Rational Design of an Ultrasensitive Quorum-Sensing Switch

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Letter

Rational design of an ultrasensitive quorum-sensing switch Weiqian Zeng, Pei Du, Qiuli Lou, Lili Wu, Haoqian M. Zhang, Chunbo Lou, Hongli Wang, and Qi Ouyang ACS Synth. Biol., Just Accepted Manuscript • Publication Date (Web): 24 Apr 2017 Downloaded from http://pubs.acs.org on April 25, 2017

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ACS Synthetic Biology

Rational design of an ultrasensitive quorum-sensing switch Weiqian Zeng1, Pei Du4, Qiuli Lou4, Lili Wu3, Haoqian M. Zhang2, Chunbo Lou,4 Hongli Wang3, and Qi Ouyang*1,2,3

1

Centre for Quantitative Biology and Peking-Tsinghua Joint Centre for Life Sciences, Peking University, Beijing, 100871, China; 2 CAS Key Laboratory of Microbial Physiological and Metabolic Engineering, Institute of Microbiology, Chinese Academy of Sciences, Beijing, China; 3 The State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China. *Correspondence: [email protected] (Q. O.) ABSTACT: One of the purposes of synthetic biology is to develop rational methods that accelerate the design of genetic circuits, saving time and effort spent on experiments and providing reliably predictable circuit performance. We applied a reverse engineering approach to design an ultrasensitive transcriptional quorum-sensing switch. We want to explore how systems biology can guide synthetic biology in the choice of specific DNA sequences and their regulatory relations to achieve a targeted function. The workflow comprises network enumeration that achieves the target function robustly, experimental restriction of the obtained candidate networks, global parameter optimization via mathematical analysis, selection and engineering of parts based on these calculations, and finally, circuit construction based on the principles of standardization and modularization. The performance of realized quorum-sensing switches was in good qualitative agreement with the computational predictions. This study provides practical principles for the rational design of genetic circuits with targeted functions. KEYWORDS: Rational design, Reverse engineering, Predictable assembly, Cell-density switch, Self-induced switch, Quorum-sensing Recent decades have witnessed advances in synthetic biology that allow the programming of functions such as logic gates (1, 2), sequential switches (3, 4), oscillators (5, 6), as well as more complex circuits (7-9). In order to accelerate the design of genetic circuits, save time and effort spent on experiments, and generate circuits that perform reliably and predictably (10-13), investigators have focused on the modularization of biological functional parts and the standardization of measurement methods, which has made possible increasing complexity, robustness, and predictability of synthetic circuits (14-16). Moreover, the development of large-scale DNA synthesis (17, 18) and new methods of DNA assembly (19, 20) have also accelerated circuit construction. Regrettably, such researches are still costly in both manpower and financial resources (21), especially considering the need for iterative design and subsequent troubleshooting. Taking advantage of systems biology to deduce biological regulatory circuits from their functions and engineer the corresponding biological systems has been considered a promising approach for the predictable design of complex genetic circuits (22-24). Among the different techniques used in this

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reverse-engineering approach, one powerful method is to enumerate all candidate network structures to find suitable ones. In that process, all possible simple network topologies are computationally enumerated and the robustness of each topology evaluated, allowing identification of the regulatory networks that are most fit for a particular function (25, 26). Topologies adapted to larger sets of parameters are presumed to be present in genetic circuits with higher tolerance of variability among components, thus with higher robustness. Further analysis of each topology can identify sensitive parameters that reveal critical genetic components of the circuit. As practical studies of the functional repertoires of networks are performed, increasingly complete computational models can be developed to capture the physical properties of biological systems (27-29). However, in this line of research, further work is needed to explore how mathematical theory can inform experimental circuit design, as well as to eliminate the “design gap” between the equations of theoretical models and the DNA sequences of real-life genetic circuits. Quorum-sensing bacteria such as Vibrio fischeri, are able to detected their own population density and implement density-based decision-making (30, 31). Using the luxI/luxR quorum-sensing system, synthetic biologists have designed a large number of devices in prokaryotic microorganisms (32, 33). Recently, Hasty et al. engineered a quorum lysis bacterium for the synchronous delivery of chemotherapeutic agents to cancer cells at a threshold population density, which led to a better therapeutic effect than traditional chemotherapy (34). Inevitably, high performance is required from such devices (35, 36), and this includes reliability, sensitivity, predictability, and adjustability. Hence, to improve the properties of population-density switches, we explored the rational design of ultrasensitive responses, in order to build a population-density switch based on topology enumeration and parameter optimization using coarse-grain theoretical models. Definition of the Target Function and Network Coarse Graining Ultrasensitive responses represent switch-like, sharply sigmoidal input/output functions, in which it takes a minimal change in an input stimulus to drive a major jump in output. The response curve can usually be described using a broader Hill function-like formula:

y = b + (V − b)

xn xn + K n

[1]

Which can be normalized as

Y=

Xn y −b xn = = X n + K n V − b xn + K n

[2]

To create an ultrasensitive switch, we defined two functional quantities: response sensitivity and response intensity (figure 1a). Response sensitivity is defined as the effective Hill exponent (n), and is related to the x9:x1 ratio in Fig. 1a (see Supporting Information for detailed deduction):

n≅

ln(81) x ln( 9 ) x1

and response intensity represents the on-off ratio via Equation 3: V −b . Intensity = b


[3]

[4]

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We limited ourselves to exploring transcriptional circuits consisting of three interacting nodes. In each network, node A receives the upstream input (population density), node C transmits the output (response), and node B is an intermediary regulator. These three nodes can positively or negatively regulate each other, giving 9 modes of directed regulation, each being positive, negative, or nonexistent. Thus, there are 39 = 19,683 possible topologies, of which 3,645 have no direct or indirect links from input to output. Consequently, we investigated the remaining 16,038 topologies in our study. As defined by Goldbeter and Koshland, a switch is ultrasensitive when n >1 (37). For this analysis, we limited ourselves to transcriptional regulatory networks and modeled network linkages using Hill equations, whereby we expected to find ultrasensitive networks (n >1) constructed from non-ultrasensitive wires (n = 1). We first built a mathematical model to describe the dynamics of the three-node systems, in which the rate of change of each node is equal to a production term minus a decay term (Eq. 5):  dA  dt = bA + FAA( A,VAA, k AA ) ⋅ FBA( B,VBA, k BA ) ⋅ FCA( C,VCA, kCA ) ⋅ I − r A ⋅ A   dB = bB + FAB( A, VAB , k AB ) ⋅ FBB( B,VBB , k BB ) ⋅ FCB( C, VCB , kCB ) − r B ⋅ B   dt  dC = bC + FAC( A, VAC , k AC ) ⋅ FBC( B, VBC , k BC ) ⋅ FCC( C,VCC , kCC ) − r C ⋅ C   dt

[5]

where Vmax,i j ⋅ i , i f i act i vat es j   i + ki j V ⋅ ki j  , i f i i nhi bi t es j ， ( i , j = A, B, C) Fi j ( i , Vi j , ki j ) =  max,i j  i + ki j  1 , i f i has no ef f ect on j  

The production term consists of a basal expression value ( bi ) and the product of all the regulation inputs ( Fij ) of the three nodes. For example, in case of a positive effect of A on B, it contributes the term:

Vmax,AB ⋅ A A + kAB

;

if the interaction is repressive, it contributes the term:

Vmax,AB ⋅ k AB A + k AB

;

if there is no regulatory signal from A to B, the corresponding value is multiplied by one. To describe the combination of a repressive and an active transcriptional input, the two terms are multiplied together; in the case of two active transcriptional regulation signals acting on one node, there are multiple and additive combinations, depending on whether the form of their interaction conforms to



an AND or an OR logic. We only used multiplication for combining two active regulations at any single node. Population-density switches are composed of elements derived from quorum-sensing systems, in which microorganisms commonly release small signal molecules that freely diffuse in and out of the cells and increase in concentration with increasing cell density. Therefore, the input was set as a multiplication factor of the production term of A (see derivation in the Supporting Information). Here, the input (I), is equal to the product of the volume of a single cell and the cell concentration (Vone*Ccell). The decay term is the combination of dilution due to cell division and protein degradation. We considered dilution to be much more significant than protein degradation, i.e. the proteins were assumed to be stable and the cellular growth rate was that of a typical model bacterium, such as E. coli. For each network topology, 10,000 sets of circuit parameters were randomly sampled from the parameter space using the Latin Hypercube Sampling method. In each network performance evaluation, the initial value of each node was set to 0.1 before calculation of the first input. The output was obtained numerically by solving the stationary steady-state equation 5 for node C with the given input. After that, the input was increased stepwise, and the initial value of each node was kept as the steady-state solution of the previous calculation. The resulting input-output response of an individual network with each parameter set was evaluated for ultrasensitivity using the criteria of V −b response sensitivity n > 6 and response intensity corresponding to ln( ) > 3 & V > 3. b Enumeration results for ultrasensitive networks For each particular network architecture, we focused on how many parameter sets reached the threshold of ultrasensitivity. The larger the number of sets (Q-value), the more robust the circuit is considered to perform the function (26). Among 16038 possible three-node networks (with up to nine links each), there were 2479 possible topologies with Q-values > 0 (figure 1b). The distribution of Q-values is illustrated in the histogram in figure 1c. The exponential decrease shows that only a small fraction of networks is robust for the ultrasensitive function. Figure 1d shows the cluster analysis from which we identified the necessary links shared with all networks with high Q-values: a positive feedback loop on A and a direct transmission from A to C (A→A and A→C). It is well known that a positive feedback loop can generate a bistable response which may also satisfy the criteria for ultrasensitivity. Therefore, we examined the possibility of hysteresis for each ultrasensitive topology and the number of parameter sets exhibiting hysteresis was defined as the q-value. There are 2381 topologies with q-value >0. We plotted a comparison of the Q-value (robustness of ultrasensitivity) and the q-value (robustness of bistability) as shown in figure 1e, and found that the corresponding scatter points are distributed close to two straight lines with different slopes. That is to say, we can classify these topologies into two groups according to q/Q; the distribution of q/Q validated this idea (figure 1f). As we discuss in the Supporting Information, these two groups of topologies have different structural characteristics. Moreover, the analytical calculations in Supporting Information further support the notion that the high q/Q topologies have higher bistable possibility (HBP), whereas the low q/Q topologies have lower bistable possibility (LBP). In order to design a population density switch, LBP topologies are much better than HBP topologies, because bistability can lead to heterogeneity in bacterial communities.


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Experimental accessibility It is worth noting that not all of the high-Q-value topologies can be realized experimentally. According to the biological features of the components, we need to develop specific topology restrictions for each parts that we intend to use in the control circuit, which we called “experimental-accessibility” (EA) condition. For instance, if the number of interactions on one part cannot be more than two, the number of edges pointing to that node is limited to two. The final topology candidates should satisfy both high-Q-value constraint and EA topology restrictions. Here, we provide an example for the definition of the EA condition, according to the parts library derived from quorum-sensing system. First of all, the mechanism of parts interaction must clarify through literature. In this particular system, the LuxR/LuxI QS system was used as the source of components to construct the cell-density-responsive switches (38); the selection of this part gave a limit in the circuit selection. The earliest and most-studied in synthetic biology, the LuxR/LuxI system comprises two critical components: LuxR, a cytoplasmic auto-inducer receptor/DNA-binding transcriptional activator, and LuxI, which is an auto-inducer synthase (39). LuxI protein produces acyl homoserine lactone (AHL), which freely diffuses in and out of the cells and accumulates in increasing concentrations with increasing cell density. Subsequently, the constraints of the use of components were found out. In this case, only LuxR with bound AHL can activate expression from the Plux promoter. Mapping the LuxR/LuxI quorum-sensing system to the three-node network topology, node A must be represented by AHL and its synthase LuxI, since the production of AHL is proportional to the concentration of LuxI (35), node B is the transcriptional activator LuxR, and node C is responsible for LuxCDABE expression, i.e. bioluminescence. Finally, the biological constraints were translated into mathematical language. Here, because a valid signal from node A to another node must be accompanied by a signal from B to that node, the sign of regulation from A to X (X = A, B, C) has to be equal to that of B to X. Based on this constraint, only 333 networks satisfied the EA criterion among the Q > 0 topologies (figure 1b). Based on further analysis (as shown in Supporting Information, Figure S1), the topologies with q/Q 50), LBP and EA criteria resulted in six topologies (figure 1g). The highest Q-value network (topology number: 10121) has Q = 90 and q/Q = 11%. Thereafter, we focused on this topology as an example to demonstrate parameter optimization and predictable performance control. The final selected topology (topology number 10121) is actually also found in the natural LuxR/LuxI quorum-sensing system, where A is equivalent to the set of LuxI and AHL, B is LuxR and C is the luciferase operon. As experimentally demonstrated by Soma et al.(35), this topology is a monostable ultrasensitive network with threshold performance, while the topology with additional positive feedback loops (topology number 10205, which is bistable ultrasensitive based on our analysis) yields a bistable response. Parameter optimization Solving each ordinary differential equation (ODE) analytically, we deduced the steady-state solution of each node, obtaining the normalized signal transfer equations between I (input) and C (output): C'=

In I + Kn n

where C’ is the normalized value of C:


[6]


C'=

rC ⋅ C − bC VBC

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[7]

The derivation process of the formulas and calculation method is described in detail in the Supporting Information. In the analytical solution, the steady-state of node B is a constant, determined by the basal expression ( bB + VB ) and decay rate ( rB ); the steady-state concentration of node A becomes a signal messenger from input (I) to output (C). Thus, based on the calculations shown in the Supporting Information, the response sensitivity of this network is determined by n=

ln(81) = I ln( 9 ) ln 81 ⋅ 9 + α I1  1 + 9α

ln(81)

[8]

 β ⋅ (1 + 9α ) + 1   ⋅ A   β A ⋅ ( 9 + α ) + 9  

where I 9 = I C '=90% , I1 = I C '=10% , α =

K AA b b , βA = A ≈ A K AC VAB VA

The response sensitivity (n) as a function of α and β is shown in figure 1f. Ultrasensitivity (n) is enhanced by a decrease of β, which is roughly equal to the reciprocal of the magnification of plux1. While for a fixed value of β, n has a maximum value as a function of α. Here, α is the ratio of two binding constants, K AA for the AHL induction of plux1 and K AC for plux2. If the analytical solution of the equation is not available, the parameter-optimization can be achieved by numerical analysis (figure 1i and Supporting Information). The most sensitive parameters,

VA , bA , K AA , K AC (figure 1i), correspond to α and β in the analytical analysis (figure 1h). Furthermore, the results of parameter sensitivity analysis are in good agreement with the analytical calculation – i.e., an increase of VA (induced saturation value of plux1) or decrease of bA (induced background value of plux1) leads to an increase of n (figure 1i), which is consistent the analysis result in which a decrease of β led to an increase of n (figure 1h). Engineering the transcriptional parts for parameter-tuning To demonstrate the predictability of our parameter optimization based on topology 10121, we implemented this network as an experimental genetic circuit (Figure 2a). It is worth noting that both the characterization of the parts and circuit construction followed the principles of modular design (14, 16, 39). For instance, a ribozyme was placed between the promoter and the ribosome binding site to act as an insulator between transcription and translation (14) (further details in the Supporting Information). In order to simplify the controllable variables, we confined the tunable parameter as

α=

K AA b , βA ≈ A K AC VA

to make valid the approximation:

βA =

bA bA b = ≈ A V A ⋅ B * VA VAB B * + K BA


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We thus ensured that the constitutive expression of node B (B*) was strong enough. Therefore, the LuxR protein was constitutively expressed from a strong promoter (BBa_J23110). Moreover, even though the nodes A and B synergistically regulate the nodes A and C via the Plux promoter, the dynamic parameters of these two regulators (Plux1 and Plux2) may differ (figure 2a). For each Plux variant, we characterized the inducer (AHL) dose-response curve using a test construct (figure 2b). By fitting the response curves to the Hill function

y = b + (V − b)

xn , (n = 1) xn + K n

we obtained the parameters of each regulation. For instance, the AHL dose-response curve of Plux1 gave the values of bA, VA, and KAA, and the curve of Plux2 provided those of bC, VC, and KAC. Translating the parameters from equation 6 to the dynamic properties of the genetic components shown in figure 2a, α equals the ratio of the dissociation constant between Plux1 (regulating LuxI) and Plux2 (regulation sfGFP), and β is the ratio of the saturation level to the basal level of Plux1. Plux consists of the lux box (20 bp) and promoter region. Using localized saturation mutagenesis, we found that the DNA sequence of the activator region (lux-box) as well as the promoter regions (-35 and -10) clearly changed the dissociation constant (K) and/or the saturation value (V): Firstly, mutations of lux-box positioned at 1-5 bp only changed K (figure 2c); secondly, mutations at positions 15-20 bp of the lux-box changed not only K, but also V (figure 2d); thirdly, deletions downstream of the -10 region changed V (figure 2e). These results indicate that the binding affinity between luxR-AHL and the lux-box is mainly affected by both ends of the lux-box, with some overlap between the last 2-3 bp of the lux-box and the -35 region of the promoter, so that these sequences change both the disassociation rate and the expression level. More details about promoter engineering can be found in the Supporting Information. Lux-box mutation K (0.1 µM AHL) A1C 1.46 A1G 1.89 C2A 2.31 C2T 6.81 C3A 15.4 C3T 47.5 Table 1. The lux-box mutations with distinct dissociation constants and constant saturation expression levels Based on these experimental results, we selected 6 lux-box mutations with different dissociation constants and a constant saturation expression level (Table1). Based on this table, we obtained a range of α values for different combinations of Plux1 and Plux2 variants (Table2). Plux1 C3T C3T C3T C3T

Plux2 A1C A1G C2A C2T

α 32.53 25.13 20.56 6.98



C3T C3A 3.08 C3T C3T 1 C3A C3T 0.32 C2T C3T 0.14 Table 2. The α values of circuits with combinations of Plux1 and 2 variants. Because β was mainly determined by the response intensity of Plux1 (regulating LuxI) , the -10 region of the promoter was engineered to lower the basal level (bA) to experimentally achieve a tunable β value, and three versions of the promoter (figures 2b and e) were designed with different maximal outputs (VA). The corresponding β values from these promoters were 0.023, 0.006, and 0.003. Experimental construction of the genetic circuit Using the library of Plux promoters, we measured two curves on the prediction surface of α-β-n: n as a function of α with fixed β, and n as a function of β with fixed α. The assembled genetic circuits were tested in continuous cultivation for >20 h, during which GFP fluorescence and OD600 were simultaneously recorded every 10 min. The density-response curves were normalized and displayed in groups with visually distinguishable response sensitivities (figures 3a-d). They were then fitted to the Hill function, to obtain the response sensitivity (n) of each circuit. We compared the n values of the experimental measurements and the trends in prediction with changing α or β values (figures 3e-j). The results have a semi-quantitative consistency. The Hill coefficient as a function of different α values showed peaks both in the experimental data and the prediction results, although the peak was at α = 1 in the experiment, while it was at > 10 in the prediction (figure 3g and j). A similar shift was found for the function of β. Discussion This work is a successful example of the rational design of a desired dynamical function through reverse engineering. Because the enumeration method used for the selection of suitable network topologies is able to search for target-functions without losing dynamic time information, it is a valuable supplement to other reverse-engineering methods, such as synthetic evolution (40) and Boolean network modeling (41, 42). Moreover, this work is the first experimental realization of network enumeration with a standardized circuit design and predictable experimental validation. Shah et al.(43) explored the robust network topologies that can generate switch-like cellular responses, opening to enzymatic and transcriptional networks. With fewer limitations, their theoretical analysis is more comprehensive than our work, but is difficult to implement in biological circuits. In this paper, we put an additional constraint (EA) on circuit selection. The EA is an additional topology restriction based on the biological features of each parts, which should be added into the automatic selection process when one decides which parts in the parts library will be used in the circuit building. Building a standard parts library is a fundamental work in synthetic biology research. We suggest that in the process of building the standard basic parts library, an annotation need to be added to provide the topological constrains on that parts. This work is not yet systematically formulized. In this paper, we just gave the definition of EA based on LuxR/LuxI system as an example.


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Several labs have engineered synthetic circuits with ultrasensitive input-output control. The mechanisms involved are positive cooperative binding (44) and molecular titration (45, 46), which requires the component itself to be ultrasensitive. The associated model calculations are also based on the biological features of those specific components. However, the main guiding hypothesis of our approach was to find ultrasensitive networks constructed from non-ultrasensitive components. This is critical because when defining a target function, the available components may have limitations and have biochemical parameters that are difficult to tune, especially their ultrasensitivity. Although the shift (Δα ≈ 10) between the experimental results and the computational prediction is significant, the fine-tuning guidance of theoretical parameter-optimization still contributes a marked reduction of the otherwise necessary labor-intensive work by trial and error. Furthermore, the semi-quantitative predictability demonstrates the validity of the outlined design principles. The most important elements of synthetic biology such as improved tools, well-characterized parts and a comprehensive understanding of how to compose circuits, were all considered in order to program cells to perform complex tasks as predicted (39). One potential feature of the measurement process may have contributed mostly to the observed shift. We used ODE to describe the transcriptional network, assuming that the concentration at each node was in a steady state – i.e., the production rate of each node was equal to its degradation rate at a steady cellular growth rate and a constant cell-density. However, in the actual measurements, fluorescence was recorded from cells growing in the logarithmic phase. To overcome this flaw, a turbidostat can be used to acquire the dose-response curves, but the results were not satisfactory in our hands. The output was the steady-state value of fluorescence at a certain cell-density. Clearly, these measurements were laborious with sparse data points, so high-throughput machine-aided platforms will be required in future work. Methods The experiments for the characterization of parts were performed as described previously (15). For density-response testing, cells (E. coli strain BW25113) from single colonies on LB agar (BD, USA) plates were grown overnight in 1 ml nutrition-rich, acid-base equilibrium medium (REM) (15.2 g/l yeast extract (BD, USA), 0.5% (NH4)2SO4, 4 mM MgSO4, 2% glucose and 24 g/l K2HPO4.3H2O, and 9.6 g/l KH2PO4) in Falcon tubes overnight (8−12 h, 1000 rpm, 37 °C, mB100-40 Thermo Shaker, AOSHENG, China). The cultures were subsequently diluted 500-fold with REM in 96-well plates, which were further incubated at 37°C in a shaker at 1000 rpm. Once the diluted cultures reached an OD600 of 0.12–0.14 (~3 h), 10 µL aliquots were transferred into 1 mL REM in 24-well plates (Corning/Costar 3524). These plates were incubated at 37°C in a Varioskan Flash (Thermo Scientific, USA) under constant shaking at 1,000 rpm for 20 h to maintain exponential growth, during which the OD600 and fluorescence values were recorded every 10 min. Blank control (REM medium only) and negative control (same strain and medium without GFP expression) were tested in the same plates at the same times. Associated Content Supporting Information The Supporting Information is available free of charge on the ACS Publication website at DOI:… Additional derivation; Bistability analysis; Figure S1 and Figure S2; Parameter optimization analysis; Figure S3; promoter sequences and engineering information; Supporting Methods; Supporting



Reference. Author Information Corresponding Author *E-mail: [email protected] (Q.O.). Author Contributions Q.O., H.W. and C.L. conceived and supervised the project. W.Z. performed the enumeration and analyzed the results. W.Z. and L.W. performed the analytical and numerical analysis. W.Z. designed and performed all the experiment and analyzed the data. P.D., H.M.Z and Q.L designed and engineered the precursor of the parts used in this work. W.Z. and Q.O. wrote the manuscript. Notes The authors declare no competing financial interest. Acknowledgments We thank Y. Q. Zong and H. W. Zhao for the plasmid template, I. Bruce for suggestions on English writing, T. Xu, T. T. Li, X. L. Chen, and X. D. Lv for helpful discussions. Part of the computational analysis was performed on the Computing Platform of the Center for Life Science. This work was supported by grants from the National Natural Science Foundation of China (11434001) and Ministry of Science and Technology of China (2012AA02A702).

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Figure legends Figure 1. (a) Definition of target functions. ( x1 , y1 ) and ( x9 , y9 ) are the corresponding values when Y = 10% and Y = 90% , where Y satisfies the normalized function

Y = X n / ( X n + K n ) = ( y − b) / (V − b) = x n / ( x n + K n ) (b) Venn diagram of the topology search results. In total, there were 19683 topologies, of which 16038 had direct or indirect links from input to output. Using the thresholds n > 6, ln[(V − b) / b] > 3 and V > 3, only 2479 topologies had Q > 0. Of these, 333 topologies satisfied the experimental accessibility (EA) condition, 1020 topologies had Q >50, and 806 topologies are LBP (q/Q < 30%). Only 6 satisfied all of the above three conditions. (c) Histogram of topologies with Q-values > 0. (d) Cluster analysis of topologies with Q-values > 27%. (e) Comparison of the Q-value (robustness of ultrasensitivity) and the q-value (robustness of bistability). (f) Histogram of q/Q. (g) The 6 topologies satisfying the high-Q, EA, and LBP criteria. The three numbers under each topology are the topology number, Q-value, and q/Q value (f) 3D surface map of response sensitivity (n) as a function of α and β for topology 10121. (g) Parameter sensitivity analysis for topology 10121. Figure 2. (a) The genetic-circuit construction of topology 10121. The parameters for each interaction are shown in brackets, and the sensitivity parameters are highlighted in blue. (b) The genetic construction used for promoter engineering and measurements. (c) mutations of the lux-box at positions 1-5 bp only changed K. (d) mutations at 15-20 bp of the lux-box changed not only K, but also V. (e) Deletions downstream of the -10 region changed V. Figure 3. (a-d) The normalized population-density response curves for different α and β values. (e-j) The experiment-prediction comparison. Pairs were grouped as e and h, f and i, g and j. The values of α and β are indicated above each diagram.


A

Topology ACS Synthetic Biology enumeration n 5

1 2 3 4

Plux1

0 60

40

0.005

α

0 0.01

20

β

parameter optimization

luxI


A

J23110 luxR

Plux2

B

0

AHL

C

C

gfp

Normalized GFP/Cell

B

Page 14 of 17

10

1

0.8

Ultrasensitive QS Switch

0.6 0.4 0.2 0 0 1 2 3 4 5 6 Density

y = b + (V − b)

10%

Intensity:

x9

x

Population Density Q > 27% (675)

Q>0 2479

ln(81) x9 ) x1

ln(

Q>50 74 656 6 40 284 476 LBP

V −b b

400 300 200 100 0

0

100 200 300 400 Q−value

Target function (e)

(g)

400

(h)

B

200 100 0

0

(f)

200 q

C

B

C

10121 90,11%

10040 72,11%

A

A

400

B C 10202 68,12%

600 400

B

C 16682 68,13% A

A

200 0

A

A

300

positive regulation negative regulation no regulation

EA 219

Q > 0 (2479)

B

C 16601 55,11%

B

ACS Paragon Plus Environment 0

0.5 q/Q

1

C 7934 53,13%

10 n 5 0 0 60 (i)

40 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8

α

20

0.005 β

0 0.01

VA bA KAA KAC VC bC KBC KBA rB VB bB

x1

Sensitivity: n =

Q

y1 b 0

90%

Number of topology

1 2 3 4 5 6 7 8(d) 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

(c)

9

Parameter Sensitivity

Output

y9

(b)

3 =19683 x n ACS Synthetic Biology n n 16038 x +K

Number of topology

y

(a) Page V 15 of 17

AHL

Topology 10121

(a)

ACS Synthetic Biology (VA,bA)

LuxI

(KBA) Plux1 LuxR

(VB,bB)

luxI (KAC)

(KBC)

(VC,bC)

J23110

GFP reporter

luxR Plux2

gfp AHL

(b)

(KAX, X=A,B,C) (Vi, bi, i=A,C)

J23110

gfp

Plux

LuxR

-35 lux box -10 ACCTGTAGGATCGTACAGGTTTACGCAAGAAAATGGTTTGTTACTTTCGAATAAA delete C/G 16-19 1-5 (c)

10

10

2

5

10 (VA)

3

10

(d)

4

(KAX)

10

10

2

1

4

(VA)

2

1

10 Paragon Plus Environment ACS −11 −9 −7 −5 −3 10

3

10 10

(KAX) 10 −11 −9 −7 −5 −3 10 10 10 10 10 AHL (M)

(e)

10

3

Output

4

10

Output

Output

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

Page 16 of 17

(KAA)

10

10 10 AHL (M)

10

1

10 −11 −9 −7 −5 −3 10 10 10 10 10 AHL (M)

2 3 4 Density

0.8 0.6 0.4 0 0

5 (e)

β=0.003 β=0.006 β=0.023

0.2 1

2 3 4 Density

(f)

0.6 0.4 0.2 0

α=1

4

(h)

10 β=bA/VAB

−1

5

−2

10 β=bA/VAB

−1

10

1.9 1.8 1.7

2

1.6

−2

10 β=bA/VAB

ACS Paragon Plus Environment 1.5

−1

10

0.2 0 0 1 2 3 4 5 6 Density

5

−3

10

−2

10 β=bA/VAB

−1

10

−2

−1

0

1

2

3

4

−2

−1

0

1

2

3

4

10 10 10 10 10 10 10 α =K /K AA AC (j)

2

3 1 −3 10

(i)

2.1

4

0.4

3

10

5

0.6

4

−3

10

α=1 α=0.32 α=0.14

6

n

10

−2

1

β=0.003

(g)

4 −3

β=0.003

0.8

0 1 2 3 4 5 6 Density

n

4.5

(d)

α=1.00 α=3.08 α=6.98 α=20.56 α=25.13 α=32.53

6

5

6

1 0.8

5

α=10.53

n

1

1

n

0

Normalized GFP/Cell

β=0.003 β=0.006 β=0.023

n

1 0.6 2 3 0.4 4 0.2 5 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

n

Normalized GFP/Cell

1 0.8

(c) α=1ACS Synthetic Biology β=0.003 Normalized GFP/Cell

(b)

Normalized GFP/Cell

(a)

Page 17 of α=10.53 17

6 5 4 3 2 1 10 10 10 10 10 10 10 α =K /K AA AC

Rational Design of an Ultrasensitive Quorum-Sensing Switch

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