Supplementary Information “Engineering modular and ...€¦ · Supplementary Information “Engineering modular and orthogonal genetic logic gates for robust digital-like synthetic

Supplementary Information

“Engineering modular and orthogonal genetic logic gates for robust digital-like

synthetic biology”

Baojun Wang1, Richard I Kitney

1, Nicolas Joly

2,3 & Martin Buck

2

1Centre for Synthetic Biology and Innovation and Department of Bioengineering, Imperial

College London, London, SW7 2AZ, UK. 2Division of Biology, Faculty of Natural Sciences,

Imperial College London, London, SW7 2AZ, UK. 3Present address: Institut Jacques Monod,

CNRS UMR 7592, Université Paris Diderot, 75205 Paris, France.

Table of Contents

Supplementary Figures S1-S12

Supplementary Tables S1-S5

Supplementary Methods

Supplementary References

Supplementary Information Wang, B. et al.

2

a

PRS

σ70 hrpR hrpS

R

R S

S

hrpL

PhrpL

σσσσ54

hrp regulon and Type III protein export complex

b

I1 I2 PhrpL

0 0 0

0 1 0

1 0 0

1 1 1

hrpR

hrpS

R

S

R

S

R SS

RBS II

P1

[I1] R1

[I2] R2

P2

RBS I

PhrpL

gfp

RBS III

c -205

GCCGGATTATGTCCGCTGAGTGGGTCACGGTCCCGGATCAGTTCCCTTGCGAAGCTGACCGATGTTTTTG

UAS

TGCCAAAAGCTGTTGTGGCAAAAAACGGTTTGCGCAAAGTTTTGTATTACAAAGAATTTCACATTTTAAA

IHF -24 -12 +1(TSS)

ATATCTTTATAAATCAATCAGTTATTTCTATTTTTAAGCTGGCATGGTTATCGCTATAGGGCTTGTAC

Supplementary Figure S1 The hrpR/hrpS hetero regulation motif in the hrp system of P. syringae and the AND gate design. a, The hrp (hypersensitive response and pathogenicity)

system in Pseudomonas syringae pv. tomato DC3000 determines its ability to cause

disease50

. The σ54

-dependent hrpL promoter is the primary regulator of this system and is

activated by the hetero HrpR and HprS bacterial enhancer-binding proteins. b, The modular

AND gate is designed on the basis of the σ54

-dependent hetero regulation module. The hrpR

and hrpS genes are placed under two separate environment-responsive promoters and gfp acts

as the output reporter. This forms a modular AND gate: the output promoter hrpL is turned

on only when both inputs are highly induced as the truth table shows. c, Sequence of hrpL

promoter. The -12 and -24 sites bind σ54

. The sequence in red is the putative UAS (upstream

activator sequence) where HrpR and HrpS bind, and the sequence in bold is the IHF

(integration host factor) binding site.


3

PlacIqPlacI gfp

PlacP

[IPTG]

ParaCParaC

PBADP

[Arab.]

PtetPluxR

PluxP

[AHL]

gfp

gfp

Promoter

Ribosome binding site

Protein coding sequence

Terminator

Supplementary Figure S2 Schematic diagram for the characterisation of the three

inducible promoters: Plac, PBAD and Plux. The gfp reporter gene (gfpmut3b) linked to RBSs

of various strengths was used to characterise: the IPTG-responsive Plac promoter, the

arabinose-responsive PBAD promoter and the AHL-responsive synthetic Plux promoter. The

sequences of RBS are listed in Table 1. The BioBrick double terminator BBa_B0015

following gfp was used to terminate transcription.

a b

0 5 10 15 20

10-1

100

time (h)

OD

60

0

6.4 mM

1.6 mM

0.4 mM

0.1 mM

0.025 mM

0.006 mM

0 5 10 15 20

0

2000

4000

6000

8000

10000

12000

time (h)

Flu

o/O

D6

00 (a

u)

6.4 mM

1.6 mM

0.4 mM

0.1 mM

0.025 mM

0.006 mM

Supplementary Figure S3 Dynamics of Plac response shows the stage of steady state. a,

Growth curves of the strain harbouring Plac-rbs30-gfp under various IPTG inductions. E. coli

MC1061 was grown in M9-glycerol in a 96 well microplate in fluorometer at 30 °C with

shaking (200 rpm) and repeating absorbance and fluorescence readings (20 min/cycle). The

exponential phase lasts several hours, i.e. between the 2 to 5 hours. b, Time course

fluorescence/OD600 values. The responses first reach to a plateau between the 5 and 8 hours

and then decrease slowly over time. The fluorescence/OD600 value after 5 hours was used to

determine the cellular response level at steady state.


4

Supplementary Figure S4 Core promoter regions and 5' UTR sequences of the three

regulated promoters. The shown 5' UTR starting from +1 site is the sequence between the

core promoter region and the RBS used for the characterisation.

a b

10-7

10-6

10-5

10-4

10-3

10-2

0

0.2

0.4

0.6

0.8

1

1.2

[IPTG] (M)

No

rma

lize

d F

luo/O

D 60

0

Plac

-rbs30-gfp

Plac

-rbs31-gfp

Plac

-rbs32-gfp

Plac

-rbs33-gfp

Plac

-rbs34-gfp

Plac

-rbsH-gfp

10

-710

-610

-510

-410

-310

-20

0.2

0.4

0.6

0.8

1

1.2

[Arabinose] (M)

No

rma

lize

d F

luo/O

D 60

0

PBAD

-rbs30-gfp

PBAD

-rbs31-gfp

PBAD

-rbs32-gfp

PBAD

-rbs33-gfp

PBAD

-rbs34-gfp

PBAD

-rbsH-gfp

c

10-12

10-11

10-10

10-9

10-8

10-7

0

0.2

0.4

0.6

0.8

1

1.2

[AHL] (M)

Norm

alize

d F

luo/O

D 60

0

Plux

-rbs30-gfp

Plux

-rbs31-gfp

Plux

-rbs32-gfp

Plux

-rbs33-gfp

Plux

-rbs34-gfp

Plux

-rbsH-gfp

Supplementary Figure S5 Normalised dose responses of the three promoters

characterised using 6 RBSs: the IPTG-responsive Plac promoter (a), the arabinose-

responsive PBAD promoter (b) and the AHL-responsive Plux promoter (c). Each curve has

similar Hill coefficient apart from Plac-rbs33-gfp construct (no response).


5

a

b c

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

G/Gmax

(model)

G/G

ma

x (

exp

eri

me

nt)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

G/Gmax

(model)

G/G

ma

x (

exp

eri

me

nt)

Supplementary Figure S6 Parameterised AND gate transfer function and model

predictions. a, The parameterised transfer function was obtained by fitting to the

experimental data (Fig. 3a). b, The Pearson correlation coefficient between the predicted and

experimentally characterised responses of the AND gate in the first context (Fig. 3c) is

0.9370. c, The Pearson correlation coefficient between the predicted and experimentally

characterised responses of the AND gate in the second context (Fig. 3c) is 0.9811.

a b

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

GNAND

/GNANDmax

(model)

GN

AN

D/G

NA

ND

ma

x (e

xp

eri

me

nt)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

GNAND

/GNANDmax

(model)

GN

AN

D/G

NA

ND

ma

x (e

xp

eri

me

nt)

Supplementary Figure S7 Comparing predicated and characterised responses of the

NAND gates. a, The Pearson correlation coefficient between the predicted and

experimentally characterised responses of the first NAND gate (Fig. 5a,c,e) is 0.8984. b,

The Pearson correlation coefficient between the predicted and experimentally characterised

responses of the second NAND gate (Fig. 5b,d,f) is 0.8568.

2

ssmax

206.1 32.5

3135 374

2.381 0.475

1.835 0.286

([ ] 7858 au, 0.9781)

R

S

R

S

K

K

n

n

G R

= ±

= ±

= ±

= ±

= =


6

a b

c

Supplementary Figure S8 Flow cytometry assays of the promoter Plac (a), PBAD (b) and

Plux (c). a, The responses of cells harbouring Plac-rbsH-gfp construct induced by 0, 3.9 × 10-4

,

1.6 × 10-3

, 6.3 × 10-3

, 2.5 × 10-2

, 0.1, 0.4, 1.6, 6.4 and 12.8 mM IPTG. b, Cellular responses

of PBAD-rbs33-gfp induced by 0, 3.3 × 10-4

, 1.3 × 10-3

, 5.2 × 10-3

, 2.1 × 10-2

, 8.3 × 10-2

, 0.33,

1.3, 5.3 and 10.7 mM arabinose. c, Cellular responses of Plux-rbs33-gfp induced by 0, 6.1 ×

10-3

, 2.4 × 10-2

, 9.8 × 10-2

, 3.9 × 10-1

, 1.6, 6.3, 25, 100 and 400 nM AHL. All data were

collected in E. coli MC1061 after 5 hours growth in M9-glycerol at 37 °C. Cells harbouring

PBAD promoter has bimodal responses at intermediate induction level (b), i.e. non-

homogenous, while the cells harbouring Plac and Plux promoters have unimodal responses at

all graded induction levels (a, c), i.e. homogenous. The non-homogeneity of the PBAD

promoter in E. coli MC1061 is consistent with the previous findings by others51

.


7

a b

c

Supplementary Figure S9 Flow cytometry assays of the engineered AND gate using Plac

and PBAD as the two inputs. a, Cellular responses with full induction of the PBAD input (1.33

mM arabinose) and graded induction of the Plac input by (bottom to top) 0, 3.9 × 10-4

, 1.6 ×

10-3

, 6.3 × 10-3

, 2.5 × 10-2

, 0.1, 0.4 and 1.6 mM IPTG. b, Cellular responses with full

induction of the Plac input (1.6 mM IPTG) and graded induction of the PBAD input by (bottom

to top) 0, 3.3 × 10-4

, 1.3 × 10-3

, 5.2 × 10-3

, 2.1 × 10-2

, 8.3 × 10-2

, 0.33 and 1.33 mM

arabinose. c, Cellular responses with graded inductions for both inputs Plac and PBAD. All data

were collected in E. coli MC1061 after 5 hours growth in M9-glycerol at 30 °C. In b and c,

the AND gate behaved with bimodal responses at intermediate inductions of PBAD. However,

the device responses are unimodal at all IPTG inductions when fully induced with arabinose

(a). The behaviour is due to that the PBAD is non-homogeneous in this host, while Plac is

homogeneous using IPTG induction.


8

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 2 4 6 8 10 12 14 16 18 20

Time (hours)

OD

60

0

WT E. coli MC1061

ref. - empty vectors

AND - noninduced

AND - induced

Supplementary Figure S10 Growth curves of E. coli MC1061 harbouring different circuit constructs. Host cells containing various circuit constructs were used: one wild type

control (WT E. coli MC1061), one reference carrying the empty vectors without the circuit

constructs (ref. – empty vectors), and one carrying the three plasmids with the functional

AND gate using Plac and PBAD as the inputs (Fig. 3a). The growth curves of the host carrying

the AND gate were performed at both on (induced with 1.3 mM arabinose and 1.6 mM IPTG)

and off (non-induced) states. The cells were grown in a 96 well microplate in fluorometer

with shaking (200 rpm) for 20 hours. The absorbance (OD600) was read every 1 h. The data

were the average of three repeats from the three colonies of each strain. Cells were grown in

M9-glycerol media at 30°C. Error bars, s.d. (n = 3).


9

Promoter characterisation for input transfer functions Plac input PBAD input Plux input

Two-input AND gate using Plac and PBAD as the inputs

Input 1 Input 2 Output

Two-input NAND gate using Plux and PBAD inputs, and the cI/Plam based NOT gate

Input 1 Input 2 Output

Supplementary Figure S11 Plasmid maps showing some of the circuit constructs used in

this study. The top three plasmids were used for the characterisation of the three inducible

promoters (Fig. 2g-i). The plasmid constructs in the middle were used for the characterisation

of the AND gate (Fig. 3a). The plasmids at the bottom were used for the NAND gate

characterisation (Fig. 5b,d,f).


10

a

PR1 reporter G

P1

[I1]

b

PR1 hrpR

P1

[I1]

PR2 hrpS

P2

[I2] reporter G

PhrpL

c

PR1

P1

[I1]

R3

P3

reporter G

d

PR1 hrpR

P1

[I1]

PR2 hrpS

P2

[I2] PhrpL

reporter GR3

P3

Supplementary Figure S12 Schematics showing the architectures of the inducible

negatively regulated promoter P1 (a), the AND gate (b), the NOT gate (c) and the

combinatorial NAND gate (d).


11

Supplementary Table S1 The best fits for the characterised responses of the cI/Plam based

NOT gate using various RBSs in the selected context (E. coli MC1061, M9-glycerol, 30°C)

NOT gate k3 (au) n3 K3 (au) α3 R2

rbs31-cI/Plam 7.538e4 ± 0.234e4 7.647 ± 1.379 111 ± 4.7 0.0527 ± 0.0144 0.9997

rbs32-cI/Plam 7.191e4 ± 0.385e4 5.09 ± 0.714 47.47 ± 5.42 0.0631 ± 0.0141 0.9997

rbs33-cI/Plam 7.5e4 ± 3.55e11 1.005 ± 5.3e6 40.01 ± 2.2e8 0.5225 ± 5.10e6 2.2e-9

rbs34-cI/Plam 7.46e4 ± 0.11e4 2.905 ± 1.028 367.8 ± 29.2 0.0509 ± 0.0108 0.9998

rbsH-cI/Plam 7.392e4 ± 0.097e4 2.967 ± 0.324 272.3 ± 15.3 0.0635 ± 0.0986 0.9999

Supplementary Table S2 Chassis compatibility assays of the AND gate shown in Fig. 6a

Chassis Function Growth

reduction Description

E. coli MC1061 Good Minor output only with two input inductions

E. coli MC4100 Poor Heavy output with two input inductions - but also

with only PBAD induction

E. coli MG1655 Poor middle output with two input inductions - but also


E. coli Top 10 Good Minor output only with two input inductions

E. coli DH5α Poor Minor output with two input inductions - but also


E. coli BW25113 Poor No output with two input inductions - but also


E. coli BL21(DE3) Poor Minor no response for any combination of inputs

Supplementary Table S3 Chassis compatibility assays of the AND gate shown in Fig. 6b

Chassis Function Growth

reduction Description

E. coli MC1061 Good Minor output only with two input inductions

E. coli MC4100 Good Heavy output only with two input inductions

E. coli MG1655 Good Heavy output only with two input inductions

E. coli Top 10 Good No output only with two input inductions

E. coli DH5α Good Minor output only with two input inductions

E. coli BW25113 Good No output only with two input inductions

E. coli BL21(DE3) Poor Minor output with all four input conditionsa

aThis unexpected behaviour may be the result of the absence of the Lon protease in this cell strain, which has

been shown to degrade the HrpR protein more prominently in Pseudomonas52

. Hence, the background level of

HrpR activators may tend to be higher in E. coli BL21(DE3) than in other chassis, leading to the expression

leakiness on the Plux input side and the elevated background level of the AND gate in this chassis.


12

Supplementary Table S4 The plasmids used in this study.

Plasmid Description Reference

pAPT110 IPTG inducible Plac promoter expression vector

p15A ori, Kanr

Polard et al., 1995

pBAD18-cm arabinose inducible PBAD promoter expression vector

pBR322 ori, Cmr

Guzman et al., 1995

pSB4A3 BioBrick vector, pSC101 ori, Ampr BioBrick Registry

pSB3K3 BioBrick vector, p15A ori, Kanr BioBrick Registry

pBWf2620 pSB3K3 carrying BBa_f2620 (PTet-rbs34-luxR-ter) This study

pBW100lac-gfp pAPT110 encoding rbs30-gfp-ter This study





pBW105lac-gfp pAPT110 encoding rbsH-gfp-ter This study

pBW200ara-gfp pBAD18-cm encoding rbs30-gfp-ter This study





pBW205ara-gfp pBAD18-cm encoding rbsH-gfp-ter This study

pBW300lux-gfp pBWf2620 encoding rbs30-gfp-ter This study





pBW305lux-gfp pBWf2620 encoding rbsH-gfp-ter This study

pBW115lac-hrpR pAPT110 encoding rbsH-hrpR-ter This study

pBW213ara-hrpS pBAD18-cm encoding rbs33-hrpS-ter This study

pBW313lux-hrpR pBWf2620 encoding rbs33-hrpR-ter This study

pBW121lac-cIgfp pAPT110 carrying rbs31-cI-ter-Plam-rbs30-gfp-ter This study




pBW125lac-cIgfp pAPT110 carrying rbsH-cI-ter-Plam-rbs30-gfp-ter This study

pBW400hrpL-gfp pSB4A3 harbouring hrpL-rbs30-gfp-ter This study

pBW412hrpL-cIgfp pSB4A3 harbouring hrpL-rbs32-cI-ter-Plam-rbs30-gfp-ter This study

pBW414hrpL-cIgfp pSB4A3 harbouring hrpL-rbs34-cI-ter-Plam-rbs30-gfp-ter This study


13

Supplementary Table S5 The oligo DNAs used in this study.

Primer (Set) Sequence (5’– 3’) Usage

pBAD18-cm F

pBAD18-cm R

ATGCCATAGCATTTTTATCC

GATTTAATCTGTATCAGG

sequencing primers set for

pBAD18-cm vector

BioBrick F

BioBrick R

TGCCACCTGACGTCTAAGAA

ATTACCGCCTTTGAGTGAGC

sequencing or analyzing parts in

BioBrick vectors

pAPT110 F

pAPT110 R

GGCTTTACACTTTATGCTTC

TGTTACCCGAGAGCTTGGCA

sequencing primer set for

pAPT110 vector

RBS30_gfp F CGTCTAGAGATTAAAGAGGAGAAATACTAG

ATGCGTAAAGGAGAAGAAC

PCR gfp with RBS30 and

relevant restriction sites

RBS31_gfp F CGTCTAGAGTCACACAGGAAAGTACTAGATG

AGTACAGGCATCGATAAG



RBS32_gfp F CGTCTAGAGTCACACAGGAAACCTACTAGATG

AGTACAGGCATCGATAAG



RBS33_gfp F CGTCTAGAGTCACACAGGACTACTAGATG

AGTACAGGCATCGATAAGG



RBS34_gfp F CGTCTAGAGAAAGAGGAGAAATACTAGATG

AGTACAGGCATCGATAAGG



RBSH_gfp F CGTCTAGAAGGAGATATACCATG

AGTACAGGCATCGATAAGGACGTC

PCR gfp with RBSH and


RBSH_hrpR F CGTCTAGAAGGAGATATACC

ATGAGTACAGGCATCGATAAGGACGTC

PCR hrpR with RBSH and


RBS33_hrpR F CGTCTAGAGTCACACAGGACTACTAG

ATGAGTACAGGCATCGATAAGG

PCR hrpR with RBS33 and


RBS33_hrpS F CGTCTAGAGTCACACAGGACTACTAG

ATGAGTCTTGATGAAAGGTTTG

PCR hrpS with RBS33 and


RBS30-H_GRS R GGGGTACCCTGCAGCGGCCGCTACTAGTATATAAA Reverse primer for PCR gfp,

hrpR, hrpS with various RBSs

RBS32_cI F CGTCTAGAGTCACACAGGAAAGTACTAG

ATGAGCACAAAAAAGAAACC

PCR cI with RBS32 and


RBS33_cI F CGTCTAGAGTCACACAGGACTACTAG

ATGAGCACAAAAAAGAAACC

PCR cI with RBS33 and


RBSH_cI F CGTCTAGAAGGAGATATACC

ATGAGCACAAAAAAGAAACCATTAACAC

PCR cI with RBSH and relevant

restriction sites

RBS31-H_cI R GGTACCCTGCAGCGGCCGCTACTAGTA

GCAACCATTATCACCGCCAG

Reverse primer for PCR cI with

the 3 various RBSs


14

Supplementary Methods

Mathematical modelling and data fitting

Computational models were developed for individual parts and modules to allow their

predictable assembly into customised devices. We focus on the average behaviour of the E.

coli population to demonstrate the performance of the engineered circuits at steady state. The

ODEs-based deterministic model was used for modelling gene regulation and expression. The

following describes the derivation of the transfer function (TF) for each genetic module and

the experimental data fitting to these models.

Deriving transfer function of the inducible promoters

Supplementary Fig. S12a shows the exemplar architecture of the inducible promoter used in

this study. The promoter P1 is negatively regulated by its constitutively expressed repressor

R1 and is responsive to exogenous inducer I1 to activate transcription of downstream reporter

gene G. The reporter gene expression can be modelled by53-54

:

1

1 1

1 11

1 1

[ ][ ] = [ ]

[ ]

n

n n

k Id Gk d G

dt I Kα

⋅⋅ + − ⋅

+ (S1)

where 1kα ⋅ is the basal constitutive activity of the promoter, 1 1 1 1[ ] ([ ] )n n nk I I K⋅ + is the

activity due to cooperative transcription activation by assuming the concentration of the

repressor is constant to model the effect of varying the concentration of the inducer 1I , and

[ ]d G⋅ is the constitutive degradation activity of protein G. 1K and 1n are the Hill constant

and coefficient relating to the promoter-regulator/inducer interaction, 1k is the maximum

expression rate due to induction and α is a constant relating to the promoter basal level due

to leakage (0 ≤ α < 1), and d is the degradation rate of G.

The steady state solution of equation S1 is given by

1 1 1

1 1 1 1([ ]) = [ ] = ( [ ] ( [ ] ))n n n

ssf I G k I K Iα + + (S2)

in which 1k k d= represents the maximum expression level due to induction. Equation S2

gives the reporter protein level at steady state for the inducible promoter P1 and is also the TF

of P1. We used this TF to fit the characterisation data of the three inducible promoters using

the nonlinear least square fitting function in Matlab. The best fit coefficients (with 95%

confidence bounds otherwise fixed at bound) are listed in Table 2.

Deriving transfer function of the AND gate

Supplementary Fig. S12b shows the architecture of the AND gate in this study. hrpL

promoter is synergistically co-activated by the hetero proteins HrpR and HrpS, which mimics

the logic AND function Based on the known mechanism underlying this hetero-regulated

module, both the bacterial enhancer-binding proteins are required to bind the UAS (upstream

activation sequence) of hrpL to remodel the conformation of σ54

-RNAP-hrpL close complex

to an open one for the transcriptional activation. The normalised AND gate TF is described

by the product of two Hill function curves:


15

max

([ ] )[ ] ([ ] )([ ] , [ ] )

[ ] 1 ([ ] ) 1 ([ ] )

R S

SR

n n

ssss ss SRss ss nn

ss ss R ss S

R KG S Kf R S

G R K S K= = ⋅

+ + (S3)

in which R

K , S

K and R

n , S

n are the Hill constants and coefficients for HrpR and HrpS.

[ ]ss

R and [ ]ss

S are the steady levels of HrpR and HrpS, whose levels are under the control of

two separate inducible promoters P1 and P2 as indicated by equation S2. max[ ]ss

G is the

maximum output level of the AND gate at steady state.

The TF was parameterised by fitting to the experimental data of the AND gate (Fig.

3a). The best fit coefficients by nonlinear least square optimisation were obtained as shown

on the right of Supplementary Fig. S6a and the parametrised TF is plotted on the left.

Supplementary Fig. S6b, c show the linear correlation between predicted and experimentally

characterised responses of the AND gate with new configurations and in different contexts

(Fig. 3c).

Deriving transfer function of the NOT gate

Supplementary Fig. S12c shows the architecture of the NOT gate in this study. The NOT gate

is designed on the basis of a repressor module ( 3R /P3). The NOT gate module is characterised

under an inducible promoter P1 in response to inducer I1. The NOT gate TF is modelled by

3 3 3

3 3 3 3 3 3([ ] ) ( ( [ ] ))n n n

ss ssf R k K K Rα= + + (S4)

in which 3K and 3n are the Hill constant and coefficient relating to 3R /P3 interaction, 3k

represents the maximum expression level due to induction, 3α is a constant relating to the

basal level of the regulated promoter (0 ≤ 3α < 1) and 3[ ]ss

R is the steady levels of 3R , whose

level is under the control of the inducible promoter as indicated by equation S2. The

characterisation data of the cI/Plam based NOT gate using various RBSs (Fig. 4) were fitted to

this transfer function model and the results are listed in Supplementary Table S1.

Deriving transfer function of the NAND Gate

Supplementary Fig. S12d shows the architecture of the NAND gate in this study. The

composite NAND gate TF is derived by directly coupling the TFs of the individual modules,

i.e. the NOT gate, AND gate and inducible promoters, in the system. The output of a forward

module acts as the input of the next module in the system cascade. Thus, the NAND gate TF

is give by

3 3 3

NAND 3 3 3 3 3 3[ ] ([ ] ) ( ( [ ] ))n n n

ss ssG f R k K K Rα= = + + (S5)

in which 3 ANDmax

([ ] ) ([ ] )[ ] ([ ] , [ ] ) [ ]

(1 ([ ] ) )(1 ([ ] ) )

SR

SR

nn

SS SS SRSS SS SS nn

SS R SS S

R K S KR f R S G

R K S K= =

+ +

where 1 1 1

1 1 1 1[ ] or [ ] ([ ]) ( [ ] ( [ ] ))n n n

SS SSR S f I k I K Iα= = + + , 1I is the inducer of the inducible

promoter for the regulation of hrpR or hrpS in the AND gate. All other parameters have the

same meaning as described in their individual TFs. The only exception is the fitted value of


16

[G]ANDmax, which needs to be adjusted according to the RBS used in the NOT gate because

the previous fitting is based on the response of the AND gate characterised with the rbs30-gfp

reporter.

Supplementary References

50 Jin, Q., Thilmony, R., Zwiesler-Vollick, J. & He, S.-Y. Type III protein secretion in

Pseudomonas syringae. Microbes Infect. 5, 301-310 (2003).

51 Siegele, D. A. & Hu, J. C. Gene expression from plasmids containing the araBAD

promoter at subsaturating inducer concentrations represents mixed populations. Proc.

Natl. Acad. Sci. USA 94, 8168-8172 (1997).

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Supplementary Information “Engineering modular and ...€¦ · Supplementary Information “Engineering modular and orthogonal genetic logic gates for robust digital-like synthetic

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