Base sequence, local helix structure, and macroscopic curvature of A-DNA and B-DNA

DNA Structure and the Golden Ratio Revisited

B-DNA, the informational molecule for life on earth, appears to contain ratios structured around the irrational number 1.618…, often known as the “golden ratio”. This occurs in the ratio of the length:width of one turn of the helix; the ratio of the spacing of the two helices; and in the axial structure of the molecule which has ten-fold rotational symmetry. That this occurs in the information-carrying molecule for life is unexpected, and suggests the action of some process. What this process might be is unclear, but it is central to any understanding of the formation of DNA, and so life.

Nature of base stacking: reference quantum-chemical stacking energies in ten unique B-DNA base-pair steps

Base-stacking energies in ten unique B-DNA base-pair steps and some other arrangements were evaluated by the second-order Møller-Plesset (MP2) method, complete basis set (CBS) extrapolation, and correction for triple (T) electron-correlation contributions. The CBS(T) calculations were compared with decade-old MP2/6-31G*(0.25) reference data and AMBER force field. The new calculations show modest increases in stacking stabilization compared to the MP2/6-31G*(0.25) data and surprisingly large sequence-dependent variation of stacking energies. The absolute force-field values are in better agreement with the new reference data, while relative discrepancies between quantum-chemical (QM) and force-field values increase modestly. Nevertheless, the force field provides good qualitative description of stacking, and there is no need to introduce additional pair-additive electrostatic terms, such as distributed multipoles or out-of-plane charges. There is a rather surprising difference of about 0.1 A between the vertical separation of base pairs predicted by quantum chemistry and derived from crystal structures. Evaluations of different local arrangements of the 5'-CG-3' step indicate a sensitivity of the relative stacking energies to the level of calculation. Thus, describing quantitative relations between local DNA geometrical variations and stacking may be more complicated than usually assumed. The reference calculations are complemented by continuum-solvent assessment of solvent-screening effects.

Comparison of molecular dynamics and harmonic mode calculations on RNA

Conformational fluctuations of a double-stranded RNA oligonucleotide have been calculated from a two nanosecond molecular dynamics simulation including explicit waters and ions and from a harmonic mode analysis. The harmonic mode analysis was performed in the absence of solvent using various effective dielectric screening functions. RNA flexibility was analyzed and compared at the level of atomic position fluctuations, helical base-pair descriptor fluctuations and global helix bending, stretching, and twisting flexibilities. Although quantitative differences were found, the qualitative pattern of atomic position and helical descriptor fluctuations along the sequence was similar for both methods. For the helical descriptor flexibility, the largest differences were observed for base-pair roll and rise that showed two times larger fluctuations in the molecular dynamics simulation. A significant overlap between the sub-space spanned by soft principal components calculated from the molecular dynamics simulation and harmonic modes was found. Both approaches predict a negative covariation for most helical base-pair step descriptors of neighboring base pair steps (with the exception of rise), which tend to stiffen the RNA at the global level. The RNA persistence length extracted from the molecular dynamics simulation (350-600 A) is smaller than the experimental value ( approximately 720 A) and estimates based on the harmonic mode approach (1100-1700 A).

Molecular dynamics simulations of small DNA plasmids: effects of sequence and supercoiling on intramolecular motions

Small (600 base pair) DNA plasmids were modeled with a simplified representation (3DNA) and the intramolecular motions were studied using molecular mechanics and molecular dynamics techniques. The model is detailed enough to incorporate sequence effects. At the same time, it is simple enough to allow long molecular dynamics simulations. The simulations revealed that large-scale slithering occurs in a homogeneous sequence. In a heterogeneous sequence, containing numerous small intrinsic curves, the centers of the curves are preferentially positioned at the tips of loops. With more curves than loop tips (two in unbranched supercoiled DNA), the heterogeneous sequence plasmid slithers short distances to reposition other curves into the loop tips. However, the DNA is immobilized most of the time, with the loop tips positioned over a few favored curve centers. Branching or looping also appears in the heterogeneous sequence as a new method of repositioning the loop tips. Instead of a smooth progression of increasing writhing with increasing linking difference, theoretical studies have predicted that there is a threshold between unwrithed and writhed DNA at a linking difference between one and two. This has previously been observed in simulations of static structures and is demonstrated here for dynamic homogeneous closed DNA. Such an abrupt transition is not found in the heterogeneous sequence in both the static and dynamic cases.

What is the basis of sequence-directed curvature in DNAs containing A tracts?

A variety of solution and gel experiments show that DNAs containing tracts of 4-8 A's repeated in phase with the helix repeat are curved. Several independent analyses of these experiments argue that curvature resides in the A tracts themselves. In x-ray crystallographic studies of several DNAs containing A tracts, however, the A tracts are uncurved, leading to models in which curvature resides in the non-A tracts. This "curved general sequence model" has several problems, in our view. We review those, and we describe recent experiments that show that the dehydrating agents commonly used in x-ray crystallography markedly reduce curvature in gels and in solution, calling into question the ability of crystallography to determine the structural basis of DNA curvature. Finally, we discuss the critical role of hydration in curved DNAs and suggest new experiments that we hope could finally determine exactly which sequences are responsible for curvature.

Static contributions to the persistence length of DNA and dynamic contributions to DNA curvature

Long molecules of DNA have the statistical properties of a worm-like coil. Deviations from linearity occur both because of small dynamic bends induced by thermal motion and from a random distribution of static bends. The latter originate in the different conformations of each of the possible base pair sequences. In this paper a statistical theory of the persistence length of DNA is developed which includes both static and dynamic effects for each base pair sequence, as well as the sequence-dependent correlations of bending angles. The result applies to a generic DNA, i.e., the average over an ensemble of all possible sequences. The theory is also applied to the generation of the average properties of curved DNAs by an analytic method that includes dynamic averaging as well as correlated bends. These results provide information which supplements that obtained by others using Monte Carlo methods. The additivity relation 1/P = 1/P(S) + 1/P(d) proposed by Trifonov et al., where P is the persistence length and P(S) and P(d) are the persistence lengths arising from purely static and dynamic effects, respectively, has been verified to be accurate to better than 0.5%. This is true for both a simplified model and one that includes a complete set of static bends at all base pair sequences.

DNA structural patterns and nucleosome positioning

There is no clear picture to date of the mechanisms determining nucleosome positioning. Generally, local DNA sequence signals (sequence-dependent positioning) or non-local signals (e.g. boundary effects) are possible. We have analyzed the DNA sequences of a series of positioned and mapped nucleosome cores in a systematic search for local sequence signals. The data set consists of 113 mapped nucleosome cores, mapped in vivo, in situ, or in reconstituted chromatin. The analysis focuses on the periodic distribution of sequence elements implied by each of six different published DNA structural models. We have also investigated the periodic distribution of all mono-, di-, and trinucleotides. An identical analysis was performed on a set of isolated chicken nucleosome cores (nucleosome data from the literature) that are presumably positioned due to local sequence signals. The results show that the sequences of the isolated nucleosome cores have a number of characteristic features that distinguish them clearly from randomly chosen reference DNA. This confirms that the positioning of these nucleosomes is mainly sequence-dependent (i.e., dependent on local octamer-DNA interactions) and that our algorithms are able to detect these patterns. Using the same algorithms, the sequences of the mapped nucleosome cores, however, are on average very similar to randomly chosen reference DNA. This suggests that the position of the majority of these nucleosomes can not be attributed to the sequence patterns implemented in our algorithms. The arrangement of positioned nucleosomes seems to be the result of a dynamic interplay of octamer-DNA interactions, nucleosome-nucleosome interactions and other positioning signals with varying relative contributions along the DNA.

Wide variations in neighbor-dependent substitution rates

The pattern of 20,200 point substitutions in the 16 unique neighbor-pair environments has been determined from aligned gene/pseudogene sequences in the current database of human DNA sequences. Substitution rates, representing averages over those for different regions of the genome, are distributed over a 60-fold range with strong biases in particular neighbor-pair environments. The rates for substitutions involving the CG doublet are the most rapid overall, where changes of the C.G pair vary over a tenfold range depending on the type of substitution and the 5' neighbor-pair. In general, the rates are fastest in alternating purine-pyrimidine sequences and slowest in purine.pyrimidine tracts, suggesting that the frequencies of one or both key molecular misadventures that can occur during replication, dNTP misinsertion and transient misalignment, may be associated with structural alternations and flexibility of the backbone. By contrast, purine.pyrimidine tracts are less flexible, less prone to substitution, and therefore their proportions accumulate in sequences over time. Characteristic biases of the content and arrangement of oligonucleotide strings or tuples in all sequence elements, but particularly in non-coding regions, appear to be due to the pattern of different neighbor-dependent substitution rates. Computer simulations of numerous replicative cycles have been carried out with substitutions occurring on the same schedule found in this study for pseudogenes. Statistical analyses of tuple frequencies at periodic intervals during the simulation experiment indicate that sequences slowly change in lexical complexity toward a quasi-equilibrium state that corresponds to that for introns.

Theoretical analysis of the base stacking in DNA: choice of the force field and a comparison with the oligonucleotide crystal structures

It follows from previous studies that changes in the base pair vertical separation (BPVS) influence the architecture of DNA much more than any other conformational parameter. This inspired us to compare BPVS in the available oligonucleotide crystal structures with the optimum values provided by nine different empirical potentials employed in the theoretical studies of DNA conformation. This comparison shows that BPVS is reproduced by three fields in all steps of the highly resolved oligonucleotide crystal structures while the remaining six empirical potentials, including AMBER, GROMOS and CHARMM, provide systematic deviations. We further find that the base pairs are poorly stacked (mostly compressed) in some other refined DNA crystal structures. Our analysis indicates that this poor stacking originates from improperly determined positions of the bases. The approach described in the present communication can be used to identify DNA structures which are not accurate enough for studies of the relationships between the base sequence and DNA conformation.

The influence of nearest neighbors on the rate and pattern of spontaneous point mutations

The numbers and local sequence environments of the two types of substitution mutation plus additions and deletions have been obtained directly in this study from differences between a large number of extant primate gene and pseudogene sequences. A total of 3786 mutations were scored in regions where similarities between pseudogene and corresponding gene sequences is greater than or equal to 85%, comprising approximately 30% of the pseudogene database of 80,584 bp. The pattern of mutations obtained in this fashion is almost identical to that obtained by Li et al. (1984) using a slightly different, more direct approach and with a smaller database. When mutations were scored, the neighbor pairs on the 5' and 3' sides were also noted, leading to a large 16 x 12 matrix of transitions and transversions. Biases of varying magnitude are found in the rates of substitution of the same base pair in different local sequence environments. The overall order for the effect of the 5' neighbor on the rates of substitution mutation of a pyrimidine is A greater than C much greater than T greater than G, and G greater than A greater than T greater than C for the 3' neighbor; where these results represent the average of substitution rates for the complement purine with complement neighbors of bases ordered above. The order for the 3' neighbor is essentially the same for the two transitions and most of the four transversions as well; however, the order for the 5' neighbor is more variable. The overall rate for the C.G----T.A transition is not unusual, however the presence of a 3' neighboring G.C pair boosts the rate substantially, presumably due to specific cytosine methylation of the CG doublet in primate DNAs. The rate of the T.A----C.G transition is also well above average when the 3' neighbor is an A.T, and to a lesser extent a G.C, pair. The latter bias is typical in that it reflects the association of alternating pyrimidine-purine sequences with increasing mutation rates. The substitution of the pyrimidine in a 5'purine-pyrimidine-purine3' sequence generally occurs much faster than in a pyrimidine tract and points to the local conformation as a major determining factor of the substitution rate. An apparent inverse relationship is found between starting and product doublet frequencies of base pairs undergoing mutations with specific 3' neighbors, indicating that differences in intrinsic substitution rates of base pairs with specific neighbors are a key factor in producing the familiar biases of nearest-neighbor frequencies.

Stabilities of double- and triple-strand helical nucleic acids

In this selected literature survey, we have seen that the stabilities of duplexes and triplexes are governed by the vertical base stacking, the horizontal specific base-paired H-bonding and the environmental parameters. The entropic contribution in the solvation/desolvation process is important in driving the aggregation of NA strands and duplex formation, but base stacking and specific H-bonding maintain the helical order. Triplex formation shares most of the physical environmental prerequisites with those of duplex NAs. However, some additional environmental conditions are often needed. Only in low pH solution is the polycytidylic strand protonated and, thus, it is possible for the strand to bind to a G.C duplex sequence to give the C+(G.C) triplex. High ionic strength is often necessary for the screening of inter-phosphate repulsion due to the high linear charge density in triplexes. The presence of specific counterions is important for complexation. In the absence of negative supercoiling, existence of an intramolecular triplex is rare except under very acidic conditions for the formation of C+(G.C)-type intramolecular triplex. As expected, the stabilities of both inter- and intramolecular triplexes increase with sequence length. The thermodynamic principles of helix-coil transition of oligo-duplex may be described by the van't Hoff relationship, which assumes a two-state cooperative melting profile. Thus, the enthalpy, entropy and free energy of transition can be evaluated from the experimental melting curves (e.g. OD, DSC). For polynucleotides, because of the non-two-state nature of transition, the simple van't Hoff relationship is no longer valid, and direct calorimetry is needed to obtain reliable thermodynamic parameters. The pH and salt concentration dependence of duplex stability can be formulated and derived from a van't Hoff equation. Base-stacking patterns are simple in duplexes but not so in triplexes due to the diversity in triplet schemes. The sequence dependence of base stacking for duplexes has been characterized and employed to predict the stability of an arbitrary sequence. In conclusion, the stability of duplex is relatively well-characterized by thermodynamic data in terms of both base stacking and specific H-bonding. Thermodynamic studies of triplexes have been far fewer in number. Oligonucleotides have found application in the detection and localization of a mRNA or its gene, the detection of bacterial or viral sequences, and the inhibition of the translation of mRNA and the transcription and replication of DNA (Englisch and Gauss, 1991). In a different approach, oligonucleotides have been targeted directly to a DNA duplex motif of a gene in order to inhibit the expression at the beginning of the transcriptional process.(ABSTRACT TRUNCATED AT 400 WORDS)

Computer simulation of DNA supercoiling

Major goals of this research are to comprehend and visualize the detailed three-dimensional arrangements of supercoiled DNA. Attention has been focused in the initial stages on mathematical procedures to generate the spatial coordinates of the B-DNA double helix constrained to specific spatial pathways and on simple energy models of chain conformation. The new treatment of superhelical DNA in terms of parametric curves is an important first step in being able to generate and examine tertiary structure systematically. The location of every residue is implicitly determined by the equation of the closed curve, with the number of computational variables sharply reduced compared to the number required for explicit specification of all chain units. Furthermore, the constraints of ring closure in cyclic chains and/or the end-to-end limitations on constrained open chains are automatically satisfied by the formulations (cubic B-splines and finite Fourier series) chosen in this work. The predicted conformations of elastic DNA do not appear to be tied to either the form of chain representation or the computer simulation method. Significantly, two very different minimization and modeling approaches come to the same structural conclusions. The most stable configurations of the closed circular elastic DNA model are found to be interwound superhelices that are critically dependent on the specified linking number difference. The total elastic energy is proportional to the imposed linking number difference, and beyond the critical linking number difference separating the circular and figure-eight forms, the writhing number of the DNA superhelices is directly proportional to delta Lk. The measured proportionality constant between Wr and delta Lk, however, is somewhat greater than that deduced from experimental observations of plectonemically interwound DNA chains and an assumed structural model. Furthermore, at large delta Lk, the interwound structures appear to curve. The treatment of the DNA double helix as an ideal elastic rod is clearly incorrect. The chain cannot bend with the same ease in all directions. The degree of bending observed in atomic level models is also tied to the angular twist so that the presumed partitioning of bending and twisting components is in error. Furthermore, the local chain bending and twisting are base sequence dependent, with certain residues able to flex more symmetrically than others. The polyelectrolyte character of the DNA is additionally expected to govern the overall folding of the chain and to influence the local secondary structure. The next step in this work is to compare the properties of such "real" DNA with conventional elastic models.(ABSTRACT TRUNCATED AT 400 WORDS)

A note on graphing helical parameters of dynamics structure of DNA

A graphical procedure for analysis of helical parameters in dynamic structure of DNA is described. The performance of the procedure is illustrated by analysis of a 20 ps dynamics simulation of the non-self-complementary ninemer, 5'CAAACAGGA:5'TCCTGTTTG, which is a part of DNA from lacI gene. The dynamics trajectory of the duplex shows sequence-dependent fluctuations of helical parameters.

Analysis of patterns of twist angles in DNA double helix

We have analysed theoretically the patterns of twist angles of B-DNA by the Tung-Harvey model mainly. It is shown that for a sequence of twist angles a smaller twist angle tends to follow a larger one and vice versa. Therefore the sequence of twist angles always takes a gentle zig-zag form. For simplicity we convert the sequence of twist angles to a symbolic sequence consisting of L and S, where L or S represents a large or a small angle, respectively. The -10 and -35 regions of 112 well-defined promoters for E. coli RNA polymerase, which were compiled by Hawley and McClure, have been analysed in terms of LS sequences in detail. The results shows that the number of LS sequences for promoters is considerably limited and the promoter mutations do not change the patterns of LS sequences in most cases. Several new ideas, which are believed to be useful in the further study, have been presented.

Molecular modeling and energy refinement of supercoiled DNA

A method is presented for constructing the complete atomic structure of supercoiled DNA starting from a linear description of the double helical pathway. The folding pathway is defined by piecewise B-spline curves and the atoms are initially positioned with respect to the local Frenet trihedra determined by the equations of the curves. The resulting chemical structure is corrected and refined with an energy minimization procedure based on standard potential expressions. The refined molecular structure is then used to study the effects of supercoiling on the local secondary structure of DNA. The minimized structure is found to differ from an isotropic elastic rod model of the double helix, with the base pairs bending in an asymmetric fashion along the supercoiled trajectory. The starting trajectory is chosen so that the refined supercoiled structure is either underwound (10.37 base pairs per turn) or overwound (9.65 base pairs per turn) compared to the standard tenfold B-DNA fiber diffraction model. The underwound supercoil is also lower in energy than the overwound duplex. The variation of base pair sequence in poly(dA).poly(dT).poly(dAT).poly(dTA) and poly(dA5T5).poly(dT5A5) is additionally found to influence the secondary structural features along a given supercoiled pathway. Finally, the detailed features of the refined structures are found to be in agreement with known X-ray crystallographic structures of DNA oligomers.

Sequence dependence of DNA conformational flexibility

By using conformational free energy calculations, we have studied the sequence dependence of flexibility and its anisotropy along various conformational variables of DNA base pairs. The results show the AT base step to be very flexible along the twist coordinate. On the other hand, homonucleotide steps, GG(CC) and AA(TT), are among the most rigid sequences. For the roll motion that would correspond to a bend, the TA step is most flexible, while the GG(CC) step is least flexible. The flexibility of roll is quite anisotropic; the ratio of fluctuations toward the major and minor grooves is the largest for the GC step and the smallest for the AA(TT) and CG steps. Propeller twisting of base pairs is quite flexible, especially of A.T base pairs; propeller twist can reach 19 degrees by thermal fluctuation. We discuss the effect of electrostatic parameters, comparison with available experimental results, and biological relevance of these results.

Sequence dependence of the B-A conformational transition of DNA

We have studied, by conformational analysis, the sequence dependence of DNA conformational transition between B- and A-forms. We have considered intramolecular interactions between base pairs, without backbone, to examine their role in the conformational transition between B- and A-forms, and found that base pairs themselves usually have intrinsic conformational preferences for the B- or A-form. Calculation of all ten possible base steps shows that the base combinations, CC (or GG), GC, AT, and TA, have tendencies to assume the A-conformation. Results show that it is particularly easy to slide along the long axis of the base pair for these steps, with AT and CC showing especially flat energies. These calculations show that a preference for the B- or A-conformation depends on the electrostatic energy parameters, in particular, on dielectric and shielding constants; the A-conformation is preferred for low dielectric constant or low shielding. Both the A- and B-conformations are mainly stabilized by electrostatic interactions between favorably juxtaposed atomic charges on base pairs; however, the B-conformation generally has more favorable van der Waals interactions than the A-form. These sequence-dependent conformational preference and environmental effects agree roughly with experimental observations, suggesting that the origin of the conformational polymorphism is attributable to the intrinsic conformational preference of base pairs.

The study of DNA sequences by their sequences of twist angles

To study the properties of DNA sequences we have transformed the sequences of bases into the sequences of twist angles along the chain of DNA double helix by using the Dickerson sum function. The Fourier transform and the auto-correlation function of the twist angles sequences have been used to study the periodicity and randomness of the original DNA sequences. Basing on the correlation coefficient, a "distance" between two DNA fragments has been defined and used to compare some realistic DNA sequences. It is hoped that the techniques developed here could be used to analyze more realistic DNA sequences.

Analysis of sequences of twist angles in DNA double helix

By assuming that the realistic DNA chains are random sequence of bases and using the Tung-Harvey formula for the prediction of twist angles, it is shown that the mean value of the sequence of twist angles is almost sequence-independent. In general the variance for the A, T-rich sequence is larger than that of G, C-rich sequence. There exists an upper bound for the variance of all possible sequences, i.e., the variance is not greater than 27 deg2. It is pointed out that the large conformational deviation from ideal DNA is an important factor for the recognition of DNA with protein/enzyme.

Sequence specificity of DNA cleavage by bis(1,10-phenanthroline)copper(I): effects of single base pair transitions on the cleavage of preferred pyrimidine-purine-pyrimidine triplets

The cleavage of DNA restriction fragments by bis(1,10-phenanthroline)copper(I) [[(OP)2CuI]+] is sequence dependent: the trimer TAT is most strongly preferred, while the trimer TGT and tetramers TAAT, TAGT, and CAGT are strongly to moderately preferred [Veal, J. M., & R. L. (1988) Biochemistry 27, 1822-1827]. [(OP)2CuI]+ cleavage of a series of oligonucleotide duplexes of the type 5'-CCCTPyPuPyCCCC-3'/3'-GGGAPuPyPuGGGG-5' (Py = pyrimidine; Pu = purine) was examined to determine the effects of purine substituents in the central triplet on specificity. The relative cleavage rates of different PyPuPy triplets in oligomers were similar to those observed for restriction fragments. The undecamer duplex containing the trimer TAT (TTATC) was most preferentially cleaved, predominantly at the central adenosine and the adjacent 3'-thymidine. Duplexes differing from TTATC by a single A.T----G.C transition in the central triplet were cleaved at significantly reduced rates relative to TTATC, the order of preference being TAT greater than TGT greater than TAC greater than CAT. By contrast, duplexes differing from TTATC by a single A.T----I.C transition were cleaved at rates similar to those for TTATC when the transition occurred at the 5'-pyrimidine or central purine [i.e., C(.I)AT and TIT]. A duplex containing the trimer TAC(.I) was cleaved at a reduced rate similar to the duplex containing TAC(.G). The guanine 2-amino group at positions 1 and 2, but not position 3, of a 5'-PyPuPy-3' trimer is therefore implicated as a strong inhibitor of DNA binding by the copper-phenanthroline complex.(ABSTRACT TRUNCATED AT 250 WORDS)

Modeling DNA supercoils and knots with B-spline functions

A method is offered to model the complex trajectories of closed circular DNA supercoils and knots. The trajectories are approximated by polygons and analytical expressions of the curves are generated from the polygons with B-spline functions. The resulting curves are used to evaluate the writhe and elastic energy of a series of interrelated supercoils, and to generate detailed atomic models of the deformed double helix.

Molecular mechanics model of supercoiled DNA

We describe a pseudo-atomic model of supercoiled DNA. Each base-pair of the DNA is represented in the model by three particles placed in a plane. The particle triplets are stacked to model stacked base-pairs in double-helical DNA, and closed circular conformations are generated to investigate supercoiling. This model is less detailed than all-atom models, which are too computationally demanding to be used to study supercoiling. On the other hand, this model contains details at the base-pair level and is therefore more elaborate than elastomechanical models. A potential energy function is written in terms of a set of internal co-ordinates defined to resemble a limited number of helical parameters. The modeled helical parameters, helical twist, base-roll, tilt and rise, are the most important parameters of the global shape of DNA. Experimentally measured mechanical properties of DNA are used to define the forces holding the particles together. We then use a procedure incorporating energy minimization and molecular dynamics to locate low energy conformations of the model DNA. The model was found to behave very much like rubber-tubing and elastomechanical models. The conformations and the effects of supercoiling pressure (a number proportional to the degree to which the total twist of the DNA has been altered from its natural value) on these conformations are all very similar to those observed in the latter two models. We also used this model to examine the effects of supercoiling pressure, base-sequence and mechanical properties on the conformations and energies of five sequences. The sequences studied include models of naturally straight DNA and DNA with static or natural bends.

Upper limit for the variances of some helical parameters in DNA double helix

Assuming that the realistic DNA chains are random sequences of purines and pyrimidines and, by using the Dickerson sum functions, it is shown that there exists an upper limit for the variance of helical twist angles, the base-plane roll angles and the other helical parameters respectively in the DNA sequences. The estimates of the variances of all the above helical parameters for the DNA sequences in the Los Alamos data base have been performed and found to be in good agreement with the theoretical results obtained in this paper.

A rigorous basepair oriented description of DNA structures

We propose new, rigorous definitions for (i) basepair fixed coordinate systems and (ii) the twist, tilt, and roll angles (called tau, t, rho) describing the relative orientation of adjacent basepairs and bases in a pair, in arbitrary DNA structures obtained from x-ray diffraction, 2D NMR, or energy calculations. In contrast to the corresponding angular parameters (tg, theta T, theta R) and coordinate systems introduced by Dickerson and co-workers and currently in use, our angular parameters and coordinate systems, together with a set of three displacement parameters, dx, dy, dz, provide a mathematically correct and general description of DNA conformations at the basepairs and/or base level. For instance, our description is applicable when the DNA structure considered is inherently curved, irregular, and/or does not possess dyad (or pseudodyad) axes. We develop a computationally convenient algorithm for rigorous DNA conformational analysis and apply it to some of the known crystal structures. We establish the connection to the currently used parameters and test the consistency and efficiency of our methodology by reconstructing the Dickerson B dodecamer using only the sequence and the set of parameters obtained from the atomic coordinates. The six parameter (tau, t, rho, dx, dy, dz) basepair level reconstruction is good but not perfect. Perfect reconstruction is obtained when one also considers each base in a basepair (consideration of propeller twist alone is not sufficient). The variation of the rigorous parameters proposed along the sequence is much larger, but their average values agree with fiber and solution data much better than in the case of the currently used set. The results of our analysis do not support Trifonov's AA.TT wedge model for DNA curvature but provide some evidence in favor of the Crothers junction-bend model. We point out some of the limitations of basepair level approaches when applied to DNA structure prediction and quantitative understanding of sequence-dependent variations in structure.

The definition of generalized helicoidal parameters and of axis curvature for irregular nucleic acids

An algorithm is presented which solves the problem of obtaining a rigorous helicoidal description of an irregular nucleic acid segment. Central to this approach is the definition of a function describing simultaneously the curvature of the nucleic acid segment in question and the corresponding stepwise variation of helicoidal parameters along the segment. Minimisation of this function leads to an optimal distribution of the conformational irregularity of the segment between these two components. Further, it is shown that this approach can be applied equally easily to single or double stranded nucleic acids. The results of this analysis yield both the absolute helicoidal parameters of individual bases/base pairs and the relative helicoidal parameters between successive bases/base pairs as well as the overall locus of the helical axis. The possibilities of this mathematical approach are demonstrated with the help of a computer program termed "Curves" which is applied to the study of a number of different nucleic acid structures.

A general procedure for generation of curved DNA molecules

A general method for generation of base-pairs in a curved DNA structure, for any prescribed values of helical parameters--unit rise (h), unit twist (theta), wedge roll (theta R) and wedge tilt (theta T), propeller twist (theta p) and displacement (D) is described. Its application for generation of uniform as well curved structures is also illustrated with some representative examples. An interesting relationship is observed between helical twist (theta), base-pair parameters theta x, theta y and the wedge parameters theta R, theta T, which has important consequences for the description and estimation of DNA curvature.

Structural basis of stable bending in DNA containing An tracts. Different types of bending

Structural determinants of DNA bending of different types have been studied by theoretical conformational analysis of duplexes. Their terminal parts were fixed either in an ordinary low-energy B-like conformation or in "anomalous" conformations with a narrowed minor groove typical of An tracts. The anomalous conformations had different negative tilt angles (up to about zero), different propeller twists and minor groove widths. Calculations have been performed for DNA fragments AnTm, TnAm, AnGCTm, AnCGTm, TmGCAn, TmCGAn which are the models of the junction of two anomalous structures on An and Tm tracts. On the AT step of the AnTm fragment the minor groove can be easily narrowed so that a whole unbent fragment of anomalous structure is formed on AnTm. According to our energy estimates, there should not be any reliable bending on AnTm. In contrast, in all other cases there was a pronounced roll-like bending into the major groove in the chemical symmetry region. Calculations of the junction between the anomalous and ordinary B-like structure for GnTm and CnAm have shown that there is an equilibrium bending with a tilt component towards the chain having the anomalous structure at the 5'-end. From our calculations it is impossible to determine precisely the direction of bending, though it can be suggested that the roll component of bending might be directed towards the major groove. The anomalous structure is the main reason of bending; alternations of pyrimidines and purines can modulate the value and the direction of equilibrium bending (only the value in the case of self-complementary fragments).(ABSTRACT TRUNCATED AT 250 WORDS)

Sequence specificity of DNA cleavage by bis(1,10-phenanthroline)copper(I)

The bis(1,10-phenanthroline)copper(I) complex is a relatively simple molecule previously shown to cause DNA cleavage with a strong preference for gene control regions such as the Pribnow box. Sequence level mapping of sites of [(Phen)2CuI]+ cleavage in greater than 2000 bases in histone genes and the plasmid pUC9 showed that the specificity for control regions is related to a predominant preference for minor groove binding at TAT triplets, which were cleaved most strongly at the adenosine sugar ring. The related sequences TGT, TAAT, TAGPy, and CAGT (Py = pyrimidine) were moderately preferred, while CAT and TAC triplets, PyPuPuPu quartets, PuPuPuPy quartets, and CG-rich PyPuPuPy quartets were cleaved with low to average frequency. Polypurine and polypyrimidine sequences were cleaved with low frequency. The sequence preferences of [(Phen)2CuI]+ can be ascribed predominantly to (i) a requirement for binding in the minor groove at a pyrimidine 3'----5' step and (ii) stereoelectronic effects of the 2-amino group of guanine in the minor groove, which inhibit binding. Although the reagent appears primarily to recognize sequence features at the triplet or quartet level, lower than expected cleavage was observed for two TAT sequences adjacent to several other preferred sequences and higher than expected cleavage was observed at CAAGC sequences, suggesting that longer range sequence-dependent DNA conformational effects influence specificity in certain cases.

An ab initio molecular orbital study on the sequence-dependency of DNA conformation: an evaluation of intra- and inter-strand stacking interaction energy

The various nearest neighbor stacking interaction energies of stacked base pairs in the DNA double helix are calculated for both A- and B-type conformations using an ab initio molecular orbital method. It is demonstrated that the sequence-dependent conformational preference for A- or B-type results from the stacking interaction. In particular, the base sequence showing the highest preference for an A-type conformation is revealed as GC/GC, and the one with the next highest preference, AT/AT; for a B-type conformation, the respective sequences are CG/CG and CA/TG. The overall conformation of a DNA fragment is not determined by these particular sequences only but is influenced by all base pair steps. An intrinsically favorable conformation is predicted from the constituent stacking interaction.

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.

A comparison of six DNA bending models

The predictions of six DNA bending models were compared with experimental relative mobility data. The study showed that all the models are reasonably accurate in predicting bending in synthetic sequences and in a natural sequence. The least accurate of these models is the Calladine-Dickerson model. The most consistent model is the ApA Wedge, possibly because it distributes the bends into base-roll and base-tilt components.

Molecular mechanics calculations of dA12.dT12 and of the curved molecule d(GCTCGAAAAA)4.d(TTTTTCGAGC)4

Using the AMBER software package (Weiner and Kollman 1981) substantially modified for electrostatic contributions, the structural energies of the double-stranded oligonucleotides dA12.dT12 and d(GCTCGAAAAA)4.d(TTTTTCGAGC)4 were minimized. Using various starting structures for the molecule dA12.dT12, one final structure is obtained which possesses the experimentally determined properties of poly(dA).poly(dT). This structure is an A-form-B-form-hybrid structure similar to that of Arnott et al. (1983). The dA-strand is similar to an A-form while the dT-strand is similar to normal B-form. This structure and separately optimized B-form sequence stretches were used to construct the double-stranded fragment d(GCTCGAAAAA)4 which again was optimized. This sequence, when imbedded in a DNA fragment as contiguous repeats, shows a gel migration anomaly which has been interpreted as stable curvature of the DNA (Diekmann 1986). The calculated structure of this sequence indeed has a curved helix axis and is discussed as a model for curved DNA. A theoretical formalism is presented which allows one to calculate the structural parameters of any nucleic acid double helix in two different geometrical representations. This formalism is used to determine the parameters of the base-pair orientations of the curved structure in terms of wedge as well as cylindrical parameters. In the structural model presented here, the curvature of the helix axis results from an alternation of two different DNA structures in which the base-pairs possess different angles with the helix axis ('cylinder tilt'). Resulting from geometric restraints, a negative cylinder tilt angle correlates strongly with the closing of the minor groove ('wedge roll'). The blocks with different structure are not exactly coincident with the dA5-blocks and the B-DNA stretches. Within the dA5 block, base-pair tilt and wedge roll adopt large values which proceed into the 3' flanking B-DNA sequence by about one base-pair. These properties of the structure calculated here are discussed in terms of different models explaining DNA curvature.

Theoretical molecular biology: prospectives and perspectives

I briefly discuss some aspects of theoretical molecular biology. Specifically, I include the issues of searches for homologies via string matchings, for patterns of specific nucleotide groupings and of sequence-structure relationship. The various approaches developed in order to achieve this end are described, attempting to convey some of the excitement in this quickly growing field.

Relationship between curved DNA conformations and slow gel migration

We propose some specific DNA conformations that explain, in terms of molecular conformations, the anomalous gel electrophoretic behavior of the sequences (VA4T4X), and (V2A3T3X2)i where V and X are either G or C. Previously (J. Biomole. Struct. Dyn. 4, 41, 1986) we considered hydrophobic interactions among aliphatic hydrocarbon groups in A/T sequences. In the sequences (T)n.(A)n, the T's are slightly bent to yield structures with tightly stacked methyl groups along one side of the major groove. By folding together the two pairs of stacked methyls on the opposite sides of the major groove. TTAA might yield a relatively sharp bend. On this basis, we show below that the sequences (VT4A4X)i might form a very tightly coiled super-helix whereas the sequences (VA4T4X)i form a broad super-helix of radius approximately 120 A for i = 25. The sequence (V2A3T3X2)i forms a slightly smaller radius super-helix. The time of passage through the gel has been taken to be inversely proportional to the smallest dimension of the molecule. Specifically we are taking the ratio of the apparent molecular weight to the actual molecular weight to be related to the moment of inertia I1 about the smallest principal axis of the molecular conformation. We find a good fit to the experimental gel mobility data of Hagerman (2) if we assume this ratio to be proportional to (I1)1/5.

A quantitative measure of DNA curvature enabling the comparison of predicted structures

A growing body of data indicates that the equilibrium structures of some DNA fragments are curved and that curvature is sequence-directed. We describe a quantitative measure of DNA curvature that can be used for evaluating and comparing current proposed models for the molecular basis of DNA curvature. We demonstrate that this measure, in conjunction with any given prediction model, enables both the comparison of experimental data to predictions and the scanning of nucleotide sequence databases for potential curved regions.