the model may be able to capture many of
the relevant trends between promoter designs and provide a quantitative
prediction of mean values, there remains work to be done
in predicting the higher moments of the distributions.
The mechanistically detailed nature of the model employed in
this work also provides the opportunity to investigate the effect of
changes in kinetic parameters that correspond to those of real biochemical
reactions. The generation rates of LacI and TetR will be
strain dependent so it may useful to understand how these rates
would affect the behavior of the system. We vary the LacI and TetR
concentrations and determine GFP expression levels. Fig. 7 shows
one of the resulting sets of simulations: a fully induced doubletetO
design—in this case with k 2 and k 3 set to zero. As expected,
GFP expression is low at higher repressor generation rates (upperright)
but high at lower rates (lower-left). The gradient is also much
steeper with increasing TetR than with increasing LacI, reflecting
the tighter binding of TetR and the presence of two tetO operator
sites rather than one lacO site. The red circle at the top of the figure
indicates the rates employed for all other simulations in this study.
These parameters were chosen with the aid of similar plots evaluated
for double-lacO systems and zero induction conditions (data
not shown).
The level of GFP expression is depicted in Fig. 8 as a function
of the leaky transcription initiation rate (at high aTc values), with
lower k 2 and k 3 (i.e., k leak ) values producing gates that express less
GFP overall, but where the amount of leaky expression is proportionally
low compared to the level of fully induced expression. This
trend correlates with in vivo observation as discussed previously. As
the rate of leaky initiation increases, the amount of GFP expressed
ceases to have a strong dependence on the presence or absence of
IPTG, as one might expect. At suitably low and commonly employed
aTc concentrations (example 10 ng/mL), however, all three systems
display AND gate functionality. Interestingly, similar leakiness reactions
were not necessary for the tetracycline operator sites. That
is, the probability of RNAp binding and transcribing DNA that is
already bound by TetR is negligible, though this probability is further
reduced by the presence of two TetR sites in each of the three
functional gates.
While all three double-tetO synthetic circuits can be considered
AND gates over some range of inducer concentrations, we observe
that knowledge of operator placement in the promoter is critical for
optimal AND gate behavior. Since the three promoters represent all
possible placements of a single lacO within a three-operator hybrid
promoter, and rates of kinetic leakiness have been obtained in each
case, these results foster meaningful predictions for subsequent
work.
In summary, we show how the integration of computational
and experimental molecular biology can rationalize the synthesis
of novel biological functionalities. We have constructed a biological
AND gate from a simple, synthetic-hybrid promoter module.
From a biological perspective, experimental results identify an
effective lacO 1 position where improved repression results due
to weak interaction between RNAp and operator-bound repressor.
We propose that this interaction plays a vital role in transcriptional
regulation as supported by the matching between models
and experiments over a wide range of induction conditions, having
taken into account the inherently stochastic behavior of the
systems. Reactions 2 and 3 and their kinetic constants quantify this
biological behavior for the first time and should prove useful in constructing
further stochastic kinetic models that involve repression
by LacI.
The models created to study this system predict the system’s
feasibility, quantify the effect of operator placement and provide
an understanding of the improved AND gate function demonstrated
by TTL. Certainly, there is not one single, direct method of conducting
simulations that precisely outlines future experimental designs.
Instead, there is an intimate interplay between simulations and
experiments, where information flows back and forth between both
computational attempts and experimental ones. In this work, the
first models constructed did not include promoter topology dependent
leakiness. Nevertheless, they were useful in demonstrating
that the designs were promising and would likely work as planned.
After the first set of experiments, it became clear that reactions
2 and 3 were required, and that different values for the kinetic
parameters would lead to correlation with the designed promoters.
What was gained was insight into the mechanism of leakiness
and a model that quantitatively captures it. It is not clear how this
biological insight would be captured with an a posteriori modeling
effort, where minimal models are built to fit observed experimental
data.
In conclusion, we believe that this approach of designing and
tailoring logical regulation of gene expression can be potentially
extended beyond transcriptional regulation to include other modular
genetic elements, search for more complex network behaviors
and assist in the forward engineering of other biological circuits.
Acknowledgements
This work was supported by a grant from the National Science
Foundation (BES-0425882, CBET-0425882 and CBET-0644792) and
the University of Minnesota Biotechnology Institute. Computational
support from the Minnesota Supercomputing Institute (MSI)
is gratefully acknowledged. This work was also supported by the
National Computational Science Alliance under TG-MCA04N033. In
addition, we would like to thank Jin Cui Tomshine for her preparation
of the schematic diagrams in Fig. 1.
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at doi:10.1016/j.bej.2009.06.014.
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