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Title:
NUCLEIC ACID BRANCHED JUNCTIONS WITH PRECISELY DEFINED MIGRATIONAL MOBILITY
Document Type and Number:
WIPO Patent Application WO/1985/000813
Kind Code:
A1
Abstract:
Nucleic acid branched junctions with precisely defined migrational mobility comprising new compositions of matter containing semi-mobile and/or immobile branched nucleic acid junctions from which at least 3-double helices emanate are described. These compositions of matter can comprise integral parts of periodic or other networks having precise molecular dimensions, thereby permitting the constitution of exact molecular architecture on the 100 to 1,000 Angstrom scale. They can be made by dissolution of at least three polynucleotides possessing minimal sequence symmetry with each other.

Inventors:
SEEMAN NADRIAN CHARLES (US)
Application Number:
PCT/US1984/001220
Publication Date:
February 28, 1985
Filing Date:
August 01, 1984
Export Citation:
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Assignee:
UNIV NEW YORK STATE RES FOUND (US)
International Classes:
C07H21/00; C12N15/10; (IPC1-7): C07G7/00; C07H21/00
Other References:
Nature, Vol. 305, issued October 1983, KALLENBACH et al, "An Immobile Nuclei Acid Junction Constructed from Oligonucleotide, " page 829-831.
Biomol. Stereodyn., Proc. Symp., Vol. 1, issued 1981, SEEMAN, NADRIAN C., "Nucleic Acid Junctions: Building Blocks for Genetic Engineering in Three Dimensions, " pages 269-277, Abstract No. 46972d.
Journal Theor. Biol., Vol. 99, No. 2, issued 1982, SEEMAN, NADRIAN C., "Nucleic Acid Junctions and Lattices, " pages 237-247, Abstract No. 13129x.
Journal Biomol. Struct. Dyn., Vol. No. 1, issued 1983, KALLENBACH et al, "Fourth Rank Immobile Nucleic Acid Junctions, " pages 159-168, Abstract No. 31050d.
Biomol. Stereodyn., Proc. Symp., Vol. 1, issued 1981, SEEMAN et al, "Stimulation of Double Stranded Branch Point Migration, " pages 279-300, Abstract No. 30108r.
Jerusalem Symp. Quantum Chem. Biochem. Vol. 16, issued 1983, SEEMAN et al, "Nucleic Acid Junctions: The Tensors of Life, " pages 183-200, Abstract No. 187473e.
Biophys. Journal, Vol. 44, No. 2, issued 1983, SEEMAN et al, "Design of Immobile Nucleic Acid Junctions, " pages 201-209, Abstract No. 2333t.
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Claims:
1. A σomposition σomprising a synthetiσ nucleic acid containing an immobile nucleiσ aσid branσhed junction.
2. A composition as claimed in claim 1 further comprising a branched junction from which at least three doublehelices emanate.
3. A σomposition as σlaimed in σlaim 2 further σomprising a branσhed junσtion from whiσh three to eight doubleheliσes emanate.
4. A σomposition as σlaimed in σlaim 3 further σomprising periodiσ or nonperiodiσ networks of branσhed junσtions whiσh at least form a substantially twodimensional struσture.
5. A σomposition as claimed in claim 4 wherein the networks are substantially threedimensional structures.
6. A composition as claimed in. claim 3 * further comprising a branched junσtion from whiσh four doubleheliσes emanate.
7. A σomposition as σlaimed in σlaim 6 σomprising four hexadeσanuσleotides.
8. A σomposition as σlaimed in σlaim 6 σomprising four dodeσanuσleotides. OMPI .
9. A composition as σlaimed in σlaim 2 wherein at least a portion of the doubleheliσes emanating from the junctions contain sticky ends.
10. A σomposition as σlaimed in σlaim 2 wherein at least a portion of the doubleheliσes emanating from the junσtions σontains blunt ends.
11. A σomposition σomprising synthetiσ nuσleiσ aσids σontaining a semimobile nuσleiσ aσid branσhed junction.
12. A composition as claimed in claim 11 further comprising a junσtion from whiσh at least three doubleheliσes emanate.
13. A σomposition as σlaimed in σlaim 12 further σomprising a branσhed junσtion from which three to eight doublehelices emanate.
14. A composition as σlaimed in σlaim 13 further σomprising periodiσ or nonperiodiσ networks of branσhed junσtions whiσh form substantially two dimensional struσtures.
15. A σomposition as σlaimed in σlaim 14 wherein the networks are substantially three dimensional.
16. A σomposition as σlaimed in σlaim 13 further σomprising a branσhed junσtion from whiσh four doubleheliσes emanate.
17. A σomposition as σlaimed in σlaim 13 σomprising four hexadeσanuσleotides.
18. A σomposition as σlaimed in σlaim 13 σomprising four dodeσanuσleotides.
19. A σomposition as σlaimed in σlaim 12 wherein at least a portion of the doubleheliσes emanating from the junσtions σontain stiσky ends.
20. *.
21. A σomposition as σlaimed in σlaim 12 wherein at least a portion of the doubleheliσes emanating from the junσtion σontain blunt ends.
22. A σomposition as σlaimed in σlaim 2 further σomprising a geometriσ nuσleiσ aσid network containing any other σhemiσal speσies bound in a speσifiσ or a nonspeσifiσ manner to an immobile nuσleiσ aσid branσhed junσtion struσture.
23. A composition as claimed in claim 12 further comprising a geometric nuσleiσ aσid network f σontaining any other σhemiσal speσies bound in a speσifiσ or nonspeσifiσ manner to a semimobile nuσleiσ aσid branσhed struσture.
24. A σomposition as σlaimed in σlaim 2 further σomprising a geometriσ nuσleiσ aσid network containing any other che iσal speσies bound in a specific or a nonspecific manner to a single or double stranded nucleiσ aσid struσture emanating from an immobile nuσleiσ aσid branσhed junσtion struσture.
25. A σomposition as σlaimed in σlaim 12 further σomprising a geometriσ nuσleiσ aσid network σontaining any other σhemiσal speσies bound in a speσifiσ or a nonspeσifiσ manner to a single or double stranded nuσleiσ aσid structure emanating from a semimobile nucleiσ aσid branσhed junσtion struσture.
26. A σomposition as σlaimed in σlaim 2 further σomprising a branσhed junσtion from whiσh at least three doubleheliσes emanate and two strands of at least one double helix are σovalently σonneσted to eaσh other at the end distal to the junσtion.
27. A σomposition as σlaimed in σlaim 12 further σomprising a branσhed junσtion from whiσh at least three doubleheliσes emanate and two strands of at least one double helix are σovalently σonneσted to eaσh other at tl\e end distal to the junσtion.
28. The method of making a σomposition σomprising a synthetiσ nuσleiσ aσid σontaining an immobile or semimobile branσhed junσtion, whiσh method * σomprises seleσting at least three double strands of nuσleiσ aσid whiσh possess minimal sequenσe symmetry with each other, dissolving said strands in a buffer at pH 6 to 9 and at a temperature from 0° to 60°C, and separating the composition containing an immobile or semimobile branched junction from said solution.
Description:
NUCLEIC ACID BRANCHED JUNCTIONS WITH PRECISELY DEFINED MIGRATIONAL MOBILITY

This application is a continuation-in-part of application Serial No. 519,928 filed August 3, 1983.

This invention relates to a new composition of matter comprising a polynucleotide containing at least one immobile or semi-mobile branched junction, and to the method of making it.

Background Art Naturally occurring oligomeriσ nucleic acids form mobile linear duplexes stabilized by hydrogen bonds between bases. Polymeric nucleic acids occasionally branch to form junction structures in nature, as shown in Figs. 1 and 1A of the drawings. These branched duplexes are unstable, and resolve to form two independent duplexes. The pre-eminent structural characteristic of stable double helical nucleic acids in nature is that the positions of all atoms in the molecule bear a well-defined relationship to a linear (although not necessarily straight) axis which exhibits no junctions (branch points). Nevertheless, conformational variability (Kim, S.H.,

Berman, H.M. , Seeman, N.C. and Newton, M.O., Acta Cryst b29, 703-710 (1973)), and backbone flexibility (Sarma, R.H., Nature London, 263, 567-572 (1976)) permit the formation of junctions which are crucial to the biological role played by nucleic acids. A replicational junction, diagram in Figure 1A is implicit in the original proposal of Watson and Crick, Nature London, 171, 737-8 (1953) for the mechanism of DNA replication. The holiday structure indicated in

Figure 1, Genet Res. 5, 282-304 (1964) is a critical intermediate in genetic recombination (Broker, T. and Lehman, I.R., J. Mol. Biol. 60, 131-149 (1971)). In addition the Platt, J.R., (Proc. Nat. Acad. Sci. (USA) 41, 181-183 (1955)) and Gierer, A., (Nature London 212, 1460-1461 (1966)) cruciform structures, closely related to the holiday structure, may play an important role in the regulation of gene expression (Gellert, M. , Mizuuchi, K., O'Dean, J.H. Ohmo , H. and Tomizawa, J-. , Cold Spring Harbor Sy p. Quant Biol. 43, 35-40

(1978)). Other types of junction structures are involved as intermediates in single-strand-displacement recombination and as transcriptional intermediates, . such as that shown in Fig. 1A. Heretofore, it has not been possible to study the structural and dynamic properties of these junctions in oligonucleotide model systems, where the junction will contribute a significant signal. This is due to the existence of sequence symmetry as illustrated in Figures 1 and 1A of the drawings. The strands there shown are unlikely to form junction structures in preference to double helices; if they did occasionally combine to form such structures, the process of branch point migration, shown in Fig. 1 will result in the rapid resolution of the junction structures into double helices (Thompson, B.J. Camien, M.N., and Warner, R.C., Proc. Nat. Acad. Sci. (USA) 73, 2299-2303 (1976)).

Disclosure of Invention The synthetic oligomeriσ nucleic acids of this invention are so constructed as to form igrationally ^ immobile or semi-mobile branched junctions. These new stable oligomeric structures, stabilized by maximizing Watson-Crick base pairing, minimize the sequence

symmetry found in their unstable analogs in living systems. The synthetic oligonuσleotide sequences of the compositions of this invention contain migrationally immobile and/or semi-mobile junction structures. In a semi-mobile junction a limited degree of configurational degeneracy is introduced into the system. These DNA junctions represent nexi, from which 3 to 8 double helices may emanate. Each junction of these compositions may be treated as a macromolecular "valence cluster" containing individual clusters which may be linked together directly, or with segments of linear DNA interspersed between them. The covalently linked compositions can be formed with a high degree of specificity, using the state-of-the-art sticky-ended ligation techniques currently employed in genetic engineering. The covalently joined three-dimensional new networks of nucleic acids containing immobile or semi-mobile junctions are periodic in connectivity and may also be periodic in space, thereby generating quasi- crystalline arrays of matter. All compositions are described herein in terms of DNA, but they also include RNA, RNA-DNA-Hybrids or nucleic acids in which the backbones or bases have been modified, but not so as to affect their pairing capabilities, via Watson-Crick or some other form of association. The junctions are then formed simply by dissolving the selected sequences in the desired proportions in a suitable liquid solvent, preferably an aqueous buffer, at a temperature from about 0° to about 60°C, usually at 20°-40°C, and at pH 6-9 and in the presence of a counterion. In the drawings.

Fig. 1 is a schematic representation of a portion of a polymeric nucleic acid containing an unstable, mobile junction as it occurs in nature;

Fig. 1A is a schematic representation of a replicational junction;

Fig. 2 is a schematic representation of a synthetic oligomeric nucleic acid containing ' an immobile junction which is one embodiment of the invention; Fig. 3 is a view of a stained gel chromatogram sheet containing the composition of Fig. 2 in lane K;

__Fig. 4 is a view of a stained gel chromatogram sheet containing the composition of Fig. 2 in lanes A to E, inclusive; - Fig. 5 is a graph showing ultraviolet absorption of the composition of Fig. 2, and of strands 1 and 2 and.of strand 3, at varying temperatures;

Fig. 6 is a flow chart showing the steps for optimizing sequences of synthetic oligomeric nucleic acid strands for making compositions of the present invention; Fig. 7 illustrates an odometer analogy to an algorithm used in the optimizing procedure of Fig. 6; Fig. 8 is a schematic representation of a composition which is a second embodiment of the invention;

Fig. 9 is a view of an autora iogram of a gel σhromatographic sheet containing the composition of Fig. 8 in lanes G and H;

Fig. 10 is a schematic representation of compositions of the invention containing immobile junctions of Rank 3 to 6;

Fig. 11 is a view of an autoradiogram of a gel chromatogram containing varying amounts of the composition of Fig. 8 in lanes B-E and in lanes G-J respectively; Fig. 12 is a schematic representation of a composition according to the invention containing a plurality of immobile junctions interconnected to form a lattice or network;

Fig. 13 is a schematic representation of a composition according to the invention containing a semi-mobile junction which is capable of existing in only the two interchangeable or isomeric forms shown;

Fig. 14 is a schematic representation of a composition according to the invention containing a Rank 3 immobile junction and of a composition containing a plurality of such junctions interconnected to form a lattice or network; and

Fig. 15A shows a portion of the NMR spectrum of the composition of Fig. 14; Fig. 15B shows the corresponding portion of the. NMR spectrum of a single strand of the composition of Fig. 14. The construction of new immobile ' junction compositions of this invention requires the ability to identify and select unique sets of sequences possessing conventional Watson-Crick base pairing patterns while at the same time minimizing sequence symmetry. Sequences containing long sequences of base pairs can be formed at higher temperatures, up to about 60°C or even higher. The probability of forming a desired junction is a function of the free energy of association of the individual strands involved. For design purposes, each strand which is chosen to

participate in the formation of an immobile or semi-mobile junction can be considered to be composed of a series of overlapping segments of a given criterion length, Nc. For example, each hexadecameric strand in the immobile junction shown in Figure 2 is a series of 13 overlapping segments of length 4. Each of these segments is termed a "criton", while the complement to a criton, i.e. the sequence of bases with which it pairs, is termed its "anti-criton". Watson-Crick pairing arrangements which compete with the desired pairing must be considered from a thermodynamic point of view for lengths less than Nc. However, if the rules indicated below for minimizing continuous lengths of sequence symmetry are obeyed, there will " be no competing Watson-Crick pairing interactions for segments of length Nc or longer. Two further terms must be defined to facilitate this discussion. A "bend" is a phosphodiester linkage which is flanked by bases paired to different strands. The "rank" of a junction is the number of the double helices which directly abut it. Thus, the junction shown in Figure 14 is of Rank 3, while those shown in Figures 2 and 8 are of Rank 4.

In order to have the new compositions of matter of this invention, i.e. uniquely paired stable structures with non-migratory junctions (for length Nc or greater), the following rules must be obeyed within the pairing regions prescribed by the architecture of a given junction. 1. Every criton in the individual strands forming the junction must be unique throughout all -strands, regardless of frame.

2. The anti-σriton to any criton which spans a bend in a strand must not be present in any strand, in any ' reading frame.

3. Self-complementary σritons are not permitted. if Nc is an odd number, this injunction holds for all σritons of size (Nc + 1).

4. The same base pair can only abut the junction twice. If it is present twice, those two occurrences must be on adjacent arms. The first three rules ensure immobility through lack of homology, except for Nσ-1 base pairs on each arm-belonging to the criton nearest the junction. The fourth restriction eliminates migratory possibilities for these bases; it should be applied sequentially " to each base pair in the criton, and perhaps beyond. The fourth rule also limits the maximum rank of junctions: Since there are only four base pairs*, A-T, T-A, G-C, C-G, and since each pair can only appear twice, junctions of rank greater than eight are not possible with the conventional bases.

These rules are limited to those cases in which Nc is less than the minimum length for stable <* stem-loop structures. In the unlikely event that this is not the case, further restrictions would be necessary to forbid those σritons capable of forming stem-loop struσtures from spanning the bends whiσh flank the junctions. Similarly, if one of the strands is not continuous at the junction, as in replication forks, the base pairs on either side of the break must be different, to avoid the sort of migration observed by Nilsen, T. and Baglioni, C. (J. Mol. Biol. 133,

319-338 (1979)). Nc is a number to be minimized, since this minimizes the strengths of σompeting interaσtion

" URE-

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by shortening the lengths involved. The most likely reason for inσreasing Nσ is that the desired junσtion cannot be generated by the 4 Nc critons available for a given value of Nσ. For example, the σonstraints applied to the generation of the immobile junσtion in Figure 2 are inσompatible with a value of Nσ less than 4.

It is easy to generate a junσtion in whiσh the limited amount of mobility is non-zero, i.e., a semi-mobile junσtion, suσh as the one shown in

Figure 13. In order to do this, the mobile bases and the phosphates which flank them must be considered part of the bend; thus, the base pairs whiσh flank the mobile bases are " now σonsidered to abut the junσtion. Once this modifiσation of the σonσept of a bend is in effeσt, the same four rules apply. Clearly, it is not possible to have more than Nσ-2 bases sinσe bends will not be properly spanned if this is not so. This junction may undergo the reactions indicated, but may not go beyond them and resolve into two linear duplexes. Thus, it constitutes a simple flip-flop. The rules of migration are satisfied for the two states shown, but the rules for non-migration come into play for any further migratory events in either direction. A FORTRAN σomputer program is desσribed hereafter whiσh generates sequenσes that fulfill these σriteria for junσtions of any design by a rapid algorithm. The program also ranks generated sequenσes on the basis of pairing fidelity relative to σompeting interaσtions at lengths shorter than Nc. The details of the algorithm and the way in which free energy considerations are taken into account for competing Watson-Crick pairing interactions (at lengths shorter

than Nσ) will be disσussed elsewhere in this desσription.

Junσtions and Networks The ability to σonstruσt junσtions of rank N (N=3, 4, 5, 6, 7, 8) makes it possible to σonstruσt highly speσifiσ geometriσal figures in whiσh suσh junσtions correspond to the vertices, while stretches of linear duplex nuσleiσ aσid correspond to the edges. These include individual polygons and polyhedra, as well as infinite N-conneσted networks and polyhedra

Wells, A.F., (Three Dimensional Networks and Polyhedra , John Wiley & Sons, New York (1977)) of double heliσal nuσleiσ aσids in two or three dimensions. These networks may be periodiσ or non-periodiσ. Examples of 3, " 4, 5, and ' 6-σonneσted three-dimensional periodiσ networks are shown in Figure 10. This σonstruσtion σan be aσσomplished by using the σonventional stiσky-ended ligation technology. That methodology involves the use of sequences in which the junction σrossroads struσture does not terminate in a "blunt ended" fashion, as shown in Figure 2. Instead, at the free end of eaσh double strand, remote from the junσtion, one strand extends beyond the end of eaσh double helix, so that a single stranded region is dangling off the end. The speσifiσity of double heliσal Watson-Criσk base pairing is then utilized to link up two different pieσes of DNA possessing complementary sticky ends to produσe a σomposition σontaining two or more immobile or semi-mobile junσtions. Among the 2- and 3-dimensional networks whiσh are possible, some are of σourse periodiσ in their σonneσtivity. Suσh networks σan also be periodiσ in spaσe and σan then σomprise unique σrystalline maσropolymers of a size suitable for

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diffraction analysis using x-rays, and perhaps neutrons. An example of such a 2-dimensional network is shown in Figure 12, illustrating formation of a two- dimensional lattice from an immobile junction with sticky ends. A is a sticky end and A' is complementary to it. A similar relationship exists between B and B'. Four of the monomeric junσtions on the left are σomplexed in-parallel orientation to yield the struσture on the right. If the inter-junσtional spaσing is large enough, a ligase would be able to σlose the overlapped gaps to make the σomplex on the right a covalently bonded struσture. Note that the σomplex has maintained open valenσes, so that it σaπ be extended by the addition of more monomers. This procedure is" not limited in theory to rank-4 junσtions, nor is it limited to two dimensions. The relative orientation of suσσessive junσtions is a funσtion of both junσtion struσture and the separation of junσtions, sinσe the σonneσting segments between junσtions are heliσal. By exploiting this faσt it should be possible to σonstruσt 3-dimensional nuσleiσ aσid networks analogous to the networks of Figure 10, wherein the arms are σomposed of double heliσal DNA of defined length and sequenσe, represented by the straight lines.

Overall Strategy For Optimized Junction Sequence Generation

The architeσture of a junσtion requires the speσifiσations of both σovalent σonneσtivity and base pairing relationships. Beσause of the σomplementary nature of the Watson-Criσk double helices which constitute the junction structure, only half of the bases must be treated as independent variables; those

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bases σomplementary to them are treated as dependent variables. Bases are enσoded as numbers on to base 4. In the σase of semi-mobile junσtions only one out of four of the mobile bases is independent. With a σomputer, new sequenσes may be generated simply by the proσess of σounting in base 4. If all of the arms of a junσtion have the same length, it is possible to fix one base at the numeriσal level, thereby decreasing the number of independent variables by one. The independent bases may be ordered by the rapidity of the rates of change of the digits representing their identities within the program. By "order" is meant an inverse measure of the rate at which the digit representing the base is incremented. Thus, the lowest ordered base will be changed on every pass, the next lowest ordered base will σhange on every "fourth pass, the next lowest ordered base on every sixteenth pass, and so on. " The σritons themselves may be ordered aσcording to the lowest ordered base within the criton. The critons are then tested for adherenσe to the rules sequentially, from highest to lowest order. Thus, if a given σriton violates one of the rules, the base σorresponding to the order of that σriton is advanσed, rather than the base of the lowest order.

Until a base at the order of violation has been σhanged, no σhanges at lower orders would σorreσt the existenσe of the violation. When a base of any order is inσremented, those bases of order lower than that of the inσremented base are, of σourse, set to their lowest value.

" This algorithm will be easier to understand if it is noted that the proσedure is analogous to the

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generation of σonfiguration of numbers with defined properties, using an odometer or σrowd σounter, as indiσated in Fig. 7. In that figure, the uniqueness of eaσh digit is the speσifiσ property required for the numeriσal σonfigurations. This property is similar to the properties involved in the σriton rules for junσtion formation. If a program operator starts at the top of the figure, with six zeroes as an initial σonfiguration, and inσrements the most rapidly σhanging digit sequentially, as shown on the left, it will take 12,345 steps to get the first suσσessful numeriσal σonfiguration. On the other hand, if the operator σorreσts the highest ordered digit whiσh is violating the uniqueness rule, that indiσated in the 10,000 's place, and-then proσeeds aσσordingly, as shown on the right, it will take 15 steps to reaσh the same point. The way in whiσh this algorithm is applied to the junσtion generation is indiσated in Figure 6.

The nine logiσal steps in this proσedure are indiσated sσhematically in Fig. 6. The two steps in double boxes must clearly be done by the programmer while the other steps are done automatically by the programs. In the first step, the covalent σonnectivity and desired base pairing are seleσted by the programmer. Speσifiσ σonstraints σan also be introduσed at this stage. In the seσond step, the σritons are ranked by the order of the most rapidly changing base which they σontain. After that, an initial numeriσal sequenσe must be assigned. (Step 3) This numeriσal sequenσe is tested against the junσtion rules (Step 4) and if it fails, a new sequenσe is generated by the fast algorithm. If the numeriσal sequence obeys the rules, its base permutations are the

tested, (step 5) against investigator selected constraints. If any of the eight sequences implied by the numerical procedures are acσeptable, their fidelities are σalσulated. (Step 6), and if these are aσσeptably high, melting σurves are σalσulated and plotted, (step 7). New sequenσes are then generated (step 8) and tested iteratively. until all possibilities have been exhausted. The programmer may then evaluate the alternatives presented by the programs. Onσe the strand sequenσes fulfill the uniqueness and nonmobility rules, thermodynamiσ σriteria-are applied to all sequenσes of length less than Nσ. The first question to σonsider is the pairing fidelity: Is the desired base pairing σonfiguration the most probable σonfiguration in which these particular sequences are to be found in solution? If so, what is its probability relative to other pairing configurations? This problem is treated in a pairwise fashion; the program routinely considers all alternative binary base pairing configurations for lengths less than Nc. The stability of an olignucleotide duplex depends on its σhain length,

•r sequenσe and σoncentration, as well as on environmental variables, suσh as pH, ioniσ strength and temperature. Data on the relative stabilities of oligoribonuσleiσ aσids in σonditions equivalent to 1 M NσCl, ρH7, have been aσσumulated by Tinoσo and his σo-workers. The effeσts of sequenσe σan be evaluated in terms of units representing adjaσent sets of two base pairs; the equilibrium σonstants σorresponding to the association within each unit are available, as is the nucleation σonstant " for initial strand interaσtion. This is denoted by β , with units M~ . A given sequenσe will

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then be paired with its σomplement by a weighting faσtor that depends on the produσt of a set of numbers:

K AB = SK 1 K 2 K 3 * " • K N-1' (1)

where N is the σhain length of σomplementary sequenσes between σhains A and B, and is the nuσleation σonstant.

The values of the K. are tabulated at 25°C by Borer et al. as:

K i = exp ( - Δ G i /RT) . To illustrate the use of equation (1) , σonsider the RNA tetramer (5 1 ) AGCϋ (3 1 )

(3') UCGA (5 « ) to be deσomposed into the three subunit "pairs",

(5') AG GC CU (3')

(3 1 ) UC CG Gϋ (5 « )

eaσh of whiσh has an approximate equilibrium σonstant assigned.

In this way, the maximum σonσentration of paired moleσules of a duplex or arbitrary sequenσe σan be prediσted. The situation for oligodeoxynuσleotides is less σompletely defined than for oligoribo- nuσleotides. However, thermodynamiσ data are available from whiσh primitive sets of Kl. ,s σan be σreated, together with rough values of the ΔH°l. ,s. Despite the unσertainties, these data m *a•ke it possible to estimate the relative σontr ibutions of different

sequenσes with reasonable aσσuraσy, particularly if appropriately scaled values from oligoribonucleotides are used. For sσaling- we alter the ΔG° values of Borer et al., so as to lower the stability of the σorresponding oligodeoxynuσleotide by 20°-45°C relative to the oligoribonuσleotide. Comparison of the values of K A „ for eaσh set of interaσtions below the σriton length then permits one to estimate the relative σontributions of the base pairing in eaσh σase. Junσtions of maximum fideltiy will be those that contain sub-σriton pairing sequences of minimal stability, relative to the stability of the complete arms. Ail binary Watson-Crick alternatives are cheσked by the program, and their stabilities are σompared with those σalσulated for the double heiσes σhosen for the arσhiteσture of the junσtion. The highest probability junσtions above a seleσted fidelity minimum are retained for further proσessing. It should be pointed out that fidelity is a funσtion of temperature. Thus, sequenσes must be σompared for relative fidelity at a standard temperature, for whiσh we use 25°C.

The information contained in the estimated „ equilibrium constants for pairing specific sequences can be used to predict approximate thermal transition profiles for junctions. In order to do this, enthalpy values, ΔH.° corresponding to the equilibrium constants K., used to assess fidelity, are required. These are considerably less certain for oligodeoxy- nuσleotides than for oligoribonuσleotides, but nonetheless reasonable estimates are available, and missing values σan be filled in by sσaling the σorresponding RNA data, as desσribed. In the σase of pairing between sequenσes on twδ non-identiσal strands.

A and B, the value of K^ and the starting σonσentrations of the two speσies uniquely σharaσterizes the equilibrium; for starting σonσentrations, C. and C B (moles per liter).

'AB (2) M =

^ " ^ 'AB' (C -B3 - C 'A-3 } '

We have disσussed how to approximate K,„; thus, C AB σan be σalσulated. This σan be done .at any temperature if the _H.° for eaσh K. is known.

Consider next the interaσtion of four oligomers. A, B, C, and D, whiσh σontains uniquely σomplementing half sequences that can lead to formation of a 4th rank junction complex. Since at equilibrium the conσentrations must be independent of the reaσtion pathway, it is suffiσient to σalσulate the junσtion σonσentration resulting from any one pathway. For example, one might seleσt:

A + B = AB (i)

C + D = CD (ii)

AB + CD = ABCD (iii)

From the values of K,_, K_,_, and

AB CD introduσing a new factor, σ _ to describe the statistical weight of the central junction "loop" structure of rank R, then conσentrations of junσtions σan be expressed in terms of known quantities. That is, C^ and C c _ σan be σalσulated by solving equation (2) , and these values σan be introduσed into reaσtion (iii) above to give:

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C A3CD

' "" YBCD

(C A3 " C AECD ) (C CD " C λBCD }

The value of K ABC _ is estimated as :

,-1

**BCD β β "V ϊC ∑W + K EC + K DA )

This is very nearly equal to S~ σ K_ A , sinσe σ _ j is not expeσted to be very different from unity, while the K's are large at low temperature. It is possible that if σ R is muσh less than 8, only negligible σonσentrations of the complete junction will be detectable, as discussed more fully below. If a junction entails no strain, we anticipate that only a simple Jacobson-Stock ayer term (Jacobson, H. and Stoσkmayer, W. (J.Chem.Phys. 18, 1600-1606- (1950)) is involved:

°R = σ o < R > "a<

where the faσtor σ refleσts the diffiσulty of forming the junσtion and the exponent a (1.5 < a < 2) is a measure of the exσluded volume.

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Conσentrations of the ternary and higher (for R > 4) intermediates σan be σalσulated, using stepwise paths suσh as:

AB + C = ABC, ABC + D = ABCD.

Thus, the equilibrium σonσentration of eaσh intermediate, as well as the junction itself can be calσulated; a series of relations exists among these intermediate of the form:

C AB + C BC = C ABC + C B'

whiσh simplifies the problem σonsiderably for this approximate treatment.

In eaσh of the examples set forth below oligodeoxynuσleotide strands synthesized from appropriately bloσked nuσleotides or dinuσleotides by standard σhemiσal procedures are placed in a glass or plastiσ vessel at room temperature in a solvent σontaining (1) a buffer system σapable of regulating pH between pH6 and pH9, so as to favor Watson-Criσk base-base hydrogen bonding and (2) a sourσe of σounterions in order to reduσe the eleσtrostatic repulsion among the strands as they form a ternary, quaternary (or higher) junction or complex. Suitable buffers include phosphate, caσodylate, tris, etc. at conσentrations from 0.001 to 1.0 M approximately. In the absenσe of buffer, the pH σan be regulated by direct titration to yield an end-point in the above range; the pH so obtained is less stable to temperature and eleσtrophoresis.

'

Satisfaσtory σounterions have been found experimentally to be (a) 1-2 molar NaCl, KCl, CsCl or any non-destabilizing monovalent neutral salt including a 2 S0 4 , K 2 S0 4 , Cs 2 S0 4 , (b) 5-10 mM Mg 2 Cl, Ca-Cl or comparable divalent neutral salt or (c) 1-5 mM spermine, spermidine or other neutral alkyl diamines NH-+-R-NH-+ or (d) σombinations of the above agents. Laσk of suitable counterions destabilize the junctions selectively relative to simpler structures (dimers, e.g.) .

Complex or junction formation can be shown to occur at temperatures below about 40°C (see the denaturat on profile monitored by ultraviolet absorbance in Fig. 5). The junctions or complexes are stable below 0°C also. As desσribed in the examples experimental σriteria for existenσe of a stable base paired σomplex or junction include:

(1) hypochromiσity of the strong ( ^ 260nm) ultraviolet absorbanσe of the bases;

(2) enhanσed σirσular diσhroism of the bases in a by duplex or higher complex;

(3) charaσteristiσ eleσtrophoretiσ mobility and

Ferguson behavior of the complex;

(4) existenσe of new proton NMR resonances corresponding to hydrogen bonds at the junction center.

Each has been applied to monitor the behavior of the σomplex shown in Fig. 2.

Example 1 The four blunt-ended oligomeriσ heliσal strands of DNA designated in Fig. 2 were seleσted by means of the rules and algorithm desσribed above, then were synthesized by σonventional phosphotriester teσhnique on a σommerσially available synthesizer from appropriately bloσked nuσleotides or dinuσleotides.

Note the laσk of symmetry around the σenter of Fig. 2., so that migration is not possible without disrupting pairing. This sequenσe also σontains no repeating GpG sequenσe longer than two, in order to restriσt..-the possibility of GG non-Watson-Criσk pairing as well. These sequenσes were lyophilized, and equal weights of the four strands were then dissolved to form a 2 mM solution in an aqueous buffer (50 mM phosphate or tris pH 7; 10 mM MgCl 2 ) at room temperature, whereupon the immobile junσtion of Fig. 1 formed spontaneously. The buffer solution was subjeσted to eleσtrophoresis on polyaσrylamide gel (10-15% acrylamide) along with solutions of other materials in separate lanes which provided mobility references. The chromatogram was stained with a σonventional dye (stains-All, Kodak) whiσh σolors single as well as double stranded nucleiσ aσids; the results were as shown in Fig. 3, in whiσh lane K σontained the desired σomposition having an immobile junσtion as shown in Fig. 2.

In preparing the σhro atogram, eaσh of the other wells or lanes σontained other materials to provide mobility referenσes only. Lanes a, b and 1 σontained restriσtion digests of PhiX-174-RF-DNA; a is the Hinf I digest, b is the Hae III digest and 1 is the Hinσ II digest. The lowest oleσular weight fragments

in these digests are: 42,48,66 and 82

(Hinf I) , 72 and 118 (Hae III) and 79 and 162

(Hinσ II). Lanes σ-f σontained strands 1, 2, 3 and 4 respeσtively. Lane g contained an equimolar mixture (based on extinction coeffiσients derived from dry weights) of strands 1, 2, and 3; lane h, strands 1, 2, and 4; lane i, strands 1, 3, and 4; and lane j, strands 2, 3, and 4. Lane k σontained an equimolar mix of strands 1, 2, 3 and 4. Lane m to r σontained equimolar mixtures of pairs of strands: m σontains 1 and 2, n 3 and 4, o 1 and 4, p 2 and 3, q 1 and 3, and r 2 and 4.

.Lane k of Fig. 3, σontaining an equimolar mixture of all four strands shown in Figure 2, -travels as a single band with a mobility lower than any of the other oligomeriσ mixtures to be seen on this gel. The highest mobility band in this digest σorresponds to a linear duplex DNA moleσule σontaining 79 base pairs. The mobility of the band in lane K, σontaining the - desired immobile junσtion σontaining 32 base pairs, σorresponds to a linear DNA duplex of 44 base pairs, measured against standards not shown here. The presenσe of a single band with appreσiable mobility in lane K σontaining the tetrameriσ σomplex or junσtion indiσates that a moleσular species with all four strands is present.

In addition, as shown in Fig. 4, electrophoresis of mixtures σontaining different ratios of two σomponents was σarried out; σomponent (i) σonsisted of an equimolar mixture of strands, 1, 2 and 4 of Fig. 2 while σomponent (ii) σonsisted of strand 3 alone, each in a different aliquot of the same buffer. Lanes G to J contained 8 micrograms of free strands 4, 3, 2 and 1, respeσtively. Lane F σontained 6

miσrograms of σomponent (i). Lanes A to E eaσh σontained 6 miσrograms of (i) , and in addition, 0.5 miσrograms (E) , 1.0 miσrograms (D) , 2.0 miσrograms (C) , 3.0 miσrograms (B) , and 4.0 miσrograms (A) of σomponent (ii). The resulting σhromatogram, after staining, is shown in Fig. 4. Eaσh of lanes A to E σontained, in varying amount, a σomposition σontaining the immobile junσtion of Fig. 2.

It σan be seen from lanes A through Ξ in Figure 4 that the intensity of σomponent (i) varies with the ratio of (ii) to (i) . It appears that σomponent. (i) is being σhased into the higher bands as more of (ii) is added. The simplest explanation for this is that a 1:1 σomplex between (i) and (ii) is being formed.

Three buffer solutions were also prepared, the first σontaining an equimolar mixture of strands 1, 2, 3 and 4 of Fig. 2 (25 M per strand) , the seσond σontaining an equimolar mixture of strands 1 and 2 (49 M per strand) ,. and the third σontaining strand 3 (98 M), and the ultraviolet absorbanσe of all three was measured at 260 nm over a range of temperatures, and the result expressed as ΔA 260 = ^ A 260 ^ /A 260 (10°C)-1). The resulting thermal transition profiles are shown in Fig. 5. Typical Δ A 260 for high molecular weight DNA duplexes approaches 30%. Actual values depend on base σomposition, length and solvent. Strand 3 alone exhibited a typiσal non-σooperative transition σharaσteristiσ of nucleic acids in the absence of base pairing. The fact that the final Δ 2g0 for the four-fold complex containing the immobile junction is roughly equivalent to twice that (per mole strand) of the individual pairs suggests that

the pairwise arms of the four-fold σomplex form additional struσture of about equal extent.

These thermal denaturation results are a measure of relative stability of the different σomplexes of strands 1 to 4. Base paired nuσleiσ aσid duplexes are hypoσhromiσ (absorb less) , relative to single strands or a mixture of their σonstituent mononuσleotides, at wave lengths near 260 nm. From the inσreased hypoσhro ism in the mixture of all four strands, it is σonσluded that approximately twiσe as muσh pairing pσσurs in this mixture as oσσurs in the same σonσentrations of the pair 1 + 2. The results of these speσtrophotometriσ experiments demonstrate that the oligonuσleotides assoσiate pairwise when mixed in that fashion ? the form of assoσiation is σlearly base pairing, as indiσated by the magnitude and σooperatively of the hypoσhromism upon melting. Furthermore, it is σoncluded from the uniphasic melt of the tetrameric σomplex that a junσtion has indeed formed as in faσt was prediσted from the sequenσe seleσtion algorithm, indicating that the base pairing associated with the formation of the junσtion has indeed oσσurred. The σomposition σontaining the immobile junσtion of Fig. 2 was obtained in solid crystalline form by cooling to 4°C, a buffer solution containing 1 mM of each of strands 1 to 4. The crystals were separated from the solution by filtration, and were found to melt as the temperature approached 40°C.

Example 2 The four dodecanuσleotides depiσted in Fig. 8 were designed by the use of the sequenσe symmetry minimization rules, supplemented by equilibrium

distribution optimization as explained above. Note the lack of symmetry around the center so that migration is not possible. These sequences also contain no repeating GpG sequence longer than two, in order to minimize competition from this form of non-Watson-Crick pairing as well. These sequences were synthesized by σonventional phosphotriester techniques.

The four strands were then end-labelled with P radioaσtive phosphate at the 5' terminus. Solutions σontaining individual labelled strands as well as mixtures were then subjeσted to eleσtrophoresis in separate lanes on polyaσrylamide gel, as follows, eaσh well σontaining 2.0 Vg of eaσh strand. Lanes A-D σontain strands 1, 2, 3 and 4, respeσtively. Lane E σontains an equimolar mixture (based on extinσtion coefficients derived from dry weights) of strands 1 and 4; lane F contains a similar mixture of strands 2 and 3. Lanes G and H each contain equimolar mixtures of strands 1, 2, 3, and 4. An autoradiogram was then made from the resulting chromatogram, as shown in Fig. 9. The composition σontaining the immobile junσtion of Fig. 8 appeared in lanes G and H and travelled as a single band with a mobility lower than that of any of strands or mixtures of the other lanes.

In interpreting Figure 9, it should be emphasized that the sequenσe optimization proσedures desσribed above are designed to make the junσtion the preferred struσture when all four strands are present. Thus, the laσk of self-assoσiation for individual strands has not been an expliσit criterion, except insofar as it detracts from the formation of the actual junction. Strand 4 aggregates rather strongly (lane

D) , but no band σorresponding to the mobility of strand 4 alone results when strand 4 is mixed with equimolar quantities of strands 1, 2 & 3 (Lanes G & H) . The mobility of the slowest band in lanes G and H σorresponds to a linear DNA duplex of 30 base pairs based on σalibration with xylene σyanol FF.

The presenσe of a single band with appreσiable mobility in the lane σorresponding to the tetrameriσ σomplex indiσates that a moleσular speσies with a well-defined stoichiometry predominates. Clearly, some dissociation of the complex ocσurs as well, in σontrast to the situation with a larger junσtion involving hexadeσanuσleotides. Higher unσlosed σomplexes (1:2:3:4:1:2:3:4:1...) do not represent a signifiσant fraction of -the total material present.

Additional solutions containing varying quantities of the labelled and unl-abelled dodecanuσleotide strands of Fig. 8 in various σombinations were subjeσted to eleσtrophoresis on polyaσryla ide gels, with the results shown in the autoradiogram of Fig. 11, as follows. It shows the stoiσhiometry of the σomplex; more speσifically, it shows that radioaσtively labelled ternary σomplexes are σhased into immobile junσtion bands by the addition of the appropriately σomplementary σold (unlabelled) missing σomponent. Lanes A-E represent an experiment in which the only radioactive material was strands 2, 3, and 4, each of which was present in 0.6 Ug quantities. Unlabelled strand 1 was present, respectively, in quantities of 0 (A), 0.15 Ug, (B) 0.3 g. (C) 0.6 g, (D) 1.2 Ug (E) . The counts in the top (junction) band are maximized in lane D, indicating 1:1:1:1 stoichiometry.

Lanes F-J represent a similar experiment in whiσh the unlabelled strand was strand 4. Labelled strands 1, 2, and 3 were eaσh present in 0.6 μg quantities in eaσh of lanes F-J. Unlabelled strand 4 was present in quantities of: 0 (F) , 0.15 μg (G) , 0.3 Ug (H) , 0.6 Ug (I) and 1.2 μg (J) . Again, the junction band saturates at 1:1:1:1 stoichiometry, corresponding to lane I.

Example 3 T three strands shown in the upper part of

Fig. 14 of the drawing were designed in aσσordanσe with the rules, and algorithm set forth above and were synthesized by σonventional phosphotriester technique. The vertical-appearing strand (containing 18 residues) W as synthesized with blunt ends, while the ones at lower left (containing 20 residues) and at lower right (containing 22 residues) were synthesized each with a sticky end, as shown. The strand at l„ower left (20 residues) was end-labelled by enzymatiσ kinase reaσtion with T4 polynuσleotide kinase enzyme using gamma P labelled ATP.

Eaσh of the three strands was dissolved in the * same speσimen of buffer (tris pH7 with 16 mM MgCl 2 ) to a σonσentration of 1 mM to form a σomposition σontaining the immobile junσtion shown in the upper part of Fig. 14 and exposed to DNA ligase, a joining enzyme, for 24 hours at room temperature, using a large exσess of the enzyme and ATP, its σofaσtor. Subsequently, the reaσtion was stopped, the mix was extraσted with phenol, bubbled with ether to remove the phenol, and dried by lyophilization to form a solid.

.When subjeσted to eleσtrophoresis in buffer, a speσimen of this σomposition exhibited several

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different bands, of whiσh those appearing as 4 and 6 multiplets of the single 20 residue band were very prominent. When the composition was subjected to digestion with the exonuclease enzyme, exo III, which catalyzes hydrolysis of linear polynucleotides stepwise from their free ends, and the solution subsequently was eleσtrophoresed on 10% polyaσrylamide gel, only the two bands at the positions of the 4- and 6-multiplets remained, showing that the σomposition was in part in the form of the 6-multiρlet hexagonal or circular unit structure or geometric network shown in the lower portion of Fig. 14, with the 20 er str-and running along the inside of the hexagon being σovalently joined; the remainder of the σomposition was in the form of a 4-multiplet square (or σircular) unit structure or geometrical network.

The NMR spectrum (low field region of 600 MH Η NMR spectrum of 2 mM solution) of another specimen of the lyophilized composition containing the three strands shown in Fig. 14 was determined, as shown in Fig. 15A. The extremely broad line widths are σharaσteristiσ of linear duplex DNA of σhain lengths in exσess of 260 base pairs, indiσating hydrogen bonding of the stiσky ends to form larger σomplexes σontaining a number of the immobile junσtions in a geometriσ network. In σontrast, the NMR speσtru of a single strand DNA σomposition, shown in Fig. 15B, exhibits σharaσteristiσally sharp lines.

Unlabelled speσimens of the σomposition σan be obtained by following the same procedure, using the autoradiogram as a guide to the location of the desired composition after electrophoresis.

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Compositions having other similar unit struσtures σan be made σontaining other immobile or semi-mobile junσtions of rank 3 to 8 using strands having either a single stiσky end or two stiσky ends. Industrial Appliσability

The first utility is that these σompositions σontaining mobile or semi-mobile nuσleiσ aσid junσtions may be used as vertiσes of n-σonnected networks of nucleiσ aσids. That is the fundamental aspeσt about this invention whiσh gives it value. They σan be used to make nuσleiσ aσid struσtures in the form of geometriσal stiσk figures where the stiσks σorrespond to double heliσal nuσleiσ aσids and the vertiσes are nuσleiσ aσid junσtions. The utility of being able to make the geometriσal figures is that this allows one to do moleσular engineering of this sort on the hundred to thousand A sσale. This, in turn, allows one to make various kinds of intriσate figures whiσh may have utility as appropriate surfaσes upon whiσh to σondense σognate mσleσules suσh as the protein depiσted in Figure 11.

The appliσation of translational symmetry to •«• this case allows one to make these figures periodic in space as well as in conneσtivity i.e. to ligate together nuσleiσ. aσids in the same form as is σurrently done with linear DNA in i^ vitro recombinant DNA work. In that σase, DNA from different sourσes is ligated together in a speσifiσ fashion. Using well known stiσky ended ligation teσhniques, one does the same thing and puts together periodiσ N-σonneσted networks of nucleic acids which will if they're periodic in space, σonstitute σrystals. These σan be used for struσtural analysis of nuσleiσ aσids by nuσleiσ

aσid-protein interaσtions and, in σombination with more sophistiσated arσhiteσture involving semi-mobile junσtions, they σan be used as well as to give informaion about nuσleiσ-aσid drug interaσtions. The more sophistiσated appliσation might also be necessary for nucleiσ aσid-protein interaσtions.

Being a periodiσ network of preσise arσhiteσture defined at the moleσular level, it should also be possible to use this σonstruσtion for doing other kinds of moleσular arσhiteσture and engineering on the 100 to thousand angstrom sσale. For example, these lattiσes may be useful as supports for miσro-eleσtroniσs struσtures. Other kinds of intriσate miσrosσopiσ struσture are available, as well: What has been devised here is the equivalent of the polyvalent (3-8) joint in the Tinkertoy TM while what previously existed in ligatable nuσleiσ aσid struσtures was only the stiσk of the Tinkertoy, and a divalent linear σonneσting pieσe. Thus one now has the polyvalent (3-8) σonneσting pieσe and anything that one wishes to make on that saσle, one can, in principle make, simply by exploiting the σombination of the prinσiples of nuσleiσ aσid junσtion formation the constraints of nucleiσ-aσid struσture, the dynamiσs of moleσular arσhiteσture and imagination. Besides periodiσ struσturing intriσate individual structures σan be σonstruσted. These inσlude σlosed σyσliσ polygons, suσh as the hexagon shown at the bottom of Figure 16, as well as open or σlosed polyhedra whose faσes are such polygons.

Another aspect that should be considered is the fact that a periodic structural network of this form would be an appropriate substrate for the investigation of any material, be it nuσleiσ aσid.

-£1JR£

_OMPI fay

something which naturally interacts with nucleiσ aσid, or otherwise. Onσe one has suσh an ordered array, one can use that, with a small amount of molecular engineering as the basis for the construσtion of an appropriate substrate on whiσh any materials σan be σrystalized. For example, a reaσtive "hook" or "hooks" σould be attaσhed to one or more residues within the unit σell to σovalently σapture and identiσally orient the moleσule of σhoiσe. Similarly, divalent antibodies σovalently and/or non-σovalently bound to nuσleiσ aσids or to σognate proteins σould aσσo plish the same goal without using σovalent reaσtions. In this vein, the junσtion lattiσ σan be used as a template for σrystallizing and struσturally σharaσterizing materials that otherwise may not be readily σrystallizable. Thus we σan look at protein folding intermediates or messenger RNA moleσules that perhaps σannot σrystallize at all. A great advantage of using junσtion lattiσes to look at suσh systems is that lattiσe forσes would only affeσt the lattiσe moleσules themselves, and not the moleσules introduσed into the lattiσe for struσtural study. Thus, protein-folding intermediates and long RNA moleσules with readily perturbed tertiary struσtures would be visible struσturally without perturbing them with lattiσe forσes.

A further thing one should consider has to do with the limited mobility junσtion, sometimes referred to as the semi-mobile junσtion. These σomplexes have an intrinsiσ dynamiσ σomponent to them and this intrinsiσ dynamiσ σomponent is a natural σonstant relating to the material. The way in whiσh any environmental or protenially mutageniσ or teratogeniσ substance perturbs that fundamental dynamic constant is

-URi

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in faσt an index of its possible effeσts within the living system. This also σonstitutes another way in whiσh drugs σan be sσreened: the way in whiσh they affeσt the dynamiσs of this system, as well as in the visualization of the statiσ way in which they interact with nuσleiσ aσids or nuσleiσ aσid junσtions in the σrystalline σontext disσussed earlier.

The use of semi-mobile junσtions as potential σomponents of a σomputer memory is apparent beσause a junσtion whiσh has two states, namely flipped or flopped, is obviously a prototype two state device since the equilibrium may be controlled by the supercoiling state of two arms, it is σlearly possible these semi-mobile junσtions σan therefore be used to store information in bit-wise fashion.

What is σlaimed is:

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