Originally published as Biophys J. BioFAST on October 27, 2006.
doi:10.1529/biophysj.105.079723
Biophysical Journal 92:769-786 (2007)
© 2007 The Biophysical Society
Orientation Preferences of Backbone Secondary Amide Functional Groups in Peptide Nucleic Acid Complexes: Quantum Chemical Calculations Reveal an Intrinsic Preference of Cationic D-Amino Acid-Based Chiral PNA Analogues for the P-form
Christopher M. Topham * and
Jeremy C. Smith 
* Institut de Pharmacologie et de Biologie Structurale, Centre National de la Recherche Scientifique UMR 5089, Toulouse, France; Computational Molecular Biophysics, IWR, Universität Heidelberg, Heidelberg, Germany; and Oak Ridge National Laboratory/University of Tennessee Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, Tennessee
Correspondence: Address reprint requests to Christopher M. Topham, E-mail: christopher.topham{at}novaleads.com.
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ABSTRACT
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Geometric descriptions of nonideal interresidue hydrogen bonding and backbone-base water bridging in the minor groove are established in terms of polyamide backbone carbonyl group orientation from analyses of residue junction conformers in experimentally determined peptide nucleic acid (PNA) complexes. Two types of interresidue hydrogen bonding are identified in PNA conformers in heteroduplexes with nucleic acids that adopt A-like basepair stacking. Quantum chemical calculations on the binding of a water molecule to an O2 base atom in glycine-based PNA thymine dimers indicate that junctions modeled with P-form backbone conformations are lower in energy than a dimer comprising the predominant conformation observed in A-like helices. It is further shown in model systems that PNA analogs based on D-lysine are better able to preorganize in a conformation exclusive to P-form helices than is glycine-based PNA. An intrinsic preference for this conformation is also exhibited by positively charged chiral PNA dimers carrying 3-amino-D-alanine or 4-aza-D-leucine residue units that provide for additional rigidity by side-chain hydrogen bonding to the backbone carbonyl oxygen. Structural modifications stabilizing P-form helices may obviate the need for large heterocycles to target DNA pyrimidine bases via PNA·DNA-PNA triplex formation. Quantum chemical modeling methods are used to propose candidate PNA Hoogsteen strand designs.
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INTRODUCTION
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More than a decade ago, Nielsen and co-workers described an electrostatically neutral chimera between nucleic acids (the nucleobases) and (pseudo-) peptides (the backbone), termed "polyamide nucleic acids", or PNAs (1
,2). These molecules, which are resistant to both nuclease and proteinase attack (3), comprise a backbone that is structurally homomorphous to the deoxyribose phosphate backbone, containing achiral N-(2-aminoethyl) glycine (aeg) units to which the nucleobase is attached via a methylene carbonyl linker (Fig. 1). PNAs form specific and highly thermally stable complexes with complementary single-stranded DNA or RNA, mediated by Watson-Crick hydrogen bonding (4). Unique among oligonucleotide analogs, PNAs are additionally able to strand invade double-stranded DNA (5,6). Their remarkable strand invasion properties, alongside demonstrations that modular PNA-conjugate constructs can cross cellular (7–9) and nuclear (10,11) membrane barriers, have made PNAs promising lead candidate molecules for the therapeutic control of gene expression (12–16).
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FIGURE 1 Schematic representation of a PNA residue junction with atom and dihedral angle nomenclature. Chiral PNA analogs based on D-aminoethylamino acid units carry side-chain (R) replacements of the pro-R hydrogen in the glycine moiety of the prototype (aeg) design.
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In practice, the efficient targeting of double-stranded DNA via (PNA·DNA-PNA) triplex formation remains essentially limited to homopurine (pu) DNA tracts (17). The use of pseudocomplementary (pc) PNA oligomers, comprising 2,4-diaminopurine and 4-thiouracil base replacements for adenine and thymine to disfavor unwanted self association of the pcPNA strands, allows mixed (pu/py) DNA sequences with a minimum 50% AT content to be targeted by a double duplex invasion mechanism (18). The future incorporation of pseudocomplementary guanine and cytosine nucleobase analogs is expected not only to increase the number of DNA sequences that can be targeted, but should also permit the covalent tethering of pcPNA oligomers as bis-pcPNAs so as to reduce the molecularity of the strand displacement process (14).
The amenability of the aeg PNA structural framework to chemical modification affords considerable advantages in the development of a pharmacologically efficacious antigene agent (19,20). The incorporation of charge and chirality, and manipulation of PNA backbone flexibility provide opportunities to increase solubility and bioavailability, and to improve selective binding to DNA targets. PNA binding to double-stranded DNA is effectively kinetically controlled (21), and the decrease in the magnitudes of association rate constants with increase in salt concentration (22–24) makes binding inhibition at physiological ionic strength a potential obstacle to in vivo applications. Marked improvements in binding rates at elevated ionic strengths obtained with bis-PNAs carrying positive charge either within the interchain linker or in the N- and C-terminal peptide tail sections (25,26) suggest that the judicious placement of charged groups on the aeg PNA backbone proper could similarly increase binding rates under physiological conditions without loss of sequence selectivity. The inherent flexibility of the prototype aeg PNA design (27–30), and the attendant entropy losses incurred upon binding to DNA, have at the same time prompted the search for conformationally constrained backbone skeletons that are preorganized so as to favor complex formation. Many strategies have focused on the covalent integration of (chiral) cyclic ring systems in designs that conform to the guiding principle of maintaining the base separation from and along the backbone by the same numbers of bonds as in DNA (see 20,31–33 for review and recent advances). In principle, rigidity may also be conferred without the creation of covalent cyclic structures by the attachment of one or more chemical substituents at pro-chiral carbon centers in the aeg PNA backbone (see Fig. 1). Much interest has been shown in the improved solubility and modified hybridization properties toward single-stranded DNA of PNA variants carrying positively charged chiral N-(2-aminoethyl) D-lysine units (34–37). A recent crystallographic study of an anti-parallel mixed-sequence PNA-DNA decamer heteroduplex, comprising a three-residue unit D-lysine "chiral box", provides evidence that increased polyamide backbone conformational rigidity can be obtained through the introduction of chiral centers (38).
The availability of experimentally determined structures of PNA complexes provides a rich knowledge base for the rational design of conformationally restricted chiral PNA analogs bearing functional groups. Experimental studies of PNA complexes have thus far revealed the existence of two distinct morphological helix forms. Crystal structures of the D-lysine-based PNA-DNA heteroduplex (38), a homopyrimidine PNA·DNA-PNA (py·pu-py) triplex (39), and four mixed (pu/py) sequence self-complementary PNA-PNA duplexes (40–43) all possess an unusual low-twist angle helical morphology, known as the P-form. These under-wound structures are characterized by 16-fold (or 18-fold) helical repeats, according to whether (or not) a partner Watson-Crick DNA strand is present, and a pronounced displacement of the bases from the helix axis. In contrast to the P-form helices, which have average (local) twist angle values in the range 19–23°, antiparallel mixed-sequence heteroduplex aeg PNA-DNA octamer (44) and aeg PNA-RNA hexamer (27) NMR solution structures have significantly higher average (local) helix twist angles of 28° and 30°, respectively. Although the C2'-endo sugar puckering observed in the aeg PNA-DNA duplex is more typical of a B-form helix, both heteroduplexes adopt similar A-like helical topologies, with displacement of inclined Watson-Crick basepairs toward the minor groove.
We have previously reported that helix morphology exerts a significant influence on PNA backbone conformation and flexibility (45). The largest conformational variation is observed experimentally in rotations around the two bonds flanking the backbone secondary amide at junctions connecting residues at positions (i) and (i + 1) in the PNA chain, described by the 
(i) and 
(i+1) dihedral angles (see Fig. 1). Values of (i) and (i+1) were shown to be highly correlated over certain ranges, providing the basis for a PNA backbone conformation classification scheme. Most notably from a design perspective, it was found that preferred Watson-Crick PNA backbone conformations in P-form helical structures differ from those in A-like helices, possibly due in part to differential solvation effects in the minor groove. These findings suggest that, in addition to restricting conformational flexibility, the incorporation of bulky and/or charged groups to the PNA backbone could be used to control the basepair stacking pattern through the selective stabilization of backbone conformers associated with a particular helical form. This thesis is supported by the existence of the D-lysine based PNA-DNA duplex as a P-form helix, rather than an A-like helical structure, although the possibility of the difference in helix morphology compared to the aeg PNA-DNA duplex studied by NMR (44) being the result of crystal packing, strand length difference and/or base sequence effects cannot as yet be completely ruled out (38). Conversely, a L-arginine based PNA T10 decamer was observed to bind a complementary DNA A10 sequence with 1:1 stoichiometry, rather than as a 2:1 (PNA·DNA-PNA) triplex as does its aeg PNA T10 counterpart (46). Notwithstanding the role of electrostatic effects or steric hindrance of Hoogsteen strand binding by the L-arginine side chain, a plausible explanation for this change in binding stoichiometry may be an inability of the 2-aminoethyl-L-arginine backbone to adopt conformations compatible with a P-form helix.
It is with this design philosophy in mind that we present here a structural analysis of the spatial orientation preferences of the backbone amide –NH and >C=O groups at residue junctions in experimental structures of PNA complexes, classified according to backbone conformation. Ambiguities concerning the controversial participation of (i + 1) backbone –NH groups in hydrogen bonding interactions with the carbonyl oxygen of the backbone-base linker at the preceding residue position (i), as proposed by Bruice and co-workers (47,48) but otherwise widely refuted (see, for example, 27,41,44,49), have been clarified using an operational definition of a hydrogen bond routinely employed in the classification of protein secondary structure (50,51). We have investigated the energetic and the structural changes involved in the binding of a water molecule to an O2 base atom in a model symmetry-restrained PNA thymine dimer (pTT) system using quantum chemical methods. Collectively the results are consistent with bound water molecules in the minor groove playing a structurally more important role in the stabilization of Watson-Crick PNA backbone conformation in aeg PNA P-form structures than in A-like hybrid double helices, where a tendency to form weak (i + 1)/(i) interresidue hydrogen bonds of less than ideal geometry is evident in at least two PNA conformation classes. Our findings shed light on conflicting results obtained in molecular dynamics simulations of solvated aeg PNA-DNA duplexes (49,52).
In another series of quantum chemical calculations on a structurally modified pTT junctions, in which the pro-R hydrogen of the aeg PNA CA atom is replaced by aliphatic chains carrying positive charge (see Fig. 1), we exploit the symmetry-restrained dimer as a model with which to investigate local backbone preorganization. In contrast to the aeg PNA junction, the P-form backbone conformation common to the D-lysine "chiral box" and the PNA·DNA-PNA triplex can be identified at minima on the chiral dimer potential energy surfaces. Shortening of the D-lysine aliphatic chain allows direct electrostatic interaction with the PNA backbone carbonyl oxygen in this conformation, suggesting that the introduction of chiral PNA analogs based on either 3-amino-D-alanine or 4-aza-D-leucine should also favor P-form helix formation.
We conclude with a proposal that conformationally restricted structural modifications preferentially stabilizing P-form helices could be exploited to promote PNA·DNA-PNA triplex formation, and in particular to target mixed-sequence double-stranded DNA via triplex invasion mechanisms using small bases and other functional groups, rather than large heterocycles, attached to Hoogsteen strand carbonyl linkers to recognize DNA pyrimidine bases in the major groove. Quantum chemical modeling methods are used in support of candidate PNA Hoogsteen strand designs.
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COMPUTATIONAL METHODS
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PNA residue junction conformer database
The database, comprising a total of 207 nonredundant PNA residue junction atom sets, was compiled from eight experimental structures of PNA complexes in the Protein Data Bank (PDB) (53). Of these, 50 and 56 atom sets were, respectively, extracted from NMR solution structures of A-like mixed (py-pu) sequence PNA-RNA (PDB code 176D; (27)) and PNA-DNA (PDB code 1PDT; (44)) heterodimers. For comparative purposes, we also included data sets obtained by constrained energy minimization of the NMR models with PNA base atoms and all atoms of the nucleic acid strands held fixed (see Topham and Smith (45)). The remaining atom sets were culled from PNA strands in P-form x-ray crystal structures of a PNA·DNA-PNA triplex (PDB code, 1PNN (32 sets); (39)), a mixed-sequence PNA-DNA heteroduplex, comprising a three-residue unit D-lysine "chiral box" (PDB code, 1NR8 (9 sets); (38)), and four self-complementary right-handed homoduplexes (PDB codes, 1PUP (16 sets), (40); 1QPY (28 sets), (41); 1HZS (10 sets), (42); 1RRU (6 sets), (43)). Hydrogen atoms were added to the Protein Data Bank crystal structures using the HBUILD (54) facility in CHARMM (55), before energy minimization with all heavy atoms held fixed. PNA force field parameters were abstracted from the distributed all-atom CHARMM22 nucleic acid (56) and protein (57) sets, supplemented as previously reported (45).
Structural analysis of PNA residue junctions
Analysis of (, ß, 
, 
, , and 
) backbone and (
1, 2, and 3) backbone-base linker dihedral angles in the residue junction database was carried out according to the contiguous atom quartet definitions given previously (45). A {æ(i), ß(i), (i), (i), ß(i+1), (i+1), (i+1)} dihedral domain vector was defined at each junction between adjacent residue positions (i) and (i + 1) in the PNA chains, where æ(i) is given by (i+1) + (i). We refer to æ as the coupling constant. Negative-signed values of æ in the range (–150° > æ 
0°) are assigned to the {æ–} domain, positive-signed values in the range (0° > æ 150°) are classed as {æ+}, and values in the range (150° > æ 210°) are assigned to the {æ-trans} domain. ß-domains are, respectively, categorized as {g+}, {trans} or {g–} for angles in the range (0° ß < 120°), (120° ß < 210°) or (210° ß < 360°). The and dihedrals are either assigned to the {+90°} domain for angle values falling in the range (0° (, ) < 180°), or the {–90°} domain for angles in the range (180° (, ) < 360°). The orientation of the carbonyl group of the PNA backbone secondary amide bond was measured using the pseudodihedral angle (
) introduced by the Orozco and Laughton groups (49). Recast in terms of the atom nomenclature used previously (39,45), and retained here (see Fig. 1), is defined at the ith residue position ((i)) by the atom quartet, CF(i)–NB(i)–C(i)–O(i).
Our PNA residue junction classification scheme allows for the coarse classification of conformers according to the {æ} domain occupied, and assignment to a particular subset or class according to the flanking {ß, , } torsion angle domain combination (45). Hierarchic flanking angle domain pattern searches are now more robustly conducted by the ordered examination of the four-component {(i), (i), ß(i+1), (i+1)} and {(i), ß(i+1), (i+1), (i+1)} vectors, before consideration of the {ß(i), (i), (i)} and {(i+1), ß(i+1), (i+1)} three-component vectors. Seven conformational classes are currently recognized (Table 1). It should be noted that all values of and were inadvertently systematically interchanged in our earlier analysis of PNA conformational preferences (45), and the {æ, ß, , } vector defining the (æ+)-ß-trans conformational class is accordingly redefined in Table 1 as {æ+, trans, +90°, –90°}. Three residue conformers in the 1PDT data set, previously assigned as (æ+)-ß-g–, are now reclassified as (æ+)-ß-trans, and one residue junction in the 1PUP data set, previously annotated (æ–)-P, is more appropriately considered as a member of a newly recognized class, (æ-trans)-P, uniquely observed in PNA-PNA duplexes. Structurally, these conformers resemble (æ–)-P conformers, with compensatory shifts in values ß, , and (i) dihedral angles permitting minor groove water bridging between the base and the backbone –NH(i+1) group to be maintained. A statistical analysis of backbone dihedral angle values in all seven conformational classes is presented in Table 2.
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TABLE 2 Statistical analysis of selected (pseudo-) dihedral angle values in seven conformational classes of PNA residue junction in experimental structures
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Electrostatic interaction energies between the backbone-base linker carbonyl group (>CE(i) = OE(i)) at residue position i and the backbone –NH(i+1) group at residue position i + 1 were calculated according to the Kabsch and Sander interatomic distance formula (50). An interresidue hydrogen bond was considered to exist when the interaction energy was <–0.5 kcal mol–1. The generous cutoff proposed by the authors allows for bifurcated hydrogen bonds and errors in coordinates.
Ab initio quantum chemical calculations on model PNA thymine dimers
Hartree-Fock (HF) calculations on a model PNA thymine dimer (pTT) system, with hydrogen atoms in place of the terminal –NH and >C=O groups, were performed using GAUSSIAN 94 (58) or 98 (59). Geometry optimizations were carried out using either the 6-31G* or 3-21G* basis set as reported in Table 3. HF/6-31G* provides a sufficiently high level of quantum chemical theory appropriate for the calculation of hydrogen bonding properties and water binding interaction energies in small stable systems (56,60,61). Input geometries were specified as a Z-matrix, and symmetry restraints applied to chemically equivalent bond lengths, valence bond angles, and dihedral angles in the two residue units. Dimer configurations existing at (local) energy minima in regions of dihedral angle space characteristic of the main P-form and A-like conformer classes were identified from geometry optimizations in the absence of constraints using starting internal coordinate values obtained from analyses of experimental structures. Other conformers in a given class were then generated by the application of a constraint to fix to a selected value within the experimentally observed range. Initial values for were calculated from the æ coupling constant. In cases such as the (æ–)-P reference model 1.2 (Table 3), where it was necessary to ensure the integrity of / dihedral angle coupling, a constraint was applied on the pseudodihedral angle without directly fixing either or . High-occupancy solvent binding in the minor groove was modeled in the dimer systems by optimization of the interaction of a water molecule with the O2 thymine base atom of the first (N-terminal) residue unit. In these calculations, water molecule (HW-OW) bond length and (HW-OW-HW) bond angle values were constrained to TIP3P reference values (62). Dimer geometries were either held fixed to their optimized configurations, determined in the absence of the water molecule, or a full optimization of the dimer-water complex performed (with dimer symmetry restraints) to explore induced conformational changes. Default convergence criteria were satisfied in all cases. All reported energy differences were determined from (Møller-Plesset) MP2 single point energy calculations on the HF/6-31G* optimized geometries, allowing for a more accurate treatment of electron correlation effects than afforded by Hartree-Fock theory.
Comparison of base stacking patterns in modeled residue junctions and experimental structures
Intrastrand base stacking patterns in four representative PNA-containing experimental structures, the standard A80 and B80 DNA fiber conformations, and the pTT model dimers were compared in a pairwise manner using (averaged) root mean square distance (RMSD) values, calculated over the (12) heavy ring atoms of stacked py/py bases (see Supplementary Material, Table S1). A total of 20 stacked py/py base atom sets were culled from (Watson-Crick) PNA strands in the 176D (chain A, 10 models) Protein Data Bank (PDB) structure, and 16 from each from the 1PDT (chain B, 8 models) and 1PNN (chains A and C) coordinate sets. None of the four experimental PNA-PNA homoduplex structures contains stacked py/py bases, and 10 stacked py/py base atom sets were generated by reconstruction of chains A and B in the 1PUP PDB structure as polypyrimidine strands using JUMNA (63,64). Helicoidal parameters were calculated using a CURVES (65,66) analysis of the original coordinates. Canonical A80 and B80 AT duplex structures were generated using JUMNA and the helicoidal parameter sets tabulated by Lavery et al. (64). Base stacking patterns were compared using principal coordinates analysis (classical scaling) techniques (67). RMSD values were loaded into a (n x n) distance (dissimilarity) matrix, and the elements normalized in a driver routine before analysis using the CMDS Fortran77 subroutine (http://astro.u-strasbg.fr/
fmurtagh//mda-sw/). The program outputs the (n – 1) eigenvalues, and projections of the base stacking pattern on the first seven principal components for plotting.
Quantum chemical modeling of interactions between Hoogsteen strand PNA analog derivative model compounds and pyrimidine bases
Geometric interactions of proposed functional groups with DNA pyrimidine bases in the major groove (see Fig. 2) were investigated using quantum chemical techniques and spatial constraints derived from the 1PNN (py·pu-py) PNA·DNA-PNA triplex x-ray crystal structure (39). Calculations were performed using the (May, 2004) GAMESS (68) implementation of the B3LYP hybrid Hartree-Fock/density functional method and the 6–311++G(d,p) basis set. The model systems (Fig. 9) comprised a pyrimidine base and N,N-dimethyl substituted alkyl amide derivatives of the functional group: (A) isopropyl (–CH(CH3)2) to target the thymine 5-methyl atom, and (B) imidazolyl (attached at the N1 position) or (C) isoxazolyl (attached at the C5 position) to hydrogen bond with cytosine. Six spatial constraints (three dihedral angles, two angles, and one distance) were imposed between the C5 and C6 atoms of the target pyrimidine base and atom positions in the model compounds analogous to the PNA backbone CA, NB, and CG atoms (Fig. 2). Pyrimidine base coordinates were obtained by conversion of the 1PNN polypurine DNA chains using JUMNA (63,64). Helicoidal parameters were calculated from a CURVES (65,66) analysis of the heterotriplex. Spatial constraints were derived from centrally positioned representative pT20·dA5 and pT18·dA3 PNA·DNA duplets (chains C and D), remote from the out-swinging Hoogsteen pC16 base in PNA chain A of the other triplex in the asymmetric unit. To take co-ordinate error into account, the CA, NB, and CG atom positions were not taken directly from the original 1PNN data, but from coordinates obtained by superposition of all heavy atoms in a HF/6-31G* geometry-optimized N,N-dimethyl thymine-1-acetamide model structure, built in the same conformation as the experimental PNA residue unit using dihedral angle constraints.
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FIGURE 2 Proposed tandem use of conformationally restricted PNA and small Hoogsteen strand functionalities to target DNA pyrimidine bases via triplex formation. (A) Solvent shielding of thymine 5-methyl group by an isopropyl group. (B) Major groove recognition of cytosine by an isoxazole base. Watson-Crick PNA strand chiral PNA analogs based on 3-amino-D-alanine (A) or 4-aza-D-leucine (B) may promote P-form helix formation.
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FIGURE 9 Spatially constrained B3LYP/6-311++G(d,p) optimized interaction geometries of N,N-dimethyl substituted amide model compounds with pyrimidine bases. (A) N,N-dimethyl-2-methylpropanamide/thymine; (B) 2-imidazol-1-yl-N,N-dimethylacetamide/cytosine; (C) 2-isoxazol-5-yl-N,N-dimethylacetamide/cytosine. Hydrogen bond interactions are represented as thin rods. Capped-stick and space-fill graphics representations were prepared using VMD (85).
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Strain energy in the model compounds in the pyrimidine base complexes was calculated from energy differences with respect to the fully geometry-optimized conformation of the isolated molecule in the absence of constraints. Calculations of atomic solvent-accessible surface area were carried out using NACCESS version 2.1.1 (69), a probe size of 1.4 Å, and the program default van der Waals radii of Chothia and co-workers for common chemical atom types. Basepair propeller and buckle parameters in the complexes of the azolyl derivatives with cytosine were calculated using CURVES (65,66) with a guanine base in place of the azole bases. Superposition was performed using the following ring atom mappings to guanine N9, C4, C5, N7, and C8 positions: N1, C2, N3, C4, C5 (imidazole); C5, O1, N2, C3, C4 (isoxazole).
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RESULTS
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Influence of / dihedral angle coupling on PNA backbone carbonyl group orientation
Our previous work drew attention to the existence of coupled rotations around the two bonds flanking the backbone secondary amide at junctions connecting residues at positions (i) and (i + 1) in the PNA chain, described by the (i) and (i+1) dihedral angles (45). Coupling of these dihedral angles operates over relatively short ranges of values characteristic of the conformer class. Fig. 3 shows that values of the pseudodihedral angle (i), describing the orientation of the carbonyl group of the PNA backbone secondary amide bond at residue positions (i), correlate closely with values of (i+1) in the seven conformational classes identified in experimental structures. The correlations indicate that coupled change in (i+1) and (i) exerts a direct effect on the orientation of the secondary amide carbonyl group.
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FIGURE 3 Dependence of PNA polyamide backbone carbonyl group orientation on the  dihedral angle at residue junctions in experimental structures. Plots of the pseudodihedral angle (i) at the ith PNA residue unit versus the (i+1) dihedral angle at the following residue position are shown. Dihedral angle pairs from four conformers identified in PNA strands in A-like aeg PNA-RNA (PDB code 176D,  ) and aeg PNA-DNA (1PDT,  ) helical structures are plotted in panels on the left-hand side. Data for three PNA conformer classes in P-form structures are shown in panels on the right-hand side: 1PNN homopyrimidine PNA·DNA-PNA triplex (Watson Crick, •, and Hoogsteen strands, O); 1PUP ( ), 1HZS ( ), 1QPY ( ), and 1RRU ( ) self-complementary PNA-PNA homoduplexes; 1NR8 ( ) PNA-DNA heteroduplex comprising a three-residue D-lysine "chiral box". Further details concerning the origins of the data are given in the Computational Methods section. The "forward" and "backward" pseudodihedral angle domains, describing 180° rotations of the PNA backbone carbonyl oxygen (O) atom around the NB-C vector with respect to the CF atom, defined by Soliva et al. (49), are, respectively, indicated as gray shaded and unshaded areas, centered at values of of 120° and –60° (300°). Solid line fits to the angle data were constructed from median estimates of ((i+1) + (i)) given in Table 2. Regression analysis of (i) on (i+1) yielded a r2 (coefficient of determination) value of 0.95 (n = 125) for combined (classified) data in the {æ–} domain, and respective r2 values of 0.71 (n = 12) and 0.83 (n = 28) for data in the {æ-trans} and {æ+} domains. Corresponding r2 values obtained from regression analysis of (i) on (i+1) are 0.97 (n = 127), 0.43 (n = 12), and 0.91 (n = 28), respectively.
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Backbone carbonyl group orientation accommodates minor groove water binding in P-form structures
The (æ–)-P conformer is present in all PNA chains of P-form crystal structures. All the experimental (æ–)-P residue junction (i) data fall within the so-called "forward" domain (Fig. 3), defined by Soliva et al. (49) for PNA residue units with backbone carbonyl groups pointing toward the helix C terminus, corresponding to values of in the range 120 ± 90°. This geometric arrangement allows the backbone –NH group at the next (ith + 1) residue position of Watson-Crick PNA chains to interact with pyrimidine O2(i) or purine N3(i) base atoms via the intermediary of a bound water molecule in the minor groove. The modeled (æ–)-P pTT dimer junction (1.2) shown in Fig. 4 A was minimized in the presence of a bridging water molecule with held fixed at the average value of 108.7° (±11.8°) for (16) residue junctions in Watson-Crick PNA chains of the PNA·DNA-PNA triplex x-ray diffraction structure (39). Base stacking in the quantum chemical model is similar to that in the homopyrimidine Watson-Crick chains of the 1PNN coordinate set, with an average RMSD value of 0.35 Å for the ring atoms.
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TABLE 4 Interresidue hydrogen bond geometry and energy analysis of HF/6-31G* geometry-optimized aeg pTT dimer models with (æ–)-ß-g+ backbone conformations
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In contrast to the (æ–)-P conformation, the backbone carbonyl group points in the opposite direction in (æ–)-Pminor residue junctions. Experimental (i) data for (æ–)-Pminor residue junctions all lie within the "backward" domain, covering the angle range –60 ± 90°. This type of P-form residue junction geometry is found in the four PNA-PNA duplexes and the first two junctions at the N-terminus of the mixed-sequence PNA-DNA decamer, carrying a centrally positioned three-residue unit D-lysine "chiral box" (38). The orientation of the carbonyl group in the experimental structures supports minor groove water bridging with pyrimidine O2 or purine N3 base atoms in the same PNA residue. The geometry-optimized reference model (2.1) of an (æ–)-Pminor pTT residue junction (Fig. 4 C) exists at an energy minimum on the pTT energy surface. The value of in the dimer model is –57.9°, in close agreement with an average value of –56° for experimental data. Base stacking in model 2.1 most closely resembles stacking in the 1PUP PNA-PNA data set, the average RMSD being 0.40 Å for the ring atoms.
Backbone carbonyl group orientation in A-like heteroduplexes associated with nonideal interresidue hydrogen bonding
The (æ–)-ß-g+ class is the most populated of the four conformational classes observed in A-like PNA-DNA and PNA-RNA heteroduplex helices studied by NMR. Average values of (i), (i+1), and (i) for this class are 90° out of phase with respect to corresponding values in (æ–)-P and (æ–)-Pminor residue junctions. The range of values of (i) in the experimental structures (200–260°) straddles the boundary at 210° (–150°) separating the "forward" and "backward" domains. The backbone carbonyl group in these conformers points toward the solvent, allowing the backbone –NH group of the next residue unit in the chain to interact with the backbone-base carbonyl (OE) oxygen, as exemplified in the geometry-optimized model (3.2) of an (æ–)-ß-g+ junction shown in Fig. 4 B. The dimer exists in a local energy minimum, with an -value of 156° and a -value of –107° (253°), as compared to respective average (i+1) and (i) values of 168° and –131° (229°) for (æ–)-ß-g+ conformers in A-like experimental structures. The OE(i)–HN(i+1) distance (2.59 Å) and OE(i)–HN(i+1)–N(i+1) angle (116.0°) in this model are close to respective average experimental values of 2.81 ± 0.39 Å and 127 ± 9° for (æ–)-ß-g+ conformers. While base stacking in model 3.2 is not particularly A-like, it being most similar to that of the 1PNN structure with an average RMSD value of 0.41 Å, a shift away from the 1PUP PNA-PNA homoduplex stacking pattern, relative to stacking in the 1.2 and 2.1 P-form reference model residue junctions, is nevertheless evident from the principal coordinates analysis in Fig. 5 A.
The chemical shifts and solvent exchange properties of HN(i+1) amide protons in the PNA-RNA (27) and PNA-DNA (44) duplexes appear to contradict the existence of interresidue hydrogen bonds (70). Indeed, respective average OE(i)–HN(i+1) distances of 2.81 (±0.39) Å and 2.69 (±0.51) Å for (æ–)-ß-g+ and pooled (æ+)-ß-trans and (æ+)-ß-g– residue junctions in the NMR solution structures are longer than the 2.5-Å limit often employed in standard definitions of hydrogen bonding (71,72). An analysis of the dependence of the electrostatic interaction energy (
) of the >CE(i)=OE(i) and –NH(i+1) groups, as a convenient single-parameter description of hydrogen bond quality, on the (i) pseudodihedral angle in the (æ–)-ß-g+ and pooled (æ+) residue junction sets is shown in Fig. 6. The results show sharp minima in as (i) approaches 240° (–120°) in (æ–)-ß-g+ conformer junctions, or alternatively as (i) tends to 120° in (æ+)-ß-trans and (æ+)-ß-g– conformers that posses dihedral angles in the –90° domain. According to the Kabsch and Sander (50) formula, a good hydrogen bond should have an electrostatic interaction energy of –3 kcal mol–1. Only in data obtained by constrained in vacuo molecular mechanics energy minimization (panels B and D) do values approach this limit. The raw solution data (panels A and C) do not support the existence of ideal interresidue hydrogen bonding.
The energetics of interresidue hydrogen bonding was further investigated in (æ–)-ß-g+ residue junctions in a series of quantum chemical calculations on the pTT dimer by varying over the experimentally observed (i+1) range from 145° to 206° (–154°). Dihedral angle values in the six geometry-optimized models (3.1, 3.2, 3.4, and 3.6–3.8) are reported in Table 3. Values of the æ coupling constant remain close to the median experimental value of –114°, at least up to -values of 180°. Inspection of the relative total energies (E in Table 4) confirms our earlier conclusions, based on molecular mechanics calculations (45), that / dihedral angle coupling in PNA chains involves little net energy change up to limiting -values of 180°. The hydrogen bonding geometry and the calculated electrostatic energy component for the (–NH(i+1)–O(i)=C(i)<) interaction vary as a function of (and consequently ) across the series (Table 4). In accordance with the analysis of the raw (æ–)-ß-g+ NMR data, the strength of the most favorable calculated electrostatic interaction energy is appreciably <–3 kcal mol–1 (–1.61 kcal mol–1). This is observed for model 3.6 ( = 180°) with a -value of 241° (–119°). Regression analysis of 
on E, with model 3.2 serving as the reference geometry, yielded a r2 value close to zero (0.05), implying that the weak hydrogen bonds do not contribute significantly to the stabilization of the (æ–)-ß-g+ conformation.
Structural and energetic analysis of base-water molecule binding in the aeg-pTT dimer
Minor groove high-occupancy water sites and spines of hydration have been observed experimentally in P-form crystal structures (38–43) and in molecular dynamics simulations of PNA-DNA and PNA-RNA heteroduplexes (49). Here we have used the symmetry-restrained pTT dimer as a model system to probe the structural and energetic influence of the binding of a water molecule in the minor groove by quantum chemical methods. Energy data for water molecule binding to the O2 atom of the N-terminal base as a function of the backbone conformation are summarized in Table 5. Variations in base-stacking patterns are represented two-dimensionally in Fig. 5 as projections on the first two components produced by principal coordinates analysis of pairwise RMSD data.
The (æ–)-P conformer permits water bridging with the backbone –NH(i+1) group, whereas neither of the –NH(i+1) and >C(i)=O(i) backbone functional groups is available in the (æ–)-ß-g+ conformer. As expected, the calculated water interaction energy (
) is higher for the (æ–)-P model 1.2 (–18.5 kcal mol–1) compared to that for the (æ–)-ß-g+ model 3.2 conformer (–11.2 kcal mol–1). Although each system nominally comprises a total of two hydrogen bonds in the presence of a water molecule, the P-form reference (æ–)-P conformer is –2.9 kcal mol–1 lower in energy than the (æ–)-ß-g+ junction. In contrast, the isolated (æ–)-P pTT dimer (model 1.2) is +4.3 kcal mol–1 higher in energy following removal of the water molecule than the (æ–)-ß-g+ conformer model 3.2, geometry-optimized in the absence of a water molecule.
Geometry optimization of (æ–)-ß-g+ model 3.2 in the presence of a water molecule targeted to the O2 atom yielded structure 1.3. Binding incurred the rupture of the weak (i + 1)/(i) interresidue hydrogen bond and the formation of a water bridge with the backbone –NH(i+1), accompanied by a marked transition in from 156° to 249° (–111°). Holding fixed at 156° or 168°, the average (i+1) value for (æ–)-ß-g+ conformers in A-like experimental structures, permitted the retention of the interresidue hydrogen bond in structures 3.3 and 3.5, respectively, obtained by optimization of starting geometries 3.2 and 3.4 in the presence of a water molecule. In both cases water molecule binding induced shifts in base-step stacking toward patterns in the four PNA experimental reference structures, and in particular the P-form 1PNN and 1PUP structures (Fig. 5 A).
The high-end -value of 249° in model 1.3 is more characteristic of P-form (æ–)-P or (æ-trans)-P conformations than A-like (æ–)-ß-g+ conformers. However, model 1.3 displays signs of / dihedral angle decoupling (æ = –90°) and has a -value of 156° that is notably higher than respective average (i) values of 118° or 81° in (æ–)-P or (æ-trans)-P experimental junctions. Removal of the bound water in model 1.3 followed by a second round of optimization led to structure 1.4, which shows even more pronounced / decoupling (æ = –79°) and a further increase in to 174°. The structural change for water binding (i.e., 
) again involves a shift in base stacking closer to stacking patterns in the P-form experimental reference structures, as does the analogous 
water-binding induced structural transition with fixed to 108.7° to provide for / dihedral angle coupling in better agreement with experimental data for triplex (æ–)-P junctions (see Fig. 5 A). Structural changes resulting from the imposition of the pseudodihedral angle constraint in the pTT dimer, respectively, incur +1.5 kcal mol–1 (
) and +2.3 kcal mol–1 (
) increases in the total energy in the presence or absence of a backbone-base bridging water molecule. The shift in base stacking relative to stacking variation in the PNA experimental structures and canonical A80 and B80 forms is highlighted in Fig. 5 B. The constraint on exerts a more pronounced effect on the and dihedral angles than on (Table 3). It is of note that reorientation of the backbone amide functional groups or shifts in base stacking closer in agreement with experimental (æ–)-P junction stacking could not be obtained by constraining either or individually.
Backbone-base water bridging in P-form (æ–)-Pminor conformers is with the >C(i)=O(i) group. As in the case of the (æ–)-P conformer, calculated water interaction energies of –15.3 or –14.4 kcal mol–1, depending on the solvent molecule-binding mode, are higher for the (æ–)-Pminor reference dimer (model 2.1) than for the (æ–)-ß-g+ conformer (
, model 3.2). Similarly, the isolated (æ–)-Pminor conformer is of significantly higher energy than (æ–)-ß-g+ model 3.2 (
). Interaction with a water molecule reduces this deficit to +0.08 kcal mol–1 for oxygen atom binding below the plane of the target base (
), or reverses it for more favorable (
) in-plane binding (
). Full geometry optimization of the (æ–)-Pminor reference model 2.1 in the presence of a water molecule yielded structures 2.2 and 2.3. Water molecule binding increases base-step rise and twist, with the result that stacking in models 2.2 and 2.3 resembles experimental patterns less than the stacking in model 2.1, as shown in Fig. 5 A. Relative to water-bound states of model 2.1 in which binding interaction geometries were optimized with the pTT dimer held fixed, the energy gains provided by full geometry optimization are modest: –0.59 kcal mol–1 for in-base-plane binding (
) and –0.77 kcal mol–1 for below base-plane binding (
). Models 2.2 and 2.3 are most similar to model 2.4 that exists in an unbound state at a local minimum on the energy surface close in / dihedral space to model 2.1 with similar energy (
).
Together these results indicate that minor groove water interactions favor conformational transitions from the (æ–)-ß-g+ to the (æ–)-P or (æ–)-Pminor states through induced rotation of the (i) and (i+1) dihedral angles and changes in base stacking. However, they also underline the inherent flexibility of the prototype aeg PNA design, and in particular, the limited ability of aeg PNA to preorganize in the (æ–)-P conformation.
Intrinsic preference of D-lysine-based pTT dimer for the P-form
Menchise et al. recently described the crystal structure of a P-form antiparallel PNA-DNA decamer heteroduplex containing a three-residue unit D-lysine "chiral box" in the PNA strand (38). The "chiral box" (i + 1)/(i) residue junctions, carrying a 4-aminobutyl side chain in place of the pro-R hydrogen of the aeg PNA glycine -carbon (CA) atom at positions (i = 5–7), exist in the (æ–)-P conformation. This prompted us to examine whether the preference of D-lysine based PNA for the (æ–)-P conformation could be observed in a modified dimer system (D-Lys-pTT) comprising the same 4-aminobutyl side-chain rotamer combination (i.e., 
1 +60°; 2, 3, 4 180°) as in the 1NR8 x-ray structure. Using aeg-pTT models 1.3 and 1.4 as starting configuration templates, geometry optimization of the D-Lys-pTT dimer in the presence or absence of a (–NH(i+1)–O2(i)) backbone-base bridging water molecule led to models 4.2 and 4.1, respectively. Both structures exist at energy minima with values of 120° in close accord with the average of 118° for (æ–)-P conformers in experimental structures. While changes in ß, , and dihedral angles are evident, reorientation of the backbone secondary amide appears to be most directly related to shifts of 42° and 45° in (see Table 3). Base-stacking patterns in models 4.2 and 4.1 are also more similar to stacking in the 1PNN triplex crystal structure than are respective patterns in the parent starting aeg-pTT models 1.3 and 1.4. D-Lys-pTT model 4.2, which is shown in Fig. 7 A, has an average RMSD value of 0.556 Å with respect to ring atoms in stacked Watson-Crick strand pyrimidine bases in the 1PNN coordinate set (c.f. 0.646 Å for model 1.3), while that for model 4.1 is 0.720 Å in the absence of a backbone-base bridging water (c.f. 0.748 Å for model 1.4).
Unlike the aeg-pTT model system, no minimum on the potential energy surface could be found for D-Lys-pTT conformers comprising -values of 160° that allow interaction between the –NH(i+1) and >CE(i)=OE(i) groups in (æ–)-ß-g+ residue junctions. Fig. 7 B shows D-Lys-pTT model 4.3, built using aeg-pTT model 3.4 as an initial template before geometry optimization with held fixed at 168°. Large negative base-step roll distorts stacking compared to experimental structures. Removal of the constraint on caused the rupture of the weak (i + 1)/(i) interresidue hydrogen bond, and resulted in model 4.1 of substantially lower energy (
).
Intrinsic preferences of hydrogen bond-locked cationic D-amino acid-based pTT dimers for the P-form
Graphical inspection of the Menchise et al. 1NR8 x-ray structure (38) reveals that the backbone >C(i)=O(i) group oxygen atom makes close contact with the D-lysine side-chain carbon atom at each of the following three (ith + 1) residue positions, the average interatomic separation being 3.17 ± 0.10 Å. This suggested to us the possibility of shortening the aliphatic D-lysine side chain by the removal of three methylene carbons allowing the protonated (i + 1) side-chain amino group in a PNA design based on 3-amino-D-alanine (D-2,3-diaminopropionic acid) to hydrogen bond with the polyamide backbone >C(i)=O(i) carbonyl. The interresidue (
) D side-chain-backbone hydrogen bonding is illustrated in Fig. 8 A, which shows a symmetry-restrained 3-amino-D-Ala-pTT model (5.2) dimer, geometry-optimized in the presence of a backbone-base bridging water molecule. Values of æ (–125°) and (113°) in model 5.2 (Table 3) are close to respective median (–116°) and average (118°) values for (æ–)-P conformers in experimental structures. The average stacked pyrimidine base RMSD value of 0.503 Å with respect to the 1PNN coordinate set is lower than that for the analogous D-Lys-pTT model 4.2. Model 5.2 comprises a 1 side-chain rotamer of +60°, defined at the ith residue position by the atom quartet NB(i) – CA(i) – Cß(i) – N(i). Rotation around the CA – Cß bond in model 5.2 to give the trans rotamer (i.e., 1 180°), followed by geometry optimization yields model 5.4, shown in Fig. 8 B. Model system 5.4 contains an intraresidue (
) D side-chain-backbone carbonyl hydrogen bond, and is only slightly higher in energy than model 5.2 (
). Values of æ (–124°) and (119°) in 3-amino-D-Ala-pTT model 5.4 are again compatible with experimental (æ–)-P residue junction geometry, and the average stacked pyrimidine base RMSD with respect to 1PNN structure stacking is further reduced to 0.426 Å. In a control calculation using the 6-31G* basis set, model 5.4 geometry remained essentially unchanged (c.f. model 5.5; Table 3). Geometry optimization of models 5.2 and 5.4 following removal of the backbone-base bridging water molecules, respectively, led to structures 5.1 and 5.3. In the absence of water bridging, values of rise respectively to 158° and 152°, and the average base-step RMSD values with respect to the 1PNN stacking show prominent increases to 0.806 and 0.784 Å, respectively. The 3-amino-D-Ala-pTT model system thus appears to be more sensitive than the D-Lys-pTT dimer to the presence of a bridging water molecule in its ability to adopt the (æ–)-P conformation.
Replacement of the 3-amino group by the bulkier charge-delocalized dimethylamino group, in an alternative PNA design based on 4-aza-D-leucine, does not hinder the formation of (i + 1)/(i) interresidue or (i)/(i) intraresidue D side-chain-backbone carbonyl hydrogen bonding in geometry-optimized 4-aza-D-Leu-pTT model dimers 6.1 and 6.2, which take up similar backbone conformations and base stacking patterns as models 5.2 and 5.4. As in the case of the 3-amino-D-Ala-pTT dimer, the trans 1 rotamer (6.2), which provides for intraresidue hydrogen bonding, is of higher energy (
) than the +60° 1 rotamer (6.1).
Geometric and energetic analysis of Hoogsteen strand PNA analog derivative model compound interactions with pyrimidine bases
The use of small bases or abasic functional groups, rather than large heterocycles, attached to Hoogsteen strand carbonyl linkers to recognize DNA pyrimidine bases in the major groove (Fig. 2) has been investigated in model systems using spatial constraints derived from the PNA·DNA-PNA triplex x-ray crystal structure (39). B3LYP/6-311++G(d,p) optimized interaction geometries of model compounds with pyrimidine bases are shown in Fig. 9. Structural comparisons of the model systems with the experimental py·pu-py triplex are summarized in Table 6.
The choice of an isopropyl group to target the thymine 5-methyl group (Fig. 9 A) was influenced by well-documented observations of the way in which valine side chains make specific van der Waals contacts with thymine 5-methyl groups at protein-DNA interfaces (73–75). Solvent shielding of the 5-methyl group rather than van der Waals interactions largely accounts for selectivity (76). The C5M carbon is the only thymine base atom to undergo a decrease in solvent-accessible surface area (of 66.5%) in the complex with the N,N-dimethyl-2-methylpropanamide. The respective approach distances of the pro-R and pro-S isopropyl methyl carbons to the C5M atom are 3.83 and 3.94 Å. The strain energy in the N,N-dimethyl-2-methylpropanamide molecule is +1.23 kcal mol–1.
Imidazole- and other azole-2'-deoxyri
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ABSTRACT
INTRODUCTION
