EQUIVALENCE OF CHEMICAL REACTION NETWORKS IN A CRN-TO-DNA COMPILER - PowerPoint PPT Presentation

EQUIVALENCE OF CHEMICAL REACTION NETWORKS IN A CRN-TO-DNA COMPILER FRAMEWORK Stefan Badelt and Erik Winfree DNA and Natural Algorithms (DNA) Group, Caltech Oxford, July, 19 , 2018 th VEMDP 2018 1

MOLECULAR PROGRAMMING (in terms of the nuskell compiler project) nucleic acids are architecture to implement algorithms chemical reaction networks are a programming language formal/experimental verification of correct implementation minimal/optimal components for biological systems verifyably correct artificial systems arbitrary algorithm Anti- Ligand Terminator scalable, correct ON promoter region protein coding region riboswitch components + Ligand - Ligand Terminator OFF information promoter region protein coding region riboswitch conditional switch processing network biological relevance is primary formal description is primary, if experiments fail, refine the method biological relevance secondary 2

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* 3

DOMAIN-LEVEL STRAND DISPLACEMENT long (branch-migration) domain: binds irreversibly short (toehold) domain: binds reversibly A B x x F2 F1 t b a + + t a x t x t b t* x* t* t* x* t* 3-way branch migration unbind bind x x x a x a t b t t t b t* x* t* t* x* t* a t x x t b i3 i1 t* x* t* i2 4

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

DOMAIN-LEVEL STRAND DISPLACEMENT long (branch-migration) domain: binds irreversibly detailed network short (toehold) domain: binds reversibly condensed network A B x x F2 F1 t b a + + t a x t x t b t* x* t* t* x* t* 3-way branch migration unbind bind x x x a x a t b t t t b t* x* t* t* x* t* a t x x t b i2 i1 t* x* t* 6

DOMAIN-LEVEL STRAND DISPLACEMENT long (branch-migration) domain: binds irreversibly short (toehold) domain: binds reversibly A B x x F2 F1 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 x a x a t b t 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} i3 i1 t* x* t* i2 7

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 VisualDSD, Lakin et al. (2012) 8

A CRN-TO-DSD COMPILER try all translation schemes sequence design experimental verify testing correctness - for all inputs - experimental setup automated workflow choose optimal scheme - synthesis cost - efficency / robustness - experimental constraints 9

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) 10

THE COMPILER FRAMEWORK condensed reaction rates nucleotide-level reaction rates CRN trajectory A B x equivalence x F1 F2 A B x a t + + t b x a t x F1 F2 x t b a t + + t b a x x t b t t* x* t* t* x* t* t* x* t* t* x* t* 3 A F2 x a a t x a t + a t x t x t* x* t* t* x* t* CRN condensation 2 domain-level reaction rates 4 A B x x F1 F2 a + + t b t a x x t b t 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 x t b a t x t t b x t b x t* x* t* t* x* t* F1 a t x x t b t b B i1 i3 t* x* t* t* x* t* 1 i2 Nuskell project Peppercorn project KinDA project Badelt et al. (2017) - Nuskell Grun et al. (2014) - Peppercorn Shin et al. (2017) - CRN pathway decomposition equivalence Johnson et al. (2018) - CRN bisimulation equivalence Berleant et al. (submitted) - KinDA 11

REACTION ENUMERATION bind / open b a b a* a* a a a a* a* 3-way branch migration 4-way branch migration c c* b b b a a b c c b b* c c* a b b* a* a a* a* b* a* b* c* c* a* a a* b* b a c d* d c b* b c c d* d c* c* a* a* 12

REACTION ENUMERATION allows all secondary structures (pseudoknots excluded) bind / open b open reactions of domains with length > L are forbidden a b a* a* a open & branch migration reactions are always unimolecular, but may lead to dissociation. a a a* bind reactions are the only valid bimolecular reactions a* 3-way branch migration 4-way branch migration c c* b b b a a b c c b b* c c* a b b* a* a a* a* b* a* b* c* c* a* a a* b* b a c d* d c b* b c c d* d c* c* a* a* 13

SEPARATION OF TIMESCALES unimolecular reactions are fast bimolecular reactions are slow t t a k α t t a A + X B t* b t* k β t* b t* resting complexes transient complex k β k α { X − → A + B ; A + B − → X } at low concentrations: k β [ A ][ B ] << k α [ X ] 14

APPROXIMATE REACTION RATE CONSTANTS a a open rate bimolecular binding a* a* unimolecular branch migration binding b b b a a b c c a a* b* a* b* c* c* h a* linker closing helix zipping c c (nucleation) c c h c* c* a* a a* a* a a* hairpin closing rate h 15

MODEL PARAMETERS negligible reactions slow reactions fast reactions bind21 bimolecular [/M/s] open (len > L) open (len < L) unimolecular [/s] bind11 branch migration unimolecular [/s] rate-independent model: simple, one parameter: L rate-dependent model: flexible, two parameters: k-slow, k-fast 16

REACTION ENUMERATION all initial complexes are included every complex has all valid fast reactions enumerated transient complexes have no slow reactions enumerated resting complexes have all valid slow reactions enumerated valid according to enumeration semantics: rate-dependent model rate-independent model max-helix semantics: reaction types are greedy reject-remote semantics: exclude remote-toehold branch migration 17

THE COMPILER FRAMEWORK condensed reaction rates nucleotide-level reaction rates CRN trajectory A B x equivalence x F1 F2 A B x a t + + t b x a t x F1 F2 x t b a t + + t b a x x t b t t* x* t* t* x* t* t* x* t* t* x* t* 3 A F2 x a a t x a t + a t x t x t* x* t* t* x* t* CRN condensation 2 domain-level reaction rates 4 A B x x F1 F2 a + + t b t a x x t b t 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 x t b a t x t t b x t b x t* x* t* t* x* t* F1 a t x x t b t b B i1 i3 t* x* t* t* x* t* 1 i2 Nuskell project Peppercorn project KinDA project Badelt et al. (2017) - Nuskell Grun et al. (2014) - Peppercorn Shin et al. (2017) - CRN pathway decomposition equivalence Johnson et al. (2018) - CRN bisimulation equivalence Berleant et al. (submitted) - KinDA 18

CRN CONDENSATION Goal: represent CRN in terms of overall slow reactions properties / requirements: all fast reactions are unimolecular reactions have arity (n,m) with n > 0 and m > 0 reactants of slow reactions must be resting states reactants and products of fast (1-2) reactions are in different SCCs (mass conservation) 19

CRN CONDENSATION Step 1: Make a graph that contains only fast (1,1) reactions 20

CRN CONDENSATION Step 2: Identify strongly connected components (SCCs) 21

CRN CONDENSATION Step 3: Define transient and resting macrostates A B C D E F 22

CRN CONDENSATION Step 4: Assign fates to complexes (or macrostates) 23

CRN CONDENSATION Step 5: Insert slow reactions & derive condensed reactions 24

DSD CONDENSATION fast (1,1) reaction b a fast (1,2) reaction x x t t b a x t t x t* x* t* t* x* t* slow (2,1) reaction i3 i4 resting macrostate {(B+F1)} {(A+F2)} transient macrostate {} set of fates detailed reactions: F1 F2 A B x x x a x A + F1 -> i1 t b t t b a t i1 -> i2 t* x* t* t* x* t* i2 -> B + F2 B + F2 -> i2 {(A)} {(F1)} {(B)} {(F2)} i2 -> i1 i1 -> A + F1 A + F2 -> i4 i4 -> A + F2 x B + F1 -> i3 x a x a x i3 -> B + F1 t t b t t b condensed reactions: t* x* t* t* x* t* i1 i2 A + F1 -> B + F2 B + F2 -> A + F1 {(A+F1), (B+F2)} 25