A central partition of molecular conformational space. II. embedding 3D structures.

A combinatorial model of molecular conformational space that was previously developed, had the drawback that structures could not be properly embedded because it lacked explicit rotational symmetry. The problem can be circumvented by sorting the elementary 3D components of a molecular system into a finite set of classes that can be separately embedded. This also opens up the possibility of encoding the dynamical states into a graph structure.

Clustering of a molecular dynamics trajectory with a Hamming distance

Based on the properties of discrete point arrangements we introduce the concept of dynamical activity, which allows one to formulate a simple double criterion for locating clusters of homologous conformers in a molecular dynamics trajectory.

Hydration of the dTn.dAn x dTn parallel triple helix: a Fourier transform infrared and gravimetric study correlated with molecular dynamics simulations.

We present a comparative analysis of the water organization around the dTn.dAn x dTn triple helix and the Watson-Crick double helix dTn.dAn respectively by means of gravimetric measurements, infrared spectroscopy and molecular dynamics simulations. The hydration per nucleotide determined by gravimetric and spectroscopic methods correlated with the molecular dynamics simulations shows that at high relative humidity (98% RH) the triple helix is less solvated than the duplex (17 +/- 2 water molecules per nucleotide instead of 21 +/-1). The experimental desorption curves are different for both structures and indicate that below 81% RH the triplex becomes more hydrated than the duplex. At this RH the FTIR spectra show the emergence of N-type sugars in the adenosine strand of the triplex. When the third strand is bound in the major groove of the Watson-Crick duplex molecular dynamics simulations show the formation of a spine of water molecules between the two thymidine strands.

Binding of Net-Fla, a netropsin-flavin hybrid molecule, to DNA: molecular mechanics and dynamics studies in vacuo and in water solution.

We have studied the binding of the hybrid netropsin-flavin (Net-Fla) molecule onto four sequences containing four A. T base pairs. Molecular mechanics minimizations in vacuo show numerous minimal conformations separated by one base pair. 400 ps molecular dynamics simulations in vacuo have been performed using the lowest minima as the starting conformations. During these simulations, the flavin moiety of the drug makes two hydrogen bonds with an amino group of a neighboring guanine. A 200 ps molecular dynamics simulation in explicit water solution suggests that the binding of Net-Fla upon the DNA substrate is enhanced by water bridges. A water molecule bridging the amidinium of Net-Fla to the N3 atom of an adenine seems to be stuck in the drug-DNA complex during the whole simulation. The fluctuations of the DNA helical parameters and of the torsion angles of the sugar-phosphate backbone are very similar in the simulations in vacuo and in water. The time auto-correlation functions for the DNA helical parameters decrease rapidly in the picosecond range in vacuo. The same functions computed from the water solution molecular dynamics simulations seem to have two modes: the rapid mode is similar to the behavior in vacuo, and is followed by a slower mode in the 10 ps range.

A molecular mechanics and dynamics study of alternate triple-helices involving the integrase-binding site of the HIV-1 virus and oligonucleotides having a 3'-3' internucleotide junction.

Triple helix formation by oligonucleotides can be extended beyond polypurine tracts with the help of specially designed linkers. In this paper we focus our attention on the integrase-binding site of the HIV-1 virus located on the U5 LTR end which contains two adjacent purine tracts on opposite strands. Two alternate triple helices with a 3'-3' junction in the third strand are considered: 5'-GGTTTTp3'-3'pTGTGT-5' and 5'-GGAAAAp3'-3'pAGAGA-5' The structural plausibility of these triplexes is investigated using molecular mechanics and dynamics simulations, both in vacuo and in aqua. The non-isomorphism of the triplets in the GpT steps in the first sequence, gives rise to non canonical conformations in the torsion angles, hydration appears to be crucial for this triplex. Sugar puckers are predominantly South during in vacuo simulations while they turn East in aqua. In the simulation in aqua the triplexes are shrouded by an hydration shell, however, we have not been able to detect any permanent hydrogen bond bridge between DNA and water. The solvation of ions as well as their radial distribution, appear to be relatively well behaved despite the artifacts known to be generated by the simulation procedure. The experimental feasibility of these structures is discussed.

Solution structure of an oncogenic DNA duplex, the K-ras gene and the sequence containing a central C.A or A.G mismatch as a function of pH: nuclear magnetic resonance and molecular dynamics studies.

The DNA duplex 5' d(GCCACCAGCTC)-d(GAGCTGGTGGC) corresponds to the sequence 29 to 39 of the K-ras gene, which contains a hot spot for mutations. This has been studied by one and two-dimensional nuclear magnetic resonance, energy minimization and molecular dynamics. The results show that it adopts a globally B-DNA type structure. We have introduced, at the central base-pair, the mismatches C.A and A.G. The mismatch position is that of the first base of the Gly12 codon, the hot spot. For the C.A mismatch we observe a structural change as a function of pH with an apparent pKa of 7.2. At low pH, the mismatch pair adopts a structure close to a classic wobble conformation with the cytidine residue displaced into the major groove. It is stabilised by two hydrogen bonds in which the adenosine residue is protonated and the cytidine residue has a significant C3'-endo population. At high pH, the mispair structure is in equilibrium between wobble and reverse wobble conformations. Similar studies are reported on the A.G mismatch, which also undergoes a transition as a function of pH. 31P spectra have been recorded on all systems and as a function of pH. No evidence for BII phosphodiester backbone conformations was found. The NMR results are well corroborated by molecular dynamics calculations performed with or without distance constraints. The dynamics at the mismatch sites have been examined. Although the overall structures are close to B-DNA, helical parameters fluctuate differently at these sites. Different hydrogen bonding alternatives in dynamic equilibrium that can involve three-centred hydrogen bonds are observed.

About the large fluctuations observed using gas-phase molecular dynamics in the K-ras gene containing a mismatch.

We describe how we can reduce the periodic bending motions in the simulation in vacuo of the molecular dynamics of a short DNA fragment containing the Gly 12 hot spot of the K-ras oncogene and having at its center a mismatch CA+.

A database of 32 DNA triplets to study triple helices by molecular mechanics and dynamics.

We present here a database of 32 deoxyribonucleotide triplets, that can be used as building blocks of triple helix forming deoxyribonucleotides on a computer. This database is made of all the pairing schemes of the triplets ATT, GCC+, ATA and GCG where the third base forms two hydrogen bonds with the purine of the first two Watson-Crick strands. The essential features of the known triple helices were preserved in the resulting structures. A triple helix can be easily built from any combination of these basic triplets. Four homogeneous and alternate triple helices thus obtained were studied by molecular mechanics and dynamics in vacuo. The results are in agreement with known experimental observations for ATT and suggest a possible structure for the GCG triple helix. In order to characterize the geometry of the structures obtained, the definitions of nucleic acid structure parameters (R.E. Dickerson et al., EMBO J. 8 (1989) 1-4) have been extended to triple helical polynucleotides.

Object Command Language: a formalism to build molecular models and to analyze structural parameters in macromolecules, with applications to nucleic acids.

We have written a programming language OCL (Object Command Language) to solve, in a general way, two recurring problems that arise during the construction of molecular models and during the geometrical characterization of macromolecules: how to move precisely and reproducibly any part of a molecular model in any user-defined local reference axes; and how to calculate standard or user-defined structural parameters that characterize the complex geometries of any macromolecule. OCL endows the user with three main capabilities: the definition of subsets of the macromolecule, called objects in OCL, with a formalism from elementary set theory or lexical analysis; the definition of sequences of elementary geometrical operations, called procedures in OCL, enabling one to build arbitrary three-dimensional (3D) orthonormal reference frames, to be associated with previously defined objects; and the transmission of these definitions to programs that allow one to display, to modify and to analyze interactively the molecular structure, or to programs that perform energy minimizations or molecular dynamics. Several applications to nucleic acids are presented.

The pH dependent configurations of the C.A mispair in DNA.

The structure of the cytosine-adenine mispair in a 7 base pair duplex has been investigated by proton NMR spectroscopy. At low pH, the predominant structure is protonated on the A residue and assumes a wobble conformation consistent with previous findings. The C residue of the mispair is found in a C2'-C3' endo equilibrium. This is confirmed by molecular dynamics calculations which suggest that the conformation of the protonated wobble is flexible and not as rigid as a normal base pair. As the solution pH is raised, a structural transition is observed with an apparent pK of 7.54 at 23 degrees C. At higher pH the predominant structure is one in which both the C and A residues are intrahelical. Evidence is presented that this structure corresponds to a reverse wobble in which the two bases are held together by one hydrogen bond. This structure is much less stable than the protonated form and even at low temperature single strands are observed in slow exchange with the neutral duplex form.

Solution conformation of an oligonucleotide containing a G.G mismatch determined by nuclear magnetic resonance and molecular mechanics.

We have determined by two-dimensional nuclear magnetic resonance studies and molecular mechanics calculations the three dimensional solution structure of the non-selfcomplementary oligonucleotide, d(GAGGAGGCACG). d(CGTGCGTCCTC) in which the central base pair is G.G. This is the first structural determination of a G.G mismatch in a oligonucleotide. Two dimensional nuclear magnetic resonance spectra show that the bases of the mismatched pair are stacked into the helix and that the helix adopts a classical B-DNA form. Spectra of the exchangeable protons show that the two guanosines are base paired via their imino protons. For the non-exchangeable protons and for some of the exchangeable protons nuclear Overhauser enhancement build up curves at short mixing times have been measured. These give 84 proton-proton distances which are sensitive to the helix conformation. One of the guanosines adopts a normal anti conformation while the other is syn or close to syn. All non-terminal sugars are C2' endo. These data sets were incorporated into the refinement of the oligonucleotide structure by molecular mechanics calculations. The G.G mismatch shows a symmetrical base pairing structure. Although the mismatch is very bulky many of its features are close to that of normal B-DNA. The mismatch induces a small lateral shift in the helix axis and the sum of the helical twist above and below the mismatch is close to that of B-DNA.

The solution structure of a DNA hairpin containing a loop of three thymidines determined by nuclear magnetic resonance and molecular mechanics.

We have determined by two-dimensional nuclear magnetic resonance studies and molecular mechanics calculations the three-dimensional solution structure of a 21 residue oligonucleotide capable of forming a hairpin structure with a loop of three thymidine residues. This structure is in equilibrium with a duplex form. At 33 degrees C, low ionic strength and in the presence of MgCl2 the hairpin form dominates in solution. Six Watson-Crick base pairs are formed topped by the loop structure. The residues 1-3 and 18-21 are not complementary and form dangling ends. Distance constraints have been derived from nuclear Overhauser enhancement measurements. These, together with molecular mechanics calculations, have been used to determine the structure. We do not observe stacking of thymidine residues either over the 3' or the 5' end of the stem.

Molecular mechanics and dynamics of an abasic frameshift in DNA and comparison to NMR data.

In a previous publication (Ph. Cuniasse, L.C. Sowers, R. Eritja, B. Kaplan, M.F. Goodman, J.A.H. Cognet, M. Le Bret, W. Guschlbauer and G.V. Fazakerley, Biochemistry 28, 2018 (1989), we determined by two dimensional NMR studies and molecular mechanics calculations the three-dimensional structure of a non-selfcomplementary oligonucleotide: [sequence; see text] where dr, at the center of the first strand, is a model abasic site. In order to explain all the results arising from NMR measurements, we found that an equilibrium between two conformations was necessary. These conformations differ mainly by the sugar pucker of G5 which is C2' endo or C3' endo. The latter is stabilized by addition of counterions between phosphate residues P3 and P4. In this paper, we have constructed systematically, all possible structures as a function of torsion angles delta of dr4 and of G5 by molecular mechanics in the presence or absence of counterions. Since these conformations were not forced with NMR distance measurements, this method allows detailed comparisons between all possible conformations and NMR data. Maps of contour lines of the potential energy, of fits to NMR distance measurements, and of helical twist as a function of torsion angles delta of dr4 and of G5 unravel the difficulties associated with the study of the G5 sugar pucker conformation equilibrium. Sugar puckers and proton distances are very sensitive criteria to monitor molecular dynamics. Relying on these experimental criteria, we have tested many molecular dynamics preparation phases and we propose a new warm-up and equilibration procedure for molecular dynamics. Thus we show with a 290 ps molecular dynamic run that G5 is in conformational equilibrium and that all NMR data are well reproduced.

The GTm6AC sequence is overwound and bent.

By a combination of distance constraints obtained from NMR spectra and molecular mechanics calculations we have determined the three dimensional structure of the self-complementary decanucleotide d(CGCGTm6ACGCG). Methylation of an adenine at a position 3' to T induces significant conformational changes relative to B-DNA. This arises from the close proximity of the four methyl groups in the large groove in the centre of the sequence. The helical twist between the two T.m6A base pairs is found to be 45 degrees, as for D-DNA, and is accompanied by a high negative value of the wedge roll angle between these base pairs. The overall nonzero wedge roll observed shows that the helix is bent. These constraints appear to be material for the absence of the sequence T-m6A in natural DNAs.

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.

Promoter recognition and transcription initiation in E. coli.

Analysis of stability maps of sequences harbouring E. coli RNA polymerase promoters shows a characteristic splitting in homostable domains, despite the heterogeneity of the sequences. Correlation of stability maps with results from static approaches giving the contact points of the enzyme on promoters and functional studies employing abortive initiation assay allow us to propose a general mechanism for recognition of promoters and transcription start.

Local stability involved in characterizing and controlling promoters in eukaryotes.

Eukaryotic promoters with known in vivo activities have been analysed for characteristic stability patterns. Correlation of transcription yield in promoter mutants with size and stability of individual domains of the promoter stability profile supports the conclusion that eukaryotic promoters are built up by at least three elements: a region enabling the transcription ("enhancer"), with a characteristic stability pattern; an activator domain, with high GC content, whose activator potential is controlled by the domain stability and length; a trap domain, with high AT content, setting the cap site. The activated enzyme undergoes a steady deactivation process, losing half of its activity upon moving 55 bases between the activator and the trap site.

Physical characteristics in eucaryotic promoters.

For a series of wild type and mutated eucaryotic gene prelude sequences (mainly "promoters" of SV40 early gene (Benoist and Chambon, Nature 290, 304 (1981); Moreau et al., Nuc. Acids Res. 9, 6047 (1982)) and of Herpes Simplex Virus TK gene (McKnight and Kingsbury, Science 217, 316 (1982)), in vivo promoter activity and local stability (denaturability) have been correlated. In agreement with the conclusions drawn in these papers, the correlation points to three major eucaryotic promoter elements and loci: (i) enzyme enabling by an enhancer sequence; SV40 and Moloney Sarcoma Virus enhancers have a striking stability homology; (ii) enzyme activation, occurring 50-70 b.p. upstream the cap site in a high stability domain; the enzyme apparently deactivates exponentially upon moving away to trap site; (iii) enzyme positioning at trap site, 30 +/- 5 b.p. upstream the cap site. The trap site contains the TATA box, or, when absent, other low stability domains downstream the activator. The number and occupancy of cap sites may depend on the stability and size of the trap site-cap site couple and its distance from the activator.

The hierarchical approach to the DNA stability problem. II. Some applications and speculations with yeast mitochondrial DNA as an example.

As discussed in the preceding article [1] hierarchical analysis of DNA sequences should make it possible to treat complex unfolding (and refolding) processes involving both equilibrium and non-equilibrium subtransitions. Hence a variety of actual experimental situations may be analyzed. This is demonstrated with the help of a 1950 bp yeast mitochondrial DNA sequence encompassing part of the 21S ribosomal RNA gene: excellent fit of complex denaturation and renaturation profiles is achieved with only two adjustable parameters. The advantage of dealing with objectively defined stability units is also apparent when stability profiles are compared to known functional maps: striking correlations may be brought out and their possible significance is briefly discussed.

The hierarchical approach to the DNA stability problem. I. Patterns in non-equilibrium denaturation and renaturation.

As proposed by Azbel (Phys. Rev. Letters, 1973, 31, 589-592), DNA sequences may be uniquely divided into embedded segments with different lengths and stabilities, each of them a potential denaturation unit. This "hierarchical" approach to the DNA stability problem was originally devised for the analysis of equilibria situations. We have extended it to deal quantitatively with various locally irreversible denaturation/renaturation processes that play a leading part in most actual experiments. Special emphasis is placed on (1) describing and delimiting major experimental domains with respect to reversibility/irreversibility, and (2) the quantitative treatment of bidirectional denaturation processes which are shown to lend themselves to an original, hierarchical analysis.