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

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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 , Casey Grun, Karthik V. Sarma, Seung Woo Shin, Brian Wolfe, and Erik Winfree Stefan Badelt DNA and Natural Algorithms (DNA) Group, Caltech FNANO-19 Snowbird, April , 2019

16th

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

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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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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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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)

• ther 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.

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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 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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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 soware package: reaction enumeration reaction condensation approximate DNA reaction rate model

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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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WHAT ARE THE CHALLENGES? WHAT ARE THE CHALLENGES?

polymerization => timescale separation size of the enumerated network => condensation

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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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MODEL PARAMETERS MODEL PARAMETERS

negligible reactions slow reactions fast reactions bimolecular [/M/s] unimolecular [/s] bind21

• pen (len > L)
• pen (len < L)

bind11 branch migration rate-independent model: simple, one parameter: L

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MODEL PARAMETERS MODEL PARAMETERS

negligible reactions slow reactions fast reactions bimolecular [/M/s] unimolecular [/s] bind21

• pen (len > L)
• pen (len < L)

bind11 branch migration unimolecular [/s] rate-independent model: simple, one parameter: L rate-dependent model: flexible, two parameters: k-slow, k-fast

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

{(K + L), (P+Q)} {(L)} {(Q)} {(P)} {(K)}

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CASE STUDIES: CONDENSED REACTION RATES CASE STUDIES: 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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CASE STUDIES: AUTOCATALYTIC SYSTEM CASE STUDIES: AUTOCATALYTIC SYSTEM

Kotani & Hughes (2017)

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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 = kfast = 10

−3

16 13 + 82 265 10 11 3 kslow = kfast = 10

−4

10 16 + 164 599 14 15 4 kslow = 10

−4, kfast = 10 −3

16 20 + 164 488 17 22 5 kslow = 10

−4, kfast = 10 −2

24 55 + 1426 6628 28 62 6 kslow = 10

−5, kfast = 10 −2

24 55 + 1426 6652 28 75

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CASE STUDIES: SEESAW SYSTEMS CASE STUDIES: SEESAW SYSTEMS

Qian & Winfree (2011)

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CASE STUDIES: SEESAW SYSTEMS CASE STUDIES: SEESAW SYSTEMS

(c) (d) (a) (b)

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CASE STUDIES: MANY SYSTEMS CASE STUDIES: MANY SYSTEMS

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THANKS TO THANKS TO

Erik Winfree Casey Grun Karthik Sarma Seung Woo Shin you Brian Wolfe

... don't forget to ask me about kernel notation. http://www.github.com/DNA-and-Natural-Algorithms-Group/peppercornenumerator 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: REACTION COMPLETION CASE STUDIES: REACTION COMPLETION

d) a*

a

b m n b* b a*

a

b m n b* b a*

a

b m n b* b

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CASE STUDIES: SEESAW SYSTEMS CASE STUDIES: SEESAW SYSTEMS

S5 c c c c t T S6

=

G5:5,6

ACTTCAAACCACCACTCTAC TGAGATGAAGTTTGGTGGTGAGATG

=

G5:5,6

S5 T* S5* T*

ACTTCAAACCACCACTCTAC TGAGATGAAGTTTGGTGGTGAGATG

T S6

ACTTCAAACCACCAC TGTTTTGAGATGAAGTTTGGTGGTG

S5* S5

Th2,5:5

s2* T*

ACTTCAAACCACCAC TGTTTTGAGATGAAGTTTGGTGGTG

Th2,5:5

T* S5* T* c* c* c* c* t* t* S5 c c S5* s2* T* c* c* c* t*

shorthand notation explicit notation Qian & Winfree (2011) - Supporting Online Material

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Designed reactions Seesawing reactions Thresholding reactions Reporting reactions Side reactions Universal toehold binding reactions Leak reactions

Sy T Sx

wx,y

T* Si* T* Si T Sk

Gi:i,k

Si T Sj

wj,i

T* Si* T* Si T Sj

Gj,i:i wi,k

Si T Sk + +

ks ks

Si* T* sj* Si

Thj,i:i waste

Si* T* sj* T Sj Si Si

waste

Si T Sj

wj,i

+ +

kf

T* Si* T* Si T Sk

Gi:i,k

Sy T Sx

wx,y

+

kf krf

Gx,y:i:i,k

T* Si* T* Si T Sk Sy T Sx

Repi

Q F Si T* Si* + + Q Si

waste

F T* Si* Si T Sj

Fluori

ks

Si T Sj

wj,i

Sy T Sx

wx,y

+

kf krf

Gj,i:i:x,y

T* Si* T* Si T Sj

Gj,i:i

Sy T Sx T* Si* T* Si T Sj Sy T Sx

wx,y

+

kf krs

Thx,y:j,i:i

Si* T* sj* Si

Thj,i:i

Si* T* sj* Si Sy T Sx

kl kl

Si T Sx

wx,i

+ T* Si* T* Si T Sj

Gj,i:i

Si T Sj

wj,i

+ T* Si* T* Si T Sx

Gx,i:i

kl kl

+ T* Si* T* Si T Sk

Gi:i,k wi,x

Si T Sx + T* Si* T* Si T Sx

Gi:i,x wi,k

Si T Sk

Repi

Q F Si T* Si* +

Repx,y:i

Q F Si T* Si* Sy T Sx

kf krf

Qian & Winfree (2011) - Supporting Online Material

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Temperature: 25 ◦C ks = 5 × 104 M−1s−1 kf = 2 × 106 M−1s−1 krs = 1. 3 s−1 krf = 26 s−1 kl = 10 M−1s−1

x1 x2 x3 x4 y1 y2

2 1 4 3 2 1

« » ¬ ¼ y y x x x x

Simulations Experiments

Qian & Winfree (2011) - Supporting Online Material

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REACTION RULES REACTION RULES

r r* r r* ? ? bind11: r ? r* r( ? ) r r* r r* ? ?

• pen: r( ? ) r ? r*

bind21: [? r ?] + [? r* ?] [? r( ? + ? ) ?] ? ? r r r* ? ? r r r* ? ? r r ? ? r r r* r* 3-way-fw: r*( ? r ? ) r*( ? ) ? r 3-way-bw: r( ? r ? ) r ? r( ? ) r r* r r* r r r* r* ? ? ? ? ? ? 4-way: r( ? r*( ? ) ? ) r( ? ) ? r( ? ) r r r* r* ? ? ? r r r* r* ? ? ? 4-way: r*( ? r( ? ) ? ) r*( ? ) ? r*( ? ) r r* ? ? ? ? + r r* ? ? ? ? + a) b) c) d) e)

x( u( y ) ) t* = <x!j u!k y u!k x!j t*\>

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CRN CONDENSATION CRN CONDENSATION

{(RM1 + R0), (R11 + R12), (R31 + R32)} fast (1,1) reaction fast (1,2) reaction slow (2,1) reaction resting macrostate transient macrostate

{}

set of fates

TC1

a b c c b d d e d* e* c* a* b*

TC2

a b c c b d d e d* e* c* a* b*

TC3

a b c c b d d e d* e* c* a* b*

R31

a c b d d e d* e* c* a* b* b c

R32

a b c d e d* e* a* b*

R11

c b d c*

R12 R0

a b c

RC2

c b d d e d* e* c* a* b* c b d d e d* e* c* a* b*

RC1 condensed reactions:

R0 + RM1 -> R11 + R12 R0 + RM1 -> R31 + R32

detailed reactions:

R0 + RC1 -> TC1 TC1 -> R0 + RC1 TC1 -> TC2 TC2 -> TC1 TC2 -> TC3 TC3 -> TC2 TC1 -> R11 + R12 TC3 -> R31 + R32

RM1 TM

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REACTION ENUMERATION 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

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SEPARATION OF TIMESCALES SEPARATION OF TIMESCALES

unimolecular reactions are fast bimolecular reactions are slow

a t t t* t* b A B a t t t* t* b kα kβ + transient complex resting complexes X

{X A + B; A + B X} − →

kα

− →

kβ

at low concentrations:

[A][B] << [X] kβ kα