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.     

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.     

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.     

Loop folds in proteins and evolutionary conservation of folding nuclei

We show that loops of close contacts involving hydrophobic residues are important in protein folding. Contrary to Berezovsky 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.     

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.     

Decisions in Force Field Development Reply to Kollman and Dill

Abstract

We reply here to several of the questions raised by Kollman and Dill (J. Biomole. Struct. Dyn. 8, 909–913, 1991) about the paper by Roterman et al. (J. Biomole. Struct. Dyn. 7, 421–453, 1989).     

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)).     

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.     

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.     

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.     

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.     

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.     

Recent Advances in GFP Folding Reporter and Split-GFP Solubility Reporter Technologies. Application to Improving the Folding and Solubility of Recalcitrant Proteins from Mycobacterium tuberculosis

We have improved our green fluorescent protein (GFP) folding reporter technology [Waldo et al., (1999) Nat. Biotechnol. 17, 691–695] to evolve recalcitrant proteins from Mycobacterium tuberculosis. The target protein is inserted into the scaffolding of the GFP, eliminating false-positive artifacts caused by expression of truncated protein variants from internal cryptic ribosome binding sites in the target RNA. In parallel, we have developed a new quantitative fluorescent protein tagging and detection system based on micro-domains of GFP. This split-GFP system, which works both in vivo and in vitro, is amenable to high-throughput assays of protein expression and solubility [Cabantous et al., (2005) Nat. Biotechnol. 23, 102–107]. Together, the GFP folding reporter and split-GFP technologies offer a comprehensive system for manipulating and improving protein folding and solubility.     

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.     

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].     

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.