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