The persistence exponent of DNA

Using the complete genome of Thermoplasma volcanium, as an example, we have examined the distribution functions for the amount of C or G in consecutive, non-overlapping blocks of m bases in this system. We find that these distributions are very much broader (by many factors) than those expected for a random distribution of bases. If we plot the widths of the C-G distributions relative to the widths expected for random distributions, as a function of the block size used, we obtain a power law with a characteristic exponent. The broadening of the C-G distributions follows from the empirical finding that blocks containing a given C-G content tend to be followed by blocks of similar C-G content thus indicating a statistical persistence of composition. The exponent associated with the power law thus measures the strength of persistence in a given DNA. This behavior can be understood using Mandelbrot's model of a fractional Brownian walk. In this model there is a hierarchy of persistence (correlation between blocks) between all parts of the system. The model gives us a way to scale the C-G distributions such that all these functions are collapsed onto a master curve. For a fractional Brownian walk, the fractal dimension of the C-G distribution is simply related to the persistence exponent for the power law. The persistence exponent for T. volcanium is found to be gamma = 0.29 while for a 10 million base segment of the human genome we obtain gamma = 0.39, similar to but not identical with the value found for the microbe.     

Free energy of proton binding in proteins

In this article we use literature data on the titration of denatured ribonuclease to test the accuracy of proton-binding distributions obtained using our recent approach employing moments. We find that using only the local slope of the titration curve at a small number of points (five, for example) we can reproduce the detailed proton-binding distribution at all pH values. Our method gives the complete proton-binding polynomial for a given protein and each coefficient in this polynomial in turn yields the free energy for binding a given number of protons in all ways to the protein. Using these net free energies, we can then compute the average proton-binding free energy per proton as a function of the fraction of protons bound. We find that this function is remarkably similar for different proteins, even for proteins that exhibit quite different titration behavior. For the special case of binding to independent sites, we obtain simple relations for the first and last terms in the free energy per-proton function. For this special case we also can calculate the distribution functions giving the probability that a molecule has a given number of positive or negative charges and the joint distribution that a molecule simultaneously has a given number of positive and negative charge.     

Stability of XGCGCp, GCGCYp, and XGCGCYp helixes: an empirical estimate of the energetics of hydrogen bonds in nucleic acids

The stabilizing effects of dangling ends and terminal base pairs on the core helix GCGC are reported. Enthalpy and entropy changes of helix formation were measured spectrophotometrically for AGCGCU, UGCGCA, GGCGCCp, CGCGCGp, and the corresponding pentamers XGCGCp and GCGCYp containing the GCGC core plus a dangling end. Each 5' dangling end increases helix stability at 37 degrees C roughly 0.2 kcal/mol and each 3' end from 0.8 to 1.7 kcal/mol. The free energy increments for dangling ends on GCGC are similar to the corresponding increments reported for the GGCC core [Freier, S. M., Alkema, D., Sinclair, A., Neilson, T., & Turner, D. H. (1985) Biochemistry 24, 4533-4539], indicating a nearest-neighbor model is adequate for prediction of stabilization due to dangling ends. Nearest-neighbor parameters for prediction of the free energy effects of adding dangling ends and terminal base pairs next to G.C pairs are presented. Comparison of these free energy changes is used to partition the free energy of base pair formation into contributions of "stacking" and "pairing". If pairing contributions are due to hydrogen bonding, the results suggest stacking and hydrogen bonding make roughly comparable favorable contributions to the stability of a terminal base pair. The free energy increment associated with forming a hydrogen bond is estimated to be -1 kcal/mol of hydrogen bond.     

基于堆积协变信息与最小自由能预测含伪结的RNA二级结构

RNA伪结预测是RNA研究的一个难点问题。文中提出一种基于堆积协变信息与最小自由能的RNA伪结预测方法。该方法使用已知结构的RNA比对序列(ClustalW比对和结构比对)测试此方法, 侧重考虑相邻碱基对之间相互作用形成的堆积协变信息, 并结合最小自由能方法对碱基配对综合评分, 通过逐步迭代求得含伪结的RNA二级结构。结果表明, 此方法能正确预测伪结, 其平均敏感性和特异性优于参考算法, 并且结构比对的预测性能比ClustalW比对的预测性能更加稳定。文中同时讨论了不同协变信息权重因子对预测性能的影响, 发现权重因子比值在l1: l2=5:1时, 预测性能达到最优。     

An algorithm for studying cooperative transitions in DNA.

Cooperative transitions in DNA (B to Z, B to A, helix to coil, etc.) are known to depend strongly on nucleotide sequence. In general the change in free energy involved in the transition can be expressed as: delta G(seq) = 2RT log (sigma) where sigma is a factor arising from the free energy associated with boundaries of different conformations along the molecule. This formula allows to infer a general algorithm with which DNA sequences can be partitioned into well defined domains in which, under suitable conditions, base pairs change state cooperatively. The different partitions of the sequence that can be generated by varying the values of the physical parameters involved in the above formula, are shown to be embedded into a binary tree hierarchy. Application to a reliable prediction of Z-DNA antibody binding sites will be illustrated for the 0X174 genome. Possible biological implications are briefly discussed.     

Methylation of cytosine in the 5-position alters the structural and energetic properties of the supercoil-induced Z-helix and of B-Z junctions

The structural and energetic consequences of cytosine methylation in the 5-position on the supercoil-dependent B-Z equilibrium in alternating dC-dG sequences cloned into recombinant plasmids were investigated. The helical parameters determined with the band shift method for right-handed [10.7 base pairs (bp)/turn] and left-handed (12.8 bp/turn) 5MedC-dG inserts were different from the helical repeat values for unmethylated dC-dG inserts (10.5 bp/turn in the right-handed and 11.5 bp/turn in the left-handed form). We analyzed the thermodynamic parameters delta GBZ (free energy difference per base pair between right-handed and left-handed helix structure), delta Gjx (free energy for formation of one B-Z junction), and b (helix unwinding at a junction region) for varying lengths of dC-dG inserts by two-dimensional gel electrophoresis and application of a statistical mechanics model. A comparison of plasmids fully methylated in vitro with HhaI methylase and their unmethylated counterparts revealed that delta Gjx is not significantly changed by cytosine methylation. However, this base modification results in an approximate 3-fold decrease of delta GBZ and an approximate 2-fold decrease of the unwinding b at B-Z junction regions. Analysis of a pair of related plasmids, each containing two dC-dG blocks, revealed qualitatively different transition behaviors. When the two dC-dG blocks were separated by 95 bp of a mixed sequence, they underwent independent B to Z transitions with separate nucleation events and junction formations. When the two blocks were separated by only a 4 bp GATC sequence, only one nucleation event was necessary, and the Z-helix spread across the nonalternating GATC region.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Using an RNA secondary structure partition function to determine confidence in base pairs predicted by free energy minimization

A partition function calculation for RNA secondary structure is presented that uses a current set of nearest neighbor parameters for conformational free energy at 37 degrees C, including coaxial stacking. For a diverse database of RNA sequences, base pairs in the predicted minimum free energy structure that are predicted by the partition function to have high base pairing probability have a significantly higher positive predictive value for known base pairs. For example, the average positive predictive value, 65.8%, is increased to 91.0% when only base pairs with probability of 0.99 or above are considered. The quality of base pair predictions can also be increased by the addition of experimentally determined constraints, including enzymatic cleavage, flavin mono-nucleotide cleavage, and chemical modification. Predicted secondary structures can be color annotated to demonstrate pairs with high probability that are therefore well determined as compared to base pairs with lower probability of pairing.     

Theoretical model for the equilibrium behavior of DNA superhelices

A statistical-mechanical model for superhelical DNA is presented. The partition function for a DNA superhelix is written by using a combinatorial approach in order to allow for the known relation between the number of superhelical twists and the states of the base pairs in the double helix. While the theory allows any factors which might contribute to the free energy of superhelical twisting to be included in the statistical weights of the superhelical twists, only the reduction in configurational entropy is considered in this paper. Similarities between an imperfectly matched DNA double helix and a DNA superhelix are used in the derivation of expressions for the entropy of superhelical DNA. Although the partition function is presented in a general form, permitting many equilibrium properties of DNA superhelices to be treated, the application considered in this paper is the calculation of helix–coil transition curves. Several experimentally observed features of such transitions are predicted. For example, the curves are bimodal, with an early and a late transition relative to that of a nicked molecule. The results are very sensitive to the volume within which two parts of the double helix must meet when forming a superhelical twist. The free energy of superhelix formation is calculated, and the results are compared with those obtained from the data of Bauer and Vinograd for ethidium bromide intercalation. In the present model, the free energy increases less sharply with an increase in the number of superhelical twists than observed experimentally, indicating that factors other than configurational entropy probably make important contributions to the free energy of superhelix formation.     

Theory of the influence of oligonucleotide chain conformation on double helix stability

We consider theoretical aspects of reactions that form base pairs in a double helix. The equilibrium constant for such reactions depends on the probability of finding the two bases in the correct orientation for pairing. This probability can be expressed in terms of the spatial and angular distribution of one micleotide around the other. In this paper we use Monte-Carlo techniques to calculate the distribution of distances between chosen phosphates in nonhclical oligonucleotide backbones, using crystallographic data for bond lengths and angles, and a screened Coulomb potential for phosphate–phosphate interactions. The model chosen is one that predicts correctly the observed dimensions of an unperturbed polynucleotide chain. Knowledge of distance distribution functions permits calculation of the dependence on loop size of the probability of closing a single backbone strand into a hairpin helix. Our results agree roughly, although not exactly, with the semiempirical ring-weighting functions determined by Schefller. Elson, and Baldwin. Further results are a comparison of intramolecular and bimolecular helix nucleation equilibrium constants and a calculation of the stacking free energy in a double helix.     

Maximum-entropy calculation of free energy distributions for two forms of myoglobin

The temperature dependence of the heat capacity of myoglobin depends dramatically on pH. At low pH (near 4.5), there are two weak maxima in the heat capacity at low and intermediate temperatures, respectively, whereas at high pH (near 10.7), there is one strong maximum at high temperature. Using literature data for the low-pH form (Hallerbach and Hinz, 1999) and for the high-pH form (Makhatadze and Privalov, 1995), we applied a recently developed technique (Poland, 2001d) to calculate the free energy distributions for the two forms of the protein. In this method, the temperature dependence of the heat capacity is used to calculate moments of the protein enthalpy distribution function, which in turn, using the maximum-entropy method, are used to construct the actual distribution function. The enthalpy distribution function for a protein gives the fraction of protein molecules in solution having a given value of the enthalpy, which can be interpreted as the probability that a molecule picked at random has a given enthalpy value. Given the enthalpy distribution functions at several temperatures, one can then construct a master free energy function from which the probability distributions at all temperatures can be calculated. For the high-pH form of myoglobin, the enthalpy distribution function that is obtained exhibits bimodal behavior at the temperature corresponding to the maximum in the heat capacity (Poland, 2001a), reflecting the presence of two populations of molecules (native and unfolded). For this form of myoglobin, the temperature evolution of the relative probabilities of the two populations can be obtained in detail from the master free energy function. In contrast, the enthalpy distribution function for the low-pH form of myoglobin does not show any special structure at any temperature. In this form of myoglobin the enthalpy distribution function simply exhibits a single maximum at all temperatures, with the position of the maximum increasing to higher enthalpy values as the temperature is increased, indicating that in this case there is a continuous evolution of species rather than a shift between two distinct population of molecules.     

Tuning of collagen triple-helix stability in recombinant telechelic polymers

The melting properties of various triblock copolymers with random coil middle blocks (100-800 amino acids) and triple helix-forming (Pro-Gly-Pro)(n) end blocks (n = 6-16) were compared. These gelatin-like molecules were produced as secreted proteins by recombinant yeast. The investigated series shows that the melting temperature (T(m)) can be genetically engineered to specific values within a very wide range by varying the length of the end block. Elongation of the end blocks also increased the stability of the helices under mechanical stress. The length-dependent melting free energy and T(m) of the (Pro-Gly-Pro)(n) helix appear to be comparable for these telechelic polymers and for free (Pro-Gly-Pro)(n) peptides. Accordingly, the T(m) of the polymers appeared to be tunable independently of the nature of the investigated non-cross-linking middle blocks. The flexibility of design and the amounts in which these nonanimal biopolymers can be produced (g/L range) create many possibilities for eventual medical application.     

Base sequence effects in double-helical DNA. II. Configurational statistics of rodlike chains

Matrix generator techniques have been adapted to account for precise structural features of the nucleotide repeating unit and to translate the primary sequence of DNA base pairs into three-dimensional structures. Chains have been constructed to reflect the local sequence-dependent differences of bending and twisting of adjacent residues and various overall chain properties, including the average unperturbed moments of the end-to-end vector r and the mean angular orientation (〈γ〉 between base pair normals, 〈?₁〉 between long axes, and 〈?₂〉 between short axes) of terminal chain residues, have been computed. The chain backbone is treated implicitly in terms of the spatial fluctuations of successive base pairs. Motions are limited to low-energy perturbations of the standard B-DNA helix. Approximate potential energy schemes are used to represent the rules governing the patterns of local base–base morphology and flexibility. Theoretical predictions are compared with experimental observations at both the local and the macro-molecular level. Initial applications are limited to the rodlike poly(dA) · poly(dT) and poly(dG) · poly(dC) helices. The former duplex is found to be more compressed and the latter more extended than random-sequence DNA of the same chain length. The flexibility of the duplexes as a whole is described in terms of the average higher moments of the displacement vector ρ = r - 〈r〉 and the likelihood of chain cyclization is estimated from the three-dimensional Hermite series expansions of the displacement tensors. Emphasis is placed on theoretical methodology and the practical relevance of the calculated chain moments to observed physical properties.     

Base-stacking interactions in double-helical DNA structures: experiment versus theory

Atom-atom potential energy calculations have been undertaken for deriving stacking energies in double-helical structures. A comparison between the energy patterns of A- and B-type double-helical fragments determined by single-crystal X-ray diffraction methods versus idealized uniform models based on fibre diffraction data shows that the van der Waals stacking energy is largely sensitive to local changes in the relative orientation of adjacent base pairs. The sequence-dependent conformational variability observed in the high-resolution structures appears to be a consequence of the equipartitioning of the stacking energy along the double helix. The large energy variations expected for a uniform structure are dampened considerably in the observed structures by means of local changes in conformational features such as helix rotation and roll angles between base pairs.     

Protein denaturant binding polynomials

We show how moments of the denaturant binding distribution function can be extracted from experimental data on the denaturation of a protein as a function of the concentration of denaturant and how in turn these moments can be used to construct the denaturant binding distribution function. This approach is similar to our recent work on using the maximum-entropy method to construct ligand-binding distributions from moments obtained from titration curves for nucleic acids and proteins. As an example we take literature data on the denaturation of ferro- and ferricytochrome c by guanidine hydrochloride and from it construct the denaturant binding polynomial and binding distribution function for the unfolded protein.     

The phylogeny of persistence in DNA

We continue our study, Poland [Biophysical Chemistry 110 (2004) 59-2], of the distribution of C or G (C-G for short) in the DNA of select organisms, in particular, the tendency for C-G to cluster on all scales with respect to the number of bases considered. We previously found that if we counted the number of C-G bases in consecutive, nonoverlapping boxes containing a total of m bases, then the width of the distribution function describing how many C-G bases are in a box increases with respect to m dramatically relative to the width expected for a random distribution. The relative width of the C-G composition distribution function was found to vary accurately as a power law with respect to m, the size of the box, over a very wide range of m values. We express the power law in terms of a characteristic exponent gamma, that is, the relative widths of the distributions vary as m(gamma). The enhanced relative width of the distribution functions is a direct consequence of the tendency for boxes of similar composition to follow one another. This tendency represents persistence in composition from box to box and hence we refer to gamma as the persistence exponent. The occurrence of a power law means that the tendency for C-G to cluster is present on all scales of sequence length (box size) up to the total length of the chromosome which for bacteria is the entire genome. The persistence exponent gamma that characterizes the power law is thus an important parameter describing the distribution of C-G on all scales from individual base pairs up to the total length of the DNA sample considered. In the present paper, we determine the characteristic exponent gamma and the associated fractal dimension of DNA samples for a selection of species representing all of the major types of organism, that is, we explore the phylogeny of the exponent gamma. Here we treat six prokaryotes and six eukaryotes which, together with the species we have previously treated, brings the total number of species we have examined to 15. We find the power law form for the C-G distribution for all of the species treated and hence this behavior seems to be ubiquitous. The values of the characteristic exponent gamma that we find tend to cluster around the value gamma=0.20 with no obvious pattern with respect to phylogeny. The extreme values that we obtain are gamma=0.057 (yeast) and gamma=0.386 (human). We conclude by showing that the persistence of C-G clustering on the scale of the length of a chromosome is dramatically illustrated by interpreting the C-G distribution as a random walk.     

Free energy contributions of G.U and other terminal mismatches to helix stability

Thermodynamic parameters of helix formation were measured spectroscopically for seven hexaribonucleotides containing a GC tetramer core and G.U or other terminal mismatches. The free energies of helix formation are compared with those for the tetramer core alone and with those for the hexamer with six Watson-Crick base pairs. In 1 M NaCl, at 37 degrees C, the free energy of a terminal G.U mismatch is about equal to that of the corresponding A.U pair. Although other terminal mismatches studied add between -1.0 and -1.6 kcal/mol to delta G0 37 for helix formation, all are less stable than the corresponding Watson-Crick pairs. Comparisons of the stability increments for terminal G.U mismatches and G.C pairs suggest when stacking is weak the additional hydrogen bond in the G.C pair adds roughly -1 kcal/mol to the favorable free energy of duplex formation.     

Base-Stacking Interactions in Double-Helical DNA Structures: Experiment Versus Theory

Abstract

Atom-atom potential energy calculations have been undertaken for deriving stacking energies in double-helical structures. A comparison between the energy patterns of A- and B-type double-helical fragments determined by single-crystal X-ray diffraction methods versus idealized uniform models based on fiber diffraction data shows that the van der Waals stacking energy is largely sensitive to local changes in the relative orientation of adjacent base pairs. The sequence-dependent conformational variability observed in the high-resolution structures appears to be a consequence of the equipartitioning of the stacking energy along the double helix. The large energy variations expected for a uniform structure are dampened considerably in the observed structures by means of local changes in conformational features such as helix rotation and roll angles between base pairs.     

Proton nuclear magnetic resonance investigations of the nucleation and propagation reactions associated with the helix-coil transition of d-ApTpGpCpApT in H2O solution.

The chemical shifts and line widths of the Watson-Crick ring NH resonances of the self-complementary duplex of d-ApTpGpCpApT have been monitored in the presence of 0.1 M phosphate at neutral pH in aqueous solution. While the resonance positions of the terminal and internal AT base pairs shift upfield and broaden as average resonances with increasing temperature (helix and coil exchange several times prior to exchange with water from the coil form), those of the central GC base pairs broaden in the absence of upfield shifts (exchange with water occurs each time helix converts to coil). The line-width changes at the AT base pairs monitor the lifetime of the coil state at these positions prior to exchange with water while the line-width changes at the GC base pairs monitor the lifetime of the helix prior to dissociation to strands. This permits the separation of the propagation reaction at the AT base pairs from the nucleation reaction at the GC base pairs during helix formation. The experimental data have been quantitatively analyzed to yield (at 20 degrees) a nucleation formation rate of approximately 10(3) sec-1 for the GC base pairs (bimolecular rate constant of approximately 6 times 10(6) l. mol-1 sec-1) and a dissociation rate of 6 times 10(2) sec-1 at these same base pairs (unimolecular dissociation to strands). The unimolecular propagation reactions at the terminal and terminal base pairs are associated with reaction rates greater than 10(4) sec-1. These values are consistent with a slow formation of a stable nucleus at the GC base pairs followed by a rapid propagation reaction at the AT base pairs. The line width of the (GC) central base pairs in the presence of phosphate is a direct measure of the lifetime of the total helix and yields an activation energy of 45 kcal for helix to coil conversion measured over a narrow temperature range. The exchange from the coil form with water is catalyzed by 0.1 M phosphate with a rate constant kHPO2-/4 = 0.2 times 10(6) 1. mol-1 sec-1.