Advertisement

Systematic Design of a Quorum Sensing-Based Biosensor for the Detection of Metal Ions in Escherichia coli

  • Bor-Sen ChenEmail author
Living reference work entry

Abstract

With the recent industrial expansion, heavy metals and other pollutants have increasingly contaminated our living surroundings. The non-degradability of heavy metals may lead to accumulation in food chains, and the resulting toxicity could cause damage in organisms. Hence, detection techniques have gradually received attention. In this study, a quorum sensing (QS)-based amplifier is introduced to improve the detection performance of metal ion biosensing. The design utilizes diffusible signal molecules, which freely pass through the cell membrane into the environment to communicate with others. Bacteria cooperate via the cell-cell communication process, thereby displaying synchronous behavior, even if only a minority of the cells detect the metal ion. In order to facilitate the design, the ability of the engineered biosensor to detect metal ions is described in a steady-state model. The design can be constructed according to user-oriented specifications by selecting adequate components from corresponding libraries, with the help of a genetic algorithm (GA)-based design method. The experimental results validate enhanced efficiency and detection performance of the quorum sensing-based biosensor of metal ions.

Introduction

Metal ions play important roles in biological metabolic pathways and affect cellular processes through a wide variety of reactions. Organisms require metal ions, which are involved in processes, such as bacterial respiration, electron transport, and peroxide reduction (Achtman and Suerbaum 2001). The uptake and efflux systems in biology regulate ion homeostasis to prevent a lack or excess of metal ions. With the recent industrial expansion, there has been either an excess of metal ions in wastewater (Ngah and Hanafiah 2008; Rezvani-Boroujeni et al. 2015; Singha and Guleria 2014; Teodosiu et al. 2014; Mulligan et al. 2001) or the intentional or careless discharge of other contaminants (Migaszewski and Galuszka 2015) into the natural environment. Metal ions can be classified based on their effects and toxicity on cells into essential ions, trace ions, and heavy metals. The stronger redox ability of heavy metals allows them to compete with essential ions and trace ions in redox actions, leading to superoxide or hydroxyl radicals (Hartwig 1995). Superoxide and hydroxyl radicals may damage lipids and proteins (Davies 2005; Raha and Robinson 2000), disrupt DNA oxidation (Hartwig 1995), and even cause cell death (Hartwig 1995). Furthermore, heavy metals are difficult to remove via metabolism and can accumulate in organs, causing permanent damage. Hence, detection techniques have gradually received great attention. In this chapter, we introduce a synthetic genetic circuit that can enhance the detection performance of metal ion biosensors and has the potential to be applied for environmental detection and environmental bioremediation.

Recent progress in research on synthetic biology (Chang et al. 2013; Danino et al. 2010; Khalil and Collins 2010; Silva-Rocha and de Lorenzo 2014; Sohka et al. 2009; Stricker et al. 2008; Wang et al. 2011; Cameron et al. 2014; Kotula et al. 2014; Teo et al. 2015) has provided an alternative means for metal ion detection aided by specific promoter elements such as derived from R. metallidurans (Taghavi et al. 1997; Hobman et al. 2012) or found in E. coli (Munson et al. 2000). In order to improve the detection performance, a metal ion-induced promoter connects to bacterial quorum sensing (QS) system. Quorum sensing is a mechanism which regulates gene expression for many functions through cell-cell communication (Brint and Ohman 1995; Darch et al. 2012; Miller and Bassler 2001; Passador et al. 1993; Pearson et al. 1995). Bacteria produce diffusible signal molecules, generally known as autoinducers (AIs) (Kaplan and Greenberg 1985; Dunlap and Kuo 1992; Fuqua et al. 1994; Ruby and Mcfallngai 1992; Ruby and Nealson 1976), and release them into the environment to communicate with others. Through this process, bacteria cooperate and thereby display synchronous behavior. The most extensively studied quorum sensing system is the autoinduction of luminescence in the marine bacterium, Aliivibrio fischeri, which is symbiotic with squids and some marine fishes (Ruby and Mcfallngai 1992; Ruby and Nealson 1976; Nealson and Hastings 1979). The luminescence here is produced by the operon acquired from V. fischeri, of which the LuxR protein is the transcriptional activator of luminescence and the LuxI protein synthesizes the specific N-acylated homoserine lactone (AHL) (Engebrecht and Silverman 1984; Hanzelka and Greenberg 1996; Val and Cronan 1998). After the LuxR protein binds AHL to form a complex, the complex can bind the target promoter sequence and activate downstream gene transcription, even if only some of the bacteria can detect the metal ions. Thus, it can be employed to enhance the detection performance by signal amplification.

To make the design of the QS-based metal ion biosensor easier, we introduce a mathematical model to describe the dynamic and steady-state regulatory behavior, which is related to transcriptional and translational processes (Chen and Wang 2014). A promoter allows RNA-polymerase molecules to latch onto a DNA strand and initialize transcription of a downstream gene into mRNA, and a RBS allows ribosome to bind and translate mRNA. A promoter combined with a RBS thus in this study is viewed as a component, of which characterizations can be identified with a reporter protein by measuring the fluorescence intensity. One can therefore use kinetic parameters as component libraries to design the circuit for QS-based metal ion detection. The design can be constructed according to user-oriented specifications by selecting adequate promoter-RBS components within a feasible range of metal ion concentrations. A long computation time is required in general when the component libraries become large. Hence, a genetic algorithm-based design method proposed here provides a simple and useful tool that saves time in evaluating and selecting components. So in summary, this study provides a systematic methodology for developments in next-generation synthetic biology, from component library construction to gene circuit assembly. When the libraries are more complete, more precise detection can be achieved.

The purposes of this chapter are fivefold: (a) The basic principles of quorum sensing are introduced as the basic background of quorum sensing-based biosensor. (b) A QS-based amplifier is introduced into a biosensor to enhance the ability for metal ion detection. (c) Based on the promoter-RBS kinetic strengths, we establish three kinds of component libraries. (d) According to user-oriented specifications, the quorum sensing (QS)-based metal ion biosensor can be constructed by selecting adequate promoter-RBS components from the corresponding libraries to achieve a desired ability for metal ion detection. (e) The proposed methodology could provide synthetic biologists with a useful tool to design metal ion biosensors.

The Basic Principles of Quorum Sensing

Before we discuss the systematic design of a quorum sensing-based biosensor for detection of metal ion in E. coli, the basic principles of quorum sensing involved in using this phenomenon are described as the basis for biosensor design and construction in the following. Quorum sensing was discovered and described in two luminous marine bacterial species over four decades, i.e., Aliivibrio fischeri and Vibrio harveyi (Achtman and Suerbaum 2001; Ruby 1996). In both species, the enzymes responsible for light production are encoded by the luciferase structural operon lux CDABE (Achtman and Suerbaum 2001; Miller and Bassler 2001; Ruby 1996), and light emission was determined to occur only at high cell population density in response to the accumulation of secreted autoinducer signaling molecules (Ruby 1996). Only a few other cases of bacterial regulation of gene expression in response to cell-cell signaling were known, for example, antibiotic production by Streptomyces spp., conjugation in Enterococcus faecalis, and fruiting body development in Myxococcus xanthus which were also recognized to be controlled by intercellular signaling. Therefore, these bacterial communication systems were considered anomalous because bacteria as a whole were not believed to use cell-cell communication in general. However, the exchange of chemical signals between cells and organisms could be assumed to be a trait highly characteristic of eukaryotes (Ruby 1996). In the recent explosion of advances in the field of cell-cell communication in bacteria, many or most bacteria have been shown to communicate using secreted chemical molecules to coordinate the behaviors of the group. Furthermore, a vast assortment of different classes of chemical signals have been employed that individual species of bacteria use more than one chemical signal and/or more than one type of signal to communicate. Therefore complex hierarchical regulatory circuits have evolved to integrate and process the sensory information, and the signals can be used to differentiate between species in consortia. Obviously, the ability to communicate both within and between species is critical for bacterial survival and interaction in natural habitats (Miller and Bassler 2001; Ruby 1996).

In the past decades quorum sensing circuits have been identified in many species of Gram-negative bacteria. The quorum sensing circuits identified in Gram-negative bacteria resemble the canonical quorum sensing circuit of the symbiotic bacterium V. fischeri. Specifically, these Gram-negative bacterial quorum sensing circuits contain homologues of two V. fischeri regulatory proteins, i.e., LuxI and LuxR, at least. The LuxI-like proteins respond for the biosynthesis of a specific acylated homoserine lactone signaling molecule (HSL) known as an autoinducer. The autoinducer concentration will increase with the increase of cell population density. The LuxR-like protein could bind cognate HSL autoinducers that cause achieved a critical threshold concentration, and the LuxR-autoinducer complexes could also activate target gene transcription (Miller and Bassler 2001). Therefore, using this quorum sensing mechanism, Gram-negative bacteria could efficiently couple gene expression to fluctuations in cell population density. Among these species of bacteria that could mediate quorum sensing by means of a LuxI/LuxR-type circuit, the V. fischeri, Pseudomonas aeruginosa, Agrobacterium tumefaciens, and Erwinia carotovora systems are the most understood (Miller and Bassler 2001).

The most intensely studied quorum sensing system is the bioluminescent marine bacterium V. fischeri. This bacterium lives in symbiotic association with a number of eukaryotic hosts. In each case the host has developed a specialized light organ that is inhabited by a pure culture of a specific strain of V. fischeri at very high cell density. In these symbiotic associations, scientists have found that the eukaryotic host supplies V. fischeri with a nutrient-rich environment in which to live. The role of V. fischeri could provide the host with light, and then each eukaryotic host uses the light which is provided by the bacteria for a specific purpose. For example, in the squid Euprymna scolopes and V. fischeri association, the squid has evolved into an antipredation strategy in which it counters and illuminates itself using the light from V. fischeri. In contrast, the fish Monocentris japonica could use the light produced by V. fischeri to attract a mate. Other uses of the V. fischeri light, such as warding off predators and attracting prey, have been documented (Miller and Bassler 2001). In general, V. fischeri culture grows to extremely high cell densities, reaching 1011 cells per ml (Ruby 1996). As V. fischeri culture grows, it could produce and release an autoinducer hormone into the extracellular environment, and the hormone is trapped inside the light organ with the bacteria. Detection of autoinducer by V. fischeri could elicit a signaling cascade that can cumulate in the emission of light. Thus, the quorum sensing system of V. fischeri has evolved to specifically enable the bacteria to produce light only under conditions in which there is a positive selective advantage for the light (Miller and Bassler 2001).

As mentioned above, the luciferase enzymes required for light production in V. fischeri are encoded by luxCDABE, which exists as part of the luxICDABE operon. Two regulatory proteins called LuxI and LuxR comprise the quorum sensing apparatus. As shown in Fig. 1, LuxI is the autoinducer synthase enzyme, and it acts in the production of an HSL, N-(3-oxohexanoyl)-homoserine lactone (Ruby 1996). LuxR functions both to bind the autoinducer and to activate transcription of the luxICDABE operon as shown in the quorum sensing system of V. fischeri in Fig. 1. Specifically, at low cell densities, the luxICDABE operon is transcribed at a low basal level. Therefore, a low level of autoinducer is produced via luxI, and because the genes encoding luciferase are located directly downstream of the luxI gene, only a low level of light is produced. The HSL autoinducer is freely diffusible across the cell membrane, so the concentration of autoinducer in the extracellular environment is the same as the intracellular concentration of the autoinducer (Miller and Bassler 2001). As the V. fischeri culture grows, autoinducer accumulates to a threshold level that is sufficient for detection and binding by the cytoplasmic LuxR protein. In this situation, the interaction of LuxR with the autoinducer unmasks the LuxR DNA-binding domain, allowing LuxR to bind the luxICDABE promoter and activate its transcription. This action results in an exponential increase in both autoinducer production and light emission. The LuxR-HSL complex also acts to negatively regulate the expression of LuxR. The negative feedback loop is a compensatory mechanism that decreases luxICDABE expression in response to the positive feedback circuit (Miller and Bassler 2001).
Fig. 1

The Aliivibrio fischeri LuxI/LuxR quorum sensing circuit. There are five luciferase structure genes (luxICDABE) and two regulatory genes (LuxR and LuxI) required for quorum sensing-controlled light emission in V. fischeri. The genes are arranged in two adjacent but divergently transcribed units. LuxR is transcribed to the left, and the luxICDABE operon is transcribed to the right. The LuxI protein is responsible for synthesis of HSL autoinducer N-(3-oxohexanoyl)-homoserine lactone. As the cell population density increases, the concentration of the autoinducer increases both intra- and extracellularly. At a critical autoinducer concentration, the LuxR protein binds the autoinducer. The LuxR-autoinducer complex binds at the luxICDABE promoter and activates transcription of this operon. This action results in an exponential increase in autoinducer synthesis via the increase in transcription of LuxR and an exponential increase in light production via the increase in transcription of luxICDABE. The LuxR-autoinducer complex also binds at the LuxR promoter. This negative action compensates for the positive action at luxICDABE promoter (Miller and Bassler 2001; Ruby 1996)

Gram-positive bacteria also regulate a variety of processes in response to increasing cell population density. However, in contrast to Gram-negative bacteria, which use HSL autoinducer, Gram-positive bacteria employ secreted peptides as autoinducer for quorum sensing. In general, the peptide is secreted via a dedicated ATP-binding cassette (ABC) transporter. Again, in contrast to the widespread use of LuxR-type proteins as autoinducer sensors by Gram-negative bacteria, Gram-positive bacteria use two-component adaptive response proteins for detection of the autoinducers. The signaling mechanism is a phosphorylation/dephosphorylation cascade. A general model for quorum sensing in Gram-positive bacteria is shown in Fig. 2. In brief, secreted peptide autoinducers increase in concentration as a function of the cell population density. Two-component sensor kinases are the detectors for the secreted peptide signals. Interaction with the peptide ligand initiates a series of phosphoryl events that culminate in the phosphorylation of cognate response regulator protein. Phosphorylation of the response regulator activates it, allowing it to bind DNA and later the transcription of the quorum sensing-controlled target genes. Several Gram-positive quorum sensing systems have been extensively studied, for example, the model systems controlling competence in Streptococcus pneumoniae, competence and sporulation in Bacillus subtilis, and virulence in Straphylococcus aureus (Miller and Bassler 2001)
Fig. 2

A general model for peptide-mediated quorum sensing in Gram-positive bacteria. In Gram-positive bacteria, a peptide signal precursor locus is translated into a precursor protein that is cleaved to produce the processed peptide autoinducer signal. Generally, the peptide signal is transported out of the cell via an ABC transporter. When the extracellular concentration of the peptide signal accumulates to the minimal stimulatory level, a histidine sensor kinase protein of a two-component signaling system detects it. The sensor kinase autophosphorylates on a conserved histidine (H) residue, and subsequently, the phosphoryl group is transferred to a cognate response regulator protein. The response regulator is phosphorylated on a conserved aspartate residue (D). The phosphorylated response regulator activates the transcription of target genes (Miller and Bassler 2001; Ruby 1996)

After we learn how quorum sensing facilitates species-specific and interspecies cell-cell communication, how quorum sensing allows populations to act synergistically, and how quorum sensing can be used to conquer competitors, we could learn about an assortment of the signals that are employed by bacteria and about the biosynthesis of these signals as well as how the information encoded in these chemical signals is processed and transduced to control gene expression. These basic principles of quorum sensing will be employed for systematic design of a quorum sensing-based biosensor for the metal ion in E.coli in the following sections.

Design Example of QS-Based Metal Ion Biosensor

In the design example, the materials and methods are given as follows:

In biosensor reagents, all restriction enzymes and DNA ligation kit are purchased from New England Biolabs. The chemicals used here are from Sigma-Aldrich. The oligonucleotides are from Integrated DNA Technologies. In bacteria strains and medium, Escherichia coli strain DH5α cells from Yeastern Biotech (ECOS) are used for the construction of the procedure and for the fluorescence measurement experiments. An M9 working medium (34 g/L Na2HPO4, 15 g/L K2HPO4, 2.5 g/L NaCl, 5 g/L NH4Cl, 2 g/L casamino acids, 2 μM vitamin B1, 2 mM MgSO4, 0.2% glucose) with proper antibiotics is used for E. coli cultivation at 37 °C and 200 r.p.m. In the plasmid construction, the DNA parts used in this study are selected from BioBrick or synthesized by MDBio Biotech Co. Ltd. All DNA parts are assembled into the backbone pSB3K3 (20–30 copies per cell), via the BioBrick standard assembly method. In the fluorescence measurement, the cells containing the genetic circuit are inoculated in the M9 working medium with 50 mg/mL kanamycin. The culture is incubated for approximately 14–16 h, after which it is diluted 250-fold and further incubated until the OD600 reaches 0.1. Different concentrations of CuSO4 are then added to the medium. The fluorescence intensity of the culture is measured subsequently by the microplate reader (BioTek, Synergy H1, GFP settings are 490/510 nm for excitation and emission).

Construction of QS-Based Metal Ion Biosensor

Recent research on synthetic biology offers an alternative means for metal ion detection using specific promoter elements derived from microorganisms. For example, PcusC and PpcoE are copper-inducible promoters regulated by CusRS, which are a part of the E. coli chromosome system and system, respectively (Bondarczuk and Piotrowska-Seget 2013). The system (cusCFBA) found in E. coli is a tetrapartite system endowing resistance to copper ion and is involved in periplasmic copper detoxification (Franke et al. 2003). The system (pcoABCDRSE) is discovered in bacteria that survive in copper-rich environments; plasmid-encoded operons in this system are known to be responsible for resistance to copper toxicity (Rouch and Brown 1997; Lee et al. 2002; Tetaz and Luke 1983). Another example of a metal ion-regulated promoter is the lead resistance promoter (Taghavi et al. 1997). The promoter is acquired from Ralstonia metallidurans strain CH34 isolated from lead-contaminated soil, containing at least seven determinants encoding resistances to toxic heavy metals (Taghavi et al. 1997; Hobman et al. 2012). Combining functions involved in uptake, efflux, and accumulation of Pb(II) ion, the lead resistance operon (pbrABCDRT) is regulated by PbrR, which belongs to the MerR family of metal regulatory proteins (Borremans et al. 2001; Brown et al. 2003).

To improve the detection performance, a metal ion-induced promoter-RBS Mi is connected to the LuxI protein-coding sequence (in Fig. 3). This allows the LuxI protein to be translated by the activation of the metal ion-induced promoter. The luxI component derived from the lux operon in V. fischeri is involved in the production of the LuxI protein, which catalyzes S-adenosyl methionine and acyl-acyl carrier protein into a specific AHL (referred to as HSL) as signal molecules (Hanzelka and Greenberg 1996; Val and Cronan 1998). HSLs may be classified into several types according to acyl group length (C4–C18). Here, the type of HSL synthesized by LuxI protein is C6-HSL. Because the lux operon is an exogenous DNA sequence for Escherichia coli (E. coli), it is required to supply LuxR protein for the activation of promoter Plux. The LuxR protein-coding sequence is connected to a constitutive promoter-RBS component Ci. When sufficient amounts of the LuxR protein is produced using a constitutive promoter-RBS component with the presence of C6-HSL, C6-HSL can then bind LuxR protein to form the LuxR complex. The complex targets the cognate QS-dependent promoter-RBS component Ak and activates the transcription of the green fluorescent protein (GFP) coding sequence, even if only some of the bacteria can detect the metal ions. This mechanism is helpful to enhance the detection ability by signal amplification.
Fig. 3

The QS-based metal ion biosensor. A metal ion-induced promoter-RBS connects with a quorum sensing system found in the marine bacterium, V. fischeri. Via the transmission of signal molecules, the output signal will be produced significantly by the activation of the QS-dependent promoter

Mathematical Model of QS-Based Metal Ion Biosensor

To construct the dynamic model, promoter-RBS regulation must be introduced. The promoter-RBS regulation function is first defined by P(Pu, Pl, TF, I), in which Pu and Pl denote the maximum and minimum promoter-RBS strengths, respectively, TF denotes transcription factor concentration, and I is inducer concentration. This function describes the biochemical aspect of the transcription and translation process. The dynamic model of the metal ion biosensor with QS-based amplifier in Fig. 3 is thus described as follows. Note that the QS-based metal ion biosensor is divided into three stages.

The first stage involves a metal ion-induced promoter-RBS Mi for producing autoinducer synthase LuxI, which catalyzes S-adenosyl methionine and acyl-acyl carrier protein into a specific AHL. The dynamics is described in the following equation (Alon 2007):
$$ {\dot{x}}_E(t)={P}_M\left({P}_{u,i},{P}_{l,i},{x}_S,{I}_M\right)-\left(d+{r}_E\right)\cdot {x}_E(t) $$
(1)
in which
$$ {P}_M\left({P}_{u,i},{P}_{l,i},{x}_S,{I}_M\right)={P}_{u,i}+\frac{P_{u,i}-{P}_{l,i}}{1+{\left(\frac{K_{SI}}{x_{SI}\left({x}_S,{I}_M\right)}\right)}^{n_{SI}}} $$
$$ {x}_{SI}\left({x}_S,{I}_M\right)=\frac{x_S}{1+\left(\frac{K_M}{I_M}\right)} $$
where xE denotes the concentration of autoinducer synthase. IM is the concentration of metal ion; xS is the total concentration of metal ion-dependent regulatory protein. xSI denotes the complex of xI and IM. i denotes the ith metal ion-induced promoter-RBS component in Table 1. PM(Pu, i, Pl, i, xS, IM) denotes the promoter-RBS regulation activity of the metal ion-induced promoter-RBS components. Pu, i and Pl, i denote the maximum and minimum promoter-RBS strengths of the ith metal ion-induced promoter-RBS component in Tables 1-3 in Appendix. rE denotes the degradation rate for autoinducter synthase. d is the dilution rate due to cell growth. KSI and nSI denote the binding affinity and binding cooperativity between the complex xSI and the corresponding promoter-RBS component, respectively. KM is the dissociation rate between the metal ion IM and the metal regulatory protein xS. Then, the dynamics for the catalysis of S-adenosyl methionine and acyl-acyl carrier protein into a specific autoinducer is given by
$$ {\dot{x}}_I(t)={ax}_E(t)-\left(d+{r}_I\right)\cdot {x}_I(t) $$
(2)
where xI is the concentration of autoinducer, a is autoinducer synthesis rate, and rI denotes the degradation rate for autoinducter.
The second stage involves a constitutive promoter-RBS part Ci for producing protein, LuxR. The change in concentration of regulatory protein LuxR with respect to time is given by (Alon 2007)
$$ {\dot{x}}_R(t)={P}_C\left({P}_{u,j},0,0,0\right)-\left(d+{r}_R\right)\cdot {x}_R(t) $$
(3)
and
$$ {P}_C\left({P}_{u,j},0,0,0\right)={P}_{u,j} $$
where xR denotes the concentration of transcriptional activator protein, LuxR. j is the jth constitutive promoter-RBS component in Table 2. PC(Pu, j, 0, 0, 0) is the regulation activity of the constitutive promoter-RBS components. Pu, j is the promoter-RBS strength of the jth constitutive promoter-RBS component in Table 2. rR denotes the degradation rate for transcriptional activator protein.
The third stage contains a QS-dependent promoter-RBS part for driving the expression of the immature reporter protein. When complex of xR and xI accumulates, it activates the QS-dependent promoter and enhances the expression of reporter gene. Therefore, the dynamics is governed by the following equation (Alon 2007):
$$ {\dot{x}}_G(t)={P}_A\left({P}_{u,k},{P}_{l,k},{x}_R,{x}_I\right)-\left(d+{r}_G\right)\cdot {x}_G(t) $$
(4)
and
$$ {P}_A\left({P}_{u,k},{P}_{l,k},{x}_R,{x}_I\right)={P}_{u,k}+\frac{P_{u,k}-{P}_{l,k}}{1+{\left(\frac{K_{RI}}{x_{RI}\left({x}_R,{x}_I\right)}\right)}^{n_{RI}}} $$
$$ {x}_{RI}\left({x}_R,{x}_I\right)=\frac{x_R}{1+\left(\frac{K_I}{x_I}\right)} $$
where xG is the concentration of immature reporter protein and represents the complex of xR and xI. k is the kth QS-dependent promoter-RBS component in Table 3. PA(Pu, k, Pl, k, xR, xI) is the activity of the QS-dependent promoter-RBS components. Pu, k and Pl, k are the maximum and minimum promoter-RBS strengths of the kth QS-dependent promoter-RBS component in Table 3. rG is the degradation rate for immature reporter protein. KRI and nRI are the binding affinity and binding cooperativity between the complex xRI and the promoter-RBS part, respectively. KI is the dissociation rate between the autoinducer xI and the transcriptional activator protein xR. Finally, the dynamics for the maturation of xG into the mature reporter protein G is given by
$$ \dot{G}(t)={mx}_G-\left(d+r\right)G(t) $$
(5)
where m is the maturation rate for the reporter protein and r is the degradation rate for mature reporter protein.
The dynamic model for the QS-based metal ion biosensor is then transformed into steady-state model by assuming that the dynamics in (1), (2), (3), (4), and (5) are equal to zero. The steady-state model of the QS-based metal ion biosensor with promoter-RBS parts Mi, Cj, and Ak being selected from the corresponding libraries in Supplementary Appendix A, respectively, is derived as follows:
$$ \left\{\begin{array}{c}{x}_{ISS}=\frac{P_M\left({P}_{u,i},{P}_{l,i},{x}_S,{I}_M\right)}{\left(d+{r}_E\right)}\cdot \frac{a}{d+{r}_I}\\ {}{x}_{RSS}={\dot{x}}_R(t)=\frac{P_C\left({P}_{u,j},0,0,0\right)}{\left(d+{r}_R\right)}\, \\ {}{x}_{GSS}=\frac{P_A\left({P}_{u,k},{P}_{l,k},{x}_R,{x}_I\right)}{d+{r}_G}\quad \\ {}{G}_{ss}=\frac{m}{d+r}{x}_G\qquad \end{array}\right. $$
(6)
where xISS, xRSS, xGSS and Gss are the steady-state concentrations of autoinducter, transcriptional activator protein, and immature reporter protein, as well as steady-state mature reporter protein, respectively. The steady-state expression of the QS-based metal ion biosensor can be obtained from the steady-state model in (6) with the regulation functions PM(Pu, i, Pl, i, xS, IM), PC(Pu, j, 0, 0, 0), as well as PA(Pu, k, Pl, k, xR, xI), respectively.
In general, a synthetic genetic circuit in vivo also suffers from extrinsic environmental cellular noise, such as transmitted noise from upstream and global noise affecting all cells (Chen and Wang 2006; Soltani et al. 2015; Kyung et al. 2015). Thus, the equation in (6) should be modified as follows:
$$ \left\{\begin{array}{c}{x}_{ISS}=\frac{P_M\left({P}_{u,i},{P}_{l,i},{x}_S,{I}_M\right)}{\left(d+{r}_E\right)}\cdot \frac{a}{d+{r}_I}+{v}_1\\ {}{x}_{RSS}={\dot{x}}_R(t)=\frac{P_C\left({P}_{u,j},0,0,0\right)}{\left(d+{r}_R\right)}+{v}_2\, \\ {}{x}_{GSS}=\frac{P_A\left({P}_{u,k},{P}_{l,k},{x}_R,{x}_I\right)}{d+{r}_G}+{v}_3\quad \\ {}{G}_{ss}=\frac{m}{d+r}{x}_G+{v}_4\qquad \end{array}\right. $$
(7)
where the Gaussian random noise vp, p = 1, 2, 3, with a zero mean and variance of \( {\sigma}_p^2 \), denotes cellular noise for both the transcriptional and translational gene expression processes at the steady state. v4 denotes cellular noise in mature protein expression at the steady state. Besides, biological components are inherently uncertain in a molecular biological system (Chen and Wang 2006). For example, the intrinsic kinetic parameters of the components including the processes of transcription and translation, the degradation rates of regulatory proteins, the dilution rates of the cells, and the maturation rate for the reporter proteins are all stochastically uncertain in vivo, as a result of gene expression noise from biochemical processes, thermal fluctuations, DNA mutation, and evolution. These perturbations are defined as follows:
$$ {\displaystyle \begin{array}{l}{P}_{u,i}\to {P}_{u,i}+\Delta {P}_{u,i}{n}_1(t),{P}_{l,i}\to {P}_{l,i}+\Delta {P}_{l,i}{n}_2(t),\\ {}{P}_{u,j}\to {P}_{u,j}+\Delta {P}_{u,j}{n}_3(t),\\ {}{P}_{u,k}\to {P}_{u,k}+\Delta {P}_{u,k}{n}_4(t),{P}_{l,k}\to {P}_{l,k}+\Delta {P}_{l,k}{n}_5(t),\\ {}{r}_E\to {r}_E+\Delta {r}_E{n}_6(t),\\ {}{r}_R\to {r}_R+\Delta {r}_R{n}_7(t),\\ {}{r}_G\to {r}_G+\Delta {r}_G{n}_8(t),\\ {}m\to m+\Delta {mn}_9(t),\\ {}r\to r+\Delta {rn}_{10}(t),\\ {}d\to d+\Delta {dn}_{11}(t)\end{array}} $$
(8)
where ΔPu, i, ΔPl, i, ΔPu, j, ΔPu, k, ΔPl, k, ΔrE, ΔrR, ΔrG, Δm, Δr, and Δd are the standard deviations of the corresponding stochastic parameters and nq(t), q = 1, 2, … , 11 denote Gaussian noise, which have zero mean and unit variance, and account for random fluctuation sources. If the kinetic parameters in the steady-state model in (7) are replaced by the parameter perturbations shown in for robust design of the gene circuit, then the QS-based metal ion biosensor can tolerate these fluctuations in vivo, i.e., a design that accounts for (8) should be able to tolerate the parameter fluctuations.

Design Specifications for QS-Based Metal Ion Biosensor

The purpose of our design is to construct a QS-based metal ion biosensor by selecting a set of suitable components from the corresponding libraries to achieve optimal tracking of a desired I/O response within a feasible range of metal ion concentrations. To achieve this, the following design specifications are needed:
  • Desired I/O response Gref(IM) of the synthetic genetic QS-based metal ion biosensor

  • A feasible range of metal ion concentrations

  • Standard derivations of cellular disturbances and parameter fluctuations to be tolerated in vivo

  • A cost function between the desired reference steady-state fluorescence intensity Gref and the steady-state fluorescence intensity Gss in within a specified range of metal ion concentrations is given to be minimized as follows:
    $$ J(S)=E\int {\left({G}_{ss}\left(S,{I}_M\right)-{G}_{ref}\left({I}_M\right)\right)}^2{dI}_M $$
    (9)
where S denotes the set of promoter-RBS components Mi, Cj, and Ak to be selected from the corresponding libraries in Appendix. If the cost function in is minimized by choosing the most appropriate set of components under design specifications, the fluorescence intensity of an engineered metal ion biosensor will be as close as possible to the specified steady-state fluorescence intensity under parameter fluctuations and environmental noise optimally. Although the cost function J(S) can be minimized by traditional conventional search methods, it will require long computation times and several trial-and-error experimentations when component libraries become large. Thus, a more effective and efficient genetic algorithm (GA)-based searching method is proposed here to save time in evaluating and selecting adequate promoter-RBS components from corresponding libraries in Appendix.

Design Procedure for the QS-Based Metal Ion Biosensor

The design procedure for a QS-based metal ion biosensor is summarized as follows:
  1. 1.

    Provide user-defined design specifications Gref(IM) for the quorum sensing-based metal ion biosensor.

     
  2. 2.

    Select an initial set S of promoter-RBS components from the corresponding libraries.

     
  3. 3.
    Calculate the cost value J(S) in for S. The relationship between the fitness value F(S) and the cost value J(S) is inversely proportional to (10)
    $$ F(S)=\frac{1}{J(S)}. $$
    (10)
    The fitness value plays a key role in natural selection for selecting a set S of promoter-RBS components to maximize the fitness value F(S) or equivalently to minimize the cost function J(S) in (9). For example
    $$ \underset{S}{\max }F(S)=\frac{1}{\underset{S}{\min }J(S)}. $$
    (11)
     
  4. 4.
    Create an offspring set S, using GA operators such as reproduction, crossover, and mutation (Chen et al. 1995).
    1. (a)

      Make copies of possible solutions, on basis of their fitness.

       
    2. (b)

      Swap values between two possible solutions.

       
    3. (c)

      Randomly alter the value in a possible solution.

       
     
  5. 5.

    Calculate the cost value of the new set S obtained by natural selection. Stop when the design goal is achieved or an acceptable solution is obtained due to a limited number of components available from the libraries. Otherwise, create the next generation and return to step 3.

     

Experimental Results

For the convenience of description and explanation, as shown in Fig. 3, a QS-based metal ion biosensor is assembled by selecting a set of components from component libraries in Appendix, namely, a metal ion-induced promoter-RBS component Mi, a constitutive promoter-RBS component Cj, and a QS-dependent promoter-RBS component Ak. The design specifications are as follows:
  • The desired fluorescence intensity to different metal ion concentrations is described as follows:
    $$ {G}_{ref}\left({I}_M\right)=65+\frac{5000}{1+{\left(\frac{10^{-1}}{I_M}\right)}^2}. $$
    (12)
  • Input operation range: 10−3 to 100 μM (National Technical Information Service 1980).

  • The standard deviations of parameter fluctuations that are supposed to be tolerated in vivo are given by
    $$ {\displaystyle \begin{array}{l}\Delta {P}_{u,i}=0.05{P}_{u,i},\Delta {P}_{l,i}=0.05{P}_{l,i},\Delta {P}_{u,j}=0.05{P}_{u,j},\\ {}\Delta {P}_{u,k}=0.05{P}_{u,k},\Delta {P}_{l,k}=0.05{P}_{l,k},\Delta {r}_E=0.05{r}_E,\\ {}\Delta {r}_R=0.05{r}_R,\Delta {r}_G=0.05{r}_G,\Delta r=0.05r,\\ {}\Delta m=0.05m,\Delta d=0.05d\end{array}} $$
    (13)
  • and the external environmental noise vp, p = 1, 2, 3, for transcription and translation processes, and noise v4, for mature reporter protein expression, are all Gaussian, with zero mean and unit variance.

  • The cost function is given by
    $$ J(S)=E\underset{10^{-3}}{\overset{10^0}{\int }}{\left({G}_{ss}\left(S,{I}_M\right)-{G}_{ref}\left({I}_M\right)\right)}^2{dI}_M $$
    (14)
In order to efficiently solve the constrained optimal matching design problem of the metal ion biosensor, a GA-based library search method is employed to search a set S from corresponding libraries in Appendix to minimize the cost function (14). The adequate promoter-RBS components from the corresponding libraries in Appendix are found to be M1, C6, and A3. The desired response is shown in Fig. 2, with the fluorescence intensity values taken from Fig. 3 under different Cu(II) ion concentrations. Clearly, the metal ion biosensor can be as close as possible to the specified I/O response despite the parameter fluctuations and environmental noise. Besides, the detection performance is better than that without quorum sensing-based amplifier in Fig. 4 (see “Appendix” for mathematical details) at the same copper ion concentrations (see Figs. 5 and 6). In particular, the QS-based metal ion biosensor increases the sensitivity to Cu(II) ion by roughly one order of magnitude and the dynamic range by roughly fourfold. It confirms the quorum sensing-based metal ion biosensor is useful for enhancing the detection ability (Figs. 7 and 8).
Fig. 4

Results for the QS-based metal ion biosensor. By minimizing the cost function in for the metal ion biosensor in Fig. 1, an adequate set S = (M1, C6, A3) is selected from the corresponding libraries in Tables 1-3 in Appendix. The green points are the experimental results (mean of three trials) by S = (M1, C6, A3). The gray solid line is the desired I/O response in (12)

Fig. 5

Time profiles for the QS-based metal ion biosensor under different concentrations of Cu(II) ion, with measurements taken every 15 min. The green points are the experimental results by S = (M1, C6, A3)

Fig. 6

Copper ion biosensor without quorum sensing-based amplifier, using metal ion-induced promoter-RBS component M1 selected from the library in Table 1 in Appendix

Fig. 7

Results for the Cu(ii) ion biosensor without QS-based amplifier. The green points are the experimental results (mean of three trials) by M1 from the library in Table 1 in Appendix

Fig. 8

Comparison of Cu(II) ion biosensors with (top) and without (bottom) QS-based amplifier. The Cu(II) concentrations from left to right are 0, 10−3, 10−2, 5 × 10−2, 10−1, 5 × 10−1 and 1 μM

Conclusion

In this chapter, a QS-based biosensor is constructed to improve the performance of metal ion detection. Based on four design specifications, the QS-based biosensor can be constructed by selecting adequate promoter-RBS components in combination with a feasible range of metal ion concentrations. The proposed GA-based searching method could provide synthetic biologists with a useful tool to save time in selecting adequate promoter-RBS components to meet a specified detection performance. The experimental results confirm that the quorum sensing-based biosensor can efficiently enhance the performance in metal ion detection. In the future, the mechanism of metal ion detection can be used for environmental bioremediation (Wang and Chen 2009). Bioremediation, which utilizes the ability of biosorption (e.g., protein) to bind the ions using biomass or biopolymers, is a promising approach for environmental treatment. Proteins for biosorption are extensively studied for their specific binding regions and are engineered as biosorbent because of their higher adsorption capacity, low cost, and reusability (Wang and Chen 2009; He and Chen 2014). Research indicates that biosorbents contain a variety of functional sites including carboxyl, phosphate, amino groups, etc., and biology materials, like bacteria, yeast, and fungi, have gained attention for their removal and recovery abilities (Wang and Chen 2009; He and Chen 2014). Ravikumar et al. used a recombinant strain based on the specific interaction of Cu(II) with metal-binding peptide, which displayed selective adsorption of Cu(II) from aqueous solutions (Ravikumar et al. 2012). Thus, the QS-based biosensor can be combined with the Cu(II) biosorption system to promote bioremediation (see Fig. 9).
Fig. 9

A copper sensing and adsorbing system in E. coli

References

  1. Achtman M, Suerbaum S (2001) Helicobacter pylori: molecular and cellular biology. Horizon Scientific, WymondhamGoogle Scholar
  2. Alon U (2007) An introduction to systems biology: Design principles of biological circuits. Chapman & Hall/CRC Press, Boca RatonGoogle Scholar
  3. National Technical Information Service (1980) Ambient water quality criteria for copper. National Technical Information Service, Washington, DC/SpringfieldGoogle Scholar
  4. Bondarczuk K, Piotrowska-Seget Z (2013) Molecular basis of active copper resistance mechanisms in gram-negative bacteria. Cell Biol Toxicol 29:397–405CrossRefGoogle Scholar
  5. Borremans B, Hobman JL, Provoost A, Brown NL, van Der Lelie D (2001) Cloning and functional analysis of the PBR lead resistance determinant of Ralstonia metallidurans CH34. J Bacteriol 183:5651–5658CrossRefGoogle Scholar
  6. Brint JM, Ohman DE (1995) Synthesis of multiple exoproducts in Pseudomonas aeruginosa is under the control of RhlR-RhlI, another set of regulators in strain PAO1 with homology to the autoinducer-responsive LuxR-LuxI family. J Bacteriol 177:7155–7163CrossRefGoogle Scholar
  7. Brown NL, Stoyanov JV, Kidd SP, Hobman JL (2003) The MerR family of transcriptional regulators. FEMS Microbiol Rev 27:145–163CrossRefGoogle Scholar
  8. Cameron DE, Bashor CJ, Collins JJ (2014) A brief history of synthetic biology. Nat Rev Microbiol 12:381–390CrossRefGoogle Scholar
  9. Chang YC, Lin CL, Jennawasin T (2013) Design of synthetic genetic oscillators using evolutionary optimization. Evol Bioinform 9:137CrossRefGoogle Scholar
  10. Chen BS, Wang YC (2006) On the attenuation and amplification of molecular noise in genetic regulatory networks. BMC Bioinform 7:52CrossRefGoogle Scholar
  11. Chen B-S, Wang Y-C (2014) Synthetic gene network: modeling, analysis, robust design methods. CRC Press, Boca RatonCrossRefGoogle Scholar
  12. Chen BS, Cheng YM, Lee CH (1995) A genetic approach to mixed H-2/H-infinity optimal pid control. IEEE Control Syst Mag 15:51–60CrossRefGoogle Scholar
  13. Danino T, Mondragon-Palomino O, Tsimring L, Hasty J (2010) A synchronized quorum of genetic clocks. Nature 463:326–330CrossRefGoogle Scholar
  14. Darch SE, West SA, Winzer K, Diggle SP (2012) Density-dependent fitness benefits in quorum-sensing bacterial populations. Proc Natl Acad Sci U S A 109:8259–8263CrossRefGoogle Scholar
  15. Davies MJ (2005) The oxidative environment and protein damage. Biochim Biophys Acta-Protein Proteom 1703:93–109CrossRefGoogle Scholar
  16. Dunlap PV, Kuo A (1992) Cell density-dependent modulation of the Vibrio-fischeri luminescence system in the absence of autoinducer and luxr protein. J Bacteriol 174:2440–2448CrossRefGoogle Scholar
  17. Engebrecht J, Silverman M (1984) Identification of genes and gene-products necessary for bacterial bioluminescence. Proc Natl Acad Sci USA Biol Sci 81:4154–4158CrossRefGoogle Scholar
  18. Franke S, Grass G, Rensing C, Nies DH (2003) Molecular analysis of the copper-transporting efflux system CusCFBA of Escherichia coli. J Bacteriol 185:3804–3812CrossRefGoogle Scholar
  19. Fuqua WC, Winans SC, Greenberg EP (1994) Quorum sensing in bacteria – the luxr-luxi family of cell density-responsive transcriptional regulators. J Bacteriol 176:269–275CrossRefGoogle Scholar
  20. Hanzelka BL, Greenberg EP (1996) Quorum sensing in Vibrio fischeri: evidence that S-adenosylmethionine is the amino acid substrate for autoinducer synthesis. J Bacteriol 178:5291–5294CrossRefGoogle Scholar
  21. Hartwig A (1995) Current aspects in metal genotoxicity. BioMetals 8:3–11CrossRefGoogle Scholar
  22. He J, Chen JP (2014) A comprehensive review on biosorption of heavy metals by algal biomass: materials, performances, chemistry, modeling simulation tools. Bioresour Technol 160:67–78CrossRefGoogle Scholar
  23. Hobman JL, Julian DJ, Brown NL (2012) Cysteine coordination of Pb(II) is involved in the PbrR-dependent activation of the lead-resistance promoter, PpbrA, from Cupriavidus metallidurans CH34. BMC Microbiol 12:109CrossRefGoogle Scholar
  24. Kaplan HB, Greenberg EP (1985) Diffusion of autoinducer is involved in regulation of the Vibrio-fischeri luminescence system. J Bacteriol 163:1210–1214PubMedPubMedCentralGoogle Scholar
  25. Khalil AS, Collins JJ (2010) Synthetic biology: applications come of age. Nat Rev Genet 11:367–379CrossRefGoogle Scholar
  26. Kotula JW, Kerns SJ, Shaket LA, Siraj L, Collins JJ, Way JC et al (2014) Programmable bacteria detect and record an environmental signal in the mammalian gut. Proc Natl Acad Sci U S A 111:4838–4843CrossRefGoogle Scholar
  27. Kyung Hyuk K, Kiri C, Bartley B, Sauro HM (2015) Controlling E. coli gene expression noise. IEEE Trans Biomed Circuits Syst 9(4):497–504CrossRefGoogle Scholar
  28. Lee SM, Grass G, Rensing C, Barrett SR, Yates CJD, Stoyanov JV et al (2002) The PCO proteins are involved in periplasmic copper handling in Escherichia coli. Biochem Biophys Res Commun 295:616–620CrossRefGoogle Scholar
  29. Migaszewski ZM, Galuszka A (2015) The characteristics, occurrence, geochemical behavior of rare earth elements in the environment: a review. Crit Rev Environ Sci Technol 45:429–471CrossRefGoogle Scholar
  30. Miller MB, Bassler BL (2001) Quorum sensing in bacteria. Annu Rev Microbiol 55:165–199CrossRefGoogle Scholar
  31. Mulligan CN, Yong RN, Gibbs BF (2001) Remediation technologies for metal-contaminated soils and groundwater: an evaluation. Eng Geol 60:193–207CrossRefGoogle Scholar
  32. Munson GP, Lam DL, Outten FW, O’Halloran TV (2000) Identification of a copper-responsive two-component system on the chromosome of Escherichia coli K-12. J Bacteriol 182:5864–5871CrossRefGoogle Scholar
  33. Nealson KH, Hastings JW (1979) Bacterial bioluminescence: its control and ecological significance. Microbiol Rev 43:496–518PubMedPubMedCentralGoogle Scholar
  34. Ngah WSW, Hanafiah MAKM (2008) Removal of heavy metal ions from wastewater by chemically modified plant wastes as adsorbents: a review. Bioresour Technol 99:3935–3948CrossRefGoogle Scholar
  35. Passador L, Cook JM, Gambello MJ, Rust L, Iglewski BH (1993) Expression of Pseudomonas aeruginosa virulence genes requires cell-to-cell communication. Science 260:1127–1130CrossRefGoogle Scholar
  36. Pearson JP, Passador L, Iglewski BH, Greenberg EP (1995) A second N-acylhomoserine lactone signal produced by Pseudomonas aeruginosa. Proc Natl Acad Sci U S A 92:1490–1494CrossRefGoogle Scholar
  37. Raha S, Robinson BH (2000) Mitochondria, oxygen free radicals, disease and ageing. Trends Biochem Sci 25:502–508CrossRefGoogle Scholar
  38. Ravikumar S, Ganesh I, Yoo IK, Hong SH (2012) Construction of a bacterial biosensor for zinc and copper and its application to the development of multifunctional heavy metal adsorption bacteria. Process Biochem 47:758–765CrossRefGoogle Scholar
  39. Rezvani-Boroujeni A, Javanbakht M, Karimi M, Shahrjerdi C, Akbari-adergani B (2015) Immoblization of thiol-functionalized nanosilica on the surface of poly(ether sulfone) membranes for the removal of heavy-metal ions from industrial wastewater samples. Ind Eng Chem Res 54:502–513CrossRefGoogle Scholar
  40. Rouch DA, Brown NL (1997) Copper-inducible transcriptional regulation at two promoters in the Escherichia coli copper resistance determinant pco. Microbiology 143:1191–1202CrossRefGoogle Scholar
  41. Ruby EG (1996) Lesson from a cooperative, bacteria-animal association: The Vibrio fischeri- Euprymna scolopes light organ symbiosis. Annu Rev Microbiol 50:591–624CrossRefGoogle Scholar
  42. Ruby EG, Mcfallngai MJ (1992) A squid that glows in the night – development of an animal-bacterial mutualism. J Bacteriol 174:4865–4870CrossRefGoogle Scholar
  43. Ruby EG, Nealson KH (1976) Symbiotic association of Photobacterium fischeri with the marine luminous fish Monocentris japonica; a model of symbiosis based on bacterial studies. Biol Bull 151:574–586CrossRefGoogle Scholar
  44. Silva-Rocha R, de Lorenzo V (2014) Engineering multicellular logic in bacteria with metabolic wires. ACS Synth Biol 3:204–209CrossRefGoogle Scholar
  45. Singha AS, Guleria A (2014) Chemical modification of cellulosic biopolymer and its use in removal of heavy metal ions from wastewater. Int J Biol Macromol 67:409–417CrossRefGoogle Scholar
  46. Sohka T, Heins RA, Phelan RM, Greisler JM, Townsend CA, Ostermeier M (2009) An externally tunable bacterial band-pass filter. Proc Natl Acad Sci USA 106:10135–10140CrossRefGoogle Scholar
  47. Soltani M, Vargas-Garcia CA, Singh A (2015) Conditional moment closure schemes for studying stochastic dynamics of genetic circuits. IEEE Trans Biomed Circuits Syst 9(4):518–526CrossRefGoogle Scholar
  48. Stricker J, Cookson S, Bennett MR, Mather WH, Tsimring LS, Hasty J (2008) A fast, robust and tunable synthetic gene oscillator. Nature 456:516–U39CrossRefGoogle Scholar
  49. Taghavi S, Mergeay M, Nies D, Vanderlelie D (1997) Alcaligenes eutrophus as a model system for bacterial interactions with heavy metals in the environment. Res Microbiol 148:536–551CrossRefGoogle Scholar
  50. Teo JJY, Sung Sik W, Sarpeshkar R (2015) Synthetic biology: a unifying view and review using analog circuits. IEEE Trans Biomed Circuits Syst 9(4):453–474CrossRefGoogle Scholar
  51. Teodosiu C, Wenkert R, Tofan L, Paduraru C (2014) Advances in preconcentration/removal of environmentally relevant heavy metal ions from water and wastewater by sorbents based on polyurethane foam. Rev Chem Eng 30:403–420CrossRefGoogle Scholar
  52. Tetaz TJ, Luke RK (1983) Plasmid-controlled resistance to copper in Escherichia coli. J Bacteriol 154(Jun):1263–1268PubMedPubMedCentralGoogle Scholar
  53. Val DL, Cronan JE (1998) In vivo evidence that S-adenosylmethionine and fatty acid synthesis intermediates are the substrates for the luxi family of autoinducer synthases. J Bacteriol 180:2644–2651PubMedPubMedCentralGoogle Scholar
  54. Wang J, Chen C (2009) Biosorbents for heavy metals removal and their future. Biotechnol Adv 27:195–226CrossRefGoogle Scholar
  55. Wang BJ, Kitney RI, Joly N, Buck M (2011) Engineering modular and orthogonal genetic logic gates for robust digital-like synthetic biology. Nat Commun 2:508CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Electric EngineeringNational Tsing Hua UniversityHsinchuTaiwan

Section editors and affiliations

  • Shimshon Belkin
    • 1
  • Paul Freemont
    • 2
  1. 1.Institute of Life SciencesThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Faculty of MedicineImperial CollegeLondonUK

Personalised recommendations