This article was downloaded by: [Purdue University] On: 20 January 2015, At: 15:58 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Journal of Biomolecular Structure and Dynamics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tbsd20
De Novo Design of Sequences for Nucleic Acid Structural Engineering Nadrian C. Seeman
a
a
Department of Chemistry , New York University , New York , NY , 10003 Published online: 21 May 2012.
To cite this article: Nadrian C. Seeman (1990) De Novo Design of Sequences for Nucleic Acid Structural Engineering, Journal of Biomolecular Structure and Dynamics, 8:3, 573-581, DOI: 10.1080/07391102.1990.10507829 To link to this article: http://dx.doi.org/10.1080/07391102.1990.10507829
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is
Downloaded by [Purdue University] at 15:58 20 January 2015
expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Journal ofBiomolecular Structure & Dynamics, /SSN 0739-1102 Volume 8, Issue Number 3 (1990), "'Adenine Press (1990).
De Novo Design of Sequences for Nucleic Acid Structural Engineering
Downloaded by [Purdue University] at 15:58 20 January 2015
Nadrian C. Seeman Department of Chemistry New York University New York, NY 10003 Asbtract An interactive procedure has been developed to assign sequences for the design of nucleic acid secondary structure. The primary goal of the procedure is to facilitate macromolecular architecture studies through the design of branched nucleic acid mono- and oligo-junction constructs in a convenient fashion. The essential feature of the sequence-symmetry minimization algorithm employed is the treatment of short sequences as vocabulary elements whose repetition decreases control over the resulting secondary structure. Both manual and semi-automatic application of this approach are available. The design of linear nucleic acid molecules or molecules containing single-stranded loops or connectors is also possible through application of the procedure.
Introduction The double helical interaction of complementary strands of DNA or RNA. mediated by Watson-Crick base pairing, is familiar to all. Our understanding of the storage, replication and expression of genetic information is primarily based on this concept, as are many protocols of the biotechnology industry. One of the salient features of DNA is the unbranched nature of the helix axis: Although the molecule maysupercoil, writhe and contort, there is currently no evidence for stable DNA structures with branched helix axes in vivo. Nevertheless, unstable branched intermediates are seen in the special processes of replication and recombination (e.g., 1, 2). In the early 1980's, the desire to model these unusual branched-topology states in oligonucleotide systems led to the development of algorithms for promoting their formation by means of sequence-symmetry minimization (3), combined with equilibrium probability calculations (4). Sequence-symmetry minimization means that the sequences are selected with the goal of minimizing sequence similarities between segments of molecules; thus, the chances of undesired associations are decreased, and control over secondary structure is improved. The sequence design process assigns sequences that assemble into otherwiseunfavorable branch points in DNA by making the maximization ofWatson-Crick base pairing contingent upon their formation. The original process for selecting the sequences of these 'branched junctions' is extremely laborious, even though it is
573
574
Seeman
Downloaded by [Purdue University] at 15:58 20 January 2015
largely automated. Once the basic features of a DNA junction are selected, that procedure examines virtually every sequence formally satisfying the architecture; sequence-symmetry is minimized, while junction-formation probability and melting behavior are estimated for each sequence tested (4), in order to determine the 'best' one. At the time the original procedure was devised, this level of analysis was warranted on several grounds: (i) The feasibility of forming branched molecules with oligonucleotides was questionable, since it had never been done. (ii) DNA synthesis was extremely expensive: As summarized in 1981, "Only a highly trained and skilled chemist could produce a single 12-unit sequence in less than 3 months" (5). (iii) Large quantities of DNA were needed for most of the physical experiments envisioned at that time. Times have changed dramatically: (i) The sequence selection algorithms are sufficiently reflective of nucleic acid chemistry that oligonucleotide junctions have now been formed and characterized by several groups ofinvestigators (6-15). (ii) It is routine today for investigators with minimal training in organic chemistry to synthesize automatically DNA strands containing 100 or more residues in a day, and the cost per residue is modest (16). (iii) The stability of newly designed branched DNA structures can be characterized by gel electrophoresis experiments using quantities of DNA in the ng-Jlg range, before proceeding with physical experiments that may demand lO's of Jlgs to mgs. As a result of these developments, there is merit in simplifying the sequence design
process, so that its use is not a major obstacle to advancing work in this area. In particular, we wish to use sequence-symmetry minimization algorithms in junctions with long arms, and in structures containing more than a single junction (3, 17-22). The same algorithms ought to be of value in directing the formation of secondary structure in other complex DNA molecules (e.g., single-stranded knots (21)), in linear duplex DNA or RNA molecules, and in single-stranded RNA molecules containing particular stem-loop structures. The change in approach that is necessary is to seek adequate sequences, without an exhaustive search for the 'best' sequence. Accordingly, the sequence-symmetry minimization approach has been encoded in an interactive menu-driven program called SEQUIN that accommodates very large structures: Up to 150 individual junction arms oflength 100 each can be included, or a linear duplex of length 15000 may be designed. Besides purely double helical structures, double helices may be mixed with single-stranded loops and connectors.
The Sequence Selection Algorithm Although it is very difficult to predict the structure of a molecule of arbitrary sequence (24,25), we have found it fairly simple to design sequences for molecules so that they will form a particular secondary structure (e.g., 6, 7, 23, 26, 27). The basic premise underlaying the procedure is that DNA will form continous perfectlypaired double helical segments in preference to other arrangements: Given enough perfect pairs, one ought to be able to force oligonucleotide strands to assume secondary
575
DE NOVO Design of Sequences
structures that would not otherwise form spontaneously. Ideally, one would prefer to have a 'vocabulary' of many different sets of complementary bases from which to draw(28), in order to form unique, yet intricate, structures. However, we have available conveniently only the two hydrogen bonding schemes defined by the classical base pairs, A-T and G-C. Therefore, we treat longer contiguous segments, i.e., trimeric, tetrameric, pentameric or hexameric sequences, as the unique components from which we may select sequences. We thereby increase our set of unique 'vocabulary elements' to 64 (trimers), 256 (tetramers), 1024 (pentamers) or 4096 (hexamers),
Downloaded by [Purdue University] at 15:58 20 January 2015
I
n II
C•G G•C C•G A•T A•T T•A C•G C•G TG~TACCG
GCACGAGT • • • • • • • • CGTGCTCA
• • • • • • • • ACTATGGC
IV
C•G C•G G•C A•T A•T T•A G•C C•G
III Figure 1: The Immobile Junction Jl. This junction is composed of4 hexadecamer strands, whose numbering is indicated. The double helical arms are indicated by roman numerals. Note that each of the individual strands may be regarded as an overlapping set of oligomers. Thus, a hexadecamer can be regarded as a set of 14 overlapping trimers, 13 overlapping tetramers, 12 overlapping pentamers or 11 overlapping hexamers. The sequence of this junction was designed using tetrameric vocabulary elements. G-C content is intentionally high (19/32 nucleotide pairs). Each end contains two G-C pairs. No more than two G' sin a row are permitted, in order to prevent G-G pairing. Note the lack of twofold symmetry in the base pairs flanking the branch point.
Downloaded by [Purdue University] at 15:58 20 January 2015
576
Seeman
depending upon the length selected. (These elements were termed' critons' in earlier work (3).) For example, the complex shown in Figure I, the well-characterized junction Jl (8, 9, 29-32), contains four hexadecamer strands designed by means of this procedure: Each hexadecamer strand consists of 13 overlapping tetramers. Each of the 52 tetramer elements in the four-stranded complex is unique. Thus, sequencesymmetry has been minimized here so that no tetrameric vocabulary element is repeated at all. To a first-order approximation, this means that competition with the designated structure comes from Watson-Crick pairing segments of length 3 or fewer (second-order analysis is discussed below). The reason for using tetramers as the vocabulary elements to design the junction is that it is too difficult (perhaps impossible) to select the 56 required unique trimers from the 64 that are available. Were it possible to use trimers, the only competitive Watson-Crick structures would be two nucleotides long. Besides being unique, none of Jl 's 52 tetramer elements is complementary to a tetramer that spans the junction. A general feature of the selection algorithm is that all sequences complementary to a region that cannot be perfectly complemented are treated as having already been used; further use would increase sequence-symmetry. Thus, in addition to the complements of elements that span junctions, elements complementary to single-stranded stretches, such as loops, are treated as having already been used, when sequence selection of additional arms or loops is done. The criticalfeature ofdesigning molecules to assume a given structure is to make it as difficult as possible for them to adopt an alternative structure. In addition to repetitive features of the sequence, branch migration at junctions can be eliminated by prohibiting twofold symmetry across the branch point. Of course, if a limited amount of branch migration is desired, this may be programmed into the sequence (3, 33). Gel electrophoresis experiments on Jl (6) and other junctions (7, 19, 26, 33, 34), conducted under native conditions, have borne out the validity of this approach. The strands have been shown to associate in the designated fashion, and the two sets of opposite strands (which are not designed to pair) have the same mobilities whether their components are run separately or mixed together. Although we must be extremely cautious about assuming that electrophoretic behavior is a perfect mirror of molecular association in solution, these results are highly encouraging about the effectiveness of designing secondary structure in this fashion. Features of the New Procedure
The earlier approach to the construction of branched nucleic acids centered on the construction of an individual junction. In the new procedure, the investigator defines double helical arms, and then specifies that they are linked together in a particular fashion. One end of an arm can terminate at a branched junction, while the other end may be linked to another arm. In this fashion, many branched junctions can be defined, and they, in tum, can be linked to form polygons, stick-polyhedra or other network components. Once the connectivity of arms is established, the symmetryminimization technique can be applied to the entire construct or to some large portion of it. No limitation is imposed on the number of arms that may flank a junction, in line with current thinking on this aspect of junction structure (35).
Downloaded by [Purdue University] at 15:58 20 January 2015
DE NOVO Design of Sequences
577
The assignment of sequence can be done in two different modes, manual or semiautomatic. In the manual mode, the designer assigns sequences one nucleotide at a time. As the user assigns the sequence of a given arm, 5' to 3', information is presented on the previous usage of the vocabulary elements (i.e., the tetramer, pentamer or hexamer ending in G, A, Tor C) that constitute the choice, as well as the selfcomplementarity of any elements selected. For example, ifone is monitoring elements oflength 4, and is setting the 5th nucleotide of an arm whose first 4 are CATC, the previous usage of ATCG, ATCA, ATCT and ATCC will be displayed. If an element is repeated, for some reason, the program will note this, but it will not object. This approach is in sharp contrast to the earlier procedure, which requires 100% stringency, with any multiple use of a specified-length vocabulary element leading to rejection of the sequence. Experience has shown that this level of stringency is unnecessary (19, 23, 33), and the current procedure is therefore more flexible. This relaxation is also warranted because errors in judgment are relatively inexpensive in time and materials. In addition to linear sequence symmetry, it is useful for the designer to be aware of twofold symmetry about the branch point, which permits branch migratory isomerization; this information is also made available. The semi-automatic mode constitutes a scan of possible sequences to fill in a region, in line with a set of specified criteria. If desired, these criteria permit complete stringency for a given set of elements, for example, no repeats of pen tamers. Alternatively, they may be relaxed to allow particular violations of minimum-symmetry rules, requiring no repeats in any new element selected, but permitting repeats in those already present. Our experience with this procedure suggests that this mode is most effective. The usual design situation involves a well-defined set of oftensymmetric sequences that must go into the structure--restriction sites, B-Z-sites, T nloops, or junction-flanking sequences--that will violate the usual stringent criteria. One wishes to design around these sequences in such a way that the rest of the molecule will assemble into a particular architecture. The program presents the user serially with all the sequences that fulfill the specified criteria for a short segment, and any of these sequences may be assigned to the segment. The more relaxed approach presented here facilitates the elimination of exhaustive scans of sequence-space seeking the 'best' sequence. If the user knows the overall characteristics of a sequence in a given region, e.g., percent GC, eschewal of GGG strings (36-38), or avoidance of polypurine tracts (39-41 ), these features can be incorporated into manual or semi-automatic sequence assignment; sequences containing unwanted features may be rejected in both assignment modes. The program readily allows the insertion or elimination of particular nucleotides. Vocabulary element usage and location are easily queried, so it is not hard to eliminate unwanted multiple usage if it arises. Since pairing interactions occur within double helical arms, it seems most logical to assign sequences in the context of defining an arm. Nevertheless, the individual covalent molecules that are synthesized, and which associate with each other to form the complex, are single-strands that participate in two or more arms. From the linkages assigned by the designer, the program figures out what the sequences of the strands are, and performs a number of diagnostic tests upon them, such as searching
578
Seeman
for inverted repeats that lead to self-pairing.
Downloaded by [Purdue University] at 15:58 20 January 2015
In addition, it is useful to test each strand against every other strand to discover unanticipated near-complementarities. These can arise from the failure of the firstorder approximation to sequence-symmetry minimization mentioned above: For example, the first-order approximation, with tetramer elements, would be insensitive to the virtual identity between ACCAATG and ACCGATG because they do not share any tetramer elements. G-Tor G-U pairing can be included as valid pairs in this form of analysis. Analysis is also facilitated with simple energy calculations using dimer energies for either DNA (42) or RNA (43). Once the connectivity of a molecule is defined, and a satisfactory sequence is worked out, it is convenient to use it as the basis for further work. Therefore, a filestructure allows the storage and retrieval of molecules: Multiple molecules may be retrieved, and aggregates can be assembled and stored. Files are in card-image format so that modifications can be made through the system text editor if desired. As an example of using a structure for further work, a DNA cube (27) was designed with both 20 and 21 nucleotide pairs per edge; the sequence of the cube with 21 nucleotide pairs was derived from the cube with 20. It is convenient that sequence-symmetry is invariant under 8 permutations of the sequence (including identity). These permutations are shown in Table I. The program allows the user to permute the sequence through any one of these transformations to arrive at a new sequence with the same sequence-symmetry properties. It is worth noting that permutations 6 and 7 are inverses of each other, while all the other permutations are self-inverse.
Application of the Procedure The key function of the program SEQUIN is tabulation of vocabulary element usage. Thus, during the assignment of sequence, the program is automatically or manually instructed to calculate element usage for all of the allowable vocabulary element lengths (trimers to hexamers ). As described above, usage includes not only explicit assignment to a given strand or complement, but also implicit assignment Table I Permutations of Nucleic Acid Sequence That Preserve Sequence Symmetry Permutation 1
2 3 4 5 6
7 8
Transformation
a-a a-a a-c a-c a-A a-A a-T a-T
A-+A A-+T A-+A A-+T
A-a
T-+T T-+A T-+T T-+A T-c
A-c
T-a
A-c
T-a
A-a
T-c
c-c c-c
c-a c-a c-T c-T c-A c-A
(Identity)
DE NOVO Design of Sequences
579
Downloaded by [Purdue University] at 15:58 20 January 2015
as the unwanted complement of a sequence that spans a branch point or forms a loop. The table containing this information is used both analytically and for purposes of further sequence assignment. The main analytical value of the table is to indicate which elements have been used repetitively; for example, adding two structures together can result in sequence repetition that one wishes to know about. Both the manual and semi-automatic sequence assignment procedures rely upon this table for keeping element repetition at a minimum. The manual assignment procedure can also keep track of nucleotides that flank junctions, thereby allowing the user to eliminate sequences with twofold symmetries that permit branch migration. The following are the steps one goes through in using the program: [1] Definition of molecular connectivity: arms of particular lengths are defined, and junction branches, single-stranded loops, and double-stranded linkages between arms are specified. (2] Fixed sequences are inserted: restriction sites, Z-loci, oligo-T loops, protein binding sites, and other regions that may contain sequence-symmetry are included if desired. [3) Sequence assignment is performed using the manual or (more likely) the semi-automatic procedure. [4] The sequence is analyzed by means of the analytical machinery of the program. [5) When satisfactory, the structure and sequence are stored, and the sequences ofthe component strands are output for synthesis. [6) The stored structure may be used as the basis for related structures.
Discussion The success of the earlier approach to DNA secondary structure design has stimulated recasting the sequence assignment procedure in an interactive format that is less restrictive. This allows the molecular architect to take advantage of the developments in nucleic acid synthesis and electrophoresis that make testing new and more intricate structural designs much less costly than they were previously. While the current algorithm is somewhat less automatic than the previous one, it is much easier to use, and much less costly. Experience shows that it is not necessary to scan and analyze every sequence consistent with the structural design. This new approach has been used to design several different structures involving branched DNA junctions. Individual objects that have been designed and successfully built include a 4-arm junction containing 25 nucleotide pairs/arm (44), and 5-arm and 6-armjunctions with 16 nucleotide pairs/arm (45). An 'eight-eared' square containing 504 nucleotides (168 internally and 336 on exocyclic arms), is an example of a large 2-dimensional object designed with SEQUIN and successfully assembled (Y. Zhang and N.C. Seeman, unpublished). The cube mentioned above contains 480 nucleotides (27), with a different restriction site on every edge. The cube was designed by the manual procedure in two pieces, neither of which contains any hexamer sequence more than once. The experience of designing the cube led to the development of the semi-automatic procedure, which we use almost exclusively now for segments that have no particular constraints on their sequences. Four logical steps are involved in the design of nucleic acid architecture (17). These are (i) choice of structure to be designed, (ii) selection of individual structural com-
580
Seeman
ponents, (iii) application of geometrical and (where available) physical constraints, and (iv) optimization of sequences to achieve structural goals. It is to be hoped that more extensive and more complicated structures with higher intricacy will be designed in the near future, and that the procedure presented here will facilitate the assignment of their sequences in a successful and convenient fashion. SEQUIN is written in FORTRAN for the VAX computer. The program and operating instructions are available upon request from the author.
Downloaded by [Purdue University] at 15:58 20 January 2015
Acknowledgments This research has been supported by grants GM-29554 from the National Institutes of Health and N00014-89-J-3078 from the Office of Naval Research. References and Footnotes 1. Kucherlapati, R. and Smith, G.R., Genetic Recombination, American Society for Microbiology, Washington, D.C. (1988). 2. Kornberg, A, DNA Replication, W.H. Freeman, New York (1980). 3. Seeman, N.C.,J. Theor. Bioi. 99,237-247 (1982). 4. Seeman, N.C. and Kallenbach, N.R., Biophys. J. 44,201-209 (1983). 5. Alvarado-Urbina, G., Sathe, G.M., Liu, W.-C., Gillen, M.F., Duck, P.D, Bender, R. and Ogilvie, K.K., Science 214, 270-274 (1981). 6. Kallenbach, N.R., Ma, R.-I. and Seeman, N.C., Nature (London) 305, 829-831 ( 1983). 7. Kallenbach, N.R., Ma, R.-I., Wand, AJ., Veeneman, G.H., van Boom, J.H., and Seeman, N.C., J. Biomol. Str. and Dyns. 1, 158-168 (1983). 8. Kallenbach, N.R. and Seeman, N.C., Cmts. on Cell. and Mol. Biophys. 4, 1-16 (1986). 9. Cooper, J.P. and Hagerman, PJ.,J. Mol. Bioi. 198,711-719 (1987). 10. Evans, D.H. and Kolodner, R.,J. Bioi. Chern. 262,9160-9165 (1987). 11. Dickie, P., McFadden, G. and Morgan, AR. ,J. Bioi. Chern. 262, 14826-14836 (1987). 12. Duckett, D. R., Murchie, A I. H., Diekmann, S., Von Kitzing, E., Kemper, B. and Lilley, D. M. J., Cell 55, 79-89 (1988). 13. Cooper, J.P. and Hagerman, P. J., Proc. Nat. Acad. Sci. (USA) 86,7336-7340 (1989). 14. Murchie, AI.H., Clegg, R.M., von Kitzing, E., Duckett, D.R., Diekmann, S., and Lilley, D.M.J., Nature 341,763-766 (1989). 15. Franz, B. and Landy, A, in Structure and Methods-, vol. 1., eds. R.H. Sarma and M.H. Sarma, Adenine Press, New York, pp. 183-192. 16. Caruthers, M. H., in Chemical and Enzymatic Synthesis of Gene Fragments, eds. Gassen, H. G. and Lang, A, Verlag Chemie, Weinheim, pp. 71-79 (1982). 17. Seeman, N.C.,J. Biomol. Str. & Dyns. 3, 11-34 (1985). 18. Seeman, N.C.,J. Mol. Graphics 3, 34-39 (1985). 19. Ma, R.-I., Kallenbach, N.R., Sheardy, R.D., Petrillo, M.L. and Seeman, N.C., Nucl. Acids- Res. 14, 9745-9753 (1986). 20. Robinson, B.H. and Seeman, N.C., Prot. Eng. 1, 295-300 (1987). 21. Seeman, N.C.,J. Biomol Str. & Dyns. 5, 997-1004 (1988). 22. Petrillo, M.L., Newton, CJ., Cunningham, R.P., R.-I. Ma, Kallenbach, N.R., and Seeman, N.C., Biopolymers 27, 1337-1352 (1988). 23. Chen, J.-H., Kallenbach, N.R. and Seeman, N.C.,J. Am. Chern. Soc.l11 6402-6407 (1989). 24. Jaeger, J.A, Turner, D.H. and Zuker, M.,Proc. Nat. Acad. Sci. (USA) 86,7706-7710 (1989). 25. Zuker, M., Science 244,48-52 (1989). 26. Kimball, A, Guo, Q., Lu, M., Cunningham, R.P., Kallenbach, N.R., Seeman, N.C. and Tullius, T.D., J. Bioi. Chern. 265, 6544-6547. (1990). 27. Chen, J. and Seeman, N.C., Submitted for publication (1990). 28. Piccirilli, J.A, Krauch, T., Moroney, S.E. and Benner, S.A, Nature 343, 33-37 (1990).
Downloaded by [Purdue University] at 15:58 20 January 2015
DE NOVO Design of Sequences
581
29. Seeman, N.C., Maestre, M.F., Ma, R-1. and Kallenbach, N.R., in Prog. Clin. & Bioi. Res. 172A: The Molecular Basis of Cancer, ed. by R. Rein, Alan Liss Inc., New York, pp. 99-108 (1985). 30. Wemmer, D.E., Wand, AJ., Seeman, N.C., and Kallenbach, N.R,Biochemistry 24,5745-5749 (1985). 31. Mark:y, LA, Kallenbach, N.R, McDonough, K.A, Seeman, N.C. and Breslauer, KJ. ,Biopolymers 26, 1621-1634 (1987). 32. Churchill, M.EA, Tullius, T.D., Kallenbach, N.R and Seeman, N.C. ,Proc. Nat. Acad. Sci. (USA) 85, 4653-4656( 1988). 33. Chen, J.-H., Churchill, M.EA, Tullius, T.D., Kallenbach, N.R and Seeman, N.C.,Biochemistry 85, 6032-6038 (1988). 34. Seeman, N.C., Chen, J.H., and Kallenbach, N.R. Electrophoresis 10, 345-354. 35. Seeman, N.C. and Kallenbach, N.R, in Molecular Structure: Chemical and Biological Activity, ed. by J.J. Stezowski, J.-L. Huang and M.-C. Shao, Oxford University Press, Oxford, 1988, pp. 189-194 (1988). 36. Williamson, J.R, Raghuraman, M.K. and Cech, T.R, Cel/59, 871-880 (1989). 37. Sundquist, W.l. and Klug, A, Nature 342, 827-829 (1989). 38. Sen, D. and Gilbert, W., Nature 344,410-414 (1990). 39. Koo, H.-S., Wu, H.-M., and Crothers, D.M.,Nature 320,501-506 (1986). 40. Lyamichev, V.I., Mirkin, S.M. and Frank-Kamenetskii, M.D. , J. Biomol. Str. & Dyns. 3, 327338(1985). 41. Htun, H. and Dahlberg, J.E., Science 241, 1791-1796 (1988). 42. Breslauer, KJ., Frank, R, Bloecker, H., and Mark:y, LA, Proc. Nat. Acad. Sci. (USA) 83, 37463750 (1986). 43. Freier, S.M., Kierzek, R., Jaeger, J.A, Sugimoto, N., Caruthers, M.H., Neilson, T., and Turner, D.H., Proc. Nat. Acad. Sci. (USA) 83,9373-9377 (1986). 44. Lu, M., Guo, Q., Seeman, N.C., and Kallenbach, N.R.,J. Bioi. Chem. 264,20851-20854 (1989). 45. Wang, Y.L., Mueller, J.E., Kemper, B., and Seeman, N.C., Submitted for publication (1990).
Date Received: June 27, 1990
Communicated by the Editor Alexander McPherson
Journal of Biomolecular Structure and Dynamics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tbsd20
De Novo Design of Sequences for Nucleic Acid Structural Engineering Nadrian C. Seeman
a
a
Department of Chemistry , New York University , New York , NY , 10003 Published online: 21 May 2012.
To cite this article: Nadrian C. Seeman (1990) De Novo Design of Sequences for Nucleic Acid Structural Engineering, Journal of Biomolecular Structure and Dynamics, 8:3, 573-581, DOI: 10.1080/07391102.1990.10507829 To link to this article: http://dx.doi.org/10.1080/07391102.1990.10507829
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is
Downloaded by [Purdue University] at 15:58 20 January 2015
expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Journal ofBiomolecular Structure & Dynamics, /SSN 0739-1102 Volume 8, Issue Number 3 (1990), "'Adenine Press (1990).
De Novo Design of Sequences for Nucleic Acid Structural Engineering
Downloaded by [Purdue University] at 15:58 20 January 2015
Nadrian C. Seeman Department of Chemistry New York University New York, NY 10003 Asbtract An interactive procedure has been developed to assign sequences for the design of nucleic acid secondary structure. The primary goal of the procedure is to facilitate macromolecular architecture studies through the design of branched nucleic acid mono- and oligo-junction constructs in a convenient fashion. The essential feature of the sequence-symmetry minimization algorithm employed is the treatment of short sequences as vocabulary elements whose repetition decreases control over the resulting secondary structure. Both manual and semi-automatic application of this approach are available. The design of linear nucleic acid molecules or molecules containing single-stranded loops or connectors is also possible through application of the procedure.
Introduction The double helical interaction of complementary strands of DNA or RNA. mediated by Watson-Crick base pairing, is familiar to all. Our understanding of the storage, replication and expression of genetic information is primarily based on this concept, as are many protocols of the biotechnology industry. One of the salient features of DNA is the unbranched nature of the helix axis: Although the molecule maysupercoil, writhe and contort, there is currently no evidence for stable DNA structures with branched helix axes in vivo. Nevertheless, unstable branched intermediates are seen in the special processes of replication and recombination (e.g., 1, 2). In the early 1980's, the desire to model these unusual branched-topology states in oligonucleotide systems led to the development of algorithms for promoting their formation by means of sequence-symmetry minimization (3), combined with equilibrium probability calculations (4). Sequence-symmetry minimization means that the sequences are selected with the goal of minimizing sequence similarities between segments of molecules; thus, the chances of undesired associations are decreased, and control over secondary structure is improved. The sequence design process assigns sequences that assemble into otherwiseunfavorable branch points in DNA by making the maximization ofWatson-Crick base pairing contingent upon their formation. The original process for selecting the sequences of these 'branched junctions' is extremely laborious, even though it is
573
574
Seeman
Downloaded by [Purdue University] at 15:58 20 January 2015
largely automated. Once the basic features of a DNA junction are selected, that procedure examines virtually every sequence formally satisfying the architecture; sequence-symmetry is minimized, while junction-formation probability and melting behavior are estimated for each sequence tested (4), in order to determine the 'best' one. At the time the original procedure was devised, this level of analysis was warranted on several grounds: (i) The feasibility of forming branched molecules with oligonucleotides was questionable, since it had never been done. (ii) DNA synthesis was extremely expensive: As summarized in 1981, "Only a highly trained and skilled chemist could produce a single 12-unit sequence in less than 3 months" (5). (iii) Large quantities of DNA were needed for most of the physical experiments envisioned at that time. Times have changed dramatically: (i) The sequence selection algorithms are sufficiently reflective of nucleic acid chemistry that oligonucleotide junctions have now been formed and characterized by several groups ofinvestigators (6-15). (ii) It is routine today for investigators with minimal training in organic chemistry to synthesize automatically DNA strands containing 100 or more residues in a day, and the cost per residue is modest (16). (iii) The stability of newly designed branched DNA structures can be characterized by gel electrophoresis experiments using quantities of DNA in the ng-Jlg range, before proceeding with physical experiments that may demand lO's of Jlgs to mgs. As a result of these developments, there is merit in simplifying the sequence design
process, so that its use is not a major obstacle to advancing work in this area. In particular, we wish to use sequence-symmetry minimization algorithms in junctions with long arms, and in structures containing more than a single junction (3, 17-22). The same algorithms ought to be of value in directing the formation of secondary structure in other complex DNA molecules (e.g., single-stranded knots (21)), in linear duplex DNA or RNA molecules, and in single-stranded RNA molecules containing particular stem-loop structures. The change in approach that is necessary is to seek adequate sequences, without an exhaustive search for the 'best' sequence. Accordingly, the sequence-symmetry minimization approach has been encoded in an interactive menu-driven program called SEQUIN that accommodates very large structures: Up to 150 individual junction arms oflength 100 each can be included, or a linear duplex of length 15000 may be designed. Besides purely double helical structures, double helices may be mixed with single-stranded loops and connectors.
The Sequence Selection Algorithm Although it is very difficult to predict the structure of a molecule of arbitrary sequence (24,25), we have found it fairly simple to design sequences for molecules so that they will form a particular secondary structure (e.g., 6, 7, 23, 26, 27). The basic premise underlaying the procedure is that DNA will form continous perfectlypaired double helical segments in preference to other arrangements: Given enough perfect pairs, one ought to be able to force oligonucleotide strands to assume secondary
575
DE NOVO Design of Sequences
structures that would not otherwise form spontaneously. Ideally, one would prefer to have a 'vocabulary' of many different sets of complementary bases from which to draw(28), in order to form unique, yet intricate, structures. However, we have available conveniently only the two hydrogen bonding schemes defined by the classical base pairs, A-T and G-C. Therefore, we treat longer contiguous segments, i.e., trimeric, tetrameric, pentameric or hexameric sequences, as the unique components from which we may select sequences. We thereby increase our set of unique 'vocabulary elements' to 64 (trimers), 256 (tetramers), 1024 (pentamers) or 4096 (hexamers),
Downloaded by [Purdue University] at 15:58 20 January 2015
I
n II
C•G G•C C•G A•T A•T T•A C•G C•G TG~TACCG
GCACGAGT • • • • • • • • CGTGCTCA
• • • • • • • • ACTATGGC
IV
C•G C•G G•C A•T A•T T•A G•C C•G
III Figure 1: The Immobile Junction Jl. This junction is composed of4 hexadecamer strands, whose numbering is indicated. The double helical arms are indicated by roman numerals. Note that each of the individual strands may be regarded as an overlapping set of oligomers. Thus, a hexadecamer can be regarded as a set of 14 overlapping trimers, 13 overlapping tetramers, 12 overlapping pentamers or 11 overlapping hexamers. The sequence of this junction was designed using tetrameric vocabulary elements. G-C content is intentionally high (19/32 nucleotide pairs). Each end contains two G-C pairs. No more than two G' sin a row are permitted, in order to prevent G-G pairing. Note the lack of twofold symmetry in the base pairs flanking the branch point.
Downloaded by [Purdue University] at 15:58 20 January 2015
576
Seeman
depending upon the length selected. (These elements were termed' critons' in earlier work (3).) For example, the complex shown in Figure I, the well-characterized junction Jl (8, 9, 29-32), contains four hexadecamer strands designed by means of this procedure: Each hexadecamer strand consists of 13 overlapping tetramers. Each of the 52 tetramer elements in the four-stranded complex is unique. Thus, sequencesymmetry has been minimized here so that no tetrameric vocabulary element is repeated at all. To a first-order approximation, this means that competition with the designated structure comes from Watson-Crick pairing segments of length 3 or fewer (second-order analysis is discussed below). The reason for using tetramers as the vocabulary elements to design the junction is that it is too difficult (perhaps impossible) to select the 56 required unique trimers from the 64 that are available. Were it possible to use trimers, the only competitive Watson-Crick structures would be two nucleotides long. Besides being unique, none of Jl 's 52 tetramer elements is complementary to a tetramer that spans the junction. A general feature of the selection algorithm is that all sequences complementary to a region that cannot be perfectly complemented are treated as having already been used; further use would increase sequence-symmetry. Thus, in addition to the complements of elements that span junctions, elements complementary to single-stranded stretches, such as loops, are treated as having already been used, when sequence selection of additional arms or loops is done. The criticalfeature ofdesigning molecules to assume a given structure is to make it as difficult as possible for them to adopt an alternative structure. In addition to repetitive features of the sequence, branch migration at junctions can be eliminated by prohibiting twofold symmetry across the branch point. Of course, if a limited amount of branch migration is desired, this may be programmed into the sequence (3, 33). Gel electrophoresis experiments on Jl (6) and other junctions (7, 19, 26, 33, 34), conducted under native conditions, have borne out the validity of this approach. The strands have been shown to associate in the designated fashion, and the two sets of opposite strands (which are not designed to pair) have the same mobilities whether their components are run separately or mixed together. Although we must be extremely cautious about assuming that electrophoretic behavior is a perfect mirror of molecular association in solution, these results are highly encouraging about the effectiveness of designing secondary structure in this fashion. Features of the New Procedure
The earlier approach to the construction of branched nucleic acids centered on the construction of an individual junction. In the new procedure, the investigator defines double helical arms, and then specifies that they are linked together in a particular fashion. One end of an arm can terminate at a branched junction, while the other end may be linked to another arm. In this fashion, many branched junctions can be defined, and they, in tum, can be linked to form polygons, stick-polyhedra or other network components. Once the connectivity of arms is established, the symmetryminimization technique can be applied to the entire construct or to some large portion of it. No limitation is imposed on the number of arms that may flank a junction, in line with current thinking on this aspect of junction structure (35).
Downloaded by [Purdue University] at 15:58 20 January 2015
DE NOVO Design of Sequences
577
The assignment of sequence can be done in two different modes, manual or semiautomatic. In the manual mode, the designer assigns sequences one nucleotide at a time. As the user assigns the sequence of a given arm, 5' to 3', information is presented on the previous usage of the vocabulary elements (i.e., the tetramer, pentamer or hexamer ending in G, A, Tor C) that constitute the choice, as well as the selfcomplementarity of any elements selected. For example, ifone is monitoring elements oflength 4, and is setting the 5th nucleotide of an arm whose first 4 are CATC, the previous usage of ATCG, ATCA, ATCT and ATCC will be displayed. If an element is repeated, for some reason, the program will note this, but it will not object. This approach is in sharp contrast to the earlier procedure, which requires 100% stringency, with any multiple use of a specified-length vocabulary element leading to rejection of the sequence. Experience has shown that this level of stringency is unnecessary (19, 23, 33), and the current procedure is therefore more flexible. This relaxation is also warranted because errors in judgment are relatively inexpensive in time and materials. In addition to linear sequence symmetry, it is useful for the designer to be aware of twofold symmetry about the branch point, which permits branch migratory isomerization; this information is also made available. The semi-automatic mode constitutes a scan of possible sequences to fill in a region, in line with a set of specified criteria. If desired, these criteria permit complete stringency for a given set of elements, for example, no repeats of pen tamers. Alternatively, they may be relaxed to allow particular violations of minimum-symmetry rules, requiring no repeats in any new element selected, but permitting repeats in those already present. Our experience with this procedure suggests that this mode is most effective. The usual design situation involves a well-defined set of oftensymmetric sequences that must go into the structure--restriction sites, B-Z-sites, T nloops, or junction-flanking sequences--that will violate the usual stringent criteria. One wishes to design around these sequences in such a way that the rest of the molecule will assemble into a particular architecture. The program presents the user serially with all the sequences that fulfill the specified criteria for a short segment, and any of these sequences may be assigned to the segment. The more relaxed approach presented here facilitates the elimination of exhaustive scans of sequence-space seeking the 'best' sequence. If the user knows the overall characteristics of a sequence in a given region, e.g., percent GC, eschewal of GGG strings (36-38), or avoidance of polypurine tracts (39-41 ), these features can be incorporated into manual or semi-automatic sequence assignment; sequences containing unwanted features may be rejected in both assignment modes. The program readily allows the insertion or elimination of particular nucleotides. Vocabulary element usage and location are easily queried, so it is not hard to eliminate unwanted multiple usage if it arises. Since pairing interactions occur within double helical arms, it seems most logical to assign sequences in the context of defining an arm. Nevertheless, the individual covalent molecules that are synthesized, and which associate with each other to form the complex, are single-strands that participate in two or more arms. From the linkages assigned by the designer, the program figures out what the sequences of the strands are, and performs a number of diagnostic tests upon them, such as searching
578
Seeman
for inverted repeats that lead to self-pairing.
Downloaded by [Purdue University] at 15:58 20 January 2015
In addition, it is useful to test each strand against every other strand to discover unanticipated near-complementarities. These can arise from the failure of the firstorder approximation to sequence-symmetry minimization mentioned above: For example, the first-order approximation, with tetramer elements, would be insensitive to the virtual identity between ACCAATG and ACCGATG because they do not share any tetramer elements. G-Tor G-U pairing can be included as valid pairs in this form of analysis. Analysis is also facilitated with simple energy calculations using dimer energies for either DNA (42) or RNA (43). Once the connectivity of a molecule is defined, and a satisfactory sequence is worked out, it is convenient to use it as the basis for further work. Therefore, a filestructure allows the storage and retrieval of molecules: Multiple molecules may be retrieved, and aggregates can be assembled and stored. Files are in card-image format so that modifications can be made through the system text editor if desired. As an example of using a structure for further work, a DNA cube (27) was designed with both 20 and 21 nucleotide pairs per edge; the sequence of the cube with 21 nucleotide pairs was derived from the cube with 20. It is convenient that sequence-symmetry is invariant under 8 permutations of the sequence (including identity). These permutations are shown in Table I. The program allows the user to permute the sequence through any one of these transformations to arrive at a new sequence with the same sequence-symmetry properties. It is worth noting that permutations 6 and 7 are inverses of each other, while all the other permutations are self-inverse.
Application of the Procedure The key function of the program SEQUIN is tabulation of vocabulary element usage. Thus, during the assignment of sequence, the program is automatically or manually instructed to calculate element usage for all of the allowable vocabulary element lengths (trimers to hexamers ). As described above, usage includes not only explicit assignment to a given strand or complement, but also implicit assignment Table I Permutations of Nucleic Acid Sequence That Preserve Sequence Symmetry Permutation 1
2 3 4 5 6
7 8
Transformation
a-a a-a a-c a-c a-A a-A a-T a-T
A-+A A-+T A-+A A-+T
A-a
T-+T T-+A T-+T T-+A T-c
A-c
T-a
A-c
T-a
A-a
T-c
c-c c-c
c-a c-a c-T c-T c-A c-A
(Identity)
DE NOVO Design of Sequences
579
Downloaded by [Purdue University] at 15:58 20 January 2015
as the unwanted complement of a sequence that spans a branch point or forms a loop. The table containing this information is used both analytically and for purposes of further sequence assignment. The main analytical value of the table is to indicate which elements have been used repetitively; for example, adding two structures together can result in sequence repetition that one wishes to know about. Both the manual and semi-automatic sequence assignment procedures rely upon this table for keeping element repetition at a minimum. The manual assignment procedure can also keep track of nucleotides that flank junctions, thereby allowing the user to eliminate sequences with twofold symmetries that permit branch migration. The following are the steps one goes through in using the program: [1] Definition of molecular connectivity: arms of particular lengths are defined, and junction branches, single-stranded loops, and double-stranded linkages between arms are specified. (2] Fixed sequences are inserted: restriction sites, Z-loci, oligo-T loops, protein binding sites, and other regions that may contain sequence-symmetry are included if desired. [3) Sequence assignment is performed using the manual or (more likely) the semi-automatic procedure. [4] The sequence is analyzed by means of the analytical machinery of the program. [5) When satisfactory, the structure and sequence are stored, and the sequences ofthe component strands are output for synthesis. [6) The stored structure may be used as the basis for related structures.
Discussion The success of the earlier approach to DNA secondary structure design has stimulated recasting the sequence assignment procedure in an interactive format that is less restrictive. This allows the molecular architect to take advantage of the developments in nucleic acid synthesis and electrophoresis that make testing new and more intricate structural designs much less costly than they were previously. While the current algorithm is somewhat less automatic than the previous one, it is much easier to use, and much less costly. Experience shows that it is not necessary to scan and analyze every sequence consistent with the structural design. This new approach has been used to design several different structures involving branched DNA junctions. Individual objects that have been designed and successfully built include a 4-arm junction containing 25 nucleotide pairs/arm (44), and 5-arm and 6-armjunctions with 16 nucleotide pairs/arm (45). An 'eight-eared' square containing 504 nucleotides (168 internally and 336 on exocyclic arms), is an example of a large 2-dimensional object designed with SEQUIN and successfully assembled (Y. Zhang and N.C. Seeman, unpublished). The cube mentioned above contains 480 nucleotides (27), with a different restriction site on every edge. The cube was designed by the manual procedure in two pieces, neither of which contains any hexamer sequence more than once. The experience of designing the cube led to the development of the semi-automatic procedure, which we use almost exclusively now for segments that have no particular constraints on their sequences. Four logical steps are involved in the design of nucleic acid architecture (17). These are (i) choice of structure to be designed, (ii) selection of individual structural com-
580
Seeman
ponents, (iii) application of geometrical and (where available) physical constraints, and (iv) optimization of sequences to achieve structural goals. It is to be hoped that more extensive and more complicated structures with higher intricacy will be designed in the near future, and that the procedure presented here will facilitate the assignment of their sequences in a successful and convenient fashion. SEQUIN is written in FORTRAN for the VAX computer. The program and operating instructions are available upon request from the author.
Downloaded by [Purdue University] at 15:58 20 January 2015
Acknowledgments This research has been supported by grants GM-29554 from the National Institutes of Health and N00014-89-J-3078 from the Office of Naval Research. References and Footnotes 1. Kucherlapati, R. and Smith, G.R., Genetic Recombination, American Society for Microbiology, Washington, D.C. (1988). 2. Kornberg, A, DNA Replication, W.H. Freeman, New York (1980). 3. Seeman, N.C.,J. Theor. Bioi. 99,237-247 (1982). 4. Seeman, N.C. and Kallenbach, N.R., Biophys. J. 44,201-209 (1983). 5. Alvarado-Urbina, G., Sathe, G.M., Liu, W.-C., Gillen, M.F., Duck, P.D, Bender, R. and Ogilvie, K.K., Science 214, 270-274 (1981). 6. Kallenbach, N.R., Ma, R.-I. and Seeman, N.C., Nature (London) 305, 829-831 ( 1983). 7. Kallenbach, N.R., Ma, R.-I., Wand, AJ., Veeneman, G.H., van Boom, J.H., and Seeman, N.C., J. Biomol. Str. and Dyns. 1, 158-168 (1983). 8. Kallenbach, N.R. and Seeman, N.C., Cmts. on Cell. and Mol. Biophys. 4, 1-16 (1986). 9. Cooper, J.P. and Hagerman, PJ.,J. Mol. Bioi. 198,711-719 (1987). 10. Evans, D.H. and Kolodner, R.,J. Bioi. Chern. 262,9160-9165 (1987). 11. Dickie, P., McFadden, G. and Morgan, AR. ,J. Bioi. Chern. 262, 14826-14836 (1987). 12. Duckett, D. R., Murchie, A I. H., Diekmann, S., Von Kitzing, E., Kemper, B. and Lilley, D. M. J., Cell 55, 79-89 (1988). 13. Cooper, J.P. and Hagerman, P. J., Proc. Nat. Acad. Sci. (USA) 86,7336-7340 (1989). 14. Murchie, AI.H., Clegg, R.M., von Kitzing, E., Duckett, D.R., Diekmann, S., and Lilley, D.M.J., Nature 341,763-766 (1989). 15. Franz, B. and Landy, A, in Structure and Methods-, vol. 1., eds. R.H. Sarma and M.H. Sarma, Adenine Press, New York, pp. 183-192. 16. Caruthers, M. H., in Chemical and Enzymatic Synthesis of Gene Fragments, eds. Gassen, H. G. and Lang, A, Verlag Chemie, Weinheim, pp. 71-79 (1982). 17. Seeman, N.C.,J. Biomol. Str. & Dyns. 3, 11-34 (1985). 18. Seeman, N.C.,J. Mol. Graphics 3, 34-39 (1985). 19. Ma, R.-I., Kallenbach, N.R., Sheardy, R.D., Petrillo, M.L. and Seeman, N.C., Nucl. Acids- Res. 14, 9745-9753 (1986). 20. Robinson, B.H. and Seeman, N.C., Prot. Eng. 1, 295-300 (1987). 21. Seeman, N.C.,J. Biomol Str. & Dyns. 5, 997-1004 (1988). 22. Petrillo, M.L., Newton, CJ., Cunningham, R.P., R.-I. Ma, Kallenbach, N.R., and Seeman, N.C., Biopolymers 27, 1337-1352 (1988). 23. Chen, J.-H., Kallenbach, N.R. and Seeman, N.C.,J. Am. Chern. Soc.l11 6402-6407 (1989). 24. Jaeger, J.A, Turner, D.H. and Zuker, M.,Proc. Nat. Acad. Sci. (USA) 86,7706-7710 (1989). 25. Zuker, M., Science 244,48-52 (1989). 26. Kimball, A, Guo, Q., Lu, M., Cunningham, R.P., Kallenbach, N.R., Seeman, N.C. and Tullius, T.D., J. Bioi. Chern. 265, 6544-6547. (1990). 27. Chen, J. and Seeman, N.C., Submitted for publication (1990). 28. Piccirilli, J.A, Krauch, T., Moroney, S.E. and Benner, S.A, Nature 343, 33-37 (1990).
Downloaded by [Purdue University] at 15:58 20 January 2015
DE NOVO Design of Sequences
581
29. Seeman, N.C., Maestre, M.F., Ma, R-1. and Kallenbach, N.R., in Prog. Clin. & Bioi. Res. 172A: The Molecular Basis of Cancer, ed. by R. Rein, Alan Liss Inc., New York, pp. 99-108 (1985). 30. Wemmer, D.E., Wand, AJ., Seeman, N.C., and Kallenbach, N.R,Biochemistry 24,5745-5749 (1985). 31. Mark:y, LA, Kallenbach, N.R, McDonough, K.A, Seeman, N.C. and Breslauer, KJ. ,Biopolymers 26, 1621-1634 (1987). 32. Churchill, M.EA, Tullius, T.D., Kallenbach, N.R and Seeman, N.C. ,Proc. Nat. Acad. Sci. (USA) 85, 4653-4656( 1988). 33. Chen, J.-H., Churchill, M.EA, Tullius, T.D., Kallenbach, N.R and Seeman, N.C.,Biochemistry 85, 6032-6038 (1988). 34. Seeman, N.C., Chen, J.H., and Kallenbach, N.R. Electrophoresis 10, 345-354. 35. Seeman, N.C. and Kallenbach, N.R, in Molecular Structure: Chemical and Biological Activity, ed. by J.J. Stezowski, J.-L. Huang and M.-C. Shao, Oxford University Press, Oxford, 1988, pp. 189-194 (1988). 36. Williamson, J.R, Raghuraman, M.K. and Cech, T.R, Cel/59, 871-880 (1989). 37. Sundquist, W.l. and Klug, A, Nature 342, 827-829 (1989). 38. Sen, D. and Gilbert, W., Nature 344,410-414 (1990). 39. Koo, H.-S., Wu, H.-M., and Crothers, D.M.,Nature 320,501-506 (1986). 40. Lyamichev, V.I., Mirkin, S.M. and Frank-Kamenetskii, M.D. , J. Biomol. Str. & Dyns. 3, 327338(1985). 41. Htun, H. and Dahlberg, J.E., Science 241, 1791-1796 (1988). 42. Breslauer, KJ., Frank, R, Bloecker, H., and Mark:y, LA, Proc. Nat. Acad. Sci. (USA) 83, 37463750 (1986). 43. Freier, S.M., Kierzek, R., Jaeger, J.A, Sugimoto, N., Caruthers, M.H., Neilson, T., and Turner, D.H., Proc. Nat. Acad. Sci. (USA) 83,9373-9377 (1986). 44. Lu, M., Guo, Q., Seeman, N.C., and Kallenbach, N.R.,J. Bioi. Chem. 264,20851-20854 (1989). 45. Wang, Y.L., Mueller, J.E., Kemper, B., and Seeman, N.C., Submitted for publication (1990).
Date Received: June 27, 1990
Communicated by the Editor Alexander McPherson
