3D QSAR studies on peroxisome proliferator-activated receptor γ agonists using CoMFA and CoMSIA

The peroxisome proliferator-activated receptors (PPARs) have increasingly become attractive targets for developing novel anti-type 2 diabetic drugs. We employed comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) to study three-dimensional quantitative structure–activity relationship (3D QSAR) based on existing agonists of PPAR (including five thiazolidinediones and 74 tyrosine-based compounds). Predictive 3D QSAR models with conventional r² and cross-validated coefficient (q²) values up to 0.974 and 0.642 for CoMFA and 0.979 and 0.686 for COMSIA were established using the SYBYL package. These models were validated by a test set containing 18 compounds. The CoMFA and CoMSIA field distributions are in general agreement with the structural characteristics of the binding pockets of PPAR, which demonstrates that the 3D QSAR models built here are very useful in predicting activities of novel compounds for activating PPAR.      

Analysis of the interactions of ribonuclease inhibitor with kanamycin

The interaction of ribonuclease inhibitor (RI) with kanamycin was studied by molecular modeling. The preliminary binding model was constructed using the Affinity module of the Insight II molecular modeling program and the key residues involved in the combination of RI binding to kanamycin were determined. Meanwhile, we determined relevant surface characteristics determining the interaction behavior. The modeling results indicated that electrostatic interactions and H-bond forces may work as major factors for the molecular interaction between kanamycin and RI. The above results are useful for elucidating the molecular principles upon which the selectivity of a kanamycin is based. The quartz-crystal microbalance (QCM) is a new method usually used to monitor the binding function of macromolecules with samples online in a flow-injection analysis (FIA) system. The experimental results demonstrate that kanamycin has an extraordinary affinity to the basic protein RI, and our result is consistent with the molecular modeling results. These principles can in turn be used to study the molecular recognition mechanism and design a mimic of kanamycin for the development of new RI binders.Figure Proposed binding model of kanamycin to RI obtained by the computer-aided docking method and optimized with molecular mechanics with the CVFF forcefield.     

Molecular modeling of the von Willebrand factor A2 Domain and the effects of associated type 2A von Willebrand disease mutations

A homology model for the A2 domain of von Willebrand factor (VWF) is presented. A large number of target–template alignments were combined into a consensus alignment and used for constructing the model from the structures of six template proteins. Molecular dynamics simulation was used to study the structural and dynamic effects of eight mutations introduced into the model, all associated with type 2A von Willebrand disease. It was found that the group I mutations G1505R, L1540P and S1506L cause significant deviations over multiple regions of the protein, coupled to significant thermal fluctuations for G1505R and L1540P. This suggests that protein instability may be responsible for their intracellular retention. The group II mutations R1597W, E1638K and G1505E caused single loop displacements near the physiologic VWF proteolysis site between Y1605–M1606. These modest structural changes may affect interactions between VWF and the ADAMTS13 protease. The group II mutations I1628T and L1503Q caused no significant structural change in the protein, suggesting that inclusion of the protease in this model is necessary for understanding their effect.Figure Homology model of the von Willebrand factor A2 domainElectronic Supplementary Material Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00894-004-0194-9     

Quantitative structure-activity relationship by CoMFA for cyclic urea and nonpeptide-cyclic cyanoguanidine derivatives on wild type and mutant HIV-1 protease

Abstact 3D-QSAR studies using the Comparative Molecular Field Analysis (CoMFA) methodology were conducted to predict the inhibition constants, K_i, and the inhibitor concentrations, IC₉₀ of 127 symmetrical and unsymmetrical cyclic urea and cyclic cyanoguanidine derivatives containing different substituent groups such as: benzyl, isopropyl, 4-hydroxybenzyl, ketone, oxime, pyrazole, imidazole, triazole and having anti-HIV-1 protease activities. A significant cross-validated correlation coefficient (q²) of 0.63 and a fitted correlation coefficient r² of 0.70 were obtained, indicating that the models can predict the anti-protease activity from poorly to highly active compounds reliably. The best predictions were obtained for: XV643 (predicted log 1/K_i=9.86), a 3,5-dimethoxy-benzyl cyclic urea derivate (molec60, predicted log 1/K_i=8.57) and a benzyl cyclic urea derivate (molec 61, predicted log 1/IC₉₀=6.87). Using the CoMFA method, we also predicted the biological activity of 14 cyclic urea derivatives that inhibit the HIV-1 protease mutants V82A, V82I and V82F. The predicted biological activities of the: (i) XNO63 (inhibitory activity on the mutant HIV-1 PR V82A), (ii) SB570 (inhibiting the mutant HIV-1 PR V82I) and also (iii) XV652 (during the interaction with the mutant HIV-1 PR V82F) were in good agreement with the experimental values.Figure Stereoview of the contour plots of the CoMFA steric and electrostatic fields. The favorable (indicated by blue polyhedra) and unfavorable (represented by red polyhedra) electrostatic areas and also the favorable (shown by green polyhedra) and unfavorable (shown by yellow polyhedra) steric areas formed around the most active molecule, 6a.     

Decomposition mechanism of 3-<Emphasis Type="Italic">N</Emphasis>-morpholinosydnonimine (<Emphasis Type="Bold">SIN-1</Emphasis>)—a density functional study on intrinsic structures and reactivities

Selected intrinsic aspects of the mode of action of 3-N-morpholinosydnonimine (SIN-1) and its follow-up products are investigated by means of density functional theory. Besides the well known radical-cationic Feelisch–Schoenafinger pathway, an alternative anionic route via a neutral radical is proposed and included in the study. The individual reaction pathways are followed. Most notably, the overall activation barrier for the cationic route is calculated to be 184.04 kcal mol^–1, while the one for the anionic route is predicted to be more favorable with 14.09 kcal mol^–1.Figure A mere conformational change is predicted by DFT theory to elicit NO ejection from the SIN-1a radical cation, formed after one electron oxidation of the N-nitrosohydrazine SIN-1a.

Prototropic tautomerism of imidazolone in aqueous solution: a density functional approach using the combined discrete/self-consistent reaction field (SCRF) models

A systematic investigation of the proton transfer in the keto-amino/enol tautomerization of imidazolone was undertaken. Calculations in aqueous solution were performed using both combined discrete/self-consistent reaction field (SCRF) and SCRF methods. Complexes containing one to three water molecules around the hydrophilic site of imidazolone were used for the combined discrete/SCRF calculations. The DFT results predict that the barrier height for non-water-assisted intramolecular proton transfer is very high (214.8 kJmol^–1). Hydrogen bonding between imidazolone and the water molecule(s) will dramatically lower the barrier by a concerted multiple proton transfer mechanism. The proton transfer process through a eight-member ring formed by imidazolone and two water molecules is found to be more efficient and the calculated barrier height is ca. 61 kJmol^–1.Figure DFT calculations in aqueous solution predict the H-bonding between imidazolone(IZ) and the water molecule(s) will dramatically lower the tautomeric barrier by a concerted multiple proton transfer mechanism, in which an eight-member ring structure formed by IZ and 2H₂O is found to be more efficient and the barrier is 60.8 kJ mol^–1, much less than 214.8 kJ mol^–1 in the non-water-assisted mechanism.     

Chiral recognition of aromatic compounds by β-cyclodextrin based on bimodal complexation

The chiral recognition of the selected aromatic chiral compounds by native -cyclodextrin (-CD) based on bimodal complexation was studied using a flexible docking algorithm FDOCK. A quantitative empirical free energy relationship model was employed to predict the complex stability constants and the preferred binding modes. The results showed that the calculated complex stability constants are in good agreement with the experimental data. Furthermore, the main force responsible for host-guest complexation is the van der Waals force and the chiral molecules are completely included into the -CD cavity. The chiral recognition for the selected aromatic chiral compounds is the result of the van der Waals force counterbalancing with the other effects, such as the electrostatic interaction and the hydrophobic effect.Figure The favorable structures for the inclusion complexes of (S)_phenylbutyric with -CD. View in the plane normal to the Z-axis. -CD is shown in surface and (S)_phenylbutyric in CPK representation.     

Organization of rhodopsin molecules in native membranes of rod cells–an old theoretical model compared to new experimental data

It has been shown that rhodopsin forms an oligomer in the shape of long double rows of monomers. Because of the importance of rhodopsin as a template for all G protein-coupled receptors, its dimeric, tetrameric and higher-oligomeric structures also provide a useful pattern for similar structures in GPCRs. New experimental data published recently are discussed in the context of a proposed model of the rhodopsin oligomer 1N3M deposited in the protein data bank. The new rhodopsin structure at 2.2 Å resolution with all residues resolved as well as an electron cryomicroscopy structure from 2D crystals of rhodopsin are in agreement with the 1N3M model. Accommodation of movement of transmembrane helix VI, regarded as a major event during the activation of rhodopsin, in a steady structure of the oligomer is also discussed.Figure Superimposition of the 1U19 (red wire), 1GZM (purple wire) and 1N3M (blue wire) rhodopsin structures. Size of the wires is proportional to thermal factors of backbone C atoms, view parallel to the membrane.      

Molecular aspects of the interaction between amphotericin B and a phospholipid bilayer: molecular dynamics studies

Amphotericin B (AmB) is a polyene macrolide antibiotic used to treat systemic fungal infections. The molecular mechanism of AmB action is still only partly characterized. AmB interacts with cell-membrane components and forms membrane channels that eventually lead to cell death. The interaction between AmB and the membrane surface can be regarded as the first (presumably crucial) step on the way to channel formation. In this study molecular dynamics simulations were performed for an AmB–lipid bilayer model in order to characterize the molecular aspects of AmB–membrane interactions. The system studied contained a box of 200 dimyristoylphosphatidylcholine (DMPC) molecules, a single AmB molecule placed on the surface of the lipid bilayer and 8,065 water molecules. Two molecular dynamics simulations (NVT ensemble), each lasting 1 ns, were performed for the model studied. Two different programs, CHARMM and NAMD2, were used in order to test simulation conditions. The analysis of MD trajectories brought interesting information concerning interactions between polar groups of AmB and both DMPC and water molecules. Our studies show that AmB preferentially took a vertical position, perpendicular to the membrane surface, with no propensity to enter the membrane. Our finding may suggest that a single AmB molecule entering the membrane is very unlikely.Figure The figure presents the whole structure of the system simulated—starting point. AmB is presented as a space-filling model, DMPC molecules—green sticks, water molecules—red sticks     

Evolutionary trace analysis of ionotropic glutamate receptor sequences and modeling the interactions of agonists with different NMDA receptor subunits

The ionotropic N-methyl-d-aspartate (NMDA) receptor is of importance in neuronal development, functioning, and degeneration in the mammalian central nervous system. The functional NMDA receptor is a heterotetramer comprising two NR1 and two NR2 or NR3 subunits. We have carried out evolutionary trace (ET) analysis of forty ionotropic glutamate receptor (IGRs) sequences to identify and characterize the residues forming the binding socket. We have also modeled the ligand binding core (S1S2) of NMDA receptor subunits using the recently available crystal structure of NR1 subunit ligand binding core which shares ~40% homology with other NMDA receptor subunits. A short molecular dynamics simulation of the glycine-bound form of wild-type and double-mutated (D481N; K483Q) NR1 subunit structure shows considerable RMSD at the hinge region of S1S2 segment, where pore forming transmembrane helices are located in the native receptor. It is suggested that the disruption of domain closure could affect ion-channel activation and thereby lead to perturbations in normal animal behavior. In conclusion, we identified the amino acids that form the ligand-binding pocket in many ionotropic glutamate receptors and studied their hydrogen bonded and nonbonded interaction patterns. Finally, the disruption in the S1S2 domain conformation (of NR1 subunit- crystal structure) has been studied with a short molecular dynamics simulation and correlated with some experimental observations.Figure The figure shows the binding mechanism of glutamate with NR2B subunit of the NMDA receptor. Glutamate is shown in cpk, hydrogen bonds in dotted lines and amino acids in blue. The amino acids shown here are within a 4-Å radius of the ligand (glutamate)     

Hydrogen-bond effects on the electronic absorption spectrum and evaluation of nonlinear optical properties of an aminobenzodifuranone derivative that exhibits the largest positive solvatochromism

In this work, for the first time, a theoretical approach to describing the influence of hydrogen-bond formation on the electronic absorption spectrum and nonlinear optical properties of an aminobenzodifuranone derivative (ABF) that exhibits the largest positive solvatochromic shift compared to other known chromophores is given. The solvent effect was included via the supermolecule (SM) method. The calculations were performed for a strong low-lying (^*) transition based on the configuration interaction singles (CIS) and time-dependent DFT (TDDFT) methods. The first-order hyperpolarizabilities () were computed using the finite-field (FF) technique combined with the Hartree–Fock (HF) theory. Reasonable agreement between theory and experiment was obtained for the solvatochromic shifts of the ABF molecule. Moreover, it was found that H-bond formation strongly influences the NLO response of the systems investigated.Figure The interaction difference-density maps of the systems studied: a II - complex ABF with NFTB; b III - complex ABF with HMPA. The red color designates an increase of the electron density caused by the intermolecular interactions, whereas blue indicates a corresponding decrease of the electron density. The isodensity contours were plotted for ±0.01 electron/bohr³ (DFT/B3LYP/6-31G(d,p)).     

ProPose: a docking engine based on a fully configurable protein–ligand interaction model

Virtual high-throughput screening of molecular databases and in particular high-throughput protein–ligand docking are both common methodologies that identify and enrich hits in the early stages of the drug design process. Current protein–ligand docking algorithms often implement a program-specific model for protein–ligand interaction geometries. However, in order to create a platform for arbitrary queries in molecular databases, a new program is desirable that allows more manual control of the modeling of molecular interactions.For that reason, ProPose, an advanced incremental construction docking engine, is presented here that implements a fast and fully configurable molecular interaction and scoring model. This program uses user-defined, discrete, pharmacophore-like representations of molecular interactions that are transformed on-the-fly into a continuous potential energy surface, allowing for the incorporation of target specific interaction mechanisms into docking protocols in a straightforward manner. A torsion angle library, based on semi-empirical quantum chemistry calculations, is used to provide minimum energy torsion angles for the incremental construction algorithm. Docking results of a diverse set of protein–ligand complexes from the Protein Data Bank demonstrate the feasibility of this new approach.As a result, the seamless integration of pharmacophore-like interaction types into the docking and scoring scheme implemented in ProPose opens new opportunities for efficient, receptor-specific screening protocols. Figure ProPose — a fully configurable protein-ligand docking program — transforms pharmacophores into a smooth potential energy surface.This revised version was published online in October 2004 with corrections to the Graphical Abstract.     

On the nature of bonding in HCOOH...Ar and HCOOH...Kr complexes

The chemical interaction in HCOOH...Ng (Ng=Ar, Kr) complex was analyzed by topological analysis of the electron density based on Atoms-In-Molecules theory. For all computationally stable equilibrium structures of 1:1 HCOOH...Ng complexes, an intermolecular bond path with a bond critical point was found and perturbation of formic acid (FA) atomic basins and electron density was observed. The intermolecular interaction between the two complex subunits can be classified, according to its nature, as a closed-shell van der Waals type of interaction. However, one of the computed structures (complex II), pictures a noble gas atom attached linearly to the acidic O–H tail of FA. In this particular case, the electron density at the intermolecular bond critical point was found to resemble a hydrogen-bonded system and thus, may be termed a hydrogen-bond-like interaction. This change in the nature of the interaction is also shown by large perturbations of the FA properties found for this complex structure. The structural and vibrational perturbations are larger than for the other three structures and they increase for the Kr complexes compared to the Ar complex.Figure Electron density analysis of HCOOH...Ng (Ng=Ar,Kr) complex.     

Local molecular properties and their use in predicting reactivity

Expressions for the local electron affinity, electronegativity and hardness are derived in analogy to the local ionization energy introduced by Sjoberg, Murray and Politzer. The local polarizability is also defined based on an additive atomic orbital polarizability model that uses Rivail's variational technique. The characteristics of these local properties at molecular surfaces and their relevance to electrophilic aromatic substitution, to S_N2 reactivity and to the nucleophilicity of enolate ions are discussed.Figure The local ionization energy at the SES surfaces of methyl benzoate. The color scale ranges from 375 (blue) to 550 kcal mol^–1 (red). The blue areas are those for which interaction with an acceptor is most favorable.     

Domain-based homology modeling and mapping of the conformational epitopes of envelope glycoprotein of west nile virus

Knowledge-based modeling has proved significantly accurate for generating the quality models for proteins whose sequence identity with the structurally known targets is greater than or equal to 40%. On the other hand, models obtained for low sequence identities are not reliable. Hence, a reliable and alternative strategy that uses knowledge of domains in the protein can be used to improve the quality of the model generated by the homology method. Here, we report a method for developing a 3D-model for the envelope glycoprotein (Egp) of west nile virus (WNV), using knowledge of structurally conserved functional domains amongst the target sequence (Egp of WNV) and its homologous templates belonging to the same protein family, flaviviridae. This strategy is found to be highly effective in reducing the root mean square deviation (RMSD) value at the C positions of the target and its experimental homologues. The 3D structure of a protein is a prerequisite for structure-based drug design as well as for identifying the conformational epitopes that are essential for the designing vaccines. The conformational epitopes are mapped from the 3D structure of Egp of WNV modeled using the concept of an antigenic domain. A total of five such epitope regions/sites have been identified. They have been found distributed in the loop regions (surface) of the whole protein model composed of dimerization, central and immunological domains. These sites are proposed as the binding sites for HLA proteins/B-cell receptors. Binding is required to activate the immune response against WNV.Figure The conformational epitopes that are distributed in all the domains. They are found out by the algorithm by Kolaskar et al.     

Structure-based method for analyzing protein–protein interfaces

Hydrogen bond, hydrophobic and vdW interactions are the three major non-covalent interactions at protein–protein interfaces. We have developed a method that uses only these properties to describe interactions between proteins, which can qualitatively estimate the individual contribution of each interfacial residue to the binding and gives the results in a graphic display way. This method has been applied to analyze alanine mutation data at protein–protein interfaces. A dataset containing 13 protein–protein complexes with 250 alanine mutations of interfacial residues has been tested. For the 75 hot-spot residues (G1.5 kcal mol^-1), 66 can be predicted correctly with a success rate of 88%. In order to test the tolerance of this method to conformational changes upon binding, we utilize a set of 26 complexes with one or both of their components available in the unbound form. The difference of key residues exported by the program is 11% between the results using complexed proteins and those from unbound ones. As this method gives the characteristics of the binding partner for a particular protein, in-depth studies on protein–protein recognition can be carried out. Furthermore, this method can be used to compare the difference between protein–protein interactions and look for correlated mutation. Figure Key interaction grids at the interface between barnase and barstar. Key interaction grid for barnase and barstar are presented in one figure according to their coordinates. In order to distinguish the two proteins, different icons were assigned. Crosses represent key grids for barstar and dots represent key grids for barnase. The four residues in ball and stick are Asp40 in barstar and Arg83, Arg87, His102 in barnase.     

Molecular modeling of the rabbit colonic (HKα2a) H<Superscript>+</Superscript>, K<Superscript>+</Superscript> ATPase

A model of the HK2a subunit of the rabbit colonic H⁺, K⁺ ATPase has been generated using the crystal structure of the Ca⁺² ATPase as a template. A pairwise sequence alignment of the deduced primary sequences of the two proteins demonstrated that they share 29% amino acid sequence identity and 47% similarity. Using O (version 7) the model of HK2a was constructed by interactively mutating, deleting, and inserting the amino acids that differed between the pairwise sequence alignment of the Ca⁺² ATPase and HK2a. Insertions and deletions in the HK2a sequence occur in apparent extra-membraneous loop regions. The HK2a model was energy minimized and globally refined to a level comparable to that of the Ca⁺² ATPase structure using CNS. The charge distribution over the surface of HK2a was evaluated in GRASP and possible secondary structure elements of HK2a were visualized in BOBSCRIPT. Conservation and placement of residues that may be involved in ouabain binding by the H⁺, K⁺ ATPase were considered and a putative location for the subunit was postulated within the structure.Figure Possible architecture of the HK2a subunit. The residue in green is the lysine (position 517, Fig. 1) that lies in the nucleotide binding pocket and the residue in red is the aspartic acid at the phosphorylation site (position 385). Based on an alignment with the Ca⁺² ATPase, ten transmembrane helices were modeled into HK2a. The ten transmembrane helices are drawn as rods and shown in different colors for clarity. From left to right, the transmembrane helix designations are M10 (blue), M7 (gray), M8 (purple), M9 (orange), M5 (pink), M6 (green), M3 (brown), M4 (cyan), M2 (teal), and M1 (almond).     

The HF-SCF energy of HIV-1 MNgp120 V3 hairpin loop conformers

The purpose of this study is to analyze the structure of the V3 loop of the HIV-1 gp120 molecule at the atomic level. The total energy of each member of the antibody-complexed 16-mer V3 conformer data set of Sharon et al. (PDB 1NJ0) was determined by the Hartree–Fock-self-consistent field (HF-SCF) method and with the GROMOS96 force field. There was no correlation between the results of the classical GROMOS96 force field analysis and the ab initio HF-SCF quantum mechanical analysis of the energy of the V3-loop-peptide conformers. HF-SCF optimization (AM1) of conformer geometries yielded structures in which HIS315 is displaced from its original position in the combining site of human antibody fragment 447-52D, but with the hairpin turn intact. The hairpin shape of the V3 loop remained detectable, albeit distorted, even with perturbation by a lithium dicationic electrostatic force field and by substitution of the PRO320 at the crown of the V3 hairpin by a GLY. These data suggest that the hairpin conformation is at least partially stable to long-range electrostatic perturbations, either with or without PRO in the tip of the crown of the V3-hairpin loop. Figure Molecular geometry of HIV-1 V3 conformer model 5 and a GLY320 substituted model 5. Space-filling models were obtained with ViewMol3D [Sharon et al. (2002) PDB 1NJ0]). Red=oxygen, blue=nitrogen, black=carbon, white=hydrogen and purple=lithium. End-to-end distance (D) was obtained with ViewMol3D and is in Ångströms. Geometry optimized GLY320 Model 5, D=4.74 ÅThis revised version was published online in October 2004 with corrections to the Graphical Abstract.     

Structure of glutathione S-transferase of the filarial parasite Wuchereria bancrofti: a target for drug development against adult worm

A three dimensional structural model of Glutathione-S-transferase (GST) of the lymphatic filarial parasite Wuchereria bancrofti (wb) was constructed by homology modeling. The three dimensional X-ray crystal structure of porcine -class GST with PDB ID: 2gsr-A chain protein with 42% sequential and functional homology was used as the template. The model of wbGST built by MODELLER6v2 was analyzed by the PROCHECK programs. Ramachandran plot analysis showed that 93.5% of the residues are in the core region followed by 5.4 and 1.1% residues in the allowed and generously allowed regions, respectively. None of the non-glycine residues is in disallowed regions. The PROSA II z-score and the energy graph for the final model further confirmed the quality of the modeled structure. The computationally modeled three-dimensional (3D) structure of wbGST has been submitted to the Protein Data Bank (PDB) (PDB ID: 1SFM and RCSB ID: RCSB021668). 1SFM was used for docking with GST inhibitors by Hex4.2 macromolecular docking using spherical polar Fourier correlations.Figure: A three-dimensional (3D) structure of Glutathione-S-transferase (GST) of the lymphatic filarial parasite Wuchereria bancrofti (wb) was constructed by homology modeling. This modeled 3D structure of wbGST has been submitted to the Protein Data Bank (PDB) (PDB ID: 1SFM and RCSB ID: RCSB021668).     

Local sequential minimization of double stranded B-DNA using Monte Carlo annealing

A software algorithm has been developed to investigate the folding process in B-DNA structures in vacuum under a simple and accurate force field. This algorithm models linear double stranded B-DNA sequences based on a local, sequential minimization procedure. The original B-DNA structures were modeled using initial nucleotide structures taken from the Brookhaven database. The models contain information at the atomic level allowing one to investigate as accurately as possible the structure and characteristics of the resulting DNA structures. A variety of DNA sequences and sizes were investigated containing coding and non-coding, random and real, homogeneous or heterogeneous sequences in the range of 2 to 40 base pairs. The force field contains terms such as angle bend, Lennard-Jones, electrostatic interactions and hydrogen bonding which are set up using the Dreiding II force field and defined to account for the helical parameters such as twist, tilt and rise. A close comparison was made between this local minimization algorithm and a global one (previously published) in order to find out advantages and disadvantages of the different methods. From the comparison, this algorithm gives better and faster results than the previous method, allowing one to minimize larger DNA segments. DNA segments with a length of 40 bases need approximately 4 h, while 2.5 weeks are needed with the previous method. After each minimization the angles between phosphate–oxygen-carbon A₁, the oxygen–phosphate–oxygen A₂ and the average helical twists were calculated. From the generated fragments it was found that the bond angles are A₁=150°±2°and A₂=130°±10°, while the helical twist is 36.6°±2° in the A strand and A₁=150°±6° and A₂=130±6° with helical twist 39.6°±2° in the B strand for the DNA segment with the same sequence as the Dickerson dodecamer.Figure The final minimized DNA segment of the Dickerson dodecamer sequence represented by ball drawings and viewed (left) perpendicular and (right) down the helical axis