Search

We study the eigenvalues of the unique connected anti-regular graph $A_n$. Using Chebyshev polynomials of the second kind, we obtain a trigonometric equation whose roots are the eigenvalues and perform elementary analysis to obtain an almost complete characterization of the eigenvalues. In particular, we show that the interval $\Omega=[\tfrac{-1-\sqrt{2}}{2}, \tfrac{-1+\sqrt{2}}{2}]$ contains only the trivial eigenvalues $\lambda = -1$ or $\lambda=0$, and any closed interval strictly larger than $\Omega$ will contain eigenvalues of $A_n$ for all $n$ sufficiently large. We also obtain bounds for the maximum and minimum eigenvalues, and for all other eigenvalues we obtain interval bounds that improve as $n$ increases. Moreover, our approach reveals a more complete picture of the bipartite character of the eigenvalues of $A_n$, namely, as $n$ increases the eigenvalues are (approximately) symmetric about the number $-\tfrac{1}{2}$. We also obtain an asymptotic distribution of the eigenvalues as $n\rightarrow\infty$. Finally, the relationship between the eigenvalues of $A_n$ and the eigenvalues of a general threshold graph is discussed., Comment: 20 pages, 6 figures, 1 table

Hematopoietic prostaglandin D synthase (HPGDS) is primarly expressed in mast cells, antigen-presenting cells, and Th-2 cells. HPGDS converts PGH2 into PGD2, a mediator thought to play a pivotal role in airway allergy and inflammatory processes. In this letter, we report the discovery of an orally potent and selective inhibitor of HPGDS that reduces the antigen-induced response in allergic sheep.

[reaction: see text] A general demonstration of orthogonal selectivity of the Liebeskind-Srogl cross-coupling protocol compared to the Suzuki-Miyaura and Stille variants is reported.

Hairpin loops are ubiquitous structures found in folded RNA and DNA sequences in nature. Recent reports have noted special stability for certain loop sequences. For example, RNA tetranucleotide loops (tetraloops) having the sequence GNRA and UUCG are more stable than other tetraloops and are highly conserved in nature.[1, 2] DNA tetraloops having the sequence GAAA, in certain contexts, are unusually stable in duplex DNA;[3] in triplex structures the loop sequence CTTTG has been reported to be especially stable as well.[4] In most or all of these cases, structural study has either implicated or identified intraloop hydrogen bonds between bases and/or phosphates as important structural features. It has long been recognized. however, that hydrogen bonds in aqueous solution are weak. In this regard a detailed study of hydrogen bonding in the GAAA tetraloop in RNA concluded that single hydrogen bonds contribute relatively little to the overall stability.[5] While less well understood, base stacking is also known to be at least as important a contribution to nucleic acid stability as hydrogen bonding.[6–8] Studies of loop structures in RNA and DNA have not generally addressed the relative importance of base stacking and hydrogen bonding in stabilizing such loops. We have undertaken a program to design and synthesize non-hydrogen-bonding nucleoside analogues to be used as probes of the biological noncovalent interactions of oligonucleotides and nucleic acids in general.[9] We now describe the incorporation of three such isosteres into DNA loops, and we have found that such substitutions can lead to significant stabilization of double- and triple-helical folded structures in DNA. Nucleosides 1 (F), 2 (B), and 3 (D) were designed to act as nearly perfect isosteres for the natural nucleosides thymidine (T) and deoxyadenosine (A) (Fig. 1). However, in contrast to the natural nucleosides, analogues 1–3 have little or no hydrogen bonding capability.[9] Compounds 1–3 are considerably more hydrophobic and less polar than the natural structures, and evidence from dangling-base studies in our laboratory indicate that they are more efficient at base stacking as well.[9b, 10] To test the effects of their properties on folded DNA structures, we incorporated 1–3 at loop positions into DNA hairpin-forming sequences and evaluated the thermal and thermodynamic stabilities of the folded structures. Fig. 1 Structural formulas and space-filling models of nonpolar nucleoside isosteres 1 (F), 2 (B), and 3 (D). Also shown are the structures of the natural nucleosides thymidine and deoxyadenosine. Nucleosides 1–3 were synthesized by using previously described methods.[9] The primary products of coupling of the bases of 1 and 2 with the α-chlorodeoxyribose toluoyl ester synthon are α-anomers,[11] which were converted to β-anomers by acid-catalyzed epimerization.[11b] Compounds 1–3 were unknown previous to our reports, although two other substituted indole nucleoside derivatives have recently been described.[12] The coupling of 1–3 in oligodeoxynucleotides using standard phosphoramidite chemistry was efficient, with stepwise yields of >95 % (trityl cation monitoring). For comparison we also synthesized analogous sequences containing the corresponding natural nucleosides at the same positions (see Tables 1 and ​and22). Table 1 Effects of natural and nonnatural nucleosides in tetranucleotide loops on the stability of double-stranded DNA hairpin structures at pH 7.0[a]. Table 2 Effects of varying the first and last nucleotides in the loop on the stability of triplexes formed between 21-nucleotide pyrimidine DNAs and complementary 8-nucleotide purine DNA strands at pH 7.0[a]. We first studied the effects of 1 (F), 2 (B), and 3 (D) in a duplex DNA hairpin loop, by using two self-complementary sequences of eight base pairs bridged by a tetranucleotide loop consisting of four identical residues. Previous studies of this sequence by Breslauer et al.[13] showed that, of sequences containing A4, C4, G4, and T4 loops, the most stable was the T4 case, and the least stable, the A4 case. We studied the properties of sequences containing F4, B4, and D4 loops, and we synthesized the natural T4 and A4 analogues for comparison. Table 1 shows data obtained for the duplex hairpin sequences. Buffer conditions were pH 7.0 (10 mm phosphate) with 100 mm NaCl. All five sequences gave melting transitions that were independent of concentration, confirming the expected hairpin structure as opposed to intermolecular complexes. The data show that the modified hairpin sequences containing 1 (F) and 2 (B) are significantly more stable than the T4 analogue. The melting temperature (Tm) for the modified F4 sequence, which contains difluorotoluene nucleosides, is 78.5 °C, or 10.8 °C higher than that of the T4 loop structure, which is the most stable tetraloop containing four identical natural nucleosides.[13] The four hairpin structures with natural nucleosides (A4, T4, C4, G4) have Tm values lying in a narrow range between 62 and 68°C.[13] Free energy values obtained by curve fitting show that the modified loop containing 1 is thermodynamically more stable than the most stable natural loop (the T4 loop) (Table 1). Similarly, the B4 hairpin sequence, with trimethylphenyl nucleosides, is almost as stable as the sequence with the F4 loop. Interestingly, just as the pyrimidine isosteres give more stable loops than a natural pyrimidine, we find that the purine analogue 3 is more stabilizing than its deoxyadenosine counterpart (ΔTm = 4.5 K). As was reported by Breslauer et a1.,[13] we find that the T4 loop is more stabilizing than the A4 loop. Moreover, we find that the nonnatural pyrimidine isosteres 1 and 2 are more stabilizing than the purine isostere 3. This difference in the natural hairpin structures has been attributed to cross-loop hydrogen bonding. Since in the nonnatural cases this difference cannot be due to hydrogen bonding, it seems likely that steric differences in the pyrimidine and purine analogues may play an important role both in the natural and nonnatural cases. Because the nonpolar thymidine isostere 1 was found to be the better stabilizing of the two analogues and because it is the best isosteric substitution, we tested it in a triple helix bridging loop. Such folded triplex-forming oligonucleotides are finding increasing use as ligands for single-stranded nucleic acids.[14] The stability of the loops in such a complex depends largely on the nature of the first and last bases in the loop.[4] The nucleoside 1 was therefore placed at these positions in a pentanucleotide loop bridging the pyrimidine strands in an eight-base triplex. For comparison we synthesized the natural T5-bridged triplex (see Table 2). We examined both 5′- and 3′-type loop orientations [4] at pH 7.0 with 100 mm NaCl and 10 mm MgCl2. The nonpolar nucleoside 1 gives complexes that are both thermally and thermodynamically more stable than structures containing the natural nucleosides (Table 2). For example, the hydrophobic nucleoside F gives complexes that are 4.8–5.4 K more thermostable than the T,T-substituted oligonucleotides, and free energies are 1.8–2.2 kcal mol−1 more favorable. Previous studies carried out with natural bases in this loop[4] have shown that the T,T case is intermediate in stability; the C,C loop is the least stable and the G,G loop the most stable. The G,G loop was found to be more stable than the T,T analogue by 1.5 kcal mol−1. [4] Thus our F,F loop is more stable than all four cases doubly substituted with the natural bases. Previous studies have described the use of simple nonnucleotide linkers as loop replacements in nucleic acids.[15] Such loops are often less stabilizing than natural nucleotide loops; this may be due both to the greater rigidity of nucleotide loops relative to the highly flexible nonnucleotide linkers and to favorable base stacking interactions in natural loops, which are missing in simple linkers. The nucleoside analogues in this study are designed to stabilize nucleic acid helices as a result of both rigidity and base stacking. In contrast to natural DNAs, loops containing nucleosides 1–3 have the added advantage of being resistant to degradation by nucleases (data not shown). In addition, such nonpolar nucleosides have been shown to pair with low affinity and low specificity with natural sequences [9b] and thus would not interfere with the expected pairing in biological systems. The present results on the incorporation of hydrophobic nucleoside analogues in oligonucleotide loops show that in general these compounds are significantly stabilizing. Because they do not undergo measurable hydrogen bonding interaction,[9b] it would seem that the best explanation for this behavior is superior base stacking propensity. This suggests a general strategy for stabilizing nucleic acid complexes containing loops: the use of arenes instead of natural bases, especially at positions adjacent to the helix, where stacking interactions are expected to make the greatest contributions. Although the present compounds cannot form stabilizing cross-loop hydrogen bonds, they may have favorable hydrophobic or van der Waals interactions. Detailed structural and physical studies will be necessary to investigate the specific origins of this stability.

Described are the design, synthesis, and structures of three nonpolar nucleoside isosteres to be used as probes of noncovalent bonding in DNA and as isosteric replacements for the natural nucleosides in designed nucleic acid structures. Reaction of substituted aryl Grignards with 3',5'-bis-O-toluoyl-α-deoxyibofuranosyl chloride and subsequent deprotection with sodium methoxide in methanol afforded the two β-C-nucleoside pyrimidine analogs 1 and 2. The dimethylindolyl nucleoside 3, a purine isostere, was obtained by a nucleophilic displacement on α-chlorodeoxyribofuranose by the sodium salt of 4,6-dimethylindole, followed by deprotection. Regio- and stereochemistry of the products were established with NOE difference spectra and (1)H NMR splitting patterns. Analogs 1 and 2 are nonpolar isosteres of thymidine, and nucleoside 3 is an isostere of 2-aminodeoxyadenosine, the triply-bonded Watson-Crick partner of thymidine. Semiempirical AM1 calculations were carried out to provide bond length information to assess structural similarities between the isosteres and their natural counterparts.

We report the use of thermodynamic measurements in a self-complementary DNA duplex (5'-dXCGCGCG)(2), where X is an unpaired natural or nonnatural deoxynucleoside, to study the forces that stabilize aqueous aromatic stacking in the context of DNA. Thermal denaturation experiments show that the core duplex (lacking X) is formed with a free energy (37 °C) of -8.1 kcal·mol(-1) in a pH 7.0 buffer containing 1 M Na(+). We studied the effects of adding single dangling nucleosides (X) where the aromatic "base" is adenine, guanine, thymine, cytosine, pyrrole, benzene, 4-methylindole, 5-nitroindole, trimethylbenzene, difluorotoluene, naphthalene, phenanthrene, and pyrene. Adding these dangling residues is found to stabilize the duplex by an additional -0.8 to -3.4 kcal·mol(-1). At 5 μM DNA concentration, T(m) values range from 41.7 °C (core sequence) to 64.1 °C (with dangling pyrene residues). For the four natural bases, the order of stacking ability is AG ≥ T = C. The nonpolar analogues stack more strongly in general than the more polar natural bases. The stacking geometry was confirmed in two cases (X = adenine and pyrene) by 2-D NOESY experiments. Also studied is the effect of ethanol cosolvent on the stacking of natural bases and pyrene. Stacking abilities were compared to calculated values for hydrophobicity, dipole moment, polarizability, and surface area. In general, hydrophobic effects are found to be larger than other effects stabilizing stacking (electrostatic effects, dispersion forces); however, the natural DNA bases are found to be less dependent on hydrophobic effects than are the more nonpolar compounds. The results also point out strategies for the design nucleoside analogues that stack considerably more strongly than the natural bases; such compounds may be useful in stabilizing designed DNA structures and complexes.

We report the properties of hydrophobic isosteres of pyrimidines and purines in synthetic DNA duplexes. Phenyl nucleosides 1 and 2 are nonpolar isosteres of the natural thymidine nucleoside, and indole nucleoside 3 is an analog of the complementary purine 2-aminodeoxyadenosine. The nucleosides were incorporated into synthetic oligodeoxynucleotides and were paired against each other and against the natural bases. Thermal denaturation experiments were used to measure the stabilities of the duplexes at neutral pH. It is found that the hydrophobic base analogs are nonselective in pairing with the four natural bases but selective for pairing with each other rather than with the natural bases. For example, compound 2 selectively pairs with itself rather than with A, T, G, or C; the magnitude of this selectivity is found to be 6.5-9.3 °C in Tm or 1.5-1.8 kcal/mol in free energy (25 °C). All possible hydrophobic pairing combinations of 1, 2, and 3 were examined. Results show that the pairing affinity depends on the nature of the pairs and on position in the duplex. The highest affinity pairs are found to be the 1-1 and 2-2 self-pairs and the 1-2 heteropair. The best stabilization occurs when the pairs are placed at the ends of duplexes rather than internally; the internal pairs may be destabilized by imperfect steric mimicry which leads to non-ideal duplex structure. In some cases the hydrophobic pairs are significantly stabilizing to the DNA duplex; for example, when situated at the end of a duplex, the 1-1 pair is more stabilizing than a T-A pair. When situated internally, the affinity of the 1-1 pair is the same as, or slightly better than, the analogous T-T mismatch pair, which is known to have two hydrogen bonds. The studies raise the possibility that hydrogen bonds may not always be required for the formation of stable duplex DNA-like structure. In addition, the results point out the importance of solvation and desolvation in natural base pairing, and lend new support to the idea that hydrogen bonds in DNA may be more important for specificity of pairing than for affinity. Finally, the study raises the possibility of using these or related base pairs to expand the genetic code beyond the natural A-T and G-C pairs.

Noncovalent interactions between aromatic molecules are widely believed to be important contributing factors in the stabilization of organized structure in biological macromolecules.1,2 Among the most significant aromatic–aromatic interactions are those found in helical nucleic acid structures. Since the identity of the nearest neighbors to a given base pair is the best single predictor of thermodynamics in DNA duplexes,3 it is clear that aromatic π–π interactions are crucial to the stabilization of these structures.4 While there have been a considerable number of theoretical studies aimed at modeling the π–π interaction in DNA,5 there have been remarkably few experimental studies specifically addressing the thermodynamics of stacking (separate from base pairing) in DNA itself.6 For that reason we have undertaken a study of aromatic stacking in the context of duplex DNA, and we hope to begin to elucidate what are the important forces which stabilize this organized structure. We report here the first experimental comparison of the stacking abilities of natural DNA bases and of nonnatural aromatic analogs in double-stranded DNA. To separate stacking from pairing (hydrogen-bonding) interactions in duplex DNA we placed the natural or nonnatural nucleotide of interest in a “dangling” position (without a pairing partner) at the end of a base-paired duplex (Figure 1).7 The resulting stabilization of the duplex by the dangling base can be measured by thermal denaturation experiments, with comparison to the duplex lacking the added nucleotide. Figure 1 Structures and DNA sequences in this study. (A) Structures of natural (1, 3) and nonnatural (2, 4–8) nucleosides examined here. (B) Illustration of how placement of a single nucleotide residue at the 5′-end of a self-complementary strand ... Electrostatic effects resulting from such localized charge have been implicated both in the stabilization and in the geometry of aromatic stacking.5 To examine such effects we compared not only natural DNA bases but also nonpolar molecules with similar shape and surface area. Thus, we compared the DNA base thymine (1) and adenine (3) with their respective nonpolar isosteres difluorotoluene (2) and 4-methylindole (4).9 We also compared the stacking of the aromatic hydrocarbons benzene (5), naphthalene (6), phenanthrene (7), and pyrene (8). The synthesis of these nucleoside analogs has been reported.10–13 Results of the thermodynamic measurements made at pH 7.0 and 1 M NaCl are presented in Table 1. We measured melting transitions (Tm) as a function of concentration for the duplexes and calculated thermodynamic parameters by plotting 1/Tm vs ln([oligonucleotide]). The linear fits were quite good (r2 ≥ 0.97), with error in free energies of approximately ±2%. The unsubstituted core duplex under these conditions has a Tm (5 μM) of 41.0(±0.5) °C and a free energy (37 °C) of −8.05(±0.16) kcal/mol. Table 1 Comparison of Stacking Affinities of Natural DNA Bases and Simple Aromatic Analogs, As Measured by Dangling End Studies in a Self-Complementary DNA Duplex (Sequence d(XCGCGCG)2)a Measurement of the duplexes with dangling thymine and adenine residues shows, perhaps not surprisingly, that the purine stacks on the duplex more strongly than the smaller pyrimidine base. The two unpaired deoxyadenosines add 2.0 kcal of stabilizing interaction to the self-complementary sequence, and thymines add 1.1 kcal to the duplex stability. This relative stacking ability is as predicted from nearest-neighbor parameters3 and is consistent with dangling-end studies carried out in RNA.7 Interestingly, the data show that the nonpolar DNA base mimics stack considerably more strongly than their natural counterparts. Difluorotoluene raises the Tm of the duplex by 13.4 °C, about twice the effect of thymine, although the two have the same size, shape, and surface area.9 Similarly, the isosteric analog 4-methylindole increases the Tm by more than does the natural base adenine. The effects on free energies of the duplexes mirror these results (Table 1). These results show clearly that surface area alone is not a good predictor of stacking affinity. It seems likely that the increased hydrophobicity of these two nonpolar analogs contributes favorably to their enhanced stacking. An alternative explanation might be differences in polarizability, which would influence van der Waals forces. However, methylindole is calculated to be only slightly more polarizable than adenine, and difluorotoluene is equally as polarizable as thymine.14 Thus it appears that hydrophobicity differences exert the largest influence here. The superior stacking of the two purine-sized compounds relative to the pyrimidine-sized cases might be explained by increased surface area, which would allow for stronger interaction with the neighboring C–G base pair. To investigate further the effects of size and hydrophobicity on stacking interactions, we then examined the series of four nucleotides in which the “base” moiety is benzene, naphthalene, phenanthrene, and pyrene (Figure 1A). The results show (Table 1) that these compounds stack relatively strongly, and the interaction generally becomes more favorable with increasing size. The benzene nucleotide stacks with slightly greater affinity than thymine. The naphthalene compound shows a large Tm increase over the unsubstituted duplex of 15.2 °C and a total stacking energy of 2.9 kcal/mol, or twice that of benzene. Interestingly, the phenanthrene nucleoside, although larger, has a stacking propensity essentially the same as that of naphthalene (compare seventh and eighth entries in Table 1). Models indicate that the third ring in phenanthrene (which is absent in naphthalene) does not contact the adjacent bases and instead is likely to protrude toward the major groove of the DNA. We surmise that lack of added contact with the nearest neighbor precludes added favorable interactions. Since phenanthrene is significantly more polarizable than naphthalene14 but does not stack more strongly, the results are most easily explained by solvophobic effects rather than dipole-induced dipole effects. The amount of nonpolar surface area excluded from solvent by stacking is expected to be similar for naphthalene and phenanthrene in these structures. The pyrene compound interacts the most strongly of all the natural and nonnatural bases studied. The duplex substituted by this species has a melting transition 23.1 °C higher than the unsubstituted duplex and 12.5 °C higher than for the case with adenine. Addition of the two pyrene residues to the self-complementary duplex adds a quite large 3.4 kcal / mol of stabilization to the helix. Models indicate that a large fraction of one face of this molecule can stack with the neighboring base pair, and so the relatively high solvophobicity is apparently put to good effect. The overall order of stacking ability of these molecules is thus found to be thymine < benzene < adenine < difluorotoluene ≤ naphthalene ∼ phenanthrene ≤ methylindole < pyrene, at least in this sequence context. It seems significant that solvophobic effects appear to be the most important factor in determining this order. When molecules of the same size are compared, we find that the less polar structure stacks more strongly than one of higher polarity. When nonpolar molecules of different sizes are compared, we find that stacking propensity appears to correlate with the surface area excluded from solvent. A number of studies aimed at measuring aromatic–aromatic interactions in smaller model systems have been reported previously.15,16 A few of these have examined interactions of DNA bases;16 and mono- and dinucleotides have been studied as models for stacking interactions.17 The present results agree with the previously known superiority of purines over pyrimidines at stacking, which was also observed by Leonard et al. using nucleobases bridged by simple trimethylene linkers.16a In a comparison of adenines and naphthalenes linked by three-carbon bridges, Gellman found evidence that naphthalene–adenine interactions were qualitatively stronger than adenine–adenine interactions,16c a result in accord with our finding of superior stacking of naphthalene over adenine. In a simple receptor system, Rebek et al. found increasing interaction of adenine with aromatics of increasing size,16b also in agreement with the present results. Our results indicate that the natural DNA bases are not particularly effective at stacking, at least in a global comparison of aromatic structures. Evolution may not have favored bases which stack too strongly, since helix unwinding is a requirement for DNA replication. For designed nucleic acid structures, where thermodynamic stability is often desirable, our results indicate that one may gain stability simply by placing large nonpolar aromatics at the ends of helical structure. It will of course be useful to study this series of compounds in additional sequence contexts to explore the generality of the conclusions. It is worth noting that in a considerably different structure (a hairpin loop) we have noted similar stabilization by nonpolar DNA base analogs.11 Since thermodynamic rather than structural evidence of stacking is presented here, it will be of significant future interest to obtain structural information18 about dangling nucleotides to better evaluate the specific interactions involved.