DNA STRAND DISPLACEMENT DNA STRAND DISPLACEMENT = Adenine = long - PowerPoint PPT Presentation

16 th 1 ENUMERATION, CONDENSATION AND SIMULATION ENUMERATION, CONDENSATION AND SIMULATION OF PSEUDOKNOT-FREE OF PSEUDOKNOT-FREE DOMAIN-LEVEL DNA STRAND DISPLACEMENT SYSTEMS DOMAIN-LEVEL DNA STRAND DISPLACEMENT SYSTEMS Stefan Badelt , Casey Grun, Karthik V. Sarma, Seung Woo Shin, Brian Wolfe, and Erik Winfree DNA and Natural Algorithms (DNA) Group, Caltech FNANO-19 Snowbird, April , 2019 http://www.github.com/DNA-and-Natural-Algorithms-Group/peppercornenumerator

2 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*

3 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 x a x a t b t t t b t* x* t* t* x* t* a t x x t b i1 i3 t* x* t* i2

4 DOMAIN-LEVEL STRAND DISPLACEMENT DOMAIN-LEVEL STRAND DISPLACEMENT detailed network long (branch-migration) domain: binds irreversibly condensed network 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 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 i1 i2 t* x* t*

5 DOMAIN-LEVEL STRAND DISPLACEMENT DOMAIN-LEVEL STRAND DISPLACEMENT detailed network long (branch-migration) domain: binds irreversibly condensed network 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 x a x a t b t t t b t* x* t* t* x* t* a t x x t b i1 i2 t* x* t*

6 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)

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

8 DSD IS A KINETIC TOOLBOX DSD IS A KINETIC TOOLBOX ... but how do you model your DSD system? per hand VisualDSD Phillips & Carelli (2009), ..., Sparcassi et al. (2018) other models Kawamata et al. (2012), Mokhtar et al. (2017), ... ? You specify the reaction types. You specify the reaction rates. You may include all(?) types of pseudoknotted conformations, and even non-DSD reactions (e.g. enzyme cleavage reactions). ... so you better know what you are doing.

9 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

10 DSD IS A KINETIC TOOLBOX ... DSD IS A KINETIC TOOLBOX ... ... that can be rigorously analyzed within the domain of the thermodynamic energy model. The Peppercorn so�ware package: reaction enumeration reaction condensation approximate DNA reaction rate model

11 bind21 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

12 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

13 WHAT ARE THE CHALLENGES? WHAT ARE THE CHALLENGES? polymerization => timescale separation size of the enumerated network => condensation

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

16 MODEL PARAMETERS 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

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

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

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

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

21 ENUMERATION / CONDENSATION ENUMERATION / CONDENSATION A B B A B m m B {(P)} {(K)} m* B* C* B m A B B* m* {(K + L), (P+Q)} C* m* B* C* {(Q)} {(L)} A B m B k A B m B m* B* B* m* C* C*

22 CASE STUDIES: CONDENSED REACTION RATES CASE STUDIES: CONDENSED REACTION RATES a) b) c) x* m* m x A A B m B m B n B k k k m* x* x A n* A B m n B B m B m x x* n* m* B* m* B* m* n* B* m* n* B* x n C* n x* C* C* C*

23 CASE STUDIES: AUTOCATALYTIC SYSTEM CASE STUDIES: AUTOCATALYTIC SYSTEM Kotani & Hughes (2017)

24 CASE STUDIES: AUTOCATALYTIC SYSTEM CASE STUDIES: AUTOCATALYTIC SYSTEM Kotani & Hughes (2017)

25 CASE STUDIES: AUTOCATALYTIC SYSTEM CASE STUDIES: AUTOCATALYTIC SYSTEM # parameters MCS RC + TC DR RM CR 1 release-cutof = 8 10 16 + 159 556 14 15 −3 2 k slow = k fast = 10 16 13 + 82 265 10 11 −4 3 k slow = k fast = 10 10 16 + 164 599 14 15 −4 , k fast = 10 −3 4 k slow = 10 16 20 + 164 488 17 22 −4 , k fast = 10 −2 5 k slow = 10 24 55 + 1426 6628 28 62 −5 , k fast = 10 −2 6 k slow = 10 24 55 + 1426 6652 28 75 INF

26 CASE STUDIES: SEESAW SYSTEMS CASE STUDIES: SEESAW SYSTEMS Qian & Winfree (2011)

27 CASE STUDIES: SEESAW SYSTEMS CASE STUDIES: SEESAW SYSTEMS (a) (b) (c) (d)

28 CASE STUDIES: MANY SYSTEMS CASE STUDIES: MANY SYSTEMS

29 THANKS TO THANKS TO Erik Winfree Casey Grun Karthik Sarma Seung Woo Shin you Brian Wolfe http://www.github.com/DNA-and-Natural-Algorithms-Group/peppercornenumerator ... don't forget to ask me about kernel notation. 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).

30 CASE STUDIES: REACTION COMPLETION CASE STUDIES: REACTION COMPLETION d) b b b m a m b a b b m a n b* a* b* n a* b* n a*

31 t* T* Th 2,5:5 T* S5* T* c* c* c* c* t* S5 Th 2,5:5 c c S5* s2* T* c* c* c* t* shorthand notation explicit notation s2* S5 S5* G 5:5,6 S5 c c c c t T S6 = G 5:5,6 = S5 S6 S5* T* T* T CASE STUDIES: SEESAW SYSTEMS CASE STUDIES: SEESAW SYSTEMS ACTTCAAACCACCACTCTAC ACTTCAAACCACCACTCTAC TGAGATGAAGTTTGGTGGTGAGATG TGAGATGAAGTTTGGTGGTGAGATG ACTTCAAACCACCAC ACTTCAAACCACCAC TGTTTTGAGATGAAGTTTGGTGGTG TGTTTTGAGATGAAGTTTGGTGGTG Qian & Winfree (2011) - Supporting Online Material