anne condon u. british columbia 100 nm · anne condon u. british columbia programming molecules...

Anne CondonU. British Columbia

Programming Molecules

Paul Rothemund, 2006

100 nm

Programming MoleculesAnne Condon, U. British Columbia

Programming Molecules | outline

motivationprinciplesexperimental successestheoryopen questionsclosing thoughts

A TCG

Programming Molecules | principles

sequencesecondary structurefolding pathway

A TCG

Programming Molecules | principles

C G

T

CCC

GGG

AA

AA

TTG

T

C

GT

C

CC

GGGA AAA

T TG T

secondary structure: set of A-T or C-G pairs of a sequence (or sequences)roughly speaking, the more base pairs, the more stable (low energy) the structure

Programming Molecules | principles

secondary structure: set of A-T or C-G pairs of a sequence (or sequences)roughly speaking, the more base pairs, the more stable (low energy) the structure

BA

C D

A

C

B

D

Programming Molecules | principles

Kinefold Web Server

folding pathway: a sequence of secondary structures that strands assume as they change from one structure to another

folding is a stochastic process; at each step one base pair forms or breaks

folding process is biased to favour low energy barrier pathways

Programming Molecules | principles

Kinefold Web Server

folding pathway: a sequence of secondary structures that strands assume as they change from one structure to another

folding is a stochastic process; at each step one base pair forms or breaks

folding process is biased to favour low energy barrier pathways

Soloveichik, Seelig, Winfree PNAS 2010

toehold-mediated DNA strand displacement (DSD)

Programming Molecules | principles

Soloveichik, Seelig, Winfree PNAS 2010

toehold-mediated DNA strand displacement (DSD)

Programming Molecules | principles

Soloveichik, Seelig, Winfree PNAS 2010

Programming Molecules | principlestoehold-mediated DNA strand displacement (DSD)

Soloveichik, Seelig, Winfree PNAS 2010

Programming Molecules | principlestoehold-mediated DNA strand displacement (DSD)

Soloveichik, Seelig, Winfree PNAS 2010

Programming Molecules | principlestoehold-mediated DNA strand displacement (DSD)

Soloveichik, Seelig, Winfree PNAS 2010

Programming Molecules | principlestoehold-mediated DNA strand displacement (DSD)

Soloveichik, Seelig, Winfree PNAS 2010

Programming Molecules | principles

A B⇌

waste byproduct( )( )auxiliary reactant

from chemical reactions to DSDs

transformer molecules

Programming Molecules | principles

Soloveichik, Seelig, Winfree PNAS 2010

A + B C + D⇌

this is a little tricky: C and D should be produced only if both A and B are present

transformer molecules are needed

from chemical reactions to DSDs

Programming Molecules | principles

Soloveichik, Seelig, Winfree PNAS 2010

A + B C + D⇌

this is a little tricky: C and D should be produced only if both A and B are present

transformer molecules are needed

from chemical reactions to DSDs

Programming Molecules | principles

Soloveichik, Seelig, Winfree PNAS 2010

A + B C + D⇌

this is a little tricky: C and D should be produced only if both A and B are present

transformer molecules are needed

from chemical reactions to DSDs

Programming Molecules | principles

Soloveichik, Seelig, Winfree PNAS 2010

A + B C + D⇌

this is a little tricky: C and D should be produced only if both A and B are present

transformer molecules are needed

from chemical reactions to DSDs

Programming Molecules | principles

Soloveichik, Seelig, Winfree PNAS 2010

from chemical reactions to DSDs

⇋

01 ⇋ 11

also doable if long domains (rather than toeholds) represent species

Programming Molecules | principles

Soloveichik, Seelig, Winfree PNAS 2010

from chemical reactions to DSDs

⇋

Programming Molecules | principles

Soloveichik, Seelig, Winfree PNAS 2010

from chemical reactions to DSDs

⇋

from chemical reactions to DSDs

Programming Molecules | principles

sequencesecondary structuresfolding pathways

A TCGDSD’s are an energy-efficient (low-

barrier) way to convert one DNA species (type of molecule) to anotherfrom a programming perspective, this is a way to change the value of a variable

BAC D

Programming Molecules | experimental successes

tiles (double-crossover molecules) adhere to a growing assembly if glue strengths (sticky end lengths) are sufficiently strong

Fu and Seeman, Biochemistry, 1993

BAC D

Programming Molecules | experimental successes

tiles (double-crossover molecules) adhere to a growing assembly if glue strengths (sticky end lengths) are sufficiently strong

Fu and Seeman, Biochemistry, 1993

Programming Molecules | experimental successes

Winfree et al., Nature, 1998; Rothemund et al., Nature, 2004

DNA self assembly

Programming Molecules | experimental successes

3D structures

Dietz, Douglas & Shih, Science, 2009

Programming Molecules | experimental successes

DNA origami

Dietz, Douglas & Shih, Science, 2009

• Short “staple” strands bring pieces of a long strand together, folding the long strand into a desired shape

100 nm

Programming Molecules | experimental successes

DNA walkers

Rothemund, Science 2004

fuel

walker has two “feet”

Programming Molecules | experimental successes

DNA walkers

Rothemund, Science 2004

fuel

walker has two “feet”

fuel

Programming Molecules | experimental successes

DNA walkers

Rothemund, Science 2004

fuel

Programming Molecules | experimental successes

DNA walkers

Rothemund, Science 2004

fuel

Programming Molecules | experimental successes

DNA walkers

Rothemund, Science 2004

fuel

Programming Molecules | experimental successes

circuit simulation

AB

CD

EF

Seelig et al., Science 2006

Programming Molecules | theory

motivationprinciplesexperimental successestheoryopen questionsclosing thoughts

A TCG

Programming Molecules | theory

principles for describing, programming and analyzing DNA at different levels of abstraction

new questions about the power and limits of (molecular) computing systems

Programming Molecules | theory

principles for describing, programming and analyzing DNA at different levels of abstraction

new questions about the power and limits of (molecular) computing systems

case study: circuit simulation

Programming Molecules | theorycase study: circuit simulation

A

BC A + B ⟶ C

D

EF

D ⟶ F

E ⟶ F

(1) express circuit as chemical reaction network (CRN)

Soloveichik, Seelig, Winfree PNAS 2010

Programming Molecules | theorycase study: circuit simulation

(2) compile CRN into DSDs

Soloveichik, Seelig, Winfree PNAS 2010

toehold-mediated

(3) design DSD domain sequences

Programming Molecules | theorycase study: circuit simulation

(1) express circuit as CRN (2) compile CRN into DSD(3) design DSD domain sequences

(4) plus more... debug, identify systematic errors, develop error-correcting techniques ...

(1)

(2,3)

Programming Molecules | theory

principles for describing, programming and analyzing DNA at different levels of abstraction

new questions about the power and limits of (molecular) computing systems

Programming Molecules | theory

can we write “volume-efficient” DNA programs?

analogous to memory/space-efficient algorithms

for example ... can we design a DSD that counts for 2^n steps using poly(n) strands/bases?

(all of the previous examples use a number of strands that grows polynomially with the number of steps)

Programming Molecules | theory

CRN and DSD programs can in principle do universal computations in an energy-efficient manner

but CRN’s and DSD’s typically use a number of molecules that is proportional to the number of reactions.

can DSD’s recycle strands to minimize volume?

put another way...

0 0 0 0 0 10 1 10 1 01 1 01 1 11 0 11 0 0

Strand Recycling Example

3-bit Gray counter

Condon et al., DNA 2011

0 0 0 0 0 10 1 10 1 01 1 01 1 11 0 11 0 0

Strand Recycling Example

– The counter state is represented by three of six signal molecules:

b3 b2 b1 (b=0,1)

– Initially the state is 03 02 01

3-bit Gray counter deterministic CRN

Condon et al., DNA 2011

0 0 0 0 0 10 1 10 1 01 1 01 1 11 0 11 0 0

Strand Recycling Example

deterministic CRN3-bit Gray counter

Condon et al., DNA 2011

0 0 0 0 0 10 1 10 1 01 1 01 1 11 0 11 0 0

Strand Recycling Example

(1) 01 ⇋ 11(2) 02 + 11 ⇋ 12 + 11(3) 03 + 12 + 01 ⇋ 13 + 12 + 01

– The counter proceeds as a random walk through the states in Gray code order

3-bit Gray counter deterministic CRN

Condon et al., DNA 2011

0 0 0 0 0 10 1 10 1 01 1 01 1 11 0 11 0 0

Strand Recycling Example

(1) 01 ⇋ 11(2) 02 + 11 ⇋ 12 + 11(3) 03 + 12 + 01 ⇋ 13 + 12 + 01

– The (atomic) reactions ensure that exactly one of 0i and 1i are present at any given time

3-bit Gray counter deterministic CRN

(1-for) (2-for)(1-rev)(3-for)(1-for)(2-rev)(1-rev)

Condon et al., DNA 2011

0 0 0 0 0 10 1 10 1 01 1 01 1 11 0 11 0 0

Strand Recycling Example

(1) 01 ⇋ 11(2) 02 + 11 ⇋ 12 + 11(3) 03 + 12 + 01 ⇋ 13 + 12 + 01

– To progress, each reaction is used alternately in forward and reverse directions: this is key to recycling

3-bit Gray counter deterministic CRN

(1-for) (2-for)(1-rev)(3-for)(1-for)(2-rev)(1-rev)

Condon et al., DNA 2011

0 0 0 0 0 10 1 10 1 01 1 01 1 11 0 11 0 0

Strand Recycling Example

3-bit Gray counter deterministic CRN

(1-for) (2-for)(1-rev)(3-for)(1-for)(2-rev)(1-rev)

Tf1 + 01 ⇋ 11 + Tr

1 Tf

2 + 02 + 11 ⇋ 12 + 11 + Tr2

Tf3 + 03 + 12 + 01 ⇋ 13 + 12 + 01 + Tr

3

– Because of the transformer molecules, direction of reactions must alternate in order to maximally recycle strands

Condon et al., DNA 2011

Strand Recycling Example

(1) 01 ⇋ 11 . . .

DSD implementation

⇋

3-bit Gray counter deterministic CRN

0 0 0 0 0 10 1 10 1 01 1 01 1 11 0 11 0 0

Condon et al., DNA 2011

0 0 0 0 0 10 1 00 1 11 0 01 0 11 1 01 1 1

Strand Recycling Example

traditional counter deterministic CRN

(1-for) (2-for)(1-for)(3-for)(1-for)(2-for)(1-for)

Tf1 + 01 ⇋ 11 + Tr

1 Tf

2 + 02 + 11 ⇋ 12 + 01 + Tr2

Tf3 + 03 + 12 + 11 ⇋ 13 + 02 + 01 + Tr

3

– In contrast, a traditional counter does not recycle molecules

Condon et al., DNA 2011

Strand Recycling: pros and cons

the n-bit Gray counter uses O(n3) volume (or equivalently, space, or total number of strand bases)

in fact, any problem in PSPACE can be solved using DSD’s using poly(n) volume

our volume-efficient DSD’s are examples of reversible computation; DSD’s are examples of physically realizable computations with arbitrarily low energetic cost, consistent with vision of Charles Bennett

Condon, Thachuk, DNA 2012

0 0 0 0 0 10 1 10 1 01 1 01 1 11 0 11 0 0

0 0 0 0 0 10 1 1

0 0 0 0 0 00 0 0

1 0 0

The two-copy system does not behave as two independent copies; thus the system is not valid.

3-bit Gray counter:single copy

3-bit Gray counter:two copies

Condon et al., DNA 2011

Strand Recycling: pros and cons

Strand Recycling: pros and cons

validity relies on single copies of counter signalswe have some results that show limits on the possibility of zero-error, volume-efficient computation with CRN’s and DSD’s when multiple copies of species are initially present

Condon et al., DNA 2011, 2012

Programming Molecules

motivationprinciplesexperimental successestheoryopen questionsclosing thoughts

A TCG

Programming Molecules | open questions

our n-bit counter is a low-barrier folding pathway of poly(n) strands that takes 2n “steps”; can a single strand of length poly(n) be designed that takes 2n “steps” on its low-barrier folding pathway?

are there ways to translate CRN's to DSD's without tags (unique transformers per reaction)?

how best to handle errors that arise experimentally such as leak (“disappearence”) of molecules, and blunt-end (rather than toehold-mediated) displacement?

Programming Molecules | closing thoughts

creative ways to program molecules are still largely unexplored:- none of the DNA-based approaches strongly leverage

3D shape, yet function follows form in nature- perhaps there’s currently an overly strong focus on

digital rather than analog approaches to programming - approaches that are stochastic, robust to noise

(varying concentrations, unintended interactions) will be important

- perhaps approaches that induce emergent behaviour could complement rational design

Programming Molecules | closing thoughts

Programming Molecules | closing thoughts

“Energy permits things to exist and to act, but programming permits things to be purposeful”- (adapted from Ware)