Molecular dynamics of an in vacuo model of duplex d(CGCGAATTCGCG) in the B-form based on the amber 3.0 force field.

The characteristics of 100 ps of molecular dynamics (MD) on the DNA dodecamer d(CGCGAATTCGCG) at 300 K are described and investigated. The simulation is based on an in vacuo model of the oligomer and the AMBER 3.0 force field configured in the manner of Singh, U. C., S. J. Weiner, and P. A. Kollman, (1985, Proc. Natl. Acad. Sci. USA. 82:755-759). The analysis of the results was carried out using the "curves, dials, and windows" procedure (Ravishanker, G., S. Swaminathan, D. L. Beveridge, R. Lavery, and H. Sklenar. 1989. J. Biomol. Struct. Dyn. 6:669-699). The results indicate this dynamical model to be a provisionally stable double helix which lies at approximately 3.2 A rms deviation from the canonical B-form. There is, however, a persistent nonplanarity in the base pair orientations which resemble that observed in canonical A-DNA. The major groove width is seen to narrow during the course of the simulation and the minor groove expands, contravariant to the alterations in groove width seen in the crystal structure of the native dodecamer (Drew, H. R., R. M. Wing, T. Takano, C. Broka, S. Tanaka, I. Itakura, and R. E. Dickerson, 1981. Proc. Natl. Acad. Sci. USA. 78:2179-2183). The propeller twist in the bases, the sequence dependence of the base pair roll and aspects of bending in the helix axis are in some degree of agreement with the crystal structure. The patterns in DNA bending are observed to follow Zhurkin theory (Zhurkin, V. B. 1985. J. Biomol. Struct. Dyn. 2:785-804.). The relationship between the dynamical model and structure in solution is discussed.     

Back to units of protein folding

In response to the criticism by A. Finkelstein (J Biomol Struct Dyn 20, 311-314, 2002) of our Communication (J Biomol Struct Dyn 20, 5-6, 2002) several issues are dealt with. Importance of the notion of elementary folding unit, its size and structure, and the necessity of further characterization of the units for the elucidation of the protein folding in vivo are discussed. The criticism (J Biomol Struct Dyn 20, 311-314, 2002) on the hierarchical protein folding is also briefly addressed.     

Bending and curvature calculations in B-DNA.

A simple program, BEND, has been written to calculate the magnitude of local bending and macroscopic curvature at each point along an arbitrary B-DNA sequence, using any desired bending model that specifies values of twist, roll and tilt as a function of sequence. The program has been used to evaluate six different DNA bending models in three categories. Two are bent non-A-tract models: (a) A new model based on the nucleosome positioning data of Satchwell et al 1986 (J. Mol. Biol. 191, 659-675), (b) The model of Calladine et al 1988 (J. Mol. Biol. 201, 127-137). Three are bent A-tract models: (c) The wedge model of Bolshoy et al 1991 (Proc. Natl. Acad. Sci. USA 88, 2312-2316), (d) The model of Cacchione et al 1989 (Biochem. 28, 8706-8713), (e) A reversed version of model (b). The last is a junction model: (f) The model of Koo & Crothers 1988 (Proc. Natl. Acad. Sci. USA 85, 1763-1767). Although they have widely different assumptions and values for twist, roll and tilt, all six models correctly predict experimental A-tract curvature as measured by gel retardation and cyclization kinetics, but only the new nucleosome positioning model is successful in predicting curvature in regions containing phased GGGCCC sequences. This model--showing local bending at mixed sequence DNA, strong bends at the sequence GGC, and straight, rigid A-tracts--is the only model consistent with both solution data from gel retardation and cyclization kinetics and structural data from x-ray crystallography.     

Persistence analysis of the static and dynamical helix deformations of DNA oligonucleotides: Application to the crystal structure and molecular dynamics simulation of d(CGCGAATTCGCG)2

A theory and graphical presentation for the analysis of helix structure and deformations in oligonucleotides is presented. The parameters “persistence” and “flexibility” as defined in the configurational statistics of polymers of infinite length are reformulated at the oligonucleotide level in an extension of J. A. Schellman's method [(1974) Biopolymers, Vol. 17, pp. 217–226], and used as a basis for a systematic “Persistence Analysis” of the helix deformation properties for all possible subsequences in the structure. The basis for the analysis is a set of link vectors referenced to individual base pairs, and is limited to sequences exhibiting only perturbed rod-like behavior, i.e., below the threshold for supercoiling. The present application of the method is concerned with a physical model for the angular component of bending, so the link vectors are defined as the unit components of a global helix axis obtained by the procedure “Curves” of R. Lavery and H. Sklenar [(1988) J. Biomol. Struct. Dynam., Vol. 6, pp. 63–91; (1989) J. Biomol. Struct. Dynam., Vol. 6, pp. 655–667]. A discussion, of the relationship between global bending and relative orientation of base pairs is provided. Our approach is illustrated by analysis of some model oligonucleotide structures with intrinsic kinks, the crystal structure of the dodecamer d (CGCGAATTCGCG)₂, and the results of two molecular dynamics simulations on this dodecamer using two variations of the GROMOS force field. The results indicate that essentially all aspects of curvature in short oligonucleotides can be determined, such as the position and orientation of each bend, the sharpness or smoothness, and the location and linearity of subsequences. In the case of molecular dynamics simulations, where a Boltzmann ensemble of structures is analyzed, the spatial extent of the deformations (flexibility) is also considered. © 1993 John Wiley & Sons, Inc.     

Sequence-dependent dynamics of TATA-Box binding sites.

We have carried out two nanosecond-length molecular dynamics simulations on a DNA oligomer, d(GCGTAAAAAAAACGC)2, which contains a weak binding site for the TATA-box binding protein. An analysis of the resulting trajectories shows that this oligomer behaves differently from a related oligomer [d(GCGTATATAAAACGC)2] studied earlier using the same protocol (Flatters, D., M. Young, D. L. Beveridge, and R. Lavery. 1997. Conformational properties of the TATA-box binding sequence of DNA. J. Biomol. Struct. & Dyn. 14:757-765), and which contains a strong binding site for the same protein. The two basepair mutations that relate these oligomers lead to significant changes in time-averaged structure and in dynamic behavior, which extend over entire length of the oligomer and appear to be compatible with the experimentally observed decrease of binding and functional activity. These results suggest that molecular dynamics simulations, taking into account explicit solvent and counterions, and avoiding the truncation of electrostatic interactions, are a powerful tool for investigating the indirect aspects of protein-nucleic acid recognition.     

Stereoelectronic factors in the interaction with DNA of small aromatic molecules substituted with a short cationic chain: importance of the polarity of the aromatic system of the molecule.

We have performed a quantitative analysis of the interaction with DNA of several unfused aromatic compounds synthesized in our laboratory and substituted with one or two short cationic chains. These and similar literature compounds, for which DNA binding data are available, bind with DNA by partial intercalation of the aromatic system, groove interaction of the linker chain, and groove electrostatic interactions of the terminal cationic group. Several independent quantitative and qualitative approaches show consistently that the strength of the interaction of the aromatic unit of the molecule with DNA binding sites depends on the direction and magnitude of polarity of the aromatic system. The phenomenon is explained in terms of the greatest negative potential in the DNA grooves, a concept extensively elaborated by Pullman and Pullman [cf. Lavery, R. and Pullman, B. [(1985) J. Biomol. Struct. Dyn. 2, 1021-1032] and references therein]. Classical, fused-ring planar intercalators do not follow the polarity-DNA affinity correlation, presumably because the intercalative forces depend more strongly on polarizability than on polarity of the aromatic system.     

Back to Units of Protein Folding

Abstract

In response to the criticism by A. Finkelstein (J. Biomol. Struct. Dyn. 20, 311–314, 2002) of our Communication (J. Biomol. Struct. Dyn. 20, 5–6, 2002) several issues are dealt with. Importance of the notion of elementary folding unit, its size and structure, and the necessity of further characterization of the units for the elucidation of the protein folding in vivo are discussed. The criticism (J. Biomol. Struct. Dyn. 20, 311–314, 2002) on the hierarchical protein folding is also briefly addressed.     

Nucleosome positioning pattern derived from oligonucleotide compositions of genomic sequences

Availability of nucleosome positioning pattern(s) is crucial for chromatin studies. The matrix form of the pattern has been recently derived (I. Gabdank, D. Barash, E. N. Trifonov. J Biomol Struct Dyn 26, 403-412 (2009), and E. N. Trifonov. J Biomol Struct Dyn 27, 741-746 (2010)). In its simplified linear form it is described by the motif CGRAAATTTYCG. Oligonucleotide components of the motif (say, triplets GRA, RAA, AAA, etc.) would be expected to appear in eukaryotic sequences more frequently. In this work we attempted the reconstruction of the bendability patterns for 13 genomes by a novel approach-extension of highest frequency trinucleotides. The consensus of the patterns reconstructed on the basis of trinucleotide frequencies in 13 eukaryotic genomes is derived: CRAAAATTTTYG. It conforms to the earlier established sequence motif. The reconstruction, thus, attests to the universality of the nucleosome DNA bendability pattern.     

Z-curve: a computer program calculating DNA helical axis coordinates for three-dimensional graphic presentation of curvature.

In order to predict curvature of DNA fragments, we previously developed a computer program for simply calculating a vectorial sum of all individual roll, tilt and twist wedge angles between the nearest base pairs for a given DNA fragment [Lee et al., (1991)]. Now, a new program, called Z-curve, was developed to calculate three-dimensional coordinates of the helical center of each base pair along the DNA, using helical axis deviations from B-form DNA by wedge angles. The output file of the new program was designed to become an input file for a graphics program, Insight II. Thus, we were able to obtain three-dimensional graphic presentations of DNA helical axis curvatures of any length. It visualized spatial details of the DNA curvature, where and how much it curves, and to which direction. It also allowed calculation of the three-dimensional distance between two ends of a DNA fragment, which could provide a measure of its curvature. Here, three DNA fragments, both curved and straight, were subjected to the Z-curve and Insight II programs. The results showed that their curvature details could be visualized to the level of the base pair, whether the DNA fragments contained an oligo(A) track or not. Their estimated curvatures were consistent with the experimental results of permutation gel mobility assay.     

Comparison of different approaches for calculation of polyelectrolyte free energy

We consider the problem of the mean field (Poisson-Boltzmann) calculation of the electrostatic free energy for a strongly charged polyelectrolyte such as DNA in a salt solution. We compare two approaches to calculate the free energy: (i) direct one starting from the statistical-mechanical expression for the electrostatic free energy and (ii) the polyion charge variation method. In the infinite dilution limit (in respect to polyion) and in excess salt (IDLES) the two approaches are fully equivalent. This is shown by straight forward algebra. We have performed specific calculations of the free energy difference for the case of B-Z transition in DNA as a function of ionic strength. As expected, the two approaches led to identical results. The ionic strength dependence of the B-to-Z free energy proves to be concaved up and as a result Z-DNA is stabilized at low ionic concentration as well as at high salt, in full agreement with our previous results (M.D.Frank-Kamenetskii et al., J. Biomol. Struct. Dyn. 3, 35-42 (1985]. Our data quantitatively agree with the results of Soumpasis (D.M.Soumpasis, J. Biomol. Struct. Dyn. 6, 563-574 (1988]. However, his claim about the absence of the effect of stabilization of Z-DNA at low salt proves to be groundless, and the criticism of our earlier approach seems to be irrelevant.     

Solvation effects on the sequence variability of DNA double helical conformations

The role of solvation on the sequence dependent conformational variabilities in DNA has been studied by calculating hydration free energies from solvent accessible surface areas for several base steps, as a function of various helical parameters, roll, twist and propeller twist. The results of roll calculations suggest opposite trends for AA and GG steps, with the former tending to have a compressed minor groove and the latter a compressed major groove. These trends are consistent with the experimental findings on sequence preferences and the nature of anisotropic bending of DNA observed in nucleosomes (Drew, H.R. and Travers, A.A., J. Mol. Biol. 186, 773-790 (1985); Satchwell, S.C., Drew, H.R. and Travers, A.A., J. Mol. Biol. 191, 659-675 (1986)) and CAP-DNA interactions (Gartenberg, M.R. and Crothers, D.M., Nature 333, 824-829, (1988)). Solvation energy profiles also indicate preferences for the base pairs in GG and AA steps to adopt low and high propeller twists, respectively. Such agreements may either reflect a coincidence of solvation effects with other energy terms or a dominance of solvent effects. The results are discussed in the context of the crystallographic observations of structural tendencies.     

Molecular dynamics simulations of beta-turn forming tetra- and hexapeptides

It was previously shown that the structural ensemble of model peptides DDKG and GKDG (H. Ishii et al. Biopolymers 24, 2045-2056, 1985), DEKS (A. Otter et al. J. Biomol. Struct. Dyn. 7, 455-476, 1989) NPGQ (F. R. Carbone et al. Int. J. Pept. Protein. Res. 26, 498-508, 1985), SALN (H. Santa et al. J. Biomol. Struct. Dyn. 16, 1033-1041, 1999), SYPFDV and SYPYDV (J. Yao et al. J. Mol. Biol. 243, 736-753, 1994), VP(D)AH and VP(D)SH (B. Imperiali et al. J. Am. Chem. Soc. 114, 3182-3188, 1992) in solution contains a significant - or in some cases dominant - proportion of beta-turn conformation. In this study, a protein database was searched for the above, unprotected sequences which incorporate only L-amino acid residues. Simulated annealing and 25 ns MD simulations of structures were also performed. The DSSP and STRIDE secondary structure-assigning algorithms and clustering were used to analyze trajectories and i, i+3 hydrogen bonds were also sought. The DSSP analysis showed a fluctuation between beta-turn and random meander structure, although bend structures were not detected because of the insufficient length of peptide chains. This alternating trend was confirmed when the STRIDE algorithm was used to analyze trajectories, but STRIDE assigned more turn structures. The population of the strongest clusters was above 40% and the middle structures adopted beta-turn structure for most sequences. These results are in good agreement with previous experimental results and support the idea of the ultra-marginal stability of turns in the absence of stabilizing long-range interactions of the neighboring segments of a polypeptide chain. However, interactions between the side-chains in tetrapeptides could also contribute to turn stability and result in unusual stability in some cases. Our observations suggest that such interactions are the consequence rather than the driving force of turn formation.     

Structure of (dG)n.(dC)n under superhelical stress and acid pH

We have recently shown that a (GA)n.(TC)n tract undergoes a sharp structural transition under superhelical stress (V.I. Lyamichev, S.M. Mirkin and M.D. Frank-Kamenetskii, J. Biomol. Struct. Dyn. 2,327 (1985]. Unlike the well studied transitions to the cruciform and to the Z form, this novel transition was strongly pH-dependent. We have found the (dG)n.(dC)n insert to undergo a pH-dependent structural transition similar to that of the (GA)n.(TC)n tract. These new data meet our earlier expectations and disagree with the data of D.E. Pulleyblank, D.B. Haniford and A.R. Morgan, Cell 42, 271 (1985). We conclude that a novel DNA structure (the H-form) is typical of homopurine-homopyrimidine mirror repeats (the H palindromes) under superhelical stress and/or acid pH. In the H-form the homopyrimidine strand forms a hairpin while half of the homopurine strand interacts with the hairpin forming a triplex, the other half of the homopurine strand being unstructured (V.I. Lyamichev, S.M. Mirkin and M.D. Frank-Kamenetskii, J. Biomol. Struct. Dyn. 2, 3, 667 (1986].     

Dependencies of Substitution Steps Number on Hamming Distance Are Identical For One-parameter Discrete Models of Both Direct and Parallel Genetic Diversity

Abstract

With the help of previously introduced enumeration procedure (M.Yu. Shchelkanov, A.N. Yudin, A.V Antonov, N.S. Starikov, A.A. Vedenov, E.V. Karamov, J. Biomol. Struct. Dyn. 15, 217–229 (1997)) and probability distribution function for the enumeration after some substitution steps (M.Yu. Shchelkanov, L.A. Soinov, V.V. Zalunin, D.A. Gumennyi, A.N. Yudin, A.A. Natan, V.B. Kireev, E.V. Karamov, J. Biomol. Struct. Dyn. 15, N 4, (1998)) we have demonstrated that dependencies of replication acts number on Hamming distance are identical for one-parameter discrete models of both direct and parallel genetic diversity.     

Comparison of Different Approaches for Calculation of Polyelectrolyte Free Energy

Abstract

We consider the problem of the mean field (Poisson-Boltzmann) calculation of the electrostatic free energy for a strongly charged polyelectrolyte such as DNA in a salt solution. We compare two approaches to calculate the free energy: (i) direct one, starting from the statistical-mechanical expression for the electrostatic free energy and (ii) the polyion charge variation method. In the infinite dilution limit (in respect to polyion) and in excess salt (IDLES) the two approaches are fully equivalent. This is shown by straight forward algebra. We have performed specific calculations of the free energy difference for the case of B-Z transition in DNA as a function of ionic strength. As expected, the two approaches led to identical results. The ionic strength dependence of the B-to-Z free energy proves to be concaved up and as a result Z-DNA is stabilized at low ionic concentration as well as at high salt in full agreement with our previous results (M.D. Frank- Kamenetskii et al, J. Biomol. Struct. Dyn. 3, 35–42 (1985)). Our data quantitatively agree with the results of Soumpasis (D. M. Soumpasis, J. Biomol. Struct. Dyn. 6, 563–574 (1988)). However, his claim about the absence of the effect of stabilization of Z-DNA at low salt proves to be groundless, and the criticism of our earlier approach seems to be irrelevant.     

Imino proton exchange in the 5S RNA of Escherichia coli and its complex with protein L25 at 490 MHz

Imino proton exchange has been examined by NMR in the 5S RNA of Escherichia coli, its principal RNase A resistant fragment, fragment 1 (bases 1-11, 69-120), and complexes between that fragment and ribosomal protein L25 by using both real-time and relaxation techniques. Fragment 1 RNA imino protons exchange at rates between 0.5 and 15 s-1 at 303 K in 5 mM cacodylate buffer, pH 7.4. In contrast with many tRNAs, intact 5S RNA contains no imino protons with exchange lifetimes as great as 1 min. Consistent with the results of Gueron and his colleagues [Leroy, J. L., Bolo, N., Figueroa, N., Plateau, P., & Gueron, M. (1985) J. Biomol. Struct. Dyn. 2,915-939; Leroy, J. L., Broseta, D., & Gueron, M. (1985) J. Mol. Biol. 184, 165-178] with tRNA, exchange in 5S RNA is catalyst-limited under conditions generally used for imino proton spectroscopy, such as those given above. Using Gueron's catalyst saturation technique, base pair opening rates have been measured for several AU and GU base pairs in fragment 1. They range from 50 to 300 s-1 at 303 K and depend on base pair type and also to some degree on context. Similar studies have been done on complexes of L25 and fragment 1. The binding of L25 to fragment 1 reduces the exchange rate of many imino protons within the region to which it binds, consistent with the hypothesis that its binding stabilizes the secondary structure of 5S RNA.