Configurational statistics of the DNA duplex: Extended generator matrices to treat the rotations and translations of adjacent residues

The base-to-base virtual bond treatment of nucleic acids used in statistical mechanical calculations of polynucleotide chain properties has been refined by incorporating the six parameters that relate the positions and orientations of sequential rigid bodies. The scheme allows for the sequence-dependent bending, twisting, and displacement of base pairs as well as for asymmetry in the angular and translational fluctuations of individual residues. Expressions are developed for the generator matrices required for the computation, as a function of chain length, of various parameters measuring the overall mean extension and shape of the DNA. Quantities of interest include the end-to-end vector r , the square of the end-to-end distance r², the square radius of gyration s², the center-of-gravity vector g , the second moments of inertia S ^×2, and the higher moments of r and g . The matrix expressions introduced in the 1960s by Flory and co-workers for the determination of configuration-dependent polymer chain averages are decomposed into their translational and orientational contributions so that the methods can be extended to the rigid body analysis of chemical moieties. The new expressions permit, for the first time, examination of the effects of sequence-dependent translations, such as the lateral sliding of residues in A- and B-helices and the vertical opening of base pairs in drug–DNA complexes, on the average extension and shape of the long flexible double helix. The approach is illustrated in the following paper using conformational energy estimates of the base sequence-dependent flexibility of successive B-DNA base pairs. © 1994 John Wiley & Sons, Inc.     

Statistical mechanical deconvolution of thermal transitions in macromolecules. III. Application to double-stranded to single-stranded transitions of nucleic acids

The statistical mechanical deconvolution theory for macromolecular conformational transitions is extended to the case of nucleic acids transitions involving strand separation. It is demonstrated that the partition function, Q, as well as all the relevant thermodynamic quantities of the system, can be calculated from experimental scanning calorimetric data. In particular, it is shown that important thermodynamic parameters such as the size of the average cooperative unit during strand separation, the mean helical segment length, and the mean coil-segment length can be calculated from the average excess enthalpy function 〈ΔH〉. The theory is applied to the double-stranded to single-stranded transition of the system poly(A)·poly(U) at different salt concentrations. It is shown that the mean helical segment length is a monotonically decreasing function of the temperature well before strand separation occurs. On the other hand, the mean coil segment length remains practically constant until temperatures very close to T_m. Both experimental findings clearly indicate that the unfolding of poly(A)·poly(U) proceeds through the formation of many short helical sequences. The cooperative unit for the strand separation is calculated to be about 120 base pairs and essentially independent of the salt concentration. The existence of a minimum helical segment length of 10 ± 2 base pairs within the double-stranded form is calculated.     

The Structure of Triple Helical Poly(U)·Poly(A)·Poly(U) Studied by Raman Spectroscopy

Abstract

Using Raman spectroscopy, we examined the ribose-phosphate backbone conformation, the hydrogen bonding interactions, and the stacking of the bases of the poly(U)·poly(A) ·poly(U) triple helix. We compared the Raman spectra of poly(U)·poly(A)·poly(U) in H₂O and D₂O with those obtained for single-stranded poly(A) and poly(U) and for double-stranded poly(A)·poly(U). The presence of a Raman band at 863 cm^?1 indicated that the backbone conformations of the two poly(U) chains are different in the triple helix. The sugar conformation of the poly(U) chain held to the poly(A) by Watson-Crick base pairing is C3′ endo; that of the second poly(U) chain may be C2′ endo. Raman hypochromism of the bands associated with base vibrations demonstrated that uracil residues stack to the same extent in double helical poly(A)·poly(U) and in the triple-stranded structure. An increase in the Raman hypochromism of the bands associated with adenine bases indicated that the stacking of adenine residues is greater in the triple helix than in the double helical form. Our data further suggest that the environment of the carbonyls of the uracil residues is different for the different strands.     

Base Sequence Effects in Double Helical DNA. I. Potential Energy Estimates of Local Base Morphology

Abstract

A series of potential energy calculations have been carried out to estimate base sequence dependent structural differences in B-DNA. Attention has been focused on the simplest dimeric fragments that can be used to build long chains, computing the energy as a function of the orientation and displacement of the 16 possible base pair combinations within the double helix. Calculations have been performed, for simplicity, on free base pairs rather than complete nucleotide units. Conformational preferences and relative flexibilities are reported for various combinations of the roll, tilt, twist, lateral displacement, and propeller twist of individual residues. The predictions are compared with relevant experimental measures of conformation and flexibility, where available. The energy surfaces are found to fit into two distinct categories, some dimer duplexes preferring to bend in a symmetric fashion and others in a skewed manner. The effects of common chemical substitutions (uracil for thymine, 5-methyl cytosine for cytosine, and hypoxanthine for guanine) on the preferred arrangements of neighboring residues are also examined, and the interactions of the sugar-phosphate backbone are included in selected cases. As a first approximation, long range interactions between more distant neighbors, which may affect the local chain configuration, are ignored. A rotational isomeric state scheme is developed to describe the average configurations of individual dimers and is used to develop a static picture of overall double helical structure. The ability of the energetic scheme to account for documented examples of intrinsic B-DNA curvature is presented, and some new predictions of sequence directed chain bending are offered.     

Sequence and conformational effects on imino proton exchange in A.T- and A.U-containing DNA and RNA duplexes

¹H-nmr relaxation has been used to study the effect of sequence and conformation on imino proton exchange in adenine–thymine (A · T) and adenine–uracil (A · U) containing DNA and RNA duplexes. At low temperature, relaxation is caused by dipolar interactions between the imino and the adenine amino and AH2 protons, and at higher temperature, by exchange with the solvent protons. Although room temperature exchange rates vary between 3 and 12s^?1, the exchange activation energies (E_α) are insensitive to changes in the duplex sequence (alternating vs homopolymer duplexes), the conformation (B-form DNA vs A-form RNA), and the identity of the pyrimidine base (thymine vs uracil). The average value of the activation energy for the five duplexes studied, poly[d(A-T)], poly[d(A) · d(T)], poly[d(A-U)], Poly[d(A) · d(U)], and poly[r(A) · r(U)], was 16.8 ± 1.3 kcal/mol. In addition, we find that the average E_α for the A.T base pairs in a 43-base-pair restriction fragment is 16.4 ± 1.0 kcal/mol. This result is to be contrasted with the observation that the E_α of cytosine-containing duplexes depends on the sequence, conformation, and substituent groups on the purine and pyrimidine bases. Taken together, the data indicate that there is a common low-energy pathway for the escape of the thymine (uracil) imino protons from the double helix. The absolute values of the exchange rates in the simple sequence polymers are typically 3–10 times faster than in DNAs containing both A · T and G · C base pairs.     

Spatial translational motions of base pairs in DNA molecules: Application of the extended matrix generator method

We have used the elementary generator matrices outlined in the preceding paper to examine the conformational plasticity of the nucleic acid double helix. Here we investigate kinked DNA structures made up of alternating B- and A-type helices and intrinsically curved duplexes perturbed by the intercalation of ligands. We model the B-to-A transition by the lateral translation of adjacent base pairs, and the intercalation of ligands by the vertical displacement of neighboring residues. We report a complete set of average configuration-dependent parameters, ranging from scalars (i.e., persistence lengths) to first- and second-order tensor parameters (i.e., average second moments of inertia), as well as approximations of the associated spatial distributions of the DNA and their angular correlations. The average structures of short chains (of lengths less than 100 base pairs) with local kinks or intrinsically curved sequences are essentially rigid rods. At the smallest chain lengths (10 base pairs), the kinked and curved chains exhibit similar average properties, although they are structurally perturbed compared to the standard B-DNA duplex. In contrast, at lengths of 200 base pairs, the curved and kinked chains are more compact on average and are located in a different space from the standard B- or A-DNA helix. While A-DNA is shorter and thicker than B-DNA in x-ray models, the long flexible A-DNA helix is thinner and more extended on average than its B-DNA counterpart because of more limited fluctuations in local structure. Curved polymers of 50 base pairs or longer also show significantly greater asymmetry than other DNAs (in terms of the distribution of base pairs with respect to the center of gravity of the chain). The intercalation of drugs in the curved DNA straightens and extends the smoothly deformed template. The dimensions of the average ellipsoidal boundaries defining the configurations of the intercalated polymers are roughly double those of the intrinsically curved chain. The altered proportions and orientations of these density functions reflect the changing shape and flexibility of the double helix. The calculations shed new light on the possible structural role of short A-DNA fragments in long B-type duplexes and also offer a model for understanding how GC-specific intercalative ligands can straighten naturally curved DNA. The mechanism is not immediately obvious from current models of DNA curvature, which attribute the bending of the chain to a perturbed structure in repeating tracts of A · T base pairs. © 1994 John Wiley & Sons, Inc.     

Parallel Double Helices of DNA. Conformational Analysis of Regular Helices with the Second Order Symmetry Axis

Abstract

We have performed a conformational analysis of DNA double helices with parallel directed backbone strands connected with the second order symmetry axis being at the same time the helix axis. The calculations were made for homopolymers poly(dA) · poly(dA), poly(dC) · poly(dC), poly(dG) poly(dG), and poly(dT) · poly(dT). All possible variants of hydrogen bonding of base pairs of the same name were studied for each polymer. The maps of backbone chain geometrical existence were constructed. Conformational and helical parameters corresponding to local minima of conformational energy of “parallel” DNA helices, calculated at atom-atom approximation, were determined. The dependence of conformational energy on the base pair and on the hydrogen bond type was analysed. Two major conformational advantageous for “parallel” DNA's do not depend much on the hydrogen-bonded base pair type were indicated. One of them coincided with the conformational region typical for “antiparallel” DNA in particular for the B-form DNA Conformational energy of “parallel” DNA depends on the base pair type and for the most part is similar to the conformational energy of “antiparallel” B-DNA.     

Spatial configurations of polynucleotide chains. 3. Polydeoxyribonucleotides

The virtual bond scheme set forth in preceding papers for treating the average properties of polyriboadenylic acid (poly rA) is here applied to the calculation of the unperturbed mean-square end-to-end distance of polydeoxyriboadenylic acid (poly dA). The modifications in structure and in charge distribution resulting from the replacement of the hydroxyl group at C_2′ in the ribose residue by hydrogen in deoxyribose produce only minor modifications in the conformational energies associated with the poly dA chain as compared to those found for poly rA. The main difference is manifested in the energy associated with rotations about the C_3′–O_3′ bond of the deoxyribose residue in the C_2′-endo conformation; accessible rotations are confined to the range between 0° and 30° relative to the trans conformation, whereas in the ribose unit the accessible regions comprise two ranges centered at approximately 35° and 85°. The characteristic ratio 〈r²〉0/nl² calculated on the basis of the conformational energy estimates is ≈9 for the poly dA chain with all deoxyribose residues in the C_3′-endo conformation and ≈21 with all residues in the C_2′-endo form. Satisfactory agreement is achieved between the theoretical values and experimental results on apurinic acid by treating the poly dA chain as a random copolymer of C_3′-endo and C_2′-endo conformational isomers present in a ratio of ～1 to 9.     

Fluctuations of an alpha-helix.

Fluctuations in backbone dihedral angles in the α-helical conformation of homopolypeptides are studied based on an assumption that the conformational energy function of a polypeptide consisting of n amino-acid residues can be approximated by a 2n-dimensional parabola around the minimum point in the range of fluctuations. A formula is derived that relates 〈Δθ_iΔθ_j〉, the mean value of the product of deviations of dihedral angles ?_i and ψ_i (collectively designated by θ_i) from their energy minimum values, with a matrix inverse to the second derivative matrix F ,_n of the conformational energy function at the minimum point. A method of calculating the inverse matrix F _n^?1 explicitly is given. The method is applied to calculating 〈Δθ_iΔθ_j〉 for the α-helices of poly(L -alanine) and polyglycine. The autocorrelations 〈(Δ?_i)²〉 and 〈(Δψ_i)²〉 at 300°K are found to be about 66 deg² and 49 deg², respectively, for poly(L -alanine), and 84 deg² and 116 deg², respectively, for polyglycine. The length of correlations of fluctuations along the chain is found for both polypeptides to be about eight residues long.     

Sequence-dependence of the CD of synthetic double-stranded RNAs containing inosinate instead of guanylate subunits

The CD spectra and melting profiles have been measured for nine synthetic double-stranded RNAs containing I · C instead of G · C base pairs: poly[r(I) · r(C)], poly[r(I-C) · r(I-C)], poly[r(A-I-C) · r(I-C-U)], poly[r(A-C) · r(I-U)], poly[r(A-I) · r(C-U)], poly[r(A-C-C) · r(I-I-U)], poly[r(A-A-C) · r(I-U-U)], poly[r(A-C-U) · r(A-I-U)], and poly[r(A-U-C) · r(I-A-U)]. CD spectra have not previously been reported for the latter six of these polymers. The substitution of inosinate for guanylate led to recognizable CD differences, with all but two of the polymers having two resolved positive bands above 230 nm. Also, the I-containing RNAs differed from their G-containing counterparts in the almost complete absence of negative CD bands at long wavelengths and in the reduction of negative CD bands near 210 nm. First-neighbor comparisons showed that the CD spectra of the I-containing RNAs were consistent with the nearest-neighbor sequences of the polymers, as previously shown for G-containing RNAs (D. M. Gray, J.-J. Liu, R. L. Ratliff, and F. S. Allen, Biopolymers (1981) 20 , 1337–1382). Moreover, two of the first-neighbor comparisons involved spectra of poly[r(A) · r(U)] and poly[r(I) · r(C)], polymers known to be in the A family of conformations in fibers (S. Arnott, D. W. L. Hukins, S. D. Dover, W. Fuller, and A. Hodgson, (1973) J. Mol. Biol. 81 , 107–122). Thus, differences in the CD spectra of I- and G-containing RNAs could be simply explained as resulting from differences in the hypoxanthine and guanine chromophores, without invoking differences in conformation. Finally, melting temperatures of the I-containing RNAs were found to vary much less with base composition than do the melting temperatures of G-containing RNAs, since A · U base pairs are closer to I · C than to G · C base pairs in stability.     

Base sequence effects in double helical DNA. I. Potential energy estimates of local base morphology

A series of potential energy calculations have been carried out to estimate base sequence dependent structural differences in B-DNA. Attention has been focused on the simplest dimeric fragments that can be used to build long chains, computing the energy as a function of the orientation and displacement of the 16 possible base pair combinations within the double helix. Calculations have been performed, for simplicity, on free base pairs rather than complete nucleotide units. Conformational preferences and relative flexibilities are reported for various combinations of the roll, tilt, twist, lateral displacement, and propeller twist of individual residues. The predictions are compared with relevant experimental measures of conformation and flexibility, where available. The energy surfaces are found to fit into two distinct categories, some dimer duplexes preferring to bend in a symmetric fashion and others in a skewed manner. The effects of common chemical substitutions (uracil for thymine, 5-methyl cytosine for cytosine, and hypoxanthine for guanine) on the preferred arrangements of neighboring residues are also examined, and the interactions of the sugar-phosphate backbone are included in selected cases. As a first approximation, long range interactions between more distant neighbors, which may affect the local chain configuration, are ignored. A rotational isomeric state scheme is developed to describe the average configurations of individual dimers and is used to develop a static picture of overall double helical structure. The ability of the energetic scheme to account for documented examples of intrinsic B-DNA curvature is presented, and some new predictions of sequence directed chain bending are offered.     

Polymorphism of DNA double helices

Native DNA duplexes in fibers exist usually in one of three well-known (A, B and C) forms depending on relative humidity, type of cations and the amount of retained salt. To determine the precise influence of these factors and the effect of base composition, as well as base sequence, on DNA secondary structure, X-ray diffraction methods have been used to study all four synthetic DNA duplexes with repeated dinucleotide sequences, eight of the 12 with repeated trinucleotide sequences and seven analogues in which guanine was replaced with hypoxanthine. The results indicate that there are at least six additional allomorphs denoted by B′, C′, C″, D, E and S.The B′ form (h = 0.329 nm) observed for poly(dA) · poly(dT), poly(dI) · poly(dC) and poly[d(A-I)] · poly[d(C-T)] is a minor variant of the traditional B form (h = 0.338 nm) of native DNA. The two C-like forms C′ for poly[d(A-G-C)] · poly-[d(G-C-T)] and poly[d(G-G-T)] · poly[d(A-C-C)] and C″ for poly[d(A-G)] · poly-[d(C-T)] have, respectively, 9₁ and 9₂ symmetries which reflect repetition of trinucleotide and dinucleotide sequences, respectively. Although isocompositional with poly(dA) · poly(dT), the existence of the rather different D form (8₁) for poly[d(A-T)] · poly[d(A-T)] or for poly[d(A-A-T)] · poly[d(A-T-T)] is a clear demonstration of the sequence effect. The I · C pair generally mimics an A · T pair, but poly[d(I-I-T)] · poly[d(A-C-C)] provides a new (E) form with approximately 15₂ screw symmetry and with 〈h〉 = 0.325 nm and 〈t〉 = 48 dg per nucleotide. The S form (6₅) observed for poly[d(G-C)] · poly[d(G-C)] and poly[d(A-C)] · poly[d(G-T)] is an unusual left-handed polydinucleotide helix and is accessible to any alternating purine-pyrimidine sequence. In it the two nucleotides have quite different conformations and involve syn purine and anti pyrimidine nucleosides.     

Studies on interaction between poly(L-lysine) and DNA of varied G + C contents

Interaction between polylysine and DNA's of varied G + C contents was studied using thermal denaturation and circular dichroism (CD). For each complex there is one melting band at a lower temperature t_m, corresponding to the helix–coil transition of free base pairs, and another band at a higher temperature t′_m, corresponding to the transition of polylysine-bound base pairs. For free base pairs, with natural DNA's and poly(dA-dT) a linear relation is observed between the t_m and the G + C content of the particular DNA used. This is not true with poly(dG)·poly(dC), which has a t_m about 20°C lower than the extrapolated value for DNA of 100% G + C. For polylysine-bound base pairs, a linear relation is also observed between the t′_m and the G + C content of natural DNA's but neither poly(dA-dT) nor poly(dG)·poly(dC) complexes follow this relationship. The dependence of melting temperature on composition, expressed as dt_m/dX_G·C, where X_G·C is the fraction of G·C pairs, is 60°C for free base pairs and only 21°C for polylysine-bound base pairs. This reduction in compositional dependence of T_m is similar to that observed for pure DNA in high ionic strength. Although the t′_m of polylysine-poly(dA-dT) is 9°C lower than the extrapolated value for 0% G + C in EDTA buffer, it is independent of ionic strength in the medium and is equal to the t_m⁰ extrapolated from the linear plot of t_m against log Na⁺. There is also a noticeable similarity in the CD spectra of polylysine· and polyarginine·DNA complexes, except for complexes with poly(dA-dT). The calculated CD spectrum of polylysine-bound poly(dA-dT) is substantially different from that of polyarginine-bound poly(dA-dT).     

Kinetic analysis of the annealing period in the formation of the poly(A)·2poly(U) triple helix

The slow kinetics of annealing processes in multistranded nucleic acids is spectrophotometrically investigated using poly(A)·2poly(U) as a model system. The absorbance changes at specific wavelengths show that double-helical (A·U) base pairs appear as transient intermediates. The annealing process is identified by the enlargement of triple-helical sequences at the cost of (A·U) base pairs and unpaired (U) residues. A large time range in the reorganization of mismatched chain configurations is characterized by a logarithmic dependence on time. This observation is quantitatively described by a kinetic model developed by Jackson. In Jackson's model the rate-limiting process in the slow annealing phase of maximizing triple-helical sequences, is the removal of strand entanglements, knots, and hairpin loops by complete unwinding of those helical stretches which stabilize the mismatched configurations. The results of the present study are briefly discussed in terms of optimum conditions for hybridization experiments and for the preparation of polynucleotide complexes commonly used to produce interferons.     

Alternative conformations of DNA modified by N-2-acetylaminofluorene

Modification of DNA by the carcinogen N-acetoxy-N-2-acetylaminofluorene gives two adducts, a major one at the C-8 position of guanine and a minor one at the N-2 position with differing conformations. Binding at the C-8 position results in a large distortion of the DNA helix referred to as the “base displacement model” with the carcinogen inserted into the DNA helix and the guanosine displaced to the outside. The result is increased susceptibility to nuclease S, digestion due to the presence of large, single-stranded regions in the modified DNA. In contrast, the N-2 adduct results in much less distortion of the helix and is less susceptible to nuclease S₁ digestion. A third and predominant adduct is formed in vivo, the deacetylated C-8 guanine adduct. The conformation of this adduct has been investigated using the dimer dApdG as a model for DNA. The attachment of aminofluorene (AF) residues introduced smaller changes in the circular dichroism (CD) spectra of dApdG than binding of acetylaminofluorene (AAF) residues. Similarly, binding of AF residues caused lower upfield shifts for the H-2 and H-8 protons of adenine than the AAF residues. These results suggest that AF residues are less stacked with neighboring bases than AAF and induce less distortion in conformation of the modified regions than AAF. An alternative conformation of AAF-modified deoxyguanosine has been suggested based on studies of poly(dG-dC)·poly(dG-dC). Modification of this copolymer with AAF to an extent of 28% showed a CD spectrum that had the characteristics of the left-handed Z conformation seen in unmodified poly-(dG-dC)·poly(dG-dC) at high ethanol or salt concentrations. Poly(dG)·poly(dC), which docs not undergo the B to Z transition at high ethanol concentrations, did not show this type of conformational change with high AAF modification. Differences in conformation were suggested by single-strand specific nuclease S₁ digestion and reactivity with anticytidine antibodies. Highly modified poly(dG-dC)·poly(dG-dC) was almost completely resistant to nuclease S₁ hydrolysis, while, modified DNA and poly(dG)·poly(dC) are highly susceptible to digestion. Two possible conformations for deoxyguanosine modified at the C-8 position by AAF are compared depending on whether its position is in alternating purine-pyrimidine sequences or random sequence DNA.     

Raman spectral studies of nucleic acids. XVI. Structures of polyribocytidylic acid in aqueous solution

Raman spectra of polyribocytidylic acid show the formation of an ordered single-stranded structure [poly(rC)] at neutral pH and an ordered double-stranded structure containing hemiprotonated bases [poly(rC)·poly(rC⁺)] in the range 5.5 > pH > 3.7. Below 40°C, poly(rC) contains stacked bases and a backbone geometry of the A-type, both of which are gradually eliminated by increasing the temperature to 90°C. Below 80°C, poly(rC)·poly(rC⁺) contains bases which are hydrogen bonded and stacked and a backbone geometry also of the A-type. In this structure the bases of each strand are shown to be structurally identical, i.e., hemiprotonated, and therefore distinct from both neutral and protonated cytosines. Infrared and Raman spectra indicate the existence of a center of symmetry with respect to the paired cytosine residues, which suggests that the additional proton per base pair is shared equally by the two hydrogen-bonded bases. Denaturation of poly(rC)·poly(rC⁺) occurs cooperatively (t_m ≈ 80°C) with elimination of base stacking, base pairing, and the A-helix geometry. Each of the separated strands of the denatured complex is shown to contain comparable amounts of both neutral and protonated cytosines, most likely in alternating sequence [poly(rC, rC⁺)]. In both poly(rC, rC⁺) and poly(rC), at 90°C, the backbones do not exhibit the phosphodiester Raman frequencies characteristic of other disordered polyribonucleotide chains. This is interpreted to mean that the single strands, though devoid of base stacking and A-type structure, contain uniformly ordered backbones of a specific type. Fully protonated poly(rC⁺), on the other hand, forms no ordered structure and may be characterized as a disordered (random chain) polynucleotide at all temperatures. Several Raman lines of poly(rC) are absent from the spectrum of poly(rC)·poly(rC⁺) and vice versa. These frequencies, assigned mainly to vibrations of the ribose groups, suggest that the furanose ring conformations are different in the single-stranded and double-stranded structures of polyribocytidylic acid. Several other Raman group frequencies have been identified and correlated with the polymer secondary structures.     

Sequence dependence of the circular dichroism of synthetic double-stranded RNAs

We have synthesized and studied the CD spectra of five new double-stranded RNA polymers: poly[r(A-G)·r(C-U)], poly[r(A-U-C)·r(G-A-U)], poly[r(A-C-U)·r(A-G-U)], poly[r(A-A-C)·r(G-U-U)], and poly[r(A-C-C)·r(G-G-U)]. Together with previously published spectra of seven other RNA sequences, the spectra of these new sequences provide a library sufficient to approximate the spectra of all other RNA sequences by first-neighbor formulas and, in addition, give four spectra with which we may test the validity of first-neighbor approximations. (1) We find that the spectra of RNA sequence isomers are very different, but that the spectra essentially do obey first-neighbor relationships. (2) We have derived tentative first-neighbor assignments of negative bands at about 295 and 210 nm in the CD spectra. (3) A test of spectral independence shows that among the 12 polymer spectra there are at least seven significant independent spectral shapes, one less than the eight needed to give the most accurate spectral analysis of an unknown RNA sequence for its first-neighbor frequencies. (4) Spectra are calculated for RNAs of random base composition, approximating natural RNAs having complex sequences. (5) A T-matrix of spectral components assigned to the first-neighbor base pairs is derived from 10 of the spectra. This matrix allows an estimation of the CD spectrum of any other known RNA sequence or an analysis of the spectrum of an unknown sequence for its distribution of first-neighbor base-pair frequencies. (6) Test analyses of two of the synthetic polymers and of two natural RNAs set a probable limit on the accuracy of first-neighbor frequency determinations using this T-matrix. (7) Finally, we summarize in an appendix the melting temperatures for all the RNA and corresponding DNA sequences; it appears that the T_m values of both DNAs and RNAs approximately obey first-neighbor relationships.     

Normal mode theory for the Brownian dynamics of a weakly bending rod: Comparison with Brownian dynamics simulations

A normal mode theory is developed for the Brownian dynamics of weakly bending rods with preset hydrodynamic interactions. The rod is replaced by a chain of contiguous spheres whose radius is chosen to yield the appropriate uniform translational and rotational diffusion coefficients. Despite the inclusion of preset hydrodynamic interactions in the dynamical operator, its normal modes are not coupled by the potential energy, so their amplitudes remain pairwise “orthogonal” under equilibrium averaging. The uniform translational and rotational diffusion coefficients obtained from Langevin theory are shown to be identical to those obtained from the Kirkwood algorithm, despite their rather different appearance. An expression is given for the mean squared angular displacement 〈Δ_xm(t)²〉 of the mth bond vector around the instantaneous x axis (perpendicular to the end-to-end vector z). Necessary algorithms are presented for the numerical evaluation of all quantities. The normal mode theory is compared with Brownian dynamics simulations for the same model by examining 3〈Δ_xm(t)²〉 for the central bond vector of rods comprising 10 and 30 subunits with various persistence lengths. The normal mode theory works very well for all times for L/P ? 0.6, where P = κ/k_BT is the persistence length and κ is the bending rigidity. With increasing flexibility, the domain of validity of the normal mode theory is restricted to shorter times, where violations of the weak bending approximation are less severe. However, increasing the length of the rod from 10 to 30 subunits yields improved agreement with the simulations for the same and even longer times. This latter effect is tentatively attributed to the greater fluctuating tension in the longer chains, which acts to retard the rotational relaxation in the simulations, but is not taken into account in the present normal mode theory.