REACTION ENUMERATION & CONDENSATION OF DOMAIN-LEVEL STRAND DISPLACEMENT SYSTEMS. Stefan Badelt DNA and Natural Algorithms (DNA) Group, Caltech

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1 REACTION ENUMERATION & CONDENSATION OF DOMAIN-LEVEL STRAND DISPLACEMENT SYSTEMS Sefn Bdel DNA nd Nurl Algorihms (DNA) Group, Clech Fe 14 h, rd TBI Winerseminr, Bled, Sloveni Grun, Bdel, Srm, Shin, Wolfe, nd Winfree (mnuscrip in preprion) hp:// 1

2 MOLECULAR PROGRAMMING (in erms of he nuskell compiler projec) nucleic cids re rchiecure o implemen lgorihms chemicl recion neworks re progrmming lnguge forml/eperimenl verificion of correc implemenion miniml/opiml componens for iologicl sysems verifyly correc rificil sysems Ani- Lignd Terminor promoer region rioswich - Lignd + Lignd ON proein coding region rirry lgorihm sclle, correc componens Terminor promoer region rioswich OFF proein coding region condiionl swich iologicl relevnce is primry if eperimens fil, refine he mehod informion processing nework forml descripion is primry, iologicl relevnce secondry 2

3 DNA STRAND DISPLACEMENT = Adenine = Thymine = long domin = shor domin = Cyosine = Gunine = 5' end = Phosphe ckone = 3' end DNA DNA * * * * 3

4 DOMAIN-LEVEL STRAND DISPLACEMENT long (rnch-migrion) domin: inds irreversily shor (oehold) domin: inds reversily A F1 F2 + + * * * * * * B unind 3-wy rnch migrion ind * i1 * * * * * i2 * * i3 * 4

5 DOMAIN-LEVEL STRAND DISPLACEMENT long (rnch-migrion) domin: inds irreversily shor (oehold) domin: inds reversily deiled nework condensed nework A F1 F2 + + * * * * * * B ind 3-wy rnch migrion unind * i1 * * * * * * * i2 * 5

6 DOMAIN-LEVEL STRAND DISPLACEMENT long (rnch-migrion) domin: inds irreversily shor (oehold) domin: inds reversily deiled nework condensed nework A F1 F2 + + * * * * * * B unind 3-wy rnch migrion ind * i1 * * * * * * * i2 * 6

7 DOMAIN-LEVEL STRAND DISPLACEMENT long (rnch-migrion) domin: inds irreversily shor (oehold) domin: inds reversily A F1 F2 + + * * * * * * B unind forml CRN forml species: {A, B} * * * i1 3-wy rnch migrion ind DSD syem specificion signl species (low concenion): {A, B} * * * fuel species (high concenrion): {F1, F2} * * * i2 i3 7

8 FROM CRN TO DSD SYSTEMS Soloveichik e l. (2010) Lkin e l. (2012) Crdelli (2011) Qin e l. (2011) Chen e l. (2012), Crdelli (2013), Srinivs (2015), Lkin e l. (2016),... Imges drwn using VisulDSD, Lkin e l. (2012) 8

9 FROM A DIGITAL CIRCUIT TO DSD Qin e l. (2011) Inpu for he nuskell compiler: 32 forml recions. soloveichik2010.s: 52 signl species, 92 fuel species, 172 inermedie species, 180 recions. verifies s correc ccording o he phwy decomposiion nd CRN isimulion equivlence Bdel, Johnson, Dong, Shin, Thchuk nd Winfree: A generl-purpose CRN-o-DSD compiler wih forml verificion, opimizion, nd simulion cpiliies. LNCS (2017) 9

10 REACTION TYPES ind / open * * * * 3-wy rnch migrion * * c c c c* * * * c* * c* c c c c* 4-wy rnch migrion c c* * * d* d * * c c* * * * * d* d 10

11 REACTION TYPES ind / open * * * * llows ll secondry srucures (pseudoknos ecluded) open recions of domins wih lengh > L re foridden open & rnch migrion recions re lwys unimoleculr, u my led o dissociion. ind recions re he only vlid imoleculr recions 3-wy rnch migrion * * c c c c* * * * c* * c* c c c c* 4-wy rnch migrion c c* * * d* d * * c c* * * * * d* d 11

12 A B * * 12

13 A B * * * * 13

14 A B * * * * 14

15 * A B * * * * * 15

16 * A B * *? * * * 16

17 * A B * *? * * * + * * + + * *.. ( + (.. + ). ( + ). ) 17

18 * mulisrnded pseudokno A B * *? * * * + * * + + * *.. ( + (.. + ). ( + ). ) 18

19 SEPARATION OF TIMESCALES unimoleculr recions re fs imoleculr recions re slow A B + * * k α k β * * X resing complees rnsien comple k α k β {X A + B; A + B X} low concenrions: k β [A][B] << k α [X] 19

20 MODEL PARAMETERS re-independen model open recions where domin-lengh > L re negligile unimoleculr recions re fs imoleculr recions re slow re-dependen model ssume ypicl re consn for every recion: k = re(rype, dlengh) unimoleculr recions wih k < k slow re negligile unimoleculr recions wih k < k fs re slow unimoleculr recions wih k k fs re fs imoleculr recions re slow 20

21 REACTION ENUMERATION every comple hs ll vlid fs recions enumered rnsien complees hve no slow recions enumered resing complees hve ll vlid slow recions enumered ll iniil complees re included vlid ccording o enumerion semnics: ll vlid, ecep open > L m-heli semnics: recion ypes re greedy proiliy hreshold for recns of imoleculr recions. proiliy hreshold for producs of unimoleculr recions. 21

22 CRN CONDENSATION Gol: represen CRN in erms of overll slow recions properies / requiremens: ll fs recions re unimoleculr recions hve riy (n,m) wih n > 0 nd m > 0 recns of slow recions mus e resing ses recns nd producs of fs (1-2) recions re in differen SCCs (mss conservion) 22

23 CRN CONDENSATION Sep 1: Mke grph h conins only fs (1,1) recions 23

24 CRN CONDENSATION Sep 2: Idenify srongly conneced componens (SCCs) 24

25 CRN CONDENSATION Sep 3: Define rnsien nd resing mcroses A B C D E F 25

26 CRN CONDENSATION Sep 4: Assign fes o complees (or mcroses) 26

27 CRN CONDENSATION Sep 5: Inser slow recions & derive condensed recions 27

28 DSD CONDENSATION fs (1,1) recion fs (1,2) recion * {(B+F1)} i3 * * * * i4 * {(A+F2)} slow (2,1) recion resing mcrose rnsien mcrose {} se of fes F1 A * * * {(A)} {(F1)} {(B)} {(F2)} * i1 * * {(A+F1), (B+F2)} B * * i2 * F2 * * * deiled recions: A + F1 -> i1 i1 -> i2 i2 -> B + F2 B + F2 -> i2 i2 -> i1 i1 -> A + F1 A + F2 -> i4 i4 -> A + F2 B + F1 -> i3 i3 -> B + F1 condensed recions: A + F1 -> B + F2 B + F2 -> A + F1 28

29 REACTION RATE CONDENSATION Consider condensed recion: P + Q K + L + M I is composed of ll deiled slow recions: p + q I weighed y he decy proiliy over ll phwys: I k + l + m where p P, q Q, k K, l L, m M nd I is mulise of inermedie species 29

30 REACTION RATE CONDENSATION Noion: deiled recion: condensed recion: given: define: hen he condensed re is: microse (comple) fs (1,1) recion slow (1,1) recion fs (1,2) recion slow (2,1) recion resing mcrose rnsien mcrose {} se of fes 30

31 REACTION RATE CONDENSATION generl form: k r = P[ ] P[ : ] r=(a,b) R A k r T B B i A i i A i T B B P[ : ] = A i P[ ] = where sionry disriuion recion decy proiliy 31

32 A DNA OSCIALLATOR Srinivs, Prkin, Seelig, Winfree, Soloveichik: Enzyme-free nucleic cid dynmicl sysems. Science (2017) 32

33 A DNA OSCIALLATOR Srinivs, Prkin, Seelig, Winfree, Soloveichik: Enzyme-free nucleic cid dynmicl sysems. Science (2017) 33

34 DETAILED VS. CONDENSED SIMULATION rnslion scheme: srinivs2017.s 34

35 REACTION ENUMERATOR model limiions no mulisrnded pseudoknos ssumpion of low concenrions ssumpion of "ypicl" recion re consns model prmeers muliple lyers of recion-semnics recion ypes m-heli noion (represenion-independen) recion re dependen enumerion 35

36 Wh he domin level cn do: enumere inended recion phwys deec uninended recion phwys very fs ssessmen of overll dynmics define CRN for sequence-level simulions Wh he domin level cnno do: include sequence-level vriions wihin he domins Wh he domin level could do: deec nd qunify priculr lek recions provide corse-grining for sochsic simulions 36

37 THANKS TO Erik Winfree Csey Grun Krhik Srm Seung Woo Shin you Brin Wolfe hp:// This reserch ws funded in prs y: The Clech Biology nd Biologicl Engineering Division Fellowship. The U.S. Nionl Science Foundion NSF Grn CCF nd NSF Grn CCF The Gordon nd Bey Moore Foundion's Progrmmle Moleculr Technology Iniiive (PMTI). 37