Marching along to an Offbeat Drum: Entrainment of Synthetic Gene

Nov 2, 2015 - Stochastic simulation of an associated model further supports that the ... of a Bacterial Synthetic Gene Oscillator through Proteolytic ...
0 downloads 0 Views 3MB Size
Download PDF
Research Article pubs.acs.org/synthbio

Marching along to an Offbeat Drum: Entrainment of Synthetic Gene Oscillators by a Noisy Stimulus Nicholas C. Butzin,† Philip Hochendoner,† Curtis T. Ogle,† Paul Hill,† and William H. Mather*,†,‡ †

Department of Physics and ‡Deptartment of Biology, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, United States S Supporting Information *

ABSTRACT: Modulation of biological oscillations by stimuli lies at the root of many phenomena, including maintenance of circadian rhythms, propagation of neural signals, and somitogenesis. While it is well established that regular periodic modulation can entrain an oscillator, an aperiodic (noisy) modulation can also robustly entrain oscillations. This latter scenario may describe, for instance, the effect of irregular weather patterns on circadian rhythms, or why irregular neural stimuli can still reliably transmit information. A synthetic gene oscillator approach has already proven to be useful in understanding the entrainment of biological oscillators by periodic signaling, mimicking the entrainment of a number of noisy oscillating systems. We similarly seek to use synthetic biology as a platform to understand how aperiodic signals can strongly correlate the behavior of cells. This study should lead to a deeper understanding of how fluctuations in our environment and even within our body may promote substantial synchrony among our cells. Specifically, we investigate experimentally and theoretically the entrainment of a synthetic gene oscillator in E. coli by a noisy stimulus. This phenomenon was experimentally studied and verified by a combination of microfluidics and microscopy using the real synthetic circuit. Stochastic simulation of an associated model further supports that the synthetic gene oscillator can be strongly entrained by aperiodic signals, especially telegraph noise. Finally, widespread applicability of aperiodic entrainment beyond the synthetic gene oscillator is supported by results derived from both a model for a natural oscillator in D. discoideum and a model for predator−prey oscillations. KEYWORDS: oscillators, entrainment, synthetic biology, systems biology, aperiodic signal, random signal

F

(noisy) component, and it has long been known that aperiodic signals can strongly entrain systems to a common behavior, e.g. in the stimulation of independent neurons,10 in the random forcing of material particles,11 or more abstractly in the theory of random iterated maps.12 Oscillator entrainment via noisy signaling has also been well-documented and simulated in physics journals.13−15 Such synchronous behavior in the context of biological systems may produce an amplified response that would otherwise not occur in asynchronous populations, greatly increasing the chance of otherwise rare events. The phenomenon of aperiodic entrainment has rarely been studied in living cells. Other than entrainment of neurons by an aperiodic signal,10,16,17 we are unaware of other biological examples in the literature with experimental support. We speculate that this situation is likely due to the difficulty of executing such experiments, or perhaps due to the concept of aperiodic entrainment being largely confined to disciplines outside of traditional biology. Regardless, we would like to highlight the relevance of this phenomenon in biological systems. In our work, we leveraged a synthetic biology approach to understanding the aperiodic entrainment of biological systems,

rom bacteria to humans, most organisms use molecular clocks to synchronize their physiology and behavior to stimuli from their environment.1 Synchronization was characterized in the 1600s by Huygens; the swinging motions of pendulum clocks were synchronized through tiny back-andforth vibrations in a wooden beam.2 Entrainment is a specific type of synchronization where an external signal leads to the bulk of oscillators in a population collectively agreeing to a common oscillatory period and phase. In humans, we use an internal clock (linked to a rhythm in gene expression) called circadian rhythm to follow the day and night cycle. This internal clock is not perfect, which can result in irregular sleep schedules. The internal clock is readjusted (entrained) by comparing its internal time to the light from the Sun.1,3 Many biological systems have been shown to be entrained by periodic signals: insulin secretion from islets of Langerhans,4 swimming of Halobacterium halobium by light and temperature signals,5 cellcycle of unicellular phytoplankton by nutrient signals,6 and rat and mice digestive system by periodic feeding,7 to mention a few (for more biological examples, see review article1). Periodic entrainment has also been predicted in silico for predator−prey systems.8,9 Periodic signals have been intensively studied in this regard, but many, if not most, natural signals contain a strong aperiodic © 2015 American Chemical Society

Received: July 15, 2015 Published: November 2, 2015 146

DOI: 10.1021/acssynbio.5b00127 ACS Synth. Biol. 2016, 5, 146−153

Research Article

ACS Synthetic Biology

Figure 1. Entrainment of a robust synthetic oscillator by an aperiodic signal. (A) Schematic view of the synthetic gene oscillator considered in this work. The synthetic oscillator is believed to have at its core a delayed negative feedback, while positive feedback tunes the circuit and can make the system more robust.19 (B) Detailed view of the synthetic oscillator. Three genes (araC, lacI, and yemGFP) are under control of the Plac/ara‑1 promoter. LacI and AraC are controlled by IPTG and arabinose, respectively, and establish negative and positive feedback loops, respectively. Each protein was engineered with an LAA-tag, which targets the resulting protein for degradation by the ClpXP protease. (C) The system in panel (B) can be entrained by an externally controlled arabinose concentration (drive signal).18 Pictured is a sinusoidal arabinose drive signal with period 15 min, 0.5% arabinose amplitude (defined as the difference between maximum and minimum signal), and a mean value 0.5% arabinose. (D) Other drive signals may lead to distinct behavior. Pictured is a telegraph noise signal with the same mean period, amplitude, and mean value as the sinusoidal drive in panel (C). A mixture of long and short plateaus in the drive signal is evident. The random distribution of time scales in the drive signal can lead to strong synchrony in an ensemble of oscillators.

loops and produces green fluorescent protein (GFP) as an indicator of the circuit state. The synthetic gene circuit consists of three genes (gf p, lacI, and araC) under control of the Plac/ara‑1 hybrid promoter.22 LacI in the absence of IPTG represses the promoter, while AraC in the presence of arabinose activates the promoter. Thus, the addition of IPTG represses LacI’s ability to inhibit transcription of all three genes, and moderate to high levels of arabinose allow AraC to activate transcription of all three genes, resulting in tunable negative and positive feedback loops, respectively. Each protein was engineered with an LAAtag (TS-linker AANDENYALAA), which targets the resulting protein for rapid degradation by the ClpXP protease. These proteins compete for degradation by ClpXP,19,23−25 which previously has been leveraged to post-translationally control the oscillator.26 We verified the possibility of aperiodic entrainment for the synthetic oscillator using a series of experiments that combined microfluidics and microscopy techniques with synthetic circuits in E. coli. As in a previous study,18 we pursued entrainment using a time-dependent arabinose concentration that can influence the circuit. A variety of different arabinose signals were considered, including sinusoidal signals (Figure 1C) and telegraph noise (Figure 1D). Other signals were considered (see Figure S1 and

using a strategy that has already been proven useful in understanding the entrainment of oscillators by periodic signaling.18 A synthetic gene oscillator in the organism E. coli19 served as an experimental model for a number of noisy oscillating systems, such as cell cycles20 and NFkB response.21 We first demonstrated with in vivo experiments that cells containing the oscillator circuit can be entrained by aperiodic signals. We then analyzed stochastic simulations of a quantitative model for this synthetic gene oscillator, which agreed with our observation that the experimental oscillator would be strongly entrained by aperiodic signals, especially telegraph noise. Finally, we tested the generalizability of these ideas to naturally occurring oscillators using in silico models for cAMP oscillations in D. discoideum and predator−prey oscillations as examples.

■

RESULTS AND DISCUSSION In vivo experiments show that synthetic gene oscillators are entrained by aperiodic signals. A previously developed synthetic oscillator19 (Figure 1A,B) has been shown to be entrained using a periodic sinusoidal signal for the arabinose concentration18 (Figure 1C). The synthetic oscillator contains coupled positive- and negative-feedback 147

DOI: 10.1021/acssynbio.5b00127 ACS Synth. Biol. 2016, 5, 146−153

Research Article

ACS Synthetic Biology

Figure 2. Synthetic oscillator driven by signals with varied periods and amplitudes. (A) The experimental synthetic oscillator can be strongly perturbed by a noisy drive signal. (Top) A coherent response of oscillators producing GFP when driven by noisy telegraph signals. Images from two different times are displayed, representing the trough and peak of mean GFP fluorescence in the microfluidic trap. The fluorescence output of GFP is indicated by green. (Middle) The drive signal for arabinose concentration was monitored by sulforhodamine 101, a red fluorescent dye, present only in the inducing medium. The red line indicates the rescaled median fluorescence of sulforhodamine 101 across a number of different locations on the microfluidic device (individual samples shown as gray lines), while the blue line indicates the desired signal sent to the microfluidic device by the controller computer. (Bottom) GFP response (filtered GFP signal, see Methods) for 4 microfluidic traps (individual trap responses shown as gray lines), with the median of these responses indicated by a red line. The times for the images at the top of the panel are indicated by dashed lines in the middle and bottom plots. (B) A single long experiment entrained cells containing the synthetic oscillator using a variety of different signals (telegraph noise and essentially sinusoidal signal) with various periods and amplitudes (see Table S1 and Videos S1−S2). As in panel (A), the red line indicates rescaled dye fluorescence, while the blue line indicates the intended drive signal. Light blue boxes indicate regions of measurement for the various signals, with a unique index for each signal appearing above each box (see Table S1 for indices). (C) The mean experimental value for the GFP response due to the signal in (B) is indicated by a red line. A model was fit to this data, and its response is indicated by a blue line, showing overall good agreement with the experiment. Measurement regions corresponding to those in panel (B) are shown. (D) Oscillators responded strongly to both periodic and aperiodic signaling. The standard deviations (across time) of the experimental and theoretical GFP mean values (across oscillators at a given time) in panel (C) were calculated to estimate response. The response to telegraph noise (indices 1−9) shows a strong response, comparable to or greater than the estimated response for drive signals that are more periodic (indices 10−14). (E) Using the fitted model that exhibits a mean period of about 35 min, we can rapidly scan different drive signals. The response of the model is defined by first calculating the mean mature GFP of all oscillators, and then calculating the standard deviation of this mean statistic across time. Oscillators without a drive signal still produce a baseline response due to statistical error (see dashed line). Strong response of the oscillators to periodic drive (blue line) occurs near resonance (the mean drive period is simply the period in this case) but is weaker for shorter period drive signals. A strong response to telegraph noise (green dots, with a smoothed red trendline) occurs uniformly for a variety of mean drive periods. Notice that spurious response for a large mean drive period can occur due to slow modulation of the amplitude of oscillators.

related discussion in the SI Methods), but sinusoidal and telegraph signals appear to sufficiently address the needs of our study. Our microfluidic device (Figure S2) allowed us to drive a controlled chemical signal across thousands of trapped cells expressing the synthetic gene oscillator, with experiments often running for days. For our signal to the cells, we kept constant the amount of IPTG at 2 mM for all experiments, but we varied the concentration of arabinose between 0% and 1% as a function of time. Each microfluidic trap in our experiments sensed this common arabinose signal. We measured the fluorescence of the protein GFP as a proxy for circuit response to signal. Since we

anticipated that our approach will be of interest to biologists using population-averaged measurements, quantitative metrics for entrainment were based on the time-dependent mean fluorescence of GFP in a microfluidic trap (see the SI Methods), which effectively averages the response of over a thousand cells per trap. Experiments reveal that cells were strongly entrained by a number of different signals (Figure 2A−D, Videos S1−S3), including by aperiodic signals and by periodic sine waves (see Table S1 for an outline of signals, and Supporting Information Figure 2_Drive_Signal.csv for the particular drive signal used in Figure 2A−D and Videos S1−S2). The response of cells was 148

DOI: 10.1021/acssynbio.5b00127 ACS Synth. Biol. 2016, 5, 146−153

Research Article

ACS Synthetic Biology

Figure 3. D. discoideum CAR1 receptor entrainment: a computational example of the importance of aperiodic signals to natural biological systems. (A) An adapted model for cAMP oscillations in D. discoideum is used to investigate how a natural system responds to aperiodic external signal.30 The cAMP oscillations require three components: CAR receptor stimulation, activation and adaptation of adenylyl cyclase (ACA), and the degradation of both the intracellular and extracellular pools of cAMP. There are four CAR receptors, but CAR1 has the highest affinity for cAMP.32 Thus, we focused our efforts on CAR1. Normally, distinct cells can synchronously oscillate by sharing a common pool of externalized cAMP, which activates the internal species CAR1 and is produced by the internal species ACA. A large portion of this oscillator network is not depicted here. (B) Single oscillators were entrained by producing additional cAMP in the external environment. The purple line shows a representative telegraph drive signal for cAMP production, with mean period 3.0 min, mean value 30.0 min−1, and minimum value zero. Corresponding sinusoidal signals are also used with given period, mean value, and minimum value of zero. (C) Strong response (in the same sense as Figure 2E) of CAR1 is found for telegraph noise (response in red) with a mean period (labeled tau) of 3.0 min, far below the natural period of the oscillator (about 7 min.). Response to sinusoidal drive is minimal for a sinusoidal drive with period 3.0 min (response in blue). Both of these responses were significant relative to oscillators with a constant drive with the same mean value (response in black). (D) Similarly as in Figure 2E, the response (standard deviation over time of the ensemble mean) of CAR1 was calculated for different values of the drive signal mean period. While the system does not respond to telegraph noise as well as sinusoidal driving near resonance (approximately a mean drive period of 7.0 min), telegraph noise strongly affects the system for a wide range of mean periods. The standard deviation was taken across the mean value of CAR1, measured from time t = 100 min to t = 1000 min. The ensemble size for each measurement is 1008.

determined. Stochastic simulations of the in silico model consistently predicted that the synthetic gene oscillator would be strongly entrained by aperiodic signals. Specifically, we often found that telegraph noise (Figure 1D) produced a strong response. To attempt to explain our particular experimental results, the model was fit to the experimental results via an automated algorithm that minimizes the difference between experimental and theoretical mean (across the ensemble of oscillators) GFP fluorescence, with each being a function of time. The model and experiment appeared to be consistent with one another after fitting was performed (Figure 2C, D). Parameter scans over different values for the signal’s mean period suggest that an aperiodic signal can entrain ensembles of oscillators to a common behavior as well as or stronger than a periodic signal (Figure 2E). Oscillator response in these investigations was quantified by measuring the standard deviation (across time) of the mean fluorescence (across the ensemble of 1000 oscillators). Using this metric, telegraph noise generated strong synchrony even when its mean period was much shorter than the natural period of the oscillator (natural period about 35 min at 0.5% arabinose), while a periodic signal with comparably short period led to very weak response in the population of oscillators. D. discoideum CAR1 receptor entrainment: a computational example of the importance of aperiodic signals to natural biological systems. We have demonstrated that a synthetic oscillator can be entrained by aperiodic signaling, but the relevance of this phenomenon to other biological oscillators remains an open question. Our modeling studies and our review of the literature on aperiodic entrainment suggest that the phenomenon of aperiodic entrainment is not limited to neurons or this synthetic oscillator. If aperiodic entrainment of biological oscillators is generic, then it may be common to many natural oscillators. We chose the cAMP oscillatory network in D. discoideum, which has been shown to be synchronized by a

highly reproducible across multiple microfluidic traps (Figure S3) and experiments (data not shown). With a constant signal (either 0% arabinose or 0.5% arabinose), cells were not synchronized (Videos S1−S2, S4), which is consistent with previously reported results.18 Our results suggest that an aperiodic signal with a mean period much shorter than the natural period of the oscillator (about 35 min for constant level 0.5% arabinose) entrained the synthetic oscillator population equally or more strongly as a periodic variation with a comparable mean period. Stochastic simulations suggest that both periodic and aperiodic signals can entrain a synthetic gene oscillator. We investigated whether these in vivo results could be reproduced using a corresponding in silico model. The mechanism behind this synthetic oscillator has been explained using an analytical degrade-and-fire model, where saturated enzymatic degradation is a major component of the oscillator period.27,28 The f ire event occurs when the LacI concentration is low and there is an abundance of nascent LacI being produced prior to its maturation and subsequent repression of the system. The f ire event causes a pulse of protein with LAA-tags that are then degraded by ClpXP. The degradation of these protein can be slow due to saturation of ClpXP, forming a queue of proteins to be degraded.24 This queue synchronizes the concentrations of LacI, GFP, and AraC so that they are flushed from the system at roughly the same time. Cycling of the production phase (f ire) followed by the degradation phase (degrade) results in oscillations of consistent frequency.28 In our theoretical investigations of the oscillator, we used an impulse-based approximation to degrade-and-fire dynamics based on earlier work,29 suitably modified for our particular experiment (see the SI Methods for details). This impulse-based formalism allows for rapid simulation of ensembles containing 1000 realizations of the model, from which the mean fluorescence of GFP as a function of time can be rapidly 149

DOI: 10.1021/acssynbio.5b00127 ACS Synth. Biol. 2016, 5, 146−153

Research Article

ACS Synthetic Biology periodic signal.30,31 The cAMP oscillatory network provides an example of a natural oscillator that is more complex than the synthetic oscillator we examined. The social amoebae D. discoideum grow as individual cells in the presence of a nutrient-rich food source, but form a multicellular organism when nutrients are low (for a detailed description of this phenomenon, see ref 32). Under starvation conditions, chemotaxis of individual cells moving toward a signaling center is essential for formation of the multicellular organism. D. discoideum cells form signaling centers that secrete cyclic adenosine monophosphate (cAMP). Cells around the signaling center move toward the cAMP source and synthesize more cAMP, which is sensed by outlying neighboring cells. This results in cells moving toward the signaling center, where cells will aggregate into a multicellular organism of ∼100,000 cells.32,33 During aggregation the synthesis and secretion of cAMP is not continuous, but is instead an outward proliferation of a complicated cAMP spiral wave-pattern with an oscillation period of ∼6 min. In the early phase of synchronization before strong spiral wave formation, it may happen that complicated fluctuations in cAMP concentrations lead to rapid synchronization of clusters of cells, which then may trigger the rapid formation of spiral centers. We conducted an early investigation of this using a previously reported model (see Figure 3A). The entrainment of the CAR1 cell receptor by an aperiodic cAMP signal was strong (Figure 3B−D), entraining much more strongly than sinusoidal variation for small mean drive period. These results are analogous to those we found in our investigation of the synthetic oscillator, supporting the general nature of aperiodic entrainment. We then hypothesize that the initially chaotic spatiotemporal pattern generated just after starvation of D. discoideum cells may rapidly select coherent spiral wave centers via aperiodic entrainment. We leave this for future work. Predator−prey entrainment: a computational example of the importance of aperiodic signals to natural biological systems. The phenomenon of aperiodic entrainment may also occur at the population level in food webs or similar networks of interacting species. These networks can be susceptible to irreversible extinction events that can drastically affect the outcome of the populations, and correspondingly, the discussion of stability of these networks is often a concern.34,35 Since external signals may lead to large fluctuations in the count of one or more species, the response of populations to external signals is of critical importance, and since many natural signals contain an aperiodic component, the study of system response to aperiodic signals is also of importance. Indeed, there has been interest in how time-dependent environments can shape the fitness landscape of microbial organisms.36,37 A full investigation of the response of interacting populations is outside the scope of this article, but to gain some insight into the role of aperiodic entrainment in a population dynamics context, we investigated an idealized model for predator−prey oscillations (Figure 4A; also see the SI Methods).38 The model includes standard reactions: prey division, predation and associated predator division, and the spontaneous death of prey and predator. This system was entrained by timedependent prey immigration from outside of the system, e.g. as may occur if the system is only a small portion of a larger system. Since such Lotka−Volterra models can describe a wide variety of real world situations, at least in a course grained sense, we chose rate constants somewhat arbitrarily to reflect time scales seen in existing synthetic ecologies.39

Figure 4. Response of a predator−prey system to aperiodic drive. (A) A simple predator−prey system (within the dashed box) was investigated. The system was augmented to include prey immigration, which occurs with a time-dependent rate. (B) For constant arrival rate (2.0 h−1) and for other particular parameters (see SI Methods), the predator−prey system exhibits oscillations with a characteristic period. For these parameters, extinction of the predator population is rare. Thus, the system for these parameters is a stable oscillator and is thus a reasonable candidate for aperiodic entrainment. (C) Response of the driven system (analogous to Figure 3D), reporting the standard deviation (over time) of the ensemble mean. In this case, the mean of the signal was 2.0 h−1, the amplitude was 1.0 h−1, and the mean drive period was scanned. As in Figure 3D, telegraph noise with a short mean period can lead to a strong response. Measurements were taken from time t = 300 h to t = 1000 h. The ensemble size was 5040.

Results for a particular representative parameter set appear in Figure 4B−C. In this investigation, we considered constant drive signal (2.0 h−1 prey immigration rate) and time-dependent drive signal with the same mean (2.0 h−1) and 50% amplitude (difference between maximum and minimum rate equal to 1.0 h−1). While a strong resonant response was observed when the system was driven periodically with a period of approximately 30.0 h, system response to telegraph noise with a fast mean period (e.g., 10.0 h) remained significant and well-exceeded response to periodic drive with a comparably fast period. Based on these results, seemingly innocuous fast (primarily nonresonant) fluctuations in the environment may be greatly amplified through the effect of aperiodic entrainment. The resulting impact on population extinction rates is anticipated to be significant, though we save this for future work.

■

CONCLUSION Here we have demonstrated that an aperiodic signal can strongly entrain a variety of different biochemical oscillators, including a synthetic gene oscillator, a natural starvation response oscillator, and an idealized predator−prey oscillator. We conclude that this phenomenon previously only associated with neuron cells and physical systems may be applied more generically to a spectrum of biological systems. For the synthetic oscillator in particular, the interplay between the experimental data generated from this work and the resulting theoretical model produced not only a validated simplified model for a synthetic gene oscillator but also the first data set exploring the effect of aperiodic fluctuations on a synthetic oscillator. Given that the central design of this synthetic oscillator is representative of many natural oscillators,19 we strongly suspect that our results will generalize to a number of native oscillators. A different question that may be asked is how often if ever are the signals sensed by cells actually dominated by an aperiodic (noisy) component? Within a single cell, it is now accepted that so-called extrinsic noise that is strong can lead to a dominant positive correlation between genes,40 especially in microbial life. We suspect that, in cells’ native context, environmental 150

DOI: 10.1021/acssynbio.5b00127 ACS Synth. Biol. 2016, 5, 146−153

Research Article

ACS Synthetic Biology fluctuations play an equally important role. What is required for us to judge the relevance of aperiodic entrainment in the natural context is then to understand the details of environmental noise. How this is done in practice is likely to be difficult, e.g. what is the environmental noise experienced by algae circulating in an ocean current, or how do irregular weather patterns statistically influence our circadian rhythm? We predict that attention to these details will resolve a number of current and future confounding results involving biochemical oscillators.

media was used to exchange nutrients, inducers, and waste between the cells and the channels. This design also allows for continuous discharge of cells, which flow to waste ports. See the SI Methods for further information. Analysis of mean GFP fluorescence. In Videos S1−3, and in Figure 2, we define “GFP response” in the following way. Define filtered mean GFP as mean GFP with its 30.0 min timesymmetric mean subtracted. GFP response is defined as filtered mean GFP divided by its standard deviation (taken across the time of the experiment). Thus, GFP response has a standard deviation (taken across time) of 1.0. This approach conveniently normalizes GFP response. When comparing models to experiment, the same filtering approach is applied to model results. Stochastic simulations of a synthetic gene oscillator with periodic and aperiodic signals. For the synthetic gene oscillator, a simplified model for degrade and fire dynamics was adapted from previous investigations.28,29 Further details concerning model definition, simulation, and analysis appear in the SI Methods. D. discoideum CAR1 receptor entrainment: a computational example of the importance of aperiodic signals to natural biological systems. We based our simulation on a previously reported model30 with a few modifications. The primary modification of the model was to systematically rescale reaction rates to reduce intracellular concentrations, thus increasing the variability of intracellular oscillations. Further details concerning model definition and simulation appear in the SI Methods. Predator−prey entrainment: a computational example of the importance of aperiodic signals to natural biological systems. A standard model for predator−prey dynamics was used to further illustrate the strength of aperiodic entrainment in the context of population dynamics. Analysis was done similarly as for the D. discoideum oscillator model. Further details appear in the SI Methods. Image analysis. All image analysis was performed using custom scripts leveraging the SciPy and OpenCV packages for Python 2.7.

■

METHODS Drive signal choice and generation. Several periodic and aperiodic arabinose signals were considered for our in vivo and in silico experiments, but we chose sinusoidal signals and telegraph noise signals as representative of periodic and aperiodic signals, respectively. We do not strive here to form a comprehensive study of the response to all possible periodic and aperiodic signals. Sinusoidal signals and telegraph noise signals were generated using standard parametrizations and techniques. Sinusoidal signals were parametrized by period and amplitude (and initial phase, but this was fixed in value). Telegraph noise signals were characterized by only a few parameters: mean period (the mean time to transition from a low value to a high value and back again) and amplitude (the difference between its high value and low value). The time to the next transition (either from a low to high value, or vice versa) in the telegraph noise signal is exponentially distributed to have a mean transition time equal to half the mean period. It is worth emphasizing that though the telegraph noise signal is stochastic, the entrainment of synthetic oscillators is possible because each cell is affected by the same realization of the noisy signal rather than each cell sensing its own independent realization of the signal. Indeed, independent realizations of internal noise for each cell can be responsible for the distinct but related phenomenon of noise-induced oscillations,41 where gene networks can generate strong (but asynchronous) oscillations due to random fluctuations. Further details concerning signal selection and generation appear in the SI Methods. Reagents. All reagents were reagent grade and purchased from Sigma-Aldrich Co., Fisher Scientific, Inc., or Thomas Scientific unless otherwise stated. Strains and plasmids. E. coli NB001 (pTDCL7) cells were used for all microfluidic experiments. The cultures were grown in Bertani’s Lysogeny Broth (LB). The plasmid pTDCL7 and the E. coli strain JS006 (pJS167CFP) were gifts from Dr. Jeff Hasty from University of California, San Diego. E. coli NB001 was constructed by passing JS006 (pJS167CFP) without selection for the plasmid antibiotic resistance, Km (50 μg/ mL), for several days. An individual colony was shown to be Km sensitive, and no plasmid was isolated from NB001, while a plasmid was isolated from JS006 (pJS167CFP), when both were grown overnight in the same volume of liquid. Microfluidics and microscopy. Microfluidic experiments were done similarly to previously described protocols.42 The microfluidic chip consists of a trapping region, a dial-a-wave mixer, and channels (Figure S2). The traps are rectangular cell chambers, 1 × 50 × 100 μm, with two opposite ends exposed to flowing LB media with 0.2% Tween-80. There are 154 traps/ chip. E. coli cells have a ∼ 1 μm diameter; the ∼1 μm trap height allows cells to be retained and to divide in the traps. Each trap has the capacity to hold over 1,000 confined cells. Flowing

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acssynbio.5b00127. Supplemental methods, discussion, and figures (PDF) Video of E. coli cells expressing the synthetic oscillator driven by an external arabinose signal (Video 1) (MOV) Video of E. coli cells expressing the synthetic oscillator driven by an external arabinose signal (Video 2) (MOV) Video of E. coli cells expressing the synthetic oscillator driven by an external arabinose signal (Video 3) (MOV) Video of E. coli cells expressing the synthetic oscillator driven by an external arabinose signal (Video 4) (MOV) Detailed captions for other SI files (PDF) Fraction of arabinose reduction (Figure 2_Drive_Signal) (CSV)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 540-231-0041. Fax: 540-2315551. 151

DOI: 10.1021/acssynbio.5b00127 ACS Synth. Biol. 2016, 5, 146−153

Research Article

ACS Synthetic Biology Author Contributions

(16) Read, H. L., and Siegel, R. M. (1996) The origins of aperiodicities in sensory neuron entrainment. Neuroscience 75, 301− 314. (17) Mori, T., and Kai, S. (2002) Noise-Induced Entrainment and Stochastic Resonance in Human Brain Waves. Phys. Rev. Lett. 88, 218101. (18) Mondragon-Palomino, O., Danino, T., Selimkhanov, J., Tsimring, L., and Hasty, J. (2011) Entrainment of a Population of Synthetic Genetic Oscillators. Science 333, 1315−1319. (19) Stricker, J., Cookson, S., Bennett, M. R., Mather, W. H., Tsimring, L. S., and Hasty, J. (2008) A fast, robust and tunable synthetic gene oscillator. Nature 456, 516−519. (20) Stamatakis, M., and Mantzaris, N. V. (2010) Intrinsic noise and division cycle effects on an abstract biological oscillator. Chaos 20, 033118. (21) Gangstad, S. W., Feldager, C. W., Juul, J., and Trusina, A. (2013) Noisy transcription factor NF-kappaB oscillations stabilize and sensitize cytokine signaling in space. Phys. Rev. E 87, 022702. (22) Lutz, R., and Bujard, H. (1997) Independent and tight regulation of transcriptional units in Escherichia coli via the LacR/O, the TetR/O and AraC/I1-I2 regulatory elements. Nucleic Acids Res. 25, 1203−1210. (23) Gottesman, S., Roche, E., Zhou, Y., and Sauer, R. T. (1998) The ClpXP and ClpAP proteases degrade proteins with carboxy-terminal peptide tails added by the SsrA-tagging system. Genes Dev. 12, 1338− 1347. (24) Cookson, N. A., Mather, W. H., Danino, T., MondragonPalomino, O., Williams, R. J., Tsimring, L. S., and Hasty, J. (2011) Queueing up for enzymatic processing: correlated signaling through coupled degradation. Mol. Syst. Biol. 7, 561. (25) Hochendoner, P., Ogle, C., and Mather, W. H. (2014) A queueing approach to multi-site enzyme kinetics. Interface Focus 4, 20130077. (26) Prindle, A., Selimkhanov, J., Li, H., Razinkov, I., Tsimring, L. S., and Hasty, J. (2014) Rapid and tunable post-translational coupling of genetic circuits. Nature 508, 387−391. (27) Smolen, P., Baxter, D. A., and Byrne, J. H. (1999) Effects of macromolecular transport and stochastic fluctuations on dynamics of genetic regulatory systems. Am. J. Physiol. 277, 777−790. (28) Mather, W.;, Bennett, M. R.; Hasty, J.; Tsimring, L. S. DelayInduced Degrade-and-Fire Oscillations in Small Genetic Circuits. Phys. Rev. Lett. 2009, 102, 10.1103/PhysRevLett.102.068105 (29) Mather, W.; Hasty, J.; Tsimring, L. S. Synchronization of Degrade-and-Fire Oscillations via a Common Activator. Phys. Rev. Lett. 2014, 113, 10.1103/PhysRevLett.113.128102. (30) Kim, J., Heslop-Harrison, P., Postlethwaite, I., and Bates, D. G. (2007) Stochastic noise and synchronisation during Dictyostelium aggregation make cAMP oscillations robust. PLoS Comput. Biol. 3, 2190−2198. (31) Laub, M. T., and Loomis, W. F. (1998) A molecular network that produces spontaneous oscillations in excitable cells of Dictyostelium. Mol. Biol. Cell 9, 3521−3532. (32) McMains, V. C., Liao, X. H., and Kimmel, A. R. (2008) Oscillatory signaling and network responses during the development of Dictyostelium discoideum. Ageing Res. Rev. 7, 234−248. (33) Dormann, D., and Weijer, C. J. (2001) Propagating chemoattractant waves coordinate periodic cell movement in Dictyostelium slugs. Development 128, 4535−4543. (34) Case, S. O., Durney, C. H., Pleimling, M., and Zia, R. K. P. (2010) Cyclic competition of four species: Mean-field theory and stochastic evolution. Europhys. Lett. 92, 58003. (35) Dobramysl, U.; Tauber, U. C. Environmental Versus Demographic Variability in Two-Species Predator-Prey Models. Phys. Rev. Lett. 2013, 110, 10.1103/PhysRevLett.110.048105 (36) Mao, J. W., Blanchard, A. E., and Lu, T. (2015) Slow and Steady Wins the Race: A Bacterial Exploitative Competition Strategy in Fluctuating Environments. ACS Synth. Biol. 4, 240−248. (37) Razinkov, I. A., Baumgartner, B. L., Bennett, M. R., Tsimring, L. S., and Hasty, J. (2013) Measuring Competitive Fitness in Dynamic Environments. J. Phys. Chem. B 117, 13175−13181.

N.C.B. performed all microfluidic experiments and wrote the manuscript. N.C.B., P.H., and W.H.M. analyzed microscopy images and created videos. P.H. and C.T.O. developed software and machinery for running microfluidic experiments. W.H.M., P.H., and N.C.B. adapted and analyzed the D. discoideum model. W.H.M. developed the E. coli synthetic oscillator model and predator−prey model. All authors contributed to the discussion and editing of the manuscript. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank Dr. Jeff Hasty from University of California, San Diego, for the plasmid pTDCL7 and the E. coli strain JS006 (pJS167CFP), and Dr. Roderick V. Jensen from Virginia Polytechnic Inst. and State University for guidance with this research. Funding for this research was provided by the National Science Foundation under Grant No. MCB-1330180.

■

REFERENCES

(1) Bell-Pedersen, D., Cassone, V. M., Earnest, D. J., Golden, S. S., Hardin, P. E., Thomas, T. L., and Zoran, M. J. (2005) Circadian rhythms from multiple oscillators: lessons from diverse organisms. Nat. Rev. Genet. 6, 544−556. (2) Bennett, M., Schatz, M. F., Rockwood, H., and Wiesenfeld, K. (2002) Huygens’s clocks. Proc. R. Soc. London, Ser. A 458, 563−579. (3) Roenneberg, T., and Merrow, M. (2007) Entrainment of the human circadian clock. Cold Spring Harbor Symp. Quant. Biol. 72, 293− 299. (4) Yi, L., Wang, X., Dhumpa, R., Schrell, A. M., Mukhitov, N., and Roper, M. G. (2015) Integrated perfusion and separation systems for entrainment of insulin secretion from islets of Langerhans. Lab Chip 15, 823−832. (5) Schimz, A., and Hildebrand, E. (1986) Entrainment and temperature dependence of the response oscillator in Halobacterium halobium. J. Bacteriol. 166, 689−692. (6) Massie, T. M., Blasius, B., Weithoff, G., Gaedke, U., and Fussmann, G. F. (2010) Cycles, phase synchronization, and entrainment in single-species phytoplankton populations. Proc. Natl. Acad. Sci. U. S. A. 107, 4236−4241. (7) Davidson, A. J., Poole, A. S., Yamazaki, S., and Menaker, M. (2003) Is the food-entrainable circadian oscillator in the digestive system? Genes, Brain Behav. 2, 32−39. (8) Pavlou, S., and Kevrekidis, I. G. (1992) Microbial predation in a periodically operated chemostat: a global study of the interaction between natural and externally imposed frequencies. Math. Biosci. 108, 1−55. (9) Aviram, I., and Rabinovitch, A. (2014) Bacteria and lytic phage coexistence in a chemostat with periodic nutrient supply. Bull. Math. Biol. 76, 225−244. (10) Mainen, Z. F., and Sejnowski, T. J. (1995) Reliability of spike timing in neocortical neurons. Science 268, 1503−1506. (11) Wilkinson, M.; Mehlig, B. Path coalescence transition and its applications. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2003, 68, 10.1103/PhysRevE.68.040101. (12) Deutsch, J. M. (1985) The effects of noise on iterated maps. J. Phys. A: Math. Gen. 18, 1457−1474. (13) Jensen, R. V. (2002) Synchronization of driven nonlinear oscillators. Am. J. Phys. 70, 607−619. (14) Pikovsky, A. S., and Kurths, J. (1997) Coherence Resonance in a Noise-Driven Excitable System. Phys. Rev. Lett. 78, 775−778. (15) Teramae, J. N., and Tanaka, D. (2004) Robustness of the noiseinduced phase synchronization in a general class of limit cycle oscillators. Phys. Rev. Lett. 93, 204103. 152

DOI: 10.1021/acssynbio.5b00127 ACS Synth. Biol. 2016, 5, 146−153

Research Article

ACS Synthetic Biology (38) Lotka, A. J. (1910) Contribution to the theory of periodic reactions. J. Phys. Chem. 14, 271−274. (39) Balagadde, F. K.; Song, H.; Ozaki, J.; Collins, C. H.; Barnet, M.; Arnold, F. H.; Quake, S. R.; You, L. C. A synthetic Escherichia coli predator-prey ecosystem. Mol. Syst. Biol. 2008, 4, 10.1038/msb.2008.24. (40) Swain, P. S., Elowitz, M. B., and Siggia, E. D. (2002) Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc. Natl. Acad. Sci. U. S. A. 99, 12795−12800. (41) Bratsun, D., Volfson, D., Tsimring, L. S., and Hasty, J. (2005) Delay-induced stochastic oscillations in gene regulation. Proc. Natl. Acad. Sci. U. S. A. 102, 14593−14598. (42) Ferry, M. S., Razinkov, I. A., and Hasty, J. (2011) Microfluidics for synthetic biology: from design to execution. Methods Enzymol. 497, 295−372.

153

DOI: 10.1021/acssynbio.5b00127 ACS Synth. Biol. 2016, 5, 146−153