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A GENERAL-PURPOSE A GENERAL-PURPOSE CRN-TO-DSD COMPILER FRAMEWORK - - PowerPoint PPT Presentation

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A GENERAL-PURPOSE A GENERAL-PURPOSE CRN-TO-DSD COMPILER FRAMEWORK CRN-TO-DSD COMPILER FRAMEWORK WITH FORMAL VERIFICATION, OPTIMIZATION, WITH FORMAL VERIFICATION, OPTIMIZATION, AND SIMULATION CAPABILITIES AND SIMULATION CAPABILITIES Stefan

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A GENERAL-PURPOSE A GENERAL-PURPOSE CRN-TO-DSD COMPILER FRAMEWORK CRN-TO-DSD COMPILER FRAMEWORK WITH FORMAL VERIFICATION, OPTIMIZATION, WITH FORMAL VERIFICATION, OPTIMIZATION, AND SIMULATION CAPABILITIES AND SIMULATION CAPABILITIES

Stefan Badelt DNA and Natural Algorithms (DNA) Group, Caltech MPP2-Finale Workshop Caltech, June , 2019

27th

peppercornenumerator, nuskell, KinDA http://www.github.com/DNA-and-Natural-Algorithms-Group

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DNA STRAND DISPLACEMENT DNA STRAND DISPLACEMENT

= Adenine = Thymine = Cytosine = Guanine = Phosphate backbone

DNA

= long domain = short domain

DNA

= 3' end = 5' end

b a* b* b b* a*

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DOMAIN-LEVEL STRAND DISPLACEMENT DOMAIN-LEVEL STRAND DISPLACEMENT

a t x x t b x* t* t* x b t x t* t* x* t a x t* t* x* t a x b t x t b x* t* t* a t x x t b x* t* t* a t x bind 3-way branch migration unbind

A B F1 F2

short (toehold) domain: binds reversibly long (branch-migration) domain: binds irreversibly

+ +

i1 i2 i3

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DOMAIN-LEVEL STRAND DISPLACEMENT DOMAIN-LEVEL STRAND DISPLACEMENT

a t x x t b x* t* t* x b t x t* t* x* t a x t* t* x* t a x b t x t b x* t* t* a t x x t b x* t* t* a t x bind 3-way branch migration unbind

A B F1 F2

short (toehold) domain: binds reversibly long (branch-migration) domain: binds irreversibly

+ +

i1 i2

detailed network condensed network

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5

DOMAIN-LEVEL STRAND DISPLACEMENT DOMAIN-LEVEL STRAND DISPLACEMENT

a t x x t b x* t* t* x b t x t* t* x* t a x t* t* x* t a x b t x t b x* t* t* a t x x t b x* t* t* a t x bind 3-way branch migration unbind

A B F1 F2

short (toehold) domain: binds reversibly long (branch-migration) domain: binds irreversibly

+ +

i1 i2

detailed network condensed network

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MANY EXPERIMENTAL DEMONSTRATIONS ... MANY EXPERIMENTAL DEMONSTRATIONS ...

0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 A B C D

Input Output

Zhang et al. (2007) Qian, Winfree, Bruck (2011) Cherry & Qian (2018)

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... MANY MORE POTENTIAL APPLICATIONS. ... MANY MORE POTENTIAL APPLICATIONS.

20 40 60 80 100 hr nM nM

Oregonator (limit cycle oscillator) Rössler (chaotic) Incrementer state machine (algorithmic) 2-bit pulse counter (digital circuit)

nM nM hr 30 60 30 60

x x(0)+y(1)

  • nw
  • nw+w(0)
  • nw+w(1)

y

logic

where where

thresholding

catalyzed by clk1 anytime z w(0)+w(0)

  • ffz

w(1)+w(1)

  • nz
  • nz+z(0)
  • nz+z(1)
  • ffz+z(1)
  • ffz+z(0)

x(1)+w(1) x(1)+w(0) y(0)+w(1) y(0)+w(0)

10 20 20 40 60 80 100 10 20 50 100 150 200 250 1 2 3 4 5

dual rail representation: species value x(0) x(1) high low low high 1 x v1 v2 + v3 c1 c2 + c3 v2 + c2 w2 w1 r1 r2+ r3 r2 + v2 d + v2 d + v1 c2 + r2 c2+ i + w1 i + w1 i + v1+ w2 v2 c2 i v3 v1 c3 c1 r3 r1 v > 0? v:=v-1 yes no w:=w+1 v:=w v:=0 w:=0 catalyzed by clk2 catalyzed by clk3 clk1 clock made from chemical

  • scillator:

clk2 clk3

A B C D

hr hr 10 20 30 40 1 2 3 4 5

Chemical Reaction Networks (CRNs)

Soloveichik et al. (2010) - DNA as a universal substrate for chemical kinetics

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DOMAIN-LEVEL STRAND DISPLACEMENT DOMAIN-LEVEL STRAND DISPLACEMENT

a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

short (toehold) domain: binds reversibly long (branch-migration) domain: binds irreversibly

+ +

x t* t* x* t a x b t x t b x* t* t* a t x x t b x* t* t* a t x bind 3-way branch migration unbind

i1 i2 i3

formal CRN formal species: {A, B} DSD sytem specification signal species (low concentation): {A, B} fuel species (high concentration): {F1, F2}

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FROM CRN TO DSD SYSTEMS FROM CRN TO DSD SYSTEMS

Cardelli (2011) Soloveichik et al. (2010) Qian et al. (2011) Lakin et al. (2012)

Chen et al. (2012), Cardelli (2013), Srinivas (2015), Lakin et al. (2016), ...

Images drawn using the DNA strand displacement analysis soware VisualDSD: Philipps & Cardelli (2009), ..., Spaccasassi et al. (2017)

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A CRN-TO-DSD COMPILER A CRN-TO-DSD COMPILER

try all translation schemes verify correctness (for all inputs) sequence design experimental testing choose

  • ptimal scheme

automated workflow

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THE CENTRAL COMPONENT: PEPPERCORN THE CENTRAL COMPONENT: PEPPERCORN

CRN trajectory equivalence

Nuskell project

a t x

A

x b t

B

x t b x* t* t*

F1

x t* t* x* t a

F2

a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

CRN condensation CRN enumeration

x t* t* x* t a x b t x t b x* t* t* a t x x t b x* t* t* a t x bind 3-way branch migration unbind a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

i1 i2 i3

Peppercorn project

condensed reaction rates domain-level reaction rates

nucleotide sequences

KinDA project

nucleotide-level reaction rates

a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

a t x

A

+

x t* t* x* t a

F2

x t* t* x* t a a x t

Grun et al. (2014) - arXiv Badelt, Grun et al. (in perparation)

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A secondary structure is a list of base pairs, where:

THERMODYNAMIC ENERGY MODEL THERMODYNAMIC ENERGY MODEL

A base may participate in at most one base pair Base pairs must not cross (no pseudoknots) Only specific base-pairs (GC, AT, GT) are allowed.

A a b c b* d e f g h B h* f* i j k l C l* m j* n

  • p

D q E q*

  • *

r d* a)

a b c b* d e f g h + h* f* i j k l + l* m j* n o p + q + q* o* r d* . ( . ) ( . ( . ( + ) ) . ( . ( + ) . ) . ( . + ( + ) ) . ) a b( c ) d( e f( g h( + ) ) i j( k l( + ) m ) n o( p + q( + ) ) r )

b) "dot-bracket" or "dot-parens-plus" notation c) "kernel" notation

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REACTION TYPES & APPROXIMATE RATES 1/2 REACTION TYPES & APPROXIMATE RATES 1/2

bind11: bind21:

  • pen:

r ? ? r* ? ? r r* r r* ? ? r r* ? ? ? ? + r r* r r* ? ? + ?

Open reactions only for toeholds with parameter: L, kslow is the only valid bimolecular reaction

bind21

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REACTION TYPES & APPROXIMATE RATES 2/2 REACTION TYPES & APPROXIMATE RATES 2/2

Figure from Kotani & Hughes (2017)

3-way-fw: ? ? r r r* ? ? r r r* ? ? r r ? ? r r r* r* 3-way-bw: r r* r r* r r r* r* ? ? ? ? ? ? ? 4-way:

unimolecular, but may lead to dissociation

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POLYMERIZATION POLYMERIZATION

a b a* b* a b a*b* s1–s2 s1–s2 s1 s2

→ →

a) a b a*b* s1–s2 s1–s2–s1–s2 s1–s2–s1–s2–s1 s1–s2–s1–s2–s1–s2 s1–s2–s1

→ → → → →...

b) a* b* a b a* b* b* a* a b

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ENUMERATION / CONDENSATION ENUMERATION / CONDENSATION

B m A B C* m* B*

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ENUMERATION / CONDENSATION ENUMERATION / CONDENSATION

B m A B C* m* B* B m A B C* m* B*

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18

ENUMERATION / CONDENSATION ENUMERATION / CONDENSATION

B m A B C* m* B* B m A B C* m* B* m B C* m* B* B A

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ENUMERATION / CONDENSATION ENUMERATION / CONDENSATION

B m A B C* m* B* B m A B C* m* B* m B C* m* B* B A

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20

ENUMERATION / CONDENSATION ENUMERATION / CONDENSATION

B m A B C* m* B* B m A B C* m* B* B m A B C* m* B* A B C* m* B* B m k m B C* m* B* B A

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CONDENSED REACTION RATES CONDENSED REACTION RATES

a) b) c)

B m A B C* m* B* A B C* m* B* B m B m A B n A B n C* m* n* B* C* m* n* B* B m n* x x* m* n x* x m x* x n n* x x* m* m k k k

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AUTOCATALYTIC SYSTEM AUTOCATALYTIC SYSTEM

Kotani & Hughes (2017)

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AUTOCATALYTIC SYSTEM AUTOCATALYTIC SYSTEM

Kotani & Hughes (2017)

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MANY SYSTEMS MANY SYSTEMS

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THE COMPILER FRAMEWORK THE COMPILER FRAMEWORK

CRN trajectory equivalence

Nuskell project

a t x

A

x b t

B

x t b x* t* t*

F1

x t* t* x* t a

F2

a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

CRN condensation CRN enumeration

x t* t* x* t a x b t x t b x* t* t* a t x x t b x* t* t* a t x bind 3-way branch migration unbind a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

i1 i2 i3

Peppercorn project

condensed reaction rates domain-level reaction rates

nucleotide sequences

KinDA project

nucleotide-level reaction rates

a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

a t x

A

+

x t* t* x* t a

F2

x t* t* x* t a a x t

Peppercorn: Badelt, Grun et al. (in perparation) KinDA: Berleant et al. (2018) NUPACK: Dirks et al. (2007) Multistrand: Schaeffer et al. (2015) Nuskell: Badelt et al. (2017) CRN pathway decomposition equivalence: Shin et al. (2017) CRN bisimulation equivalence: Johnson et al. (2018)

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THE COMPILER FRAMEWORK THE COMPILER FRAMEWORK

CRN trajectory equivalence

Nuskell project

a t x

A

x b t

B

x t b x* t* t*

F1

x t* t* x* t a

F2

a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

CRN condensation CRN enumeration

x t* t* x* t a x b t x t b x* t* t* a t x x t b x* t* t* a t x bind 3-way branch migration unbind a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

i1 i2 i3

Peppercorn project

condensed reaction rates domain-level reaction rates

nucleotide sequences

KinDA project

nucleotide-level reaction rates

a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

a t x

A

+

x t* t* x* t a

F2

x t* t* x* t a a x t

Peppercorn: Badelt, Grun et al. (in perparation) KinDA: Berleant et al. (2018) NUPACK: Dirks et al. (2007) Multistrand: Schaeffer et al. (2015) Nuskell: Badelt et al. (2017) CRN pathway decomposition equivalence: Shin et al. (2017) CRN bisimulation equivalence: Johnson et al. (2018)

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THE COMPILER FRAMEWORK THE COMPILER FRAMEWORK

CRN trajectory equivalence

Nuskell project

a t x

A

x b t

B

x t b x* t* t*

F1

x t* t* x* t a

F2

a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

CRN condensation CRN enumeration

x t* t* x* t a x b t x t b x* t* t* a t x x t b x* t* t* a t x bind 3-way branch migration unbind a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

i1 i2 i3

Peppercorn project

condensed reaction rates domain-level reaction rates

nucleotide sequences

KinDA project

nucleotide-level reaction rates

a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

a t x

A

+

x t* t* x* t a

F2

x t* t* x* t a a x t

Peppercorn: Badelt, Grun et al. (in perparation) KinDA: Berleant et al. (2018) NUPACK: Dirks et al. (2007) Multistrand: Schaeffer et al. (2015) Nuskell: Badelt et al. (2017) CRN pathway decomposition equivalence: Shin et al. (2017) CRN bisimulation equivalence: Johnson et al. (2018)

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CRN EQUIVALENCE CRN EQUIVALENCE

A -> A + A A + A -> A A + B -> B + B B -> A + C -> C -> C + C C + C -> C

Johnson et al. (2018) - CRN bisimulation equivalence translation scheme: qian2011_3D_var1.ts

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CRN EQUIVALENCE CRN EQUIVALENCE

A -> A + A A + A -> A A + B -> B + B B -> A + C -> C -> C + C C + C -> C f14 + C -> e1428 + f15 e853 + f12 -> C + f13 A + f4 -> f3 + e71 f2 + e25 -> A + f1 A + e25 -> f2 + e7 e996 + f3 -> A + f10 e1428 + f15 -> f14 + C f3 + e71 -> A + f4 e465 + B -> e418 + f6 e614 + f9 -> e611 + e730 e996 + C -> e1040 + f12 e465 + f5 -> e514 + e368 e308 + f7 -> f8 + B e418 + B -> e371 + f6 C + f13 -> e853 + f12 A + f1 -> f2 + e25 B + e71 -> e319 + f7 f2 + e7 -> A + e25 e1040 + f11 -> e1162 + e1163 + e1158 e319 + f7 -> B + e71 e308 + f9 -> e614 + e615 + e611 e371 + f6 -> e418 + B e1040 + f12 -> e996 + C f8 + B -> e308 + f7 e319 + f5 -> e372 + e371 + e368 f3 + e7 -> A + f0 e853 + f15 -> e1428 + C e1428 + C -> e853 + f15 A + f10 -> e996 + f3 e1163 + f11 -> e1158 + e1246 e418 + f6 -> e465 + B A + f0 -> f3 + e7

Johnson et al. (2018) - CRN bisimulation equivalence translation scheme: qian2011_3D_var1.ts

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CRN EQUIVALENCE CRN EQUIVALENCE

A -> A + A A + A -> A A + B -> B + B B -> A + C -> C -> C + C C + C -> C f14 + C -> e1428 + f15 e853 + f12 -> C + f13 A + f4 -> f3 + e71 f2 + e25 -> A + f1 A + e25 -> f2 + e7 e996 + f3 -> A + f10 e1428 + f15 -> f14 + C f3 + e71 -> A + f4 e465 + B -> e418 + f6 e614 + f9 -> e611 + e730 e996 + C -> e1040 + f12 e465 + f5 -> e514 + e368 e308 + f7 -> f8 + B e418 + B -> e371 + f6 C + f13 -> e853 + f12 A + f1 -> f2 + e25 B + e71 -> e319 + f7 f2 + e7 -> A + e25 e1040 + f11 -> e1162 + e1163 + e1158 e319 + f7 -> B + e71 e308 + f9 -> e614 + e615 + e611 e371 + f6 -> e418 + B e1040 + f12 -> e996 + C f8 + B -> e308 + f7 e319 + f5 -> e372 + e371 + e368 f3 + e7 -> A + f0 e853 + f15 -> e1428 + C e1428 + C -> e853 + f15 A + f10 -> e996 + f3 e1163 + f11 -> e1158 + e1246 e418 + f6 -> e465 + B A + f0 -> f3 + e7 C -> e1428 e853 -> C A -> e71 e25 -> A A + e25 -> e7 e996 -> A e1428 -> C e71 -> A e465 + B -> e418 e614 -> e611 + e730 e996 + C -> e1040 e465 -> e514 + e368 e308 -> B e418 + B -> e371 C -> e853 A -> e25 B + e71 -> e319 e7 -> A + e25 e1040 -> e1162 + e1163 + e1158 e319 -> B + e71 e308 -> e614 + e615 + e611 e371 -> e418 + B e1040 -> e996 + C B -> e308 e319 -> e372 + e371 + e368 e7 -> A e853 -> e1428 + C e1428 + C -> e853 A -> e996 e1163 -> e1158 + e1246 e418 -> e465 + B A -> e7

Johnson et al. (2018) - CRN bisimulation equivalence translation scheme: qian2011_3D_var1.ts

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CRN EQUIVALENCE CRN EQUIVALENCE

f14 + C -> e1428 + f15 e853 + f12 -> C + f13 A + f4 -> f3 + e71 f2 + e25 -> A + f1 A + e25 -> f2 + e7 e996 + f3 -> A + f10 e1428 + f15 -> f14 + C f3 + e71 -> A + f4 e465 + B -> e418 + f6 e614 + f9 -> e611 + e730 e996 + C -> e1040 + f12 e465 + f5 -> e514 + e368 e308 + f7 -> f8 + B e418 + B -> e371 + f6 C + f13 -> e853 + f12 A + f1 -> f2 + e25 B + e71 -> e319 + f7 f2 + e7 -> A + e25 e1040 + f11 -> e1162 + e1163 + e1158 e319 + f7 -> B + e71 e308 + f9 -> e614 + e615 + e611 e371 + f6 -> e418 + B e1040 + f12 -> e996 + C f8 + B -> e308 + f7 e319 + f5 -> e372 + e371 + e368 f3 + e7 -> A + f0 e853 + f15 -> e1428 + C e1428 + C -> e853 + f15 A + f10 -> e996 + f3 e1163 + f11 -> e1158 + e1246 e418 + f6 -> e465 + B A + f0 -> f3 + e7 C -> e1428 e853 -> C A -> e71 e25 -> A A + e25 -> e7 e996 -> A e1428 -> C e71 -> A e465 + B -> e418 e614 -> e611 + e730 e996 + C -> e1040 e465 -> e514 + e368 e308 -> B e418 + B -> e371 C -> e853 A -> e25 B + e71 -> e319 e7 -> A + e25 e1040 -> e1162 + e1163 + e1158 e319 -> B + e71 e308 -> e614 + e615 + e611 e371 -> e418 + B e1040 -> e996 + C B -> e308 e319 -> e372 + e371 + e368 e7 -> A e853 -> e1428 + C e1428 + C -> e853 A -> e996 e1163 -> e1158 + e1246 e418 -> e465 + B A -> e7 C -> C C + C -> C A -> A A -> A A + A -> A + A A -> A C -> C A -> A B -> B

  • >

A + C -> A + C

  • >

B -> B B + B -> B + B C -> C + C A -> A B + A -> A + B A + A -> A + A A + C -> A + B -> B + A B -> B + B -> B + B A + C -> A + C B -> B A + B -> B + B A + A -> A C + C -> C + C C + C -> C + C A -> A

  • >

B -> B A -> A + A

A => A B => B C => C e1040 => A, C e1158 => e1162 => e1163 => e1246 => e1428 => C e25 => A e308 => B e319 => A, B e368 => e371 => B, B e372 => e418 => B e465 => e514 => e611 => e614 => e615 => e7 => A, A e71 => A e730 => e853 => C, C e996 => A

Interpretation (CRN-bisimulation):

A -> A + A A + A -> A A + B -> B + B B -> A + C -> C -> C + C C + C -> C

Johnson et al. (2018) - CRN bisimulation equivalence translation scheme: qian2011_3D_var1.ts

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33

FROM A DIGITAL CIRCUIT TO DSD FROM A DIGITAL CIRCUIT TO DSD

Qian et al. (2011)

Input for the nuskell compiler: 32 formal reactions. soloveichik2010.ts: 52 signal species, 92 fuel species, 172 intermediate species, 180 reactions. verifies as correct according to the pathway decomposition and CRN bisimulation equivalence Badelt, Shin, Johnson, Dong, Thachuk and Winfree: A general-purpose CRN-to-DSD compiler with formal verification, optimization, and simulation capabilities. LNCS (2017)

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... that can be rigorously analyzed within the domain of the thermodynamic energy model. formal verification, choose optimal translation scheme, simulation using approximate reaction rates

CONCLUSION CONCLUSION

STRAND DISPLACEMENT IS A KINETIC TOOLBOX ... STRAND DISPLACEMENT IS A KINETIC TOOLBOX ...

CRN trajectory equivalence

Nuskell project

a t x

A

x b t

B

x t b x* t* t*

F1

x t* t* x* t a

F2

a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

CRN condensation CRN enumeration

x t* t* x* t a x b t x t b x* t* t* a t x x t b x* t* t* a t x bind 3-way branch migration unbind a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

i1 i2 i3

Peppercorn project

condensed reaction rates domain-level reaction rates

nucleotide sequences

KinDA project

nucleotide-level reaction rates

a t x x t b x* t* t* x b t x t* t* x* t a

A B F1 F2

+ +

a t x

A

+

x t* t* x* t a

F2

x t* t* x* t a a x t

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35

THANKS TO THANKS TO

Erik Winfree Seung Woo Shin Casey Grun Joseph Berleant Robert F. Jonhson Chris Thachuk Frits Dannenberg Chris Berlind Karthik V. Sarma Qing Dong Joseph M. Schaeffer Brian Wolfe http://www.github.com/DNA-and-Natural-Algorithms-Group/nuskell http://www.github.com/DNA-and-Natural-Algorithms-Group/peppercornenumerator http://www.github.com/DNA-and-Natural-Algorithms-Group/KinDA This research was funded in parts by: The Caltech Biology and Biological Engineering Division Fellowship. The U.S. National Science Foundation NSF Grant CCF-1213127 and NSF Grant CCF-1317694. The Gordon and Betty Moore Foundation's Programmable Molecular Technology Initiative (PMTI).

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CASE STUDIES: AUTOCATALYTIC SYSTEM CASE STUDIES: AUTOCATALYTIC SYSTEM

Kotani & Hughes (2017)

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37

CASE STUDIES: AUTOCATALYTIC SYSTEM CASE STUDIES: AUTOCATALYTIC SYSTEM

Kotani & Hughes (2017)

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CASE STUDIES: AUTOCATALYTIC SYSTEM CASE STUDIES: AUTOCATALYTIC SYSTEM

INF

# parameters MCS RC + TC DR RM CR 1 release-cutof = 8 10 16 + 159 556 14 15 2 kslow = kfa st = 10− 3 16 13 + 82 265 10 11 3 kslow = kfa st = 10− 4 10 16 + 164 599 14 15 4 kslow = 10− 4, kfa st = 10− 3 16 20 + 164 488 17 22 5 kslow = 10− 4, kfa st = 10− 2 24 55 + 1426 6628 28 62 6 kslow = 10− 5, kfa st = 10− 2 24 55 + 1426 6652 28 75