Appendix Appendix A: Construction of Promoter-rbs Libraries Construction of Constitutive Promoter-rbs Libraries

Before we construct the promoter-RBS libraries, we select the GFP (BBa_E0040) to measure the fluorescence of protein. The fluorescence of GFP can respond to the upstream signal variations. For the construction of the constitutive promoter-RBS constitutive promoter-RBS components. After a constitutive promoter-RBS component is inserted at the upstream of the reporter protein as shown in Figure A1(i), the reporter protein could be produced continually. The reporter protein could be diluted by cell growth, degraded by protease and matured by the post-translation modification. Similarly, the mature reporter protein can be diluted and degraded, too. The dynamic model of reporter protein under the regulation of constitutive promoter-RBS component with the environmental disturbances is shown as follows [32, A1]. const c im x m x x c t p P m x c t v t g c t mx c t g c t v t µ γ µ γ = − + + + = − + + (A1) where () , x c t and () , g c t denote the concentrations of the immature and mature reporter protein, respectively; () 1 v t and () 2 v t denote the environmental disturbances of the immature and mature reporter protein, respectively; µ denotes the dilution rate, m denotes the mature rate of the reporter protein, and , im x γ and , m x γ denote the degradation rates of the immature and mature reporter protein , respectively. The procedure for constructing constitutive promoter-RBS libraries shown in Figure A1 can be divided into four steps: (i) select the candidate constitutive


Background
Synthetic biology aims to perform various specific functions in organisms by inserting a designed gene network. In the past, synthetic biology could be classified as having two broad purposes. The first was to create artificial life from natural biology using the synthetic methods. The other was to assemble some functional components using interchangeable natural components which are nonexistent in natural biology [1]. A lot of the recent literature focuses on performing electronic circuit behaviors in organisms using genetic devices such as toggle switches [2][3][4][5], oscillators [6][7][8][9][10][11][12][13], pulse generators [14,15], logic gates [16][17][18][19], and filters [20][21][22]. Synthetic biologists also design various types of genetic circuits with different functionalities by employing genetic devices to solve useful tasks, such as biosensor decisions or edge detection [23,24].
In many industries, such as the electronics and manufacturing industries, the characterization and standardization of components and the institution of specifications are already key elements in the production line. In the synthetic biology, the expression of a specific protein needs a promoter, a ribosome binding side (RBS), a protein coding sequence and a terminator, which are DNA fragments. The Registry of Biological Standard Parts (http://www.partsregistry.org), formed by MIT, shows many standard BioBricks, and these standard biological components provide synthetic biologists with a quick and standardized way of constructing gene circuits. Also, BioFAB provides some sorts of biobricks (see http://biofab.org/data), enabling the rapid design and prototyping of genetic constructs. However, in the past, the strength of a promoter and an RBS, which are the main components of transcription and translation, were defined according to their relative strength with other promoters and RBSs. Now, however, the promoter-RBS strength can be quantified by measuring the fluorescence of proteins whose coding gene is constructed at the downstream of the promoter-RBS component.
Based on the kinetic strengths of promoter-RBS components, promoter-RBS libraries are constructed for gene circuit design. In our gene circuit design, promoter-RBS libraries are built based on kinetic parameters of the dynamic gene regulation, which are identified by the nonlinear least squares method based on experimental data. We formulate the design specifications of desired gene circuits in advance and choose an adequate set of promoter-RBS components from the promoter-RBS libraries based on the characterized, standardized and quantified components. For our promoter-RBS libraries, we select three kinds of promoters, i.e., constitutive promoters, repressor-regulated promoters and activator-regulated promoters, to combine with RBSs as the promoter-RBS components. Each of these is constructed using the green fluorescent protein in Escherichia coli. and characterized to allow for the construction of the following three types of promoter-RBS libraries: constitutive promoter-RBS libraries, repressorregulated promoter-RBS libraries and activator-regulated promoter-RBS libraries.
To date, several researchers have demonstrated that synthetic gene circuits have the functionality of amplification or switching [25][26][27][28][29]. These gene circuits can amplify the input signal or switch the output signal as it exceeds a specific threshold level. Often shown in these genetic amplifiers is the use of a two-stage cascade of promoters to achieve the function of amplification. However, these circuits only amplify a low level of input signal or low concentration of inducer at the first stage while the second stage consists of the promoter-RBS activity being fixed. On the other hand, switching circuits switch the output signal using an external inducer. When the inducer is externally increased, the circuit is on, and vice versa. Nevertheless, at present, the on-state, or high level, of switching has not been clearly defined.
In this paper, we demonstrate that a simple repressive gene circuit can work like an electrical transistor as an amplifier or a switch. The amplification gains or switch levels of the genetic transistor are regulated by the concentrations of inducer and different combinations of promoters with RBSs. For the convenience of measurement and application, reporter genes are constructed as the measurable input and output. We show that the I/O characteristics of the repressive gene circuit regulated by inducer concentration can be effectively predicted by adequate selection of promoter-RBS components from our libraries. Thus, based on these promoter-RBS libraries, a look-up table is built to quickly select adequate promoter-RBS components for the design of genetic transistors with different design specifications.
In the following sections, we first construct the promoter-RBS libraries based on the promoter-RBS strength through the dynamic regulatory model of promoter-RBS components. Then, we describe the I/O characteristics of a genetic transistor with different kinetic strengths of promoter-RBS components in the promoter-RBS libraries and different concentrations of inducers. Finally, a look-up table (or genetic transistor library) is constructed for genetic transistor design requiring prescribed I/O characteristics, which is used by searching the most appropriate sets of promoter-RBS components and concentrations of inducers via the genetic algorithm (GA).

Construction of the promoter-RBS libraries for genetic transistors
In this section, we introduce the characterization and standardization of promoter-RBS libraries and employ a dynamic mathematical model to construct the promoter-RBS libraries according to the identified kinetic strengths of promoter-RBS components, populated via experimental data.

Promoter-RBS libraries based on the identified kinetic strengths of promoter-RBS components
In a systematic design procedure, the characterization and standardization of components are important preparatory tasks before practical design process. These can save designers a significant amount of time and avoid unnecessary trial-and-error attempts. In the field of synthetic biology, a particular technique was developed to create standard interchangeable biological components called BioBricks [30,31]. These allow the synthetic biologists to focus on the design of more complex genetic circuits rather than the basic construction of the gene components.
BioBricks are DNA fragments with specific functions, and include promoters, ribosome binding sites (RBS), repressors, activators, reporters and terminators. In the database, there are only a few BioBrick components that are well-characterized. The well-characterized BioBrick components are conducive to the systematic design of synthetic genetic circuits. In order to facilitate the design of synthetic gene circuits, wider libraries of wellcharacterized BioBricks need to be constructed.
In our promoter-RBS libraries, the library indexes are the kinetic strengths of promoter and RBS, which are considered together as a promoter-RBS component because the gene expression is regulated by a promoter-RBS component. The kinetic strength of a promoter-RBS component can be systematically identified by a stochastic model which simulates the dynamic behavior of promoter-RBS components under some external molecular or environmental noises. In order to identify the kinetic strength of a promoter-RBS component, the green fluorescence gene is embedded into the downstream of the promoter-RBS component. By measuring the fluorescence dynamic time profile and using the nonlinear least squares method [32], we identify the kinetic strengths of the promoter-RBS components to be used as the indexes of promoter-RBS libraries.
The construction procedure of the promoter-RBS libraries can be generally divided into four steps [33]: (i) choose the required promoter-RBS components, (ii) select the suitable reporter protein and growth conditions, (iii) measure the time-profile data of the dynamic behavior, and (iv) construct the dynamic regulatory model for identifying kinetic strengths of promoter-RBS components to be used as library indexes according to the nonlinear least squares method. In the first step, some promoters can be regulated by specific transcription factors, and different combinations of promoters with RBSs give different kinetic strengths of promoter-RBS components, which increase the diversity of the libraries. In order to rapidly obtain a variety of kinetic strengths of promoter-RBS components, a mutation technique was used to create different kinetic strengths of promoters and RBSs to increase the varieties of promoter-RBS components through the mutation of a specific region on promoters or RBSs [18,33]. In the second and third step, since different reporter proteins, such as the green fluorescent protein or red fluorescent protein have different degradation rates, the measurement times may differ. Further, the cell growth conditions have an effect on the results of the measurement. Biological component can be characterized at different cellular growth phases, under different culture conditions, or at different resolutions. In our experiment, the GFP is selected as the reporter protein and the time profiles of fluorescence are measured by the microplate reader. In the final step, a mathematical dynamic model is built to describe the time profile of protein expression. Using the protein expression time profile measurements, the nonlinear least squares method is employed to identify the kinetic strengths of promoter-RBS components to be used as the library indexes with the mathematical model. For the systematic design of genetic transistors, we construct three kinds of promoter-RBS libraries, i.e., constitutive, repressor-regulated and activator-regulated promoter-RBS libraries. The promoter-RBS components in promoter-RBS libraries and all BioBrick components used in this study are listed in Additional file 1, respectively. The detailed construction procedures of constitutive, repressorregulated and activator-regulated promoter-RBS libraries are described in Additional file 1.

Construction and design of the genetic transistor
After the introduction of regulatory functions of promoter-RBS components and the construction of the promoter-RBS libraries, we design a synthetic genetic circuit, similar to a transistor, with prescribed I/O characteristics of amplification or switching through the external inducer. Before the construction of the synthetic genetic transistor, we introduce the simply operation of an electronic transistor in Additional file 1 to which the genetic transistor will be designed accordingly following.

Construction of the genetic transistor
A genetic transistor is shown in Figure 1(a). The transistor is constructed to obtain the output protein concentration x protein of the transistor for amplification or switching behavior. The genetic transistor consists of the repressorregulated promoter-RBS component c 3 and a repressor coding gene. The input repressor x repressor2 to the genetic transistor is controlled by the repressor-regulated promoter-RBS component c 2 , which is regulated by the corresponding repressor. The input repressor x repressor2 will form the complex and restrict the production of output protein x protein by binding the corresponding repressorregulated promoter-RBS component c 3 to decrease its kinetic strength. However, when the inducer is added, this inducer will bind input repressor x repressor2 and prevent it from binding to the repressor-regulated promoter-RBS component c 3 . Then, both the kinetic strength of repressor-regulated promoter-RBS component c 3 and the production of output protein x protein will increase. The dynamic model of a genetic transistor is described as follows: where x repressor2 and x protein denote the concentrations of input repressor2 and the output protein of the genetic transistor, respectively, and γ protein denotes the degradation rate of the protein.
However, the protein concentration is difficult to directly measure and quantify. To determine characteristics of the synthetic genetic transistor, a genetic transistor with measurement circuit is constructed as shown in Figure 1(b). In Figure 1(b), we construct an additional repressor-regulated promoter-RBS component c 2 so that the input reporter protein x 1 can be measured by input fluorescence g 1 and the output reporter protein x 2 can be measured by output fluorescence g 2 . Note that RFP is used to measure input while GFP is used to measure output. Additionally, for the convenience of the input regulation, we construct an input signal generation device with the concentration of inducer I 1 to control the input g 1 of the genetic transistor circuit. Then, the dynamic model of a synthetic genetic transistor circuit with I/O measure devices under environmental disturbances is described by the following set of equations: where m 1 and m 2 denote the maturation rates of reporter1 x 1 and reporter2 x 2 , respectively, and v i (t), i = 1, 2, ⋯, 6 denote the noises. To explore the I/O characteristics of a synthetic genetic transistor with the function of amplification or switching, the steady state model of (2) is given by where v s i , i = 1, 2, ⋯, 6 denote the noises at the steady state.
From (3), if m 1 ≈ m 2 , γ m;x 1 ≈γ m;x 2 and γ im;x 1 ≈γ im;x 2 , then the I/O characteristic can be regarded as input/output = x repressor2 /x protein ≈ x 1 /x 2 ≈ g 1 /g 2 , i.e., we could use the x 1 / x 2 or g 1 /g 2 ratio to replace the I/O characteristic of the synthetic genetic transistor. Further, the I/O characteristic can be controlled and regulated by the selection of promoter-RBS components c 3 and inducer concentration I 2 . Therefore, we need to define the I/O characteristic of synthetic genetic transistor circuits to design a genetic transistor with the desired I/O characteristic. This is done as follows: where y ss (c 3 , I 2 , g 1 ) denotes the I/O response of the synthetic genetic transistor circuit between input signal g 1 and output signal g 2 , and g 1e and g 1n denote the lower bound and upper bound of g 1 . a.u. stands for arbitrary unit. In Figure 1(b), promoter-RBS components c 1 and c 2 can be selected to control input signals x repressor1 (c 1 ) and x repressor2 (c 2 , I 1 ) in (3). In general, genetic components are inherently uncertain in the biological system as a result of gene expression noises in transcription or translation processes, thermal fluctuations, DNA mutations, evolutions, context-dependence between promoters, 5′UTRs, and coding sequences, as well as parameter estimation errors [34][35][36][37]. Hence, we model the uncertain kinetic strengths of promoter-RBS components, degradation rate of proteins and transcription/ translation rates as stochastic processes in the following model: γ im;x2 →γ im;x2 þ Δγ im;x2 n 3 t ð Þ; γ m;x2 →γ m;x2 þ Δγ m;x2 n 3 t ð Þ; where ΔP c 1 , ΔP M;c 2 , ΔP m;c 2 , ΔP M;c 3 , ΔP m;c 3 , Δγ repressor1 , Δγ repressor2 , Δγ im;x 1 , Δγ m;x 1 , Δγ im;x 2 , Δγ m;x 2 , Δm 1 , Δm 2 and Δμ denote the standard deviations of stochastic parameters to be tolerated and could be specified before design and n i (t), i = 1, 2, 3 denote Gaussian noises with zero mean and unit variance. Therefore, ΔP c 1 , ΔP M;c 2 , ΔP m;c 2 , ΔP M;c 3 , ΔP m;c 3 , Δγ repressor1 , Δγ repressor2 , Δγ im;x 1 , Δγ m;x 1 , Δγ im;x 2 , Δγ m;x 2 , Δm 1 , Δm 2 and Δμ denote the deterministic parts of parameter variations and n i (t), i = 1, 2, 3 denote different random fluctuation sources. For robust design of the genetic transistor circuit, these parameter fluctuations in (5) will henceforth be considered in the design procedure so that the synthetic genetic transistor can tolerate these kinds of parameter fluctuations in vivo.
With fixed concentration of inducer I 2 , we expect that the input signal g 1 /output signal g 2 (I/O) characteristics of the synthetic genetic transistor in (4) would be similar to the voltage I/O characteristics of the electronic transistor shown in Additional file 1. When the inducer concentration I 1 increases, the kinetic strength of promoter-RBS component c 2 increases along with the fluorescence of the input signal g 1 , which means that the repressor concentration x repressor2 increases. Due to the fixed concentration of inducer I 2 , the redundant repressors x repressor2 , which are not bound by the inducer I 2 , will repress the promoter-RBS component c 3 , and the fluorescence of output signal g 2 will decrease. Therefore, the I/O characteristic of the synthetic genetic transistor is similar to Additional file 1. Additionally, from Additional file 1, we see that if input signal is in the operation range of linear amplification, the input signal would be inversely amplified. Now, consider the alternative viewpoint, i.e., the voltage I/O characteristics of an electronic transistor. When R 2 /R 1 increases, the reverse amplification gain will become large and the operation region of linear amplification will narrow as shown in (B1)-(B3) and Additional file 1. In the synthetic genetic transistor, we expect that when the concentration of inducer I 2 changes as per the R 2 /R 1 ratio in (B2)-(B3), the I/O characteristics would be similar to the voltage I/O characteristics of electronic transistor in Additional file 1. Due to different concentrations of inducer I 2 , the effect of the inducer on the input repressor can vary. When the inducer concentration I 2 decreases, the I/O characteristics would sharpen, so the reverse amplification gain becomes large in the operation region of linear amplification.
Finally, when R 2 /R 1 is large enough in (B2)-(B3), the operation region of linear amplification will become too narrow and result in a sharp change in this region. Correspondingly with a synthetic genetic transistor, when the inducer concentration I 2 is low enough, the input signal g 1 will produce a small variation, and the output signal g 2 will have an acute change like a switch. Therefore, according to the analysis above, we could obtain varying reverse amplification gains and switch levels by changing the concentration of inducer I 2 .

Systematic design of a genetic transistor based on design specification
According to the above analysis in Figure 1(b), we can obtain different reverse amplification gains or switch behaviors via regulation of different concentrations of inducer I 2 . Additionally, due to the output signal g 2 being under the controlled by promoter-RBS component c 3 , we could change the output range by selecting different repressor-regulated promoter-RBS components c 3 from the repressor-regulated promoter-RBS libraries. In this way, we can control the I/O characteristics of a synthetic genetic transistor to obtain different reverse amplification gains or switch levels by choosing different concentrations of inducer I 2 and selecting different repressor-regulated promoter-RBS components c 3 from the repressor-regulated promoter-RBS libraries.
In Figure 1(b), the input signal generation device consists of a constitutive promoter-RBS component c 1 , and a repressor-regulated promoter-RBS component c 2 and an inducer I 1 . The constitutive promoter-RBS component c 2 is selected to produce the input repressor continually. Further, for convenience of design, the repressor-regulated promoter-RBS component c 2 is selected from the corresponding promoter-RBS library to have sufficient kinetic strength to obtain an adequate maximum regulation range of input signal regulated by inducer I 1 . However, the operation region of linear amplification is still limited in the amplifier design of genetic transistor, and the input signal range might not be fully contained in the operation region of linear amplification. Therefore, the input signal range should be considered in relation to the design purpose. In the procedure of amplifier design, the input operation range g 1 ∈ [g 1,l , g 1,u ] can be set by transforming the inducer concentration I 1 into the input fluorescence according to (2)

or (3) as follows
Input operation range: where I 1 and g 1 denote the inducer concentration and input fluorescence, respectively, I 1,l and I 1,u denote the lower and upper bound of inducer concentrations, respectively, and g 1,l and g 1,u denote the lower and upper bound of input fluorescences respectively. Note that, in the future, when the promoter-RBS libraries are large enough, the promoter-RBS components c 1 and c 2 can be designed and selected to match the input operation range. However, due to the limited size of our promoter-RBS libraries and for the convenience of design, we will select the repressor-regulated promoter-RBS component c 2 from the corresponding promoter-RBS library.
From the above analysis, the design purpose of an amplifier will lead to the selection of a suitable repressor-regulated promoter-RBS component c 3 from the repressor-regulated promoter-RBS libraries and concentration of inducer I 2 , i.e., {c 3 , I 2 }, so that the I/O characteristics of the synthetic genetic transistor in (4) in a specific input range g 1 ∊ [g 1,l , g 1,u ] can match the desired I/O response similar to (B2), i.e., y d g 1 ð Þ ¼ gain⋅ðg 1 −g 1;l Þ þ g 2;u ; g 1 ∈½g 1l ; g 1u a:u: ð Þ where g 1,l and g 2,u denote the lower bound of input fluorescence g 1 and upper bound of output fluorescence g 2 , respectively, and gain denotes the amplification gain of the genetic transistor. On the other hand, the switching behavior will occur when the input signal has a small variation (see Additional file 1), i.e., a high level signal can be switched into a low level signal and vice versa. In the switching behavior of synthetic genetic transistor, each promoter-RBS component has its own basal level. Thus, when the input signal increases, the output signal will rapidly decrease to the basal level. Therefore, the desired I/O response of a switch is described as follows: where H s and L s denote the high level and low level of switching, respectively, and g t denotes the transition point of input fluorescence. Moreover, the input signal range of I/O characteristics of the switch can be set by (6). Finally, for matching the desired I/O response of an amplifier or switch, the genetic algorithm (GA) is employed to select an adequate repressor-regulated promoter-RBS component c 3 in the repressor-regulated promoter-RBS libraries and the concentration of inducer I 2 to minimize the following cost function [38], respectively, i.e., min c 3 ∈Lib repressor ;I 2 ∈ I 2;l ;I 2;u ½ J c 3 ; I 2 ð Þ ¼ min c 3 ∈Lib repressor ;I 2 ∈ I 2;l ;I 2;u ½ E Z g 1;u g 1;l y ss c 3 ; To summarize the above design procedure of a biological amplifier and switch, a genetic transistor design procedure of by the promoter-RBS library searching method using GA is proposed as follows [38]: 1. Construct the genetic transistor circuit such as in Figure 1(a). 2. Build the dynamic and steady state mathematical model in (2) and (3), respectively. 3. Provide the design specification of amplifier with the desired I/O response as in (6) and (7) or switch with the desired I/O response as in (6) and (8) Based on the design procedure of a genetic transistor using the promoter-RBS library searching method with GA, the promoter-RBS component c 3 is selected from the corresponding repressor-regulated promoter-RBS library and the inducer concentration I 2 is selected within [I 2,l , I 2,u ], while the cost function is calculated in each iteration of the selection process. Then, GA would select the most adequate promoter-RBS component c 3 from the corresponding repressor-regulated promoter-RBS library and inducer concentration I 2 ∊ [I 2,l , I 2,u ] to minimize the cost function.

In silico synthetic genetic transistor design examples based on promoter-RBS libraries
We have presented the construction and design procedure of a synthetic genetic transistor. In this section, the synthetic genetic transistor is designed and simulated to verify the I/O characteristics of amplification and switching. Subsequently, based on our promoter-RBS libraries, the amplification gain in a specific input operation range and switching level are designed by employing GA to select the most adequate promoter-RBS components and inducer concentrations. Finally, to support future application of this method, a look-up table for genetic transistors is built for different genetic transistor design specifications.

Amplifier design example of synthetic genetic transistor
Consider the amplifier design of the synthetic genetic transistor. Firstly, to obtain the I/O characteristics of amplifier, promoter-RBS components {c 1 , c 2 } = {J 6 , L 3 } are selected to obtain the maximum input operation range. The dynamic model and the steady state model have been described in (2) and (3). The input operation range and desired I/O response of genetic transistor are specified as follows: Input operation range: and where −2 is the desired amplification gain as shown in Figure 2. Note that the standard deviations of parameter fluctuations that are supposed to be tolerated in vivo are given by ΔP c1 ¼ 0:05P c1 ; ΔP M;ci ; ΔP m;ci È É ¼ 0:05P M;ci ; 0:05P m;ci È É ; i ¼ 2; 3 Δγ LacI ¼ 0:05γ LacI ; Δγ TetR ¼ 0:05γ TetR Δγ im;x1 ¼ 0:05γ im;x1 ; Δγ m;x1 ¼ 0:05γ m;x1 Δγ im;x2 ¼ 0:05γ im;x2 ; Δγ m;x2 ¼ 0:05γ m;x2 Δm 1 ¼ 0:05m 1 ; Δm 2 ¼ 0:05m 2 ; Δμ ¼ 0:05Δμ ð12Þ and the environmental disturbances v i (t) are independent Gaussian noises with zero mean and unit variance. Finally, GA is employed to search a set {c 3 , I aTc } from corresponding libraries to minimize the following cost function: Then, the most adequate promoter-RBS component from the corresponding library and aTc concentration are found to be {c 3 , I aTc } = {T 3 , 0 ng/ml}. The estimation of I/O response of genetic transistor based on experimental results is shown in Figure 2, with experimental details summarized in Additional file 1. Clearly, the I/O characteristics of genetic transistor can match the desired I/O response in a workable input range g 1 ∊ [298, 431] under the intrinsic fluctuations and environmental disturbances.

Switch design example of synthetic genetic transistor
Consider the switch design of the synthetic genetic transistor. The switch design procedure is similar to the amplifier design procedure of a synthetic genetic transistor. Firstly, to obtain the complete I/O characteristics of switching, promoter-RBS components {c 1 , c 2 } = {J 6 , L 3 } are selected to obtain the maximum input operation range. The dynamic model and the steady state model have been described in (2) and (3), respectively. The input operation range and desired I/O switch response are specified as follows: Input operation range: and where L s denotes the low level of switching or basal level of promoter-RBS component c 3 . Note that the standard deviations of parameter fluctuations that are supposed to be tolerated in vivo and from environmental disturbances are the same as in (12). Finally, GA is employed to search a set {c 3 , I aTc } from corresponding libraries to minimize the following cost function:   For the convenience of synthetic genetic transistor design for synthetic biologists, one look-up table has been built for the various design specifications as shown in Table 1 via selecting adequate promoter-RBS components from the corresponding libraries and adequate inducer concentration to achieve the optimal matching in (9). Based on various amplification gains in some specific operation range, the synthetic genetic transistors can be designed by first checking the look-up table. In future, more promoter-RBS components and inducer concentrations for different I/O characteristics of synthetic genetic transistors can be accumulated to build much larger look-up tables to match a lot of design specifications. From this look-up table, based on the desired design specifications, we can select the adequate promoter-RBS components and inducer concentrations to synthesize the genetic transistors with desired I/O responses. Thus, less time will be spent on the design procedure as a designer will be able to easily construct transistors with the desired I/O characteristics.

Discussion
One major aim of synthetic biology is to construct a gene circuit with the desired functionality of an organism. Recently, promoter libraries and promoter-RBS libraries have been built to simulate the in vivo behavior of a gene circuit [30,38,39]. By identifying the kinetic strengths of promoter-RBS components, the protein expressions in the gene circuit can be estimated and predicted. However, in the process of constructing promoter-RBS library, the identified kinetic parameters in the promoter-RBS library can be affected by several conditions, including the medium, copy number of plasmid, terminator and so on. Therefore, for the extensive application of promoter-RBS libraries, the construction conditions of promoter-RBS libraries need to be unified and standardized. This will allow standardized promoter-RBS libraries, similar to electronic component libraries, which can be easily used and expanded by other gene circuit designers.
In this study, by the promoter-RBS libraries we established, a genetic transistor has been constructed and implemented. Additionally, the synthetic genetic transistor can perform amplification and switching like an electronic transistor according to its I/O characteristics. The I/O characteristics of the synthetic genetic transistor circuit are simulated by a mathematic model with random parameter fluctuation to guarantee the robustness of the design in vivo. The design specification of amplification or switching in the genetic transistor can be achieved by the library-searching method using GA. By optimally matching the desired I/O response of amplification or switching, the most adequate set of promoter-RBS component and inducer concentration {c 3 , I 2 } can be selected to construct a genetic transistor with the desired design specifications. The librarysearching method using GA is introduced to reduce the number of trial-and-error attempts, as well as the searching time in libraries when the libraries have a large number of components. Furthermore, for the convenience of synthetic genetic transistor design for synthetic biologists, one look-up table has been built for the various design specifications as shown in Table 1. From this look-up table, based on the desired design specifications, we can select the adequate promoter-RBS components and inducer concentrations to synthesize the genetic transistors with desired I/O responses. Thus, less time will be spent on the design procedure as a designer will be able to easily construct transistors with the desired I/O characteristics.
For applications of the genetic transistor, the various biological components need to be characterized and standardized. By using characterized and standardized genetic components, the design specification of a genetic transistor can be set and the look-up tables can be used to support the genetic circuit design. The genetic transistor described here has a number of potential applications. The amplifier can be used to amplify the oscillation signal reversely and linearly. Based on the designed oscillatory genetic circuits [7,[11][12][13][40][41][42] in oscillatory metabolic pathways [43][44][45], an adequate genetic transistor selected from the look-up tables according to the oscillation range and desired amplification gain can be inserted into these circuits directly to amplify the oscillatory signal. In this way, the original genetic circuits do not need to be redesigned. On the other hand, the switch can be used to detect some signals and act like a detector or biosensor [25,29,46,47]. When the input signal changes, the output signal will switch to the other state and make the downstream circuit respond to Given the desired amplification gains and their input signal ranges, we could select adequate promoter-RBS component and inducer concentration from the table to achieve the minimum matching error in (9).