Automated Design Framework for Synthetic Biology Exploiting Pareto

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Automated Design Framework for Synthetic Biology exploiting Pareto Optimality Irene Otero-Muras, and Julio R. Banga ACS Synth. Biol., Just Accepted Manuscript • DOI: 10.1021/acssynbio.6b00306 • Publication Date (Web): 28 Mar 2017 Downloaded from http://pubs.acs.org on March 30, 2017

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ACS Synthetic Biology is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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ACS Synthetic Biology

∗

ACS Paragon Plus Environment


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 58 59 60 ACS Paragon Plus Environment

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B Constraint: Sustained Oscillation

A Library of Parts cIR

lasR

tetR

lasI

Ptet

araC

ccdB

Pbad

lacI

ccdA

luxI

Plac

Ter

level

RBS

Pλ

ccdA2

time

luxR

Objective 1: Tunability of the Period Maximum number of devices: 3

Objective 2: Stability of the Limit Cycle

C

Pareto front of trade-off solutions

P1

-1.5

× 10-3

-1.6 Ptet

lacI

Plac

Pbad

araC

tetR

NP (Repressilator)

Pλ

lacI

Plac

tetR

Ptet

-1.7

-Limit cycle stability

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 58 59 60


cIR

P3

P1 NP

-1.8 -1.9 -2

P2

-2.1 -2.2

Pλ

tetR

Ptet

araC

Pbad

cIR

-2.3

P2 -2.4 Plac

araC

Pbad

cIR

Pλ

lacI

P3 U -2.5 -0.98 0.96 -0.94 0.92

-0.9

-0.88 0.86 -0.84 0.82

-0.8

-Period tunability

nG

nR


nP


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 58 59 60

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nT M = nG×nR×nP ×nT

i = 1, . . . , M

y ∈ ZM

yi

i

y

x

x, y

z(t) ˙ = N (y)v(x, y, k)

N (y)

v(x, y, k)

k


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cIR tetR araC lacI luxI luxR lasR lasI ccdB ccdA ccdA2

y



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 58 59 60

Gi

yij ∈ {−1, 0, 1}

Gj (−1)

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(0)

xij ∈ R>0

(1)

N2

N N2

Gi

χi =

n !

ωji zj + αi I

j=1

ωji = yji xji

αi I

Gi αi = 0

zi

Gi

z˙i =

1 − δzi 1 + exp(a − b(χi ))


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a

b δ

A B

C

1 − δA 1 + exp(a − b(I + ωAA A + ωBA B + ωCA C))) 1 B˙ = − δB 1 + exp (a − b(ωAB A + ωBB B + ωCB C)) 1 C˙ = − δC. 1 + exp (a − b(ωAC A + ωBC B + ωCC C)) A˙ =

N



A Hypergraph

B Decision variables

yAB yBB yCB yAC yBC y CC xAB xBB xCB xAC xBC x CC

A

Protein C (steady state) Max

B

ωBB

ω BC

C

Protein levels (pl)

ωAB

ωAC ωCB

Additional constraints

Min

maximum number of active connections: 6 (unconstrained)

ωCC

Cell index (ci)

Objective 1: Stripe quality Objective 2: Protein production cost

C Pareto front of optimal trade-offs

0 0 5

8

pl 10 B

10

C

.1 15

0

7

10 15 20 25 30 ci

450

Protein Cost

5 10 15 20 25 30 ci

3.53

300

P4

20 A

NP1

0

0 0

200 20 A

NP4 P8

-0.95

-0.9

-0.85

-0.8

-0.75

-0.7

-0.65

-0.6

0.5

B 2.2

pl 10 0

pl 10

5 10 15 20 25 30 ci

A

1

3 B 0.0 .18 4 C

0 0

0.5

10 15 20 25 30 ci

5

10 15 20 25 30 ci

20

20 A

7

5

P8 (IFF1)

P7 (IFF1) 20

0

-0.5

-Stripe Quality Score

0.6

5 10 15 20 25 30 ci

NP4 (IFF1)

-1

2.75 5 10 15 20 25 30 ci

B pl 10

6.8

P5

1 B 0.1 4 8.3 C

0

.2

0

A pl 10

10

5.2

C

250

P6 (IFF1)

3

2 B 0.2 3 9.4 C

P3

C

20 1.1

350

5 10 15 20 25 30 ci

5 10 15 20 25 30 ci

NP3 (IFF1)

P7

P5 (IFF1)

0 0

NP3

50

0

5.5

NP2

100

pl 10

B pl 10

10 15 20 25 30 ci

P6

0

A

5

150

20 9

2 B 0.4 0 4.1 C

0

11.2

5.72

P4 (IFF1) 1.7

C

pl 10 0

9

4

0

P2

0

A

B

pl 10

400

2

7 C 0.5 6 8.4 C

0.4 4.2

20

A

1.8

5 10 15 20 25 30 ci

P1

20 2.4

C 0

P3 (IFF1) A

20 A

2.2

3

pl 10

1.4

1.63

6 B

7.5

NP2 (IFF1)

20 A

3.6

1.7

C

NP1 (IFF1)

P1 (IFF3) 20

3

2.14

5.8

50

9.37

A

10

P2 (IFF1)

3.8

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 58 59 60

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0.4

2 B 0.0 .21 4 C

pl10 0

pl 10 0 0

0

5

10 15 20 25 30 ci


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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 58 59 60


yAB , yBB , yCB , yAC , yBC xAB , xBB , xCB , xAC , xBC

∈ {−1, 0, 1}

R>0

xCC

I = M dc

A

yCC

M

d c

c = 1, 2, . . . , N

A B

C c

P 1, . . . , P 8



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 58 59 60

B

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C B

C

N P 1, . . . , N P 4

A A B

C

C


y AA yBA yCA yAB yBB y CB yACy BC yCC

-4

ωAB

x AA xBA xCA xAB xBB x CB x AC xBC xCC

-6

ωBB

-Amplitude

B

ω BC

C ω CC

5 0 20 10 time

A

-12

time

10

0

-8

-10

Additional constraints

2 connections (C) 3 connections (D)

Stim.

-2

ωAA

ω BA ωAC ωCB

ωCA

0

C

Objective 1: Speed Objective 2: Amplitude

Stimulus

A

B

Decision variables

Hypergraph

B

-14

Amplitude

Response

A

-16

Speed -1

C

-18 -20

time

Max: 2 active connections 0

1

2

3

4

5

6

7

8

9

10

Speed -1

P7

-6

P8

20 P6 10

-Amplitude

Resp. Resp. Resp. Resp.

Resp.

P6

0

0 20 P7 10 0 20 P8

P10 P11

-10

P13 P14

-12

20 P9 10 0

-16

-20 200

300 time

∈ {−1, 0, 1}

P15

A

P16

0

0.05

P13

10 0 20

P14

10 0 20 P15 10

P19

IFF1 0.1

P20

0.15

0.2

0.25 Speed -1

20 P16 10 0 20 P17 10

20 P19 10 0 20 P20 10

0 P18

C

0 20

0 20 P18 10

P17

B

-18

100

Pareto Front

P12

-14

20 P12 10

0

P9

-8

10 0

20 P10 10 0 -100 0

Resp.

P5

P5

10

Resp.

P4

-4

Resp.

P3

Resp.

0 20

-2

time

Max: 3 active connections

P2 P4

0

time

Resp.

10

0

time

P1

20 P11 10

Resp.

10 0 20

0

0

P3

5

Resp.

0 20

10

20 P1 10

Resp.

10

Stim.

P2

Resp.

20

Resp.

Resp.

Resp.

Resp.

Resp.

D

Resp.

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 58 59 60


Resp.

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0.3

0.35

0.4

0.5

0 -100

0

100

200

300 time

yAA , yBA , yCA , yAB , yBB , yCB , yAC , yBC

yCC

xAA , xBA , xCA , xAB , xBB , xCB , xAC , xBC

xCC

R>0

C C




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yAA , yBA , yCA , yAB , yBB , yCB , yAC , yBC

yCC


xCC


A Stimulus

0 2-fold change

Amplitude speed

speed

-6 time

same response

-Amplitude

time

B

-2 -4

Amplitude

R>0

Pareto Front obtained for IFF1 and NLIF architectures P1 P2 P3 P4 P5 P6 P7 P8 P9 P10

-8

P11 P12

-10

P13 P14 P15

-12

Architectures with FCD property

∈ {−1, 0, 1}

xCC

C

Fold Change Detection (FCD)

Response

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 58 59 60


-14

P16 P17

-16

A

A

P18 P19

B

B C

IFF1

C

NLIF

-18

-20 0

P20

0.05

0.1

0.15

0.2

0.25

Speed -1


0.3

0.35

0.4

0.5


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 58 59 60

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z(t) ˙ = f (z, y, x, k), z(0) = z0 z ∈ RN x ∈ RR y ∈ ZM k ∈ RK

J(z, ˙ z, x, y, k) J J = (J1 , J2 , . . . , JS )


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x ∈ RR

y ∈ ZM

J = (J1 , J2 , . . . , JS )

min J1 (z, ˙ z, x, y, k), J2 (z, ˙ z, x, y, k), . . . , JS (z, ˙ z, x, y, k) x,y

z

k

ξ(z, ˙ z, x, y, k) = 0, z(t0 ) = z0 ,

h(z, x, y, k) = 0,

g(z, x, y, k) ≤ 0,

xL ≤ x ≤ x U , yL ≤ y ≤ yU .

(x∗ , y ∗ ) J(x∗ , y ∗ ) J(x∗ , y ∗ ) ≤ J(x∗∗ , y ∗∗ )

Ji i = 1, . . . , S


J(x∗∗ , y ∗∗ )


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 58 59 60

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ε

ε

J1

J2

(x∗1 , y1∗ ), (x∗2 , y2∗ )

J1 = J1 (x∗1 , y1∗ ), J1 = J1 (x∗2 , y2∗ ), J2 = J2 (x∗2 , y2∗ ), J2 = J2 (x∗1 , y1∗ ).

[J1 J2 ]

[J1 J2 ]


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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 58 59 60


J1

m J2

J2

ε = [ε1 , . . . , εi , . . . , εm+1 ]

ε1 ≤ J 2 εm+1 ≥ J 2

ε1 < ε2 < . . . < εm+1

min J1 (z, ˙ z, x, y, k) w,y

εk ≤ J2 (z, ˙ z, x, y, k) < εk+1 k = 1, . . . , m m J2 (z, ˙ z, x, y, k) < εk+1 J2 (z, ˙ z, x, y, k) ≤ εk+1 − ϵ


ϵ>0


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 58 59 60

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A) MO-MINLP

J2

ε-constraint strategy

P1

Interval 1

P2 P3 MINLP

MINLP

MINLP

MINLP

MINLP

ε m+1

Interval 2

Pareto Front (optimal trade-offs)

P4

hybrid MINLP solvers

... P1

P2

P3

ε2

Pm Interval m

Pm

P4

ε1 J1

B)

Inferring patterns and their evolution:

Additional criterion for forward design:

Continuous Pareto (example)

J2

E)

D)

C)

Discontinuous Pareto (example)

J2

J2

Extreme 1

J2

Clustering Pareto solutions

Dominated solution

Pareto Front (optimal trade-offs) interval with no feasible solution

Knee Point Extreme 2

Pareto Front (black squares)

Utopia point J1

J1

ε

ε ε


J1

J1

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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 58 59 60

R+M

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R

S


M

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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 58 59 60


Objective Space

Decision Space y2

J2 Nadir point

Pareto Front Utopia point y1

J1

yx yBB xBB yCB xCB yAC xAC yBC xBC yCC xCC k


yAB xAB



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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 58 59 60


Ptet2 LacI

Pλ LacI

Ptet2 LacI

Pλ araC

Plac1 tetR Pλ LacI


Pλ araC


aTc

18000

Ptet 2

Plac1

LacI

tetR

LacI

aTc

Ptet 2

Plac1

LacI

tetR

LacI

16000 P

λ

IPTG

Plac1

LacI

14000

IPTG LacI

12000

Cost

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 58 59 60

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10000 8000

aTc

Ptet 2

Plac1

LacI

tetR

LacI

LacI

tetR

LacI

aTc

6000

Ptet 2

Plac1

4000 P

λ

IPTG

Plac4 LacI

2000 0 -1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-Performance score

m

m


-0.2

-0.1

IPTG LacI

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Library 1 (16 decision variables) 25 eSS-MISQP

Average CPU time (s)

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 58 59 60

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MITS-MISQP

ACO-MISQP

20

15

10

5

0 3 devices

5 devices


9 devices

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• •




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ACS Synthetic Biology MULTIOBJECTIVE AUTOMATED DESIGN FRAMEWORK

Objective 1

Topologies that optimally trade-off objectives 1 and 2:

Topology search-space

Pareto Optimal Solutions

Global Multiobjective Mixed Integer Optimization Objective 2

(optimize topology and parameters simultaneously)

REVERSE DESIGN

FORWARD DESIGN Library of Parts Pλ

RBS

All possible N-gene networks cIR

lasR

tetR

lasI

Ptet

araC

ccdB

Pbad

lacI

ccdA

luxI

Plac

Ter

ccdA2

luxR

Best circuit for implementation

Patterns/motifs with given function A

A

B

B tetR

Ptet

araC

Pbad

C

cIR

IFF1

stimulus

Pλ

C

NLIF

2-fold change

response

level

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 58 59 60

time

Example: Synthetic oscillator with optimal stability and tunability of the period.

Example: Fold-Change detection architectures with optimal speed and amplitude


Automated Design Framework for Synthetic Biology Exploiting Pareto

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