A Clocked DNA-Based Replicator
Bernard Yurke1,2 and David Zhang2
1
2
Bell Laboratories, 600 Mountain Ave., Murray Hill NJ 07974
California Institute of Technology, Pasadena, California 91125
{yurke, dzhang}@dna.caltech.edu
Abstract. A stepped replicator is described that uses the energy of hybridization to pry the product from the template in order to prevent
product inhibition of replication. Toehold-mediated strand displacement
is used to reset the system to its initial state after a round of replication. It is argued that the formation of dimers between structures in the
process of replicating should not be able to form and, consequently, the
system should exhibit exponential growth.
1
Introduction
The ability to reproduce is one of the defining characteristics of life. This ability
arises from a process by which DNA serves as its own template to make copies
of itself [1]. There is considerable interest in the construction of synthetic systems that are also capable of template-directed replication [2]. For our purposes
synthetic systems will mean systems that do not take advantage of biologically
derived polymerases to achieve replication of nucleic acids. Much of the interest
in synthetic replication systems comes from the insights they might provide on
how life originated or functions [3, 4]. There is interest also from the point of
view of what template replication may have to offer for manufacturing. Replication by living organisms is an exponential growth process. In a manufacturing
setting this kind of replication would alow for easy scale-up of the volume of
units produced. Another feature exhibited by living organisms is that the replication process is not perfect. This allows for Darwinian evolution. The power
of directed evolution has been exploited in research and manufacturing settings
[5]. Error-prone synthetic replicators may also allow for the directed evolution
of useful products.
A number of synthetic chemical systems have been constructed which exhibit template-directed replication [6] or self-replication in oligonucleotide-based
systems [7]-[15], peptide-based systems [16]-[20], and other chemical systems [21][27]. A characteristic problem of these systems is that the product remains bound
to the template or competes with monomers for binding with the template. Such
systems exhibit parabolic rather than exponential growth. The replication process tends to stall as the concentration of product increases. Exponential growth
is a prerequisite for selection in the Darwinian sense [28, 29]. The sub-exponential
growth exhibited by these systems is thus nonconducive to Darwinian evolution.
C. Ferretti, G. Mauri and C. Zandron (Eds.): DNA10, LNCS 3384, pp. 445–457, 2005.
c Springer-Verlag Berlin Heidelberg 2005
446
B. Yurke and D. Zhang
Recently a self-replicating system based on a ligase ribozyme has been constructed [30] that, at least, at early times exhibits exponential growth.
Recently exponential growth has also been demonstrated for a system employing a stepwise ’feeding’ procedure and immobilization of the product on a
support [31]. In this system a template is immobilized on a solid support. Fragments of the product that bind to the template are introduced. The fragments are
then ligated together to produce the product. Next, a denaturing step releases
the product which is then immobilized on fresh solid support. The problem of
the binding of a template with its product is thus overcome by immobilization.
Various DNA-based nanostructures [32]-[38] and nanomachines [39]-[46] have
been constructed. For a recent review see [38]. This suggests that DNA may be
a suitable medium for the construction of synthetic replicators. Most of the
DNA-based nanomachines that have been constructed [40]-[46] to date use the
energy of hybridization to activate the machines. In addition, strand displacement through competitive binding mediated by toeholds is generally used to
return the machine to its initial state. The operation of these machines involves
stepwise feeding and, hence, are clocked in the sense that the operator controls
when the machine advances to its next state through the addition of the appropriate DNA strand to the solution containing the machines. Here we argue
that clocked replicators can be constructed in which the energy of hybridization
is used to pull the template-replicated product from the template to allow for
template replication. Toehold-mediated strand displacement is used to clear the
spent replication machinery from the template and product to prepare for the
next round of template replication. The replication process proceeds in a clocked
manner in which the replication process is sequenced through a series of steps
via the addition of DNA strands in an appropriate sequence. In the discussion
that follows it will be assumed that the DNA strands are added in stoichiometry
and that one waits for the reaction at each step to go to completion. Alternatively, strands or components could be added in excess, if a means is provided for
removing the unreacted excess before one proceeds to the next step. This could,
in principle, be achieved through the use of magnetic beads functionalized with
the appropriate base sequences to scavenge the unreacted strands. It is argued
that the replication scheme we propose is not stalled by product-template binding and exhibits exponential growth. If the template-directed replication process
is made a bit faulty this system could, in principle, be subjected to directed
evolution.
2
The Replicator
The components from which the replicating structures are constructed are shown
in Figure 1. Key components are a set of structures we will refer to as ”bases”
labeled Bi where i is an integer index distinguishing members of the set. These
structures will play a role very similar to individual bases on a DNA strand.
Each base Bi consists of two strands of DNA held together by complementary
regions labeled n and n̄. We will refer to this as the neck region of the base. For
A Clocked DNA-Based Replicator
E
Bi
L
g
h
e
ne
F
h
g
f
e
f
n
n
e
f
nf
be
bi
b'i
bf
be
bi
b'i
b'f
n'e
447
f'
e'
n'
n'
e'
f'
n'f
f'
e'
g'
h'
h'
g'
L
E
Bi
F
Fig. 1. The components from which the structures to be template-replicated are constructed. The Bi are referred to as bases and the B̄i as their complements. The linker
strands L and L̄ allow the bases or the complements, respectively, to polymerize into
linear chains. The DNA strands E, Ē, F , and F̄ serve as chain terminators. The recognition groups be , bf , and the bi and bi allow for binding with the complements via the
complementary sequences b̄e , b̄f , and the b̄i and b̄i . See the text for further details
each base Bi there is a corresponding structure labeled B̄i which we will refer to
as the complement of the base. This complement also consists of two strands of
DNA held together by complementary regions labeled n and n̄ . A base Bi and
its complement B̄i can bind through hybridization of the single-stranded regions
bi and bi of the base with the corresponding complementary regions b̄i and b̄i
of the complement of the base. In addition to the bases, we have two strands of
DNA labeled E and F which can be viewed as a half of a base. Associated with
E and F are Ē and F̄ that will be referred to as the complements of E and F ,
respectively. E can bind with Ē via complementary base paring of be with b̄e .
Similarly, F can bind with F̄ via complementary base paring of bf with b¯f .
The base sequences of the regions labeled e, f , g, and h are the same for all
the bases Bi . In addition, the sequences e and h also appear in E. Similarly, the
sequences f and g also appear in F . The sequences e , f , g , and h are likewise
shared among Ē, F̄ , and the B̄i . By using identical sequences in portions of
these structures one can reduce the size of the set of maximally noninteracting
base sequences that one needs to design. The sequences ne , ne , nf , and nf
are a set of maximally noninteracting base sequences which are also maximally
noninteracting with n, n and their complements. The base sequences g, g , h,
and h will provide regions for the attachment of the replication machinery, to
be discussed in Section 3.
The regions labeled e and f allow the bases Bi to be linked end to end in a
polymer chain. E and F provide chain terminations, since L can bind with these
strands only at one end. The linkage is performed by the strand labeled L in
448
B. Yurke and D. Zhang
Fig. 1 that consists of the concatenation of ē and f¯, the complements of e and
f . Similarly, the complements B̄i can be linked together via the strand labeled
L̄. For the complements, Ē and F̄ serve as chain terminators.
Figure 2 shows the simplest chain that can be constructed for the complements of the bases. It consists of the termination Ē, a single base complement
B̄i , and the termination F̄ . These units are held together by the linker strand
L̄. More generally, one could have an arbitrary sequence of the B̄i between the
two terminations. However, to keep the complexity of the figures and the discussion at a manageable level, we will consider this three-unit system with the
understanding that the discussion can be easily extended to the case of a general
sequence of B̄i .
The recognition groups b̄e , b̄f , b̄i , and b̄i allow template-guided ordering of
E, F , and the Bi when they are added to a solution containing the construct of
Fig. 2. This is shown in Fig. 3. Because E and F are not connected, the singlestranded pairs be with b̄e , bi with b̄i , bi with b̄i , and bf with b̄f are able to wrap
around each other to form a double helix.
b'i
bi
be
b'f
L
L
g'
h'
E
g'
h'
F
Bi
Fig. 2. A trimer consisting of the units Ē, B̄i , and F̄ linked together by the strand L̄.
The single-stranded regions b̄e , b̄i , b̄i , and b̄f sever as recognition sites for the templatedirected construction of the complementary trimer
E
Bi
h
be
f
e
be
F
g
h
bi
b'i
bi
b'i
E
e
f
Bbf
b'f
L
L
h'
g
g'
h'
Bi
g'
F
Fig. 3. The construct, consisting of Ē, B̄i , and F̄ linked together by L̄ strands, allows
the template-guided arrangement of E, Bi , and F through the pairing of complementary regions be with b̄e , bi with b̄i , bi with b̄i , and bf with b̄f
A Clocked DNA-Based Replicator
E
Bi
h
449
F
g
h
bi
b'i
bi
b'i
g
L
L
be
be
bf
b'f
L
L
g'
h'
E
g'
h'
F
Bi
Fig. 4. Addition of L strands to the solution forms the template-constructed polymer
consisting of the three units E, Bi , and F . This is the structure that is to be repeatedly
template-replicated
It should be noted that the base sequences n and n̄ are noncomplementary to
the base sequences n and n̄ , and the base sequences bi and b̄i are noncomplementary to the base sequences bi and b̄i . As a consequence, the Holiday junction
formed when Bi binds to B̄i , as depicted in Figs. 3 and 4, is stable.
s
s
r
r
h
h
g
g
m'
m'
m
m
h'
h'
g'
g'
s'
s'
r'
r'
Fig. 5. The DNA strands that constitute the replication machinery. See the text for
an explication of the function of these strands. The base sequences m, m , m̄, and m̄
involved in pulling apart the complementary polymers are indicated by thicker lines
for emphasis
450
B. Yurke and D. Zhang
As shown in Fig. 5, the strands L can now be added to the solution to link
the e and f sequences of neighboring units. Because there is a nick between
the e and f strands attached to a given L and because one has a pivot where
be is joined with e and where f is joined with bi , for example, there should be
sufficient freedom for L to form a double helix with the e and f strands. The
repeated template replication of this structure will now be discussed.
3
The Functioning of the Template-Replication
Machinery
Once the structure of Fig. 4 has been formed, in order to have further template
replication the two polymers EBi F and Ē B̄i F̄ must be pulled apart to expose
the sequences be , bi , bi , and bf and the complements b̄e , b̄i , b̄i , and b̄f . The
template-replication procedure described here uses the DNA strands shown in
Fig. 5. The strands consisting of the sequences r̄ḡ m̄ḡ r̄ and s̄h̄m̄ h̄ s̄ are able
to bind with the structure of Fig. 4 through the base sequences ḡ, g¯ , h̄, and
h̄ . The strand m and m can hybridize with r̄ḡ m̄ḡ r̄ and s̄h̄m̄ h̄ s̄ , respectively,
and will supply the energy to pry apart the two complementary polymers. The
strands rg, g r , sh, and h s will allow the removal of the replication machinery,
once a round of replication has taken place.
Figure 6. shows the r̄ḡ m̄ḡ r̄ and s̄h̄m̄ h̄ s̄ attached to the structure to be
replicated. Since the g, g , h, and h regions are attached to the structure at only
one end, it is clear that these are not inhibited from forming double-stranded
DNA with complementary regions of r̄ḡ m̄ḡ r̄ and s̄h̄m̄ h̄ s̄ . To insure that the
r̄ḡ m̄ḡ r̄ and s̄h̄m̄ h̄ s̄ strands only connect between complementary units rather
Bi
E
h
s
r
s
r
h
g
h
g
m'
h'
E
F
m
m'
g
m
be
bi
b'i
bf
be
bi
b'i
b'f
h'
g'
h'
g'
s'
r'
s'
r'
Bi
g'
F
Fig. 6. Upon addition to the solution, the r̄ḡ m̄ḡ r̄ and s̄h̄m̄ h̄ s̄ strands attach to the
construct of Fig. 4 as shown. For clarity, tick marks indicating the individual bases of
the sequences m̄ and m̄ have been suppressed
A Clocked DNA-Based Replicator
451
than across units, such as from Bi to F̄ , L and L̄ and the sequences e and f that
it hybridizes with should be sufficiently long to prevent the r̄ḡ m̄ḡ r̄ and s̄h̄m̄ h̄ s̄
strands from reaching between complementary regions on neighboring units. We
will assume that the structure is sufficiently linear so that folding will not be a
problem. How long a polymer is allowed is determined by the persistence length
of the polymer.
Upon the addition of m and m to solution they hybridize with the complementary regions in the strands r̄ḡ m̄ḡ r̄ and s̄h̄m̄ h̄ s̄ . As the double helix
is formed m̄ and m̄ begin to straighten and pull the structure into two complementary polymers. Since for each base torn apart between, for example, be
and b̄e , one is formed between, in this case, m and s̄h̄m̄ h̄ s̄ , one has a random
walk process that eventually breaks apart the complementary pairs of sequences
(be , b̄e ), (bi , b̄i ), (bi , b̄i ), and (bf , b̄f ). Since double helices are being unwound
during this process, the unit consisting of E and Ē must rotate relative to the
unit consisting of Bi and B̄i . That it can do so is evident from the fact that it is
connected to the Bi B̄i unit through the single duplex strand consisting of be and
b̄e In fact, the link between the E Ē unit and the Bi B̄i becomes a single duplex
strand at two places, the one already mentioned and the strand consisting of
bi and b̄i . The unit consisting of F and F̄ is similarly free to rotate relative to
the Bi B̄i unit. This argument is easily extended to polymers with multiple Bi B̄i
Bi
E
h
F
s
r
s
r
h
g
h
g
L
L
be
m'
b'i
bi
m
m'
bf
m
m'
bi
b'i
be
E
m'
m
m
b'f
L
L
h'
g
h'
g'
h'
g'
s'
r'
s'
r'
Bi
g'
F
Fig. 7. The construct of Fig. 6 after the motor strands m and m have been added and
the two complementary polymers have been pulled apart
452
B. Yurke and D. Zhang
Bi
E
H
F
S
R
S
R
H
G
H
G
L
L
Be
M'
B'i
Bi
M
M'
M
Be
Be
Bf
M'
Bi
B'i
Bi
B'i
E
M'
M
M
Bf
B'f
L
L
H'
G
H'
G'
H'
G'
S'
R'
S'
R'
Bi
G'
F
Fig. 8. The construct of Fig. 7 after the addition of the monomers E, Bi , and F . The
polymer unit Ē B̄i F̄ serves as a template to put the E, Bi , and F into the correct order.
The g and h regions of the monomers have been drawn folded back on themselves with
ticks representing individual bases suppressed. Thick lines have been used to represent
these regions. This representation will reduce the amount of clutter in Figs. 9 through 11
units. However, the number of turns the end units have to make relative to each
other grows linearly with the number of units.
Once the two complementary polymers have been pulled apart, the monomers
E, Bi , and F can be added to solution and allowed to hybridize with complementary base sequences on the Ē B̄i F̄ polymer, as shown in Fig. 8. This process
takes place in much the same way as discussed in connection with Fig. 3. Again,
because there is a free end, the double helices are not inhibited from forming.
It may be of concern that the complementary polymers, when pulled apart,
have a propensity to form dimers in which two neighboring constructs, like the
one depicted in Fig. 7, bind together, the exposed be , bi , bi bf sites of one
construct binding with the complements of another. It is noted that this process is geometrically hindered. In the case when the template and product are
pulled apart, each pair of units was free to rotate relative to neighboring pairs
by virtue of the fact that in the link between neighboring units are the single
duplex strands that need to be unwound. In the present situation this is not the
case, because each unit is linked to its neighbors to form a ladder-like structure.
The rungs of the ladder are the r̄ḡ m̄ḡ r̄ and s̄h̄m̄ h̄ s̄ strands hybridized, re-
A Clocked DNA-Based Replicator
Bi
E
h
F
s
r
s
r
h
g
h
g
L
L
bi
b'i
bf
be
bi
b'i
b'f
m
m'
m
m'
be
bi
b'i
m
m
bi
b'i
bf
b'f
L
L
E
m'
L
L
be
h'
g
be
m'
453
h'
g'
h'
g'
s'
r'
s'
r'
Bi
g'
F
Fig. 9. The construct of Fig. 8 after the addition of the L strands. Now the monomers
E, Bi , and F attached to Ē B̄i F̄ are assembled into the linear polymer EBi F
spectively, with the m and m strands. The rails of the ladder are the template
and its product. Also, apart from the single-stranded recognition regions, the
rungs and rails of the ladder are made of stiff double-stranded DNA. Two such
ladders forming a dimer do not provide the freedom for a monomer unit and
its complement to rotate relative to neighboring pairs of units in order to form
duplex DNA. Hence, the duplexes will be incompletely formed. Under such circumstances, monomers will be able to attach themselves to the portions of the
recognition regions that remain single-stranded. Then, by competitive binding
the monomers will be able to break the duplex bonds. Hence, this system should
not exhibit the product inhibition of replication that occurs in most synthetic
systems so far devised.
Next the monomers E, Bi , and F are linked together using the L strands.
This is shown in Fig. 9. The mechanics of this process is essentially the same as
that discussed in connection with figure 4.
Once the new EBi F polymer has been completed, one adds the monomers
Ē, B̄i and F̄ to the solution. The recognition sequences of these monomers
hybridize with complementary exposed sequences of the upper EBi F polymer
shown in Fig. 9. With the addition of L̄ strands a new Ē B̄i F̄ polymer is formed
as shown in Fig. 10. Now to produce two copies of the construct of Fig. 4 it is
only necessary to remove the hybridization machinery strands.
454
B. Yurke and D. Zhang
Bi
E
h
s
h
F
r
s
r
g
h
g
L
L
be
be
bi
b'i
bi
b'i
bf
b'f
L
L
m'
m
m'
m
m'
be
bi
b'i
m
m
bi
b'i
bf
b'f
L
L
E
m'
L
L
be
h'
g
h'
g'
h'
g'
s'
r'
s'
r'
Bi
g'
F
Fig. 10. The construct of Fig. 9 after the addition of monomers Ē, B̄i , and F̄ , followed
by the addition of L̄. Note that one now has two copies of the construct of Fig. 4, but
linked together with the replication machinery strands
The hybridization machinery strands are removed through the addition of the
sh, h s , rg, and g r strands of Fig. 5. These attach themselves to the r̄ḡ m̄ḡ r̄
and s̄h̄m̄ h̄ s̄ strands via the toeholds provided by the base sequences r̄, r̄ , s̄,
and s̄ . Then, by three-way branch migration, the r̄ḡ m̄ḡ r̄ and s̄h̄m̄ h̄ s̄ strands
along with the m and m strands are displaced. As depicted in Fig. 11 the result
is two released constructs of the type depicted in Fig. 4 for each initial construct.
In addition, the freed hybridization machinery strands are double-stranded over
their entire length and, hence, neutral to the addition of further DNA strands
to repeat the replication process.
4
Conclusions
We have described a clocked DNA-based template-replication system. It was
argued that product inhibition of template formation should not be a problem for
this system because geometrical constraints imposed by the attached replication
machinery prevent dimer formation between templates and products at the stage
when new monomers are added to the system. The system should, thus, exhibit
exponential amplification. The system could be made error-prone by choosing the
A Clocked DNA-Based Replicator
s
s
h
h
F
Bi
E
h
g
h
bi
b'i
be
bi
b'i
b'f
m
L
L
be
be
bi
b'i
bi
b'i
s'
h'
E
bf
b'f
L
L
s'
g
bf
m'
h'
g
L
L
h'
r
L
L
be
g
r
455
g'
h'
Bi
g'
F
g'
g'
r'
r'
Fig. 11. The addition of strands sh, h s , rg, and g r to the construct of Fig. 10
results in the displacement of the hybridization strands from the polymers through
competitive binding. The result is the release of two constructs of the same structure
as the starting construct, depicted in Fig. 4. Although the hybridization machinery
strands are drawn with short displaced segments, these should be viewed as nicks so
that, in fact, these strands are double-stranded over their entire length
recognition sequences bi and bi such that the bases Bi are capable of binding to
an inappropriate site. In principle, circumstances could be devised where strands
with different Bi sequences could compete with each other in a Darwinian fashion
where both mutation and selection take place. It is also worth noting that the
ladder-like structure formed by the replication machinery as the template and
its product are pulled apart can be viewed as a kind of compartmentalization
which prevents interference, in this case dimer formation and product inhibition,
by neighboring replicators. Also, note that as in biological systems where, during
replication, two duplex strands are made from one, here also duplex structures
are being duplicated.
References
1. B. Alberts, ”DNA replication and recombination,” Nature 421, 431-435 (2003).
2. E. A. Wintner, M. M. Conn, and J. Rebek, ”Studies in molecular replication,”
Acc. Chen. Res. 27, 198-203 (1994).
3. L. S. Penrose, ”Self-Reproducing Machines,” Scientific American 200(6), 105-114
(1959).
456
B. Yurke and D. Zhang
4. L. E. Orgel, ”Unnatural Selection in Chemical Systems,” Acc. Chem. Res. 28,
109-118 (1995).
5. J. J. Bull and H. A. Wichman, ”Applied Evolution,” Annu. Rev. Ecol. Syst. 32,
183-271 (2001).
6. W. K.Johnston, P. J. Unrau, M. S. Lawrence, M. E. Glasner, and D. P. Bartel, ”RNA-Catalyzed RNA Polymerization: Accurate and General RNA-Templated
Primer Extension,” Science 292, 1319-1325 (2001).
7. G. von Kiedrowski, ”A self-replicating hexadeoxynucleotide,” Angew. Chem. Int.
Edn Engl. 25, 932-935 (1986).
8. W. S. Zielinski and L. E. Orgel, ”Autocatalytic synthesis of a tetranucleotide analogue,” Nature 327, 346-347 (1987).
9. G. von Kiedrowski, B. Wlotzka, J. Helbing, M. Matzen, and S. Jordan, ”Parabolic
growth of a hexadeoxynucleotide analogue bearing a 3’-5’-phosphoamidate link,”
Angew. Chem. Int. Edn Engl. 30, 423-426, 892 (1991).
10. T. Achilles and G. von Kiedrowski, ”A self-replicating system from three precursors,” Angew. Chem. Int. Edn 32, 1198-1201 (1993).
11. D. Sievers and G. von Kiedrowski, ”Self-replication of complementary nucleotidebased oligomers,” Nature 369, 221-224 (1994).
12. T. Li and K. C. Nicolaou, ”Chemical self-replication of palindromic duplex DNA,”
Nature 369, 218 (1994).
13. B. Martin, R. Micura, S. Pitsch, and A. Eschenmoser, ”Pyranosyl-RNA: further
observations on replication,” Helv. Chim. Acta 80, 1901-1951 (1997).
14. D. Sievers and G. von Kiedrowski, ”Self-replication of hexadeoxynucleotide analogues: autocatalysis versus cross-catalysis,” Chem. Eur. J. 4, 629-641 (1998).
15. H. Schöneborn, J. Bülle, and G. von Kiedrowski, ”Kinetic monitoring of selfreplicating systems through measurement of fluorescence resonance energy transfer,” Chembiochem 2, 922-927 (2001).
16. D. H. Lee, J. R. Granja, J. A. Martinez, K. Severin, and M. R. Ghadiri, ”A selfreplicating peptide,” Nature 382, 525-528 (1996).
17. K. S. Severin, D. H. Lee, J. A. Martinez, and M. R. Ghadiri, ”Peptide selfreplication via template-directed ligation,” Chem. Eur. J. 3, 1017-1024 (1997).
18. K. Severin, D. H. Lee, J. A. Martinez, M. Vieth, and M. R. Ghadiri, ”Dynamic
error correction in autocatalytic peptide networks,” Angew, Chem. Int. Edn Engl.
37, 126-128 (1998).
19. S. Yao, I. Ghosh, R Zutshi, and J. A. Chmielewski, ”A self-replicating peptide
under ionic control,” Angew. Chem. Int. Edn Engl. 37, 478-481 (1998).
20. A. Saghathelian, Y. Yokobayashi, K. Soltani and M. R. Ghadiri, ”A chiroselective
peptide replicator,” Nature 409, 797-801 (2001).
21. T. Tjivikua, P. Ballester, and J. A. Rebek, ”A self-replicating system,” J. Am.
Chem. Soc. 112, 1249-1250 (1990).
22. A. Terfort and G. von Kiedrowski, ”Self-replication during condensation of 3aminobenzamidines with 2-formylphenoxyacetic acids,” Angew. Chem. Int. Edn
Engl. 31, 654-656 (1992).
23. J.-I. Hong, Q. Fang, V. Rotello, and J. Rebek, ”Competition, cooperation, and
mutation improving a synthetic replicator by light irradiation,” Science 255, 848850 (1992).
24. Q. Fang, T. K. Park, and J. Rebek, ”Crossover reactions between synthetic replicators yield active and inactive recombinants,” Science 256, 1179-1180 (1992).
25. R. J. Pieters, I. Huc, and J. Rebek, ”Reciprocal template effect in a replication
cycle,” Angew. Chem. Int. Edn Engl. 106, 1579-1581 (1994).
A Clocked DNA-Based Replicator
457
26. D. N. Reinhoudt, D. M. Rudkevich, and F. de Jong, ”Kinetic analysis of the Rebek
self-replicating system: Is there a controversy?” J. Am. Chem. Soc. 118, 6880-6889
(1996).
27. B. Wang and I. O. Sutherland, ”Self-replication in a Diels-Alder reaction,” Chem.
Commun. 16, 1495-1496 (1997).
28. E. Szathmáry and I. Gladkih, ”Sub-exponential growth and coexistence of nonenzymatically replicating templates,” J. Theor. Biol. 138, 55-58 (1989).
29. P. R. Wills, S. A. Kauffman, and B. M. R. Stadler, ”Selection dynamics in autocatalytic systems: Templates replicating through binary ligation,” Bull. Math.
Bio. 60, 1073-1098 (1998).
30. N. Paul and G. F. Joyce, ”A self-replicating ligase ribozyme,” PNAS 99, 1273312740 (2002).
31. A. Luther, R. Brandsch, and G. von Kiedrowski, ”Surface-promoted replication
and exponential amplification of DNA analogues,” Nature 396, 245-248 (1998).
32. J. Chen and N. C. Seeman, ”The synthesis from DNA of a molecule with the
connectivity of a cube,” Nature 350, 631-633 (1991).
33. N. C. Seeman, ”Nucleic acid nanostructures and topology,” Angew. Chem. Int.
Edn Engl. 37, 3220-3238 (1998).
34. E. Winfree, F. Liu, L. A. Wenzler, N. C. Seeman, ”Design and self-assembly of
two-dimensional DNA crystals,” Nature 394, 539-544 (1998).
35. C. Mao, W. Sun, N. C. Seeman, ”Designed two-dimensional DNA Holiday junction
arrays visualized by atomic force microscopy” J. Am. Chem. Soc. 121, 5437-5443
(1999).
36. T. H. LaBean, H. Yan, J. Kopatsch, F. Liu, E. Winfree, J. H. Reif, N. C. Seeman, ”Construction, analysis, ligation, and self-assembly of DNA triple crossover
complexes,” J. Am. Chem. Soc. 122, 1848-1860 (2000).
37. C. Mao, T. H. LaBean, J. H. Reif, and N. C. Seeman, ”Logical computation using
algorithmic self-assembly of DNA triple-crossover molecules,” Nature 407, 493-496
(2000).
38. N. C. Seeman, ”DNA in a material world,” Nature 421, 427-431 (2003).
39. C. Mao, W. Sun, Z. Shen, and N. C. Seeman, ”A nanomechanical device based on
the B-Z transition of DNA,” Nature 297, 144-146 (1999).
40. B. Yurke, A. J. Turberfield, A. P. Mills, Jr., F. C. Simmel, and J. L. Neumann, ”A
DNA-fuelled molecular machine made of DNA,” Nature 406, 605-608 (2000).
41. F. C. Simmel and B. Yurke, ”Using DNA to construct and power a nanoactuator,”
Phys. Rev. E 63, art. no. 041913 (2001).
42. F. C. Simmel and B. Yurke, ”A DNA-based molecular device switchable between
three distinct mechanical states,” Appl. Phys. Lett. 80, 883-885 (2002).
43. H. Yan, X. Zhang, Z. Shen, and N. C. Seeman, ”A robust DNA mechanical device
controlled by hybridization topology,” Nature 415, 62-65 (2002).
44. J. J. Li and W. Tan, ”A single DNA molecular nanomotor,” Nano Lett. 2, 315-318
(2002).
45. P. Alberti and J-L Mergny ”DNA duplex-quadruples exchange as the basis for a
nanomolecular machine,” PNAS 100, 1569-1573 (2003).
46. L. Feng, S. H. Park, J. H. Reif, H. Yan, ”A two-state DNA lattice switched by
DNA nanoactuator,” Angew. Chem. Int. Ed. 42, 4342-4346 (2003).