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.     

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.     

Decisions in Force Field Development: An Alternative to Those Described by Roterman et al.

Abstract

We attempt to give an alternate point of view of the analysis by Roterman et al. (J. Biolmol. Struct. Dyn. 7, 415 (1989)). In particular, we argue for the use of flexible geometry and explicit inclusion of solvent effects in analyzing φ psi; maps of peptides.     

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.     

Loop Folds in Proteins and Evolutionary Conservation of Folding Nuclei

Abstract

We show that loops of close contacts involving hydrophobic residues are important in protein folding. Contrary to Berezovsky and Trifonov (J. Biomol. Struct. Dyn. 20, 5–6, 2002) the loops important in protein folding usually are much larger in size than 23–31 residues, being instead comparable to the size of the protein for single domain proteins. Additionally what is important are not single loop contacts, but a highly interconnected network of such loop contacts, which provides extra stability to a protein fold and which leads to their conservation in evolution.     

OnionTree XML: A Format to Exchange Gene-Related Probabilities

Abstract

Combined use of shielding constant computations, measurements of chemical shifts and NOE studies reveal that poly(dG-dC)?(poly)dG-dC) in low salt solutions exist as a right- handed B-DNA double helix described by Gupta, Dhingra, Sarma, Sarma, Rajagopalan and Sasisekharan, J. Biomole. Str. Dyn. 1, 395, 1983. We present a simple and direct method to determine the handedness of DNA double helices from NOE difference spectra. This method takes advantage of the NOE between base protons and the H2′H2” sugar protons; and in the difference NOE spectra in the H2′H2” region the signatures of the right and left-handed helices become imprinted.     

Molecular Dynamics Simulations of β-turn Forming Tetra- and Hexapeptides

Abstract

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^DAH and VP^DSH (B. Imperiali et al. J. Am. Chem. Soc. 114, 3182–3188, 1992) in solution contains a significant—or in some cases dominant—proportion of β-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 β-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 β-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

Abstract

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)).     

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.     

An Automatic Search for Similar Spatial Arrangements of α-Helices and β-Strands in Globular Proteins

Abstract

A fast search algorithm to reveal similar polypeptide backbone structural motifs in proteins is proposed. It is based on the vector representation of a polypeptide chain fold in which the elements of regular secondary structures are approximated by linear segments (Abagyan and Maiorov, J. Biomol. Struct. Dyn. 5, 1267–1279 (1988)). The algorithm permits insertions and deletions in the polypeptide chain fragments to be compared. The fast search algorithm implemented in FASEAR program is used for collecting βαβ supersecondary structure units in a number of α/β proteins of Brookhaven Data Bank. Variation of geometrical parameters specifying backbone chain fold is estimated. It appears that the conformation of the majority of the fragments, although almost all of them are right-handed, is quite different from that of standard βαβ units. Apart from searching for specific type of secondary structure motif, the algorithm allows automatically to identify new recurrent folding patterns in proteins. It may be of particular interest for the development of tertiary template approach for prediction of protein three-dimensional structure as well for constructing artificial polypeptides with goal-oriented conformation.     

Internal DNA Modes Below 25 cm−1: A Resonance Raman Spectroscopy Observation

Abstract

The first resonance Raman scattering observation of the low-frequency (LF) region (below 40 up to 12 cm^?1) of DNA motions is presented. Since the concentration of the studied DNA solution was very low (1 mg/ml), the spectra features reflect internal vibrations of the macro-molecule. The decomposition of the spectra into Lorentzians clearly indicate three intrahelical DNA modes: the corresponding peaks are located at the frequencies 16,19, and 23 (±1) cm^?1. This result is in agreement with our quasi-continuity model of the LF B-form DNA dynamics (V. Lisy, P. Miskovsky and P. Schreiber, J. Biomol. Struct. Dyn. 13, 707 (1996)). The fit of the experimental frequencies to the theory, using the Genetic Algorithms approach, allowed us to make some conclusions about the model force constants which could be found by independent conformational energy calculations. Possible positions of five lowest-frequency DNA peaks, predicted by the model, are discussed.     

Structures of Homopurine-homopyrimidine Tract in Superhelical DNA

Abstract

For homopurine-homopyrimidine tracts in superhelical DNA, we propose a structure involving Watson-Crick and Hoogsteen paired triple helixes, hairpin loops and unstructured domains. Topologically, the whole structure is equivalent to an open region. The proposed structure is consistent with available SI cleavage, pH and alkylation data and energetics under superhelical stress; this new structure is a much more probable candidate than the one proposed by us recently (V.I. Lyamichev, S.M. Mirkin &; M.D. Frank-Kamenetskii, J. Biomole. Str. Dyns 3, 327-338, 1985).     

A note on ‘A generalized two-sex logistic model’

We re-visit the recently published paper on a generalization of the two-sex logistic model by Maxin and Sega [A generalized two-sex logistic model, J. Biol. Dyn. 7(1) (2013), pp. 302–318]. We show that the logistic assumption of a non-increasing birth rate can be replaced by a more general assumption of a non-increasing ratio between the female/male birth and mortality rate. In this note we indicate the changes necessary in the proofs of the theorems in [D. Maxin and L. Sega, A generalized two-sex logistic model, J. Biol. Dyn. 7(1) (2013), pp. 302–318] and discuss several situations where this new assumption is useful.     

Structure of Poly(dA)·Poly(dT) is not Identical to the AT Rich Regions of the Single Crystal Structure of CGCGAATTBrCGCG. The Consequence of this to Netropsin Binding to Poly(dA)·Poly(dT)

Abstract

The basic assumption of Dickerson and Kopka (J. Biomole. Str. Dyns. 2, 423, 1985) that the conformation of poly(dA)·poly(dT) in solution is identical to the AT rich region of the single crystal structure of the Dickerson dodecamer is not supported by any experimental data. In poly(dA)·poly(dT), NOE and Raman studies indicate that the dA and dT units are conformationally equivalent and display the (anti-S-type sugar)-conformation; incorporation of this nucleotide geometry into a double helix leads to a conventional regular B-helix in which the width of the minor groove is 8A. The derived structure is consistent with all available experimental data on poly(dA)·poly(dT) obtained under solution conditions. In the crystal structure of the dodecamer, the dA and dT units have distinctly different conformations—dA residues adopt (anti, S-type sugar pucker), while dT residues belong to (low anti, N-type sugar pucker). These different conformations of the dA and dT units along with the large propeller twist can be accommodated in a double helix in which the minor groove is shrunk from 8A to less than 4A. In the conventional right handed B-form of poly(dA)·poly(dT) with the 8A wide minor groove, netropsin has to bind asymmetrically along the dA strand to account for the NOE and chemical shift data and to generate a stereochemically sound structure (Sarma et al, J. Biomole. Str. Dyns. 2, 1085, 1985).     

Relationship Between Curved DNA Conformations and Slow Gel Migration

Abstract

We propose some specific DNA conformations that explain, in terms of molecular conformations, the anomalous gel electrophoretic behavior of the sequences (VA₄T₄X)₁, and (V₂A₃X₂)₁ where V and X are either G or C. Previously (J. Biomole. Struct. Dyn. 4, 41, 1986) we considered hydrophobic interactions a mong 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)₁ might form a very tightly coiled super-helix whereas the sequences (VA₄T₄X)₁ form a broad super-helix of radius ~ 120 A for i = 25. The sequence (V₂A₃T₃X₂)₁ forms a slightly smaller radius super-helix. The time of passage through the gel has been taken to be inversely proportional to the smallesuiimension 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.     

Bh-DNA: Variations of the Poly[d(A)] · Poly[d(T)] Structure within the Framework of the Fibre Diffraction Studies

Abstract

A refinement of the recent results for poly[d(A)] · poly[d(T)] (Alexeev et al., J. Biomol. Struct. Dyn. 4, 989 (1987)) involving additional parameters of the base-pair structure and of the sugar- phosphate backbone expands the conformational potential of this polynucleotide of the B type to include the possibility of bifurcated hydrogen bonds of the kind recently discovered in crystalline deoxyoligonucleotide with lone d(A)_n · d(T)_n stretch (Nelson et al., Nature 330, 221 (1987)).

Still, analysis of the available data and energy calculations do not seem to indicate that the bifurcated H-bonds are a crucial factor responsible for the anomalous structure of the d(A)_n · d(T)_n sequence. The unique structural properties of poly [d(A)] · poly[d(T)] can hardly be explained without taking into account its interactions with the double-layer hydration spine in the minor groove. In view of the hydration mechanism stabilizing poly [d(A)] · poly [d(T)] and of the polynucleotide's heteronomous prehistory (Arnott et al., Nucleic Acids Res. 11, 4141 (1983)) we suggest that this B-type structure be called B_h.     

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.     

Unusual Protonated Structure in the Homopurine · Homopyrimidine Tract of Supercoiled and Linearized Plasmids Recognized by Chemical Probes

Abstract

Plasmid pEJ4, which is a derivative of pUC19 containing an insert with 60-bp-long · homopurine homopyrimidine tract from sea urchin P. miliaris histone gene spacer, was studied by chemical probes of the DNA structure osmium tetroxide and glyoxal. The former probe reacts with pyrimidine bases, while the latter forms a stable product only with guanine residues. These probes can thus be applied as specific probes for the homopyrimidine and homopurine strands, respectively.

At pH 6.0 the site-specific modification of the homopurine · homopyrimidine tract by both probes was observed at native superhelical density of the plasmid. In the linear plasmid under the same conditions this modification was absent; it appeared, however, at more acid pH values. In supercoiled DNA the hypersensitivity of the homopurine homopyrimidine tract to osmium tetroxide did not substantially change when pH was decreased from 6.0 to 4.0. Changes in NaCl concentration at pH 4.5 did not influence the hypersensitivity to osmium tetroxide; at pH 6.0 this hypersensitivity decreased with increasing NaCl concentration. These results thus show that the chemical probes recognize an unusual protonated structure containing unpaired bases or non-Watson-Crick base pairs. At pH 5.6 the site-specific modification occurred at or near to the middle of the homopurine · homopyrimidine tract, suggesting that a hairpin may be involved in the unusual structure under the given conditions. From the models suggested so far for the unusual structure of homopurine · homopyrimidine tracts our results fit best the protonated triplex H form suggest by V.I. Lyamichev, S.M. Mirkin and M.D. Frank-Kamenetskii, J. Biomol. Struct. Dyn. 3, 667 (1986).