Communication

Programming Microbes Using Pulse Width
Modulation of Optical Signals

Eric A. Davidson 1 , Amar S. Basu 2 and Travis S. Bayer 1
1 - Centre for Synthetic Biology and Innovation and Division of Molecular Biosciences, Imperial College London,
London SW7 2AZ, UK
2 - Department of Electrical Engineering, Wayne State University, Detroit, MI 48202, USA

Correspondence to Travis S. Bayer: Department of Biochemistry, University of Oxford, South Parks Road, Oxford
OX1 3QU, UK. travis.bayer@oriel.ox.ac.uk
http://dx.doi.org/10.1016/j.jmb.2013.07.036
Edited by M. Gottesman

Abstract
Cells transmit and receive information via signalling pathways. A number of studies have revealed that
information is encoded in the temporal dynamics of these pathways and has highlighted how pathwayarchitecture can influence the propagation of signals in time and space. The functional properties of pathwayarchitecture can also be exploited by synthetic biologists to enable precise control of cellular physiology. Here,we characterised the response of a bacterial light-responsive, two-component system to oscillating signals ofvarying frequencies. We found that the system acted as a low-pass filter, able to respond to low-frequency
oscillations and unable to respond to high-frequency oscillations. We then demonstrate that the low-passfiltering behavior can be exploited to enable precise control of gene expression using a strategy termed pulse
width modulation (PWM). PWM is a common strategy used in electronics for information encoding thatconverts a series of digital input signals to an analog response. We further show how the PWM strategy
extends the utility of bacterial optogenetic control, allowing the fine-tuning of expression levels, programmingof temporal dynamics, and control of microbial physiology via manipulation of a metabolic enzyme.
© 2013 The Authors. Published by Elsevier Ltd. All rights reserved.

Cells have evolved signal transduction pathways
to fine-tune metabolic and physiological processes
according to environmental conditions [1]. Many
biological systems use temporal encoding of signals
to propagate information, much like human engineered communication systems. Living organisms
are composed of interconnected signalling networks
that coordinate functions such as stress response,
metabolism, cell cycle, and inflammation. These
networks are composed of architectural motifs thathave dynamic modulatory properties, including
filtering of signals, oscillations, and hysteresis [2].
Given the importance of signal dynamics on
biological function, precise control of gene expression
is critical for living cells and for many applications in
genetic engineering, where robust and predictive
specification of protein levels is required to build andanalyse complex systems [3]. Furthermore, strategies
for easily programming signal perturbations allow for

the mechanisms of how signal transduction pathwayarchitectures respond to and modulate dynamicallychanging signals. From a bioengineering point ofview, an ideal control strategy would allow rational,
rapid tuning of expression over a range of levels andwould allow for the kinetics of induction and repressionof expression to be dictated experimentally. Optogenetic systems, in which gene expression is controlledby specific wavelengths of light via light-responsive
receptors, are powerful tools for encoding spatial
control of biological systems and have been used tomanipulate neuron function, cell motility, and patternformation [4–7].
Here, we sought to extend the usefulness andflexibility of a green-light-inducible system in
Escherichia coli based on a two-component systemfrom cyanobacteria (Fig. 1a) [8,9]. In the presence ofgreen light, the histidine kinase ccaS phosphorylates
the response regulator ccaR, increasing transcription

0022-2836/$ - see front matter © 2013 The Authors. Published by Elsevier Ltd. All rights reserved.

J. Mol. Biol. (2013) 425, 4161–4166

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(a)

Microbes and Pulse Width Modulation

(b)

(c)

(d)

(e)

Fig. 1. PWM of optical signals allows graded control of gene expression. (a) An engineered hardware and genetic systemfor perturbing gene expression. A computer-controlled 8 × 12 array of dual (red and green) LEDs illuminates a 96-well,clear-bottom microplate. Red and green light from the LEDs is used to control the ccaS/ccaR two-component signaltransduction pathway. Green light activates ccaS, increasing transcription of the GFP gene, while red light inhibits ccaS,
decreasing transcription of the GFP gene. (b) The optogenetic system shows a sharp transition between repressed andinduced states in response to input signal intensity. Light intensity is represented as a percentage of maximal LED intensity(approximately 30 W/m 2), with increasing red light intensity denoted by increasingly negative values for visualisation. (c) The
GFP output of the system tracks input optical signal at low frequencies, but not at high frequencies. The pattern of applied lightis represented within each graph in green and red. From left to right, cells were induced with oscillating green and red signals
with a frequency equal to 0.0083 min −1, 0.017 min −1, 0.033 min −1, and 0.1 min −1 and with a duty cycle of 0.25. (d) The
relationship between input frequency and output amplitude indicates a low-pass filtering effect. The amplitude of oscillation is
calculated as the difference between the maximal and minimal fluorescence values observed in (c), where 1.0 is the maximum
difference between fully induced (green light) and fully repressed (red light) states. The frequency value for the 0.0014 min −1
data point (shown in red) is calculated based on a duty cycle of 0.25 and ~180 min required to transition from fully repressed to
fully induced and represents the maximum amplitude. (e) System output shows a dependence on the duty cycle of oscillating
input signals, allowing tuning along the entire range of expression. An oscillating square wave at a frequency of 0.1 min −1 wasapplied to cells. For all graphs, connecting lines are visual guides; gene expression points are an average of at least three
independent GFP fluorescence measurements scaled from repressed (0.0) to induced (1.0) to show progression from “off” to“on” states; error bars are standard deviations.

of the reporter gene by approximately 2-fold (Supplementary Fig. 1). Red light inhibits this process,decreasing transcription. We developed an optical

microtiter plate consisting of light emitting diodes(LEDs) corresponding to the induction and repression
wavelengths of the cyanobacterial system (design

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Microbes and Pulse Width Modulationand construction detailed in Supplementary Information and Supplementary Fig. 2). The optical microtiterplate is computer controlled, allowing automatedmanipulation of optical signals over time. Each well
can be programmed independently to enable ahigh-throughput workflow.
We first characterised the signal response of the
optogenetic system by varying red and green lightintensity in each well. The system shows repression
under red light and induction under green light, withan extremely sharp transition between the two states(Fig. 1b). This is not optimal as a control strategy, asintermediate levels of gene expression are difficult toaccess by manipulating signal intensity.
Transforming a sharp response to a graded
response is conceptually analogous to the conversion
between digital and analog information in electronics. A
common strategy to perform digital-to-analog conversion in control of electronic devices is pulse widthmodulation (PWM) [10,11]. PWM controls the power toa device by switching the supplied voltage on and off at
rapid rates. The duty cycle (the fraction of time thevoltage is on) determines the average power of thesystem. Given that duty cycle can be controlled
digitally, PWM provides precise, linear control of thetime-averaged power (an analog output). While PWM
is widely used in electronics, it has not been used tocontrol biological systems. Here, duty cycle represents
the fraction of a wave period in which the LED is shining
green light at maximum intensity, with the remainder ofthe period at maximum intensity red. The implemen-

(a)

(b)

tation of a PWM control strategy requires that switching
between on and off signals occur more rapidly than thesystem can respond so that the system “averages” thepulse signal input to return an output. To examine thesuitability of the optogenetic system for PWM control,
we characterised the response to periodic input signals
at varying frequencies (Fig. 1c). At low frequencies(less than 0.03 min −1), the system tracked the input
with a delay, resulting in an oscillation of output
expression. At high frequencies, the system is unable
to track the input signal. The magnitude of theoscillation amplitude is plotted against the signal
frequency in Fig. 1d. The signal transduction systemacts as a low-pass filter that attenuates input signals
when the frequency is high and “passes” the input
when the frequency is low.
At high input signal frequencies, the system cannot
respond fast enough to track input signals for induction
and repression, which is ideal for PWM control. We
next examined the response of the system to varying
duty cycle at high frequency (frequency = 0.1 min −1).
Reporter gene expression shows a graded response
to duty cycle variation, allowing access to expression
levels between the minimum and maximum states(Fig. 1e). This is a graded response at the single celllevel, which is evident from flow cytometer assays ofreporter gene expression (Supplementary Fig. 3).
The dynamics of gene expression in response toenvironmental and cellular stimuli are known to play
an important role in biological regulation and adaptation [12]. In the mammalian NF-κB signalling pathway,(c)Fig. 2. Programming temporal dynamics of gene expression. Gene expression was programmed for slow (triangle),
moderate (diamond), or rapid with overshoot (square) induction profiles, each targeted to three different final expression levels[low expression (a), medium expression (b), and high expression (c)]. Graph legends (below) show the induction/repression
pattern for each gene expression curve. Green-filled blocks denote green-light induction; red-filled blocks denote red-light
repression; alternating green/red are duty cycle induction [where duty cycle equals 0.1 for (a), 0.2 for (b), and 0.3 for (c), all at afrequency of 0.1 min −1]. For all graphs, connecting lines are visual guides; red broken lines are visual guides indicating thetarget gene expression level; gene expression points are an average of at least three independent GFP fluorescencemeasurements scaled from repressed (0.0) to induced (1.0) to show progression from “off” to “on” states; error bars are
standard deviations.

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Microbes and Pulse Width Modulationfor example, different inflammatory stimuli induce
distinct patterns of NF-κB activity [13,14]. The
properties of these patterns include the rate of increase and decrease of expression, the “overshoot”
kinetics, and the delay of induction or repression after a
stimulus is applied. Experimental tuning of theseproperties is difficult to achieve with conventional
inducible promoters, which has limited the understanding of how signals are propagated and “interpreted” bycellular networks. For example, it would be useful tocharacterise the biological effects of inducing gene
expression at different initial rates that reach the samesteady-state value. This would allow experimental testsof the relative contribution of the parameters of
temporal dynamics on cellular signalling, metabolism,
and physiology. Dynamic input–output studies of
biological systems are valuable for revealing genetic
network structure, parameters, and robustness [15–17].
We next sought to manipulate the dynamics of gene
expression and to independently program temporal
properties using a series of tailored pulsed signals. We
tested whether the time to reach a target steady-statevalue could be tuned. Using experimentally derived
parameters for the duty cycle transfer function (Fig. 1e)and the temporal induction and repression curves(Supplementary Fig. 4), we developed simple protocols programming gene expression to progress
towards a pre-set steady-state value by three distinct
induction profiles: slow, moderate, and rapid withovershoot. The program for a slow approach transitions directly from a repressed state (duty cycle = 0.0)
to the final duty cycle. The program for a moderate
approach applies maximal induction (duty cycle = 1.0)

(a)

(b)

until 20 min prior to the time at which the desired final
gene expression level is reached under maximal
induction. The induction is then changed to the final
state duty cycle to hold gene expression at the desired
value. A rapid approach with overshoot is programmedusing maximal induction (duty cycle = 1.0) until 20 min
past the point at which the desired gene expression
level was reached. At this point, transcription isrepressed (duty cycle = 0.0) for 20 min and then the
final state duty cycle is applied, causing the final gene
expression level to be approached from above. These
protocols were applied successfully to three different
final gene expression levels (corresponding to duty
cycles of 0.1, 0.2, and 0.3; Fig. 2a–c), demonstratingthat a range of expression values and temporal
dynamics can be accessed using this control scheme.
In addition, a wide range of signal frequencies can beused to control gene expression using PWM (Supplementary Fig. 5).
The ability to precisely manipulate gene expression
levels and dynamics is a powerful tool to perturb
cellular metabolism and physiology. To further test
PWM as a control methodology, we constructed agenetic system to place an E. coli metabolic pathway
under the control of the optogenetic system. Light is an
ideal tool to manipulate bacterial physiology, as it canbe reversibly applied to a culture without physically
perturbing the cells. We cloned the metE gene into the
optogenetic system (Fig. 3a). metE is a methyltransferase involved in methionine biosynthesis and is an
essential gene for growth in media lacking methionine.
Thus, we predict that the growth rate of bacteria inculture media lacking methionine will be dependent on
metE expression level. We introduced this construct(c)Fig. 3. Control of bacterial growth rate by PWM of a metabolic protein. (a) The E. coli methyltransferase metE wasplaced under control of the optogenetic system and transformed into a metE genomic deletion strain that does not grow in
the absence of methionine (Supplementary Fig. 6). (b) Growth curves of the optically controlled metE strain in media
lacking methionine, subjected to varying duty cycles of light perturbation. The red line indicates full repression of thesystem while the green line indicates full induction. Grey lines indicate cultures subjected to varying duty cycles, from 0.1
to 0.8. All lines represent absorbance averages for three independent cultures. (c) Growth rate is dependent on duty cycle
applied, showing a graded increase in rate with higher duty cycle. Growth rate is calculated as described in the methods
section. Growth rate data are averages from three independent growth rate calculations; error bars are standard
deviations.

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Microbes and Pulse Width Modulation

into a strain with a genomic metE deletion and controlled expression by varying the duty cycle of green
and red light pulses. Engineered strains showed
growth rates proportional to duty cycle applied (Fig. 3b
and c), demonstrating that the PWM strategy can beused to control bacterial metabolism. A control strain
expressing GFP (green fluorescent protein) rather thanmetE showed no growth in the absence of methionine,while the wild-type strain showed no growth response
to light (Supplementary Fig. 6). The growth rates ofengineered cultures at high duty cycles are similar tothat of the wild-type strain, indicating that a wide rangeof growth rates can be achieved (Supplementary Fig.
6). We also note that the transfer function of thedependence of growth rate on duty cycle closely
matches the GFP–duty cycle curve (Fig. 1e), indicating a reliable dose–response curve for both thefluorescent reporter and a metabolic output.
The interface between electronic and biologicalsystems is a promising area with the potential todevelop tools for probing living cells and to deliver novel
applications. We have demonstrated that a control
strategy from electronics, along with genetic andhardware engineering, is a viable methodology for
programming gene expression levels, temporal dynamics, and cell physiology. We anticipate that PWM
can be used in analogous biological systems, bothbacterial and eukaryotic, where signal input canbe rapidly switched relative to the system response
and output, which likely encompasses a large classof electronic–biological interfaces. For example, thehigh-osmolarity sensing pathway in Saccharomyces
cerevisiae is known to function as a low-pass filter andtherefore should be amenable to analog control
through PWM [18]. Given the transformative impact ofdigital information processing in electronics and communications, strategies to control biology using similar
principles could enable a step change in synthetic
biology.

Acknowledgements
We thank John Heap, Oliver Windram, Diego
Oyarzun, and Jeff Tabor for helpful discussions. We
thank Jeff Tabor and J. Clark Lagarias for providing
plasmids. This work was supported by Engineeringand Physical Sciences Research Council grant EP/
G036004/1.
Author Contributions: E.A.D. and T.S.B. conceived and designed experiments. A.S.B. designed
and constructed the optical microtiter plate and wrote
the control software. E.A.D. performed experiments
and analyzed data. E.A.D., A.S.B., and T.S.B. wrote
the paper.
Conflict of Interest: The authors declare that they
have no conflict of interest.

Appendix A. Supplementary data
Supplementary data to this article can be foundonline at http://dx.doi.org/10.1016/j.jmb.2013.07.036.
Received 30 May 2013;
Received in revised form 21 June 2013;
Accepted 21 July 2013
Available online 6 August 2013
Keywords:
low-pass filter;
optogenetics;
pulse width modulation;
signal transduction
This is an open-access article distributed under the terms of theCreative Commons Attribution–Noncommercial–No Derivative
Works License, which permits non–commercial use, distribution,and reproduction in any medium, provided the original author andsource are credited.

Abbreviations used:
PWM, pulse width modulation; LED, light emitting diode.

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