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

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 27 th http://www.github.com/DNA-and-Natural-Algorithms-Group peppercornenumerator, nuskell, KinDA 1

DNA STRAND DISPLACEMENT DNA STRAND DISPLACEMENT = Adenine = long domain = Thymine = short domain = Cytosine = Guanine = 5' end = Phosphate = 3' end backbone DNA DNA b b a* a* b* b* 2

DOMAIN-LEVEL STRAND DISPLACEMENT DOMAIN-LEVEL STRAND DISPLACEMENT long (branch-migration) domain: binds irreversibly short (toehold) domain: binds reversibly A B x x F1 F2 t b + + a t a x t x t b t* x* t* t* x* t* 3-way branch migration unbind bind x x a x a x t t b t t b t* x* t* t* x* t* a t x x t b i1 i3 t* x* t* i2 3

DOMAIN-LEVEL STRAND DISPLACEMENT DOMAIN-LEVEL STRAND DISPLACEMENT long (branch-migration) domain: binds irreversibly detailed network short (toehold) domain: binds reversibly condensed network A B x x F1 F2 t b + + a t a x t x t b t* x* t* t* x* t* 3-way branch migration bind unbind x x a x a x t t b t t b t* x* t* t* x* t* a t x x t b i1 i2 t* x* t* 4

DOMAIN-LEVEL STRAND DISPLACEMENT DOMAIN-LEVEL STRAND DISPLACEMENT long (branch-migration) domain: binds irreversibly detailed network short (toehold) domain: binds reversibly condensed network A B x x F1 F2 t b + + a t a x t x t b t* x* t* t* x* t* 3-way branch migration unbind bind x x a x a x t t b t t b t* x* t* t* x* t* a t x x t b i1 i2 t* x* t* 5

MANY EXPERIMENTAL DEMONSTRATIONS ... MANY EXPERIMENTAL DEMONSTRATIONS ... 0 1 0 1 Output 1 1 0 0 Input 1 1 1 0 0 1 1 0 A B C D Qian, Winfree, Bruck (2011) Zhang et al. (2007) Cherry & Qian (2018) 6

... MANY MORE POTENTIAL APPLICATIONS. ... MANY MORE POTENTIAL APPLICATIONS. Chemical Reaction Networks (CRNs) A B Oregonator (limit cycle oscillator) Rössler (chaotic) nM nM 5 5 4 4 3 3 2 2 1 1 0 50 100 150 200 250 hr 0 10 20 30 40 hr C 2-bit pulse counter D Incrementer state machine (algorithmic) nM v:=0 (digital circuit) nM w:=0 60 20 30 10 v > 0? 0 0 no yes where 60 20 w:=w+1 v:=v-1 30 v:=w 10 0 0 0 20 40 60 80 100 hr 0 20 40 60 80 100 hr x clock made where catalyzed by clk1 catalyzed by clk2 catalyzed by clk3 z logic thresholding y from chemical r1 r2+ r3 v2 v1 v2 + v3 v3 v1 oscillator: x(0)+y(1) on w w(1)+w(1) on z dual rail c2 c1 c2 + c3 c3 c1 clk1 on w +w(0) on w +w(1) w(0)+w(0) off z representation: i r3 r1 w2 w1 species value x(1)+w(1) x(1)+w(0) on z +z(0) on z +z(1) x x(0) x(1) anytime y(0)+w(1) y(0)+w(0) off z +z(1) off z +z(0) r2 + v2 d + v2 c2 + r2 c2+ i + w1 v2 + c2 high low 0 clk2 clk3 d + v1 i + w1 i + v1+ w2 low high 1 Soloveichik et al. (2010) - DNA as a universal substrate for chemical kinetics 7

DOMAIN-LEVEL STRAND DISPLACEMENT DOMAIN-LEVEL STRAND DISPLACEMENT long (branch-migration) domain: binds irreversibly short (toehold) domain: binds reversibly A B x x F1 F2 t b + + a t a x t x t b t* x* t* t* x* t* 3-way branch migration unbind bind DSD sytem specification formal CRN x x a x a x t t b t t b formal species: {A, B} signal species (low concentation): {A, B} t* x* t* t* x* t* a t x x t b fuel species (high concentration): {F1, F2} i1 i3 t* x* t* i2 8

FROM CRN TO DSD SYSTEMS FROM CRN TO DSD SYSTEMS Soloveichik Lakin Cardelli (2011) Qian et al. (2011) et al. (2010) et al. (2012) Chen et al. (2012), Cardelli (2013), Srinivas (2015), Lakin et al. (2016), ... Images drawn using the DNA strand displacement analysis so�ware VisualDSD: Philipps & Cardelli (2009), ..., Spaccasassi et al. (2017) 9

A CRN-TO-DSD COMPILER A CRN-TO-DSD COMPILER try all translation schemes sequence design experimental verify testing correctness (for all inputs) automated workflow choose optimal scheme 10

THE CENTRAL COMPONENT: PEPPERCORN THE CENTRAL COMPONENT: PEPPERCORN condensed reaction rates nucleotide-level reaction rates CRN trajectory A B x equivalence x A B F1 F2 t b x a t + + x x a t x F1 F2 t b a t + + t b a t x x t b t* x* t* t* x* t* t* x* t* t* x* t* A F2 x a a t x a t + a t x t x t* x* t* t* x* t* CRN condensation domain-level reaction rates A B x x F1 F2 a t + + t b a t x x t b nucleotide t* x* t* t* x* t* a t x unbind bind A sequences x F2 CRN enumeration a t x 3-way branch migration x t* x* t* a t x t b a t x t b x t b x t* x* t* t* x* t* F1 a t x x t b B t b i1 i3 t* x* t* t* x* t* i2 Nuskell project Peppercorn project KinDA project Grun et al. (2014) - arXiv Badelt, Grun et al. (in perparation) 11

THERMODYNAMIC ENERGY MODEL THERMODYNAMIC ENERGY MODEL A secondary structure is a list of base pairs, where: 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) A E b d* q* D r d b* o* q b) "dot-bracket" or "dot-parens-plus" notation c e o p 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* . ( . ) ( . ( . ( + ) ) . ( . ( + ) . ) . ( . + ( + ) ) . ) f n c) "kernel" notation f* g i a b( c ) d( e f( g h( + ) ) i j( k l( + ) m ) n o( p + q( + ) ) r ) h* j* j B h m k l* l C 12

REACTION TYPES & APPROXIMATE RATES 1/2 REACTION TYPES & APPROXIMATE RATES 1/2 r ? r* r ? bind11 : ? r* ? ? r ? ? r bind21 : + + ? ? r* ? ? r* r r* ? r open : ? r* Open reactions only for toeholds with parameter: L , k slow is the only valid bimolecular reaction bind21 13

REACTION TYPES & APPROXIMATE RATES 2/2 REACTION TYPES & APPROXIMATE RATES 2/2 Figure from Kotani & Hughes (2017) r r* ? r ? r ? r* r r r ? ? 4-way : ? ? 3-way-fw : ? r* r r ? r* r* r* ? ? r r r ? ? r 3-way-bw : ? r* r* ? unimolecular, but may lead to dissociation 14

POLYMERIZATION POLYMERIZATION a) s1 a b b b → → a a a*b* a*b* s2 a* b* s1–s2 s1–s2 b) a* b* a* → ... b* → → b* → → a* a a b b s1–s2 s1–s2–s1 s1–s2–s1–s2 s1–s2–s1–s2–s1 s1–s2–s1–s2–s1–s2 15

ENUMERATION / CONDENSATION ENUMERATION / CONDENSATION B m A B m* B* C* 16

ENUMERATION / CONDENSATION ENUMERATION / CONDENSATION B A B m B m B* m* C* A B m* B* C* 17

ENUMERATION / CONDENSATION ENUMERATION / CONDENSATION A B B A B m B m B* m* C* B m A B B* m* C* m* B* C* 18

ENUMERATION / CONDENSATION ENUMERATION / CONDENSATION A B B A B m B m B* m* C* B m A B B* m* C* m* B* C* 19

ENUMERATION / CONDENSATION ENUMERATION / CONDENSATION A B B A B m B m B* m* C* B m A B B* m* C* m* B* C* A B m B k A B m B m* B* B* m* C* C* 20

CONDENSED REACTION RATES CONDENSED REACTION RATES a) b) c) m x x* m* A A B m B m B n B k k k m* x* x A A n* B m B m B n B m x n* x* m* B* m* B* m* B* m* n* B* n* n x C* n x* C* C* C* 21

AUTOCATALYTIC SYSTEM AUTOCATALYTIC SYSTEM Kotani & Hughes (2017) 22

AUTOCATALYTIC SYSTEM AUTOCATALYTIC SYSTEM Kotani & Hughes (2017) 23

MANY SYSTEMS MANY SYSTEMS 24

THE COMPILER FRAMEWORK THE COMPILER FRAMEWORK condensed reaction rates nucleotide-level reaction rates CRN trajectory A B x equivalence x A B F1 F2 t b x a t + + x x a t x F1 F2 t b a t + + t b a t x x t b t* x* t* t* x* t* t* x* t* t* x* t* A F2 x a a t x a t + a t x t x t* x* t* t* x* t* CRN condensation domain-level reaction rates A B x x F1 F2 a t + + t b a t x x t b nucleotide t* x* t* t* x* t* a t x unbind bind A sequences x F2 CRN enumeration a t x 3-way branch migration x t* x* t* a t x t b a t x t b x t b x t* x* t* t* x* t* F1 a t x x t b B t b i1 i3 t* x* t* t* x* t* i2 Nuskell project Peppercorn project KinDA project 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) 25