J. Mol. Biol. (1991) 221, 271-292
Solution Structure of [d(GTATATAC)], via Restrained Molecular Dynamics Simulations with Nuclear Magnetic Resonance Constraints Derived from Relaxation Matrix Analysis of Two-dimensional Nuclear Overhauser Effect Experiments Uli Schmitz, David A. Pearlman and Thomas L. James-f Departments
of Pharmaceutical Chemistry and Radiology University of California San Francisco, CA 94143-0446, U.S.A.
(Received 18 January
1991; accepted 17 April
1991)
Two-dimensional nuclear Overhauser effect (2D NOE) spectra have been used as the experimental basis for determining the solution structure of the duplex [d(GTATATAC)], employing restrained molecular dynamics (rMD) simulations. The MARDIGRAS algorithm has been employed to construct a set of 233 interproton distance constraints via iterative complete relaxation matrix analysis utilizing the peak intensities from the 2D NOE spectra obtained for different mixing times and model structures, The upper and lower bounds for each of the constraints, defining size of a flat-well potential function term used in the rMD simulations, were conservatively chosen as the largest or smallest value calculated by MARDIGRAS. Three different starting models were utilized in several rMD calculations: energy-minimized A-DNA, B-DNA, and a structure containing wrinkled D-DNA in the interior. Considerable effort was made to define the appropriate force constants to be employed with the NOE terms in the AMBER force field, using as criteria the average constraints deviation, the constraints violation energy and the total energy. Of the 233 constraints, one was generated indirectly, but proved to be crucial in defining the structure: the cross-strand A&H2 A5-H2 distance. As those two protons resonate isochronously for the self-complementary duplex, the distance cannot be determined directly. However, the general pattern of 2D NOE peak intensities, spin-lattice relaxation time (T,) values, and 31P nuclear magnetic resonance spectra lead to use of the A3-H2 AT-H2 distance for A5-H2 A5-H2 as well. Five rMD runs, with different random number seeds, were made for each of the three starting structures with the full distance constraint set. The average structure from all 15 runs and the five-structure averages from each starting structure were all quite similar. Two rMD runs for each starting structure were made with the A5-H2 A5-H2 constraint missing. The average of these six rMD runs revealed differences in structure, compared to that with the full set of constraints, primarily for the middle two base-pairs involving the missing cross-strand constraint but global deviations also were found. Conformational analysis of the resulting structures revealed that the inner four to six basepairs differed in structure from the termini. Furthermore, an alternating structure was suggested with features alternating for the A-T and T-A steps. Keywords: 2D n.m.r. of DNA; molecular dynamics; alternating A-T sequences; NOE restraints; complete relaxation matrix analysis
1. Introduction Recently,
$ Abbreviations used: n&r., nuclear magnetic resonance; 2D NOE, two-dimensional nuclear
techniques based on nuclear magnetic (n.m.r.1) have become the method of
resonance choice for solution
structure
determination
Overhauser effect; 2&F-COSY, double-quantum-filtered correlated spectroscopy; ISPA, isolated spin-pair approximation; rMD, restrained molecular dynamics; r.m.s., root-mean-square; rMIN, restrained energyminimization; EGTA, [ethylenebis(oxyethylenenitrilo)]tetra-acetic acid.
of pro-
7 Author to whom all correspondence should be addressed. 0022~2836/91/170271-22
$03.00/O
271
0
1991 Academic Press Limited
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teins, oligosaccharides and oligonucleotides. In general, interproton distance information extractable from two-dimensional nuclear Overhauser effect (2D NOE) spectra and, to a smaller degree, torsion angle information deduced from various COSY experiments, are used in conjunction with the distance geometry algorithm (Crippen & Havel, 1988) and restrained molecular dynamics (rMD) (van Gunsteren et al., 1983) to establish high-resolution structures. Several reviews have been published recently (Scheek et al., 1989; Clore & Gronenborn, 1989; Gippert et al., 1996; Karplus & Petsko, 1996), but no standard procedure for determination of solution structures has been agreed upon. Duplex oligonucleotide analysis encounters a broader methodological range, since the general structural motif, i.e. base-paired helix, is a prerequisite and some of the subtle structural features of interest might not be deducible solely from n.m.r. data (Lane, 1996; Pardi et al., 1988). One major obstacle to establishing accurate oligonucleotide structures is the extraction of a sufficiently large number of accurate interproton distances from 2D NOE cross-peak intensities due to the nature of NOE-based distances and peak overlap, especially for highly repetitive sequences. The commonly applied method for converting intensities into distances, the isolated spin-pair approximation (ISPA), imposes another limitation, since it genuinely cannot account for spin-diffusion, which was shown to affect 2D NOE experiments obtained even for short mixing times (Keepers & James, 1984; Borgias & James, 1988, 1989). A complete relaxation matrix analysis, employed in MARDIGRAS (Borg& & James, 1989, 1996), IRMA (Boelens et al., 1988) and MORASS (Post et al., 1990) algorithms, augments the accuracy of the distance information derived, especially for longer distances accessible via the NOE. Nevertheless, several strategies have been proposed (Nilges et al., 1987a; Pieters et al., 1996; Baleja et al., 1996o) describing how the inaccurate distances derived from ISPA can be implemented as the initial constraints in molecular dynamics simulations. Restrained molecular dynamics (rMD) simulations allow conformational space to be searched for structures that simultaneously satisfy the NOE-derived restraints and correspond to a reasonable potential energy. However, an optimal set of parameters that appropriately balances the influences of potential energy and experimental restraints’ violations, has not yet been established. A major drawback of almost all (Torda et al., 1999) the refinement strategies currently employed is the bias inherent in interpreting n.m.r.-based constraints in terms of only one rigid conformer, which may be contradictory to the dynamic nature of DNA molecules (Pearlman & Kollman, 1991). Comparison of 2D NOE intensities calculated for the resultant rMD structures with the original experimental intensities seems to be a prudent final step. A refinement procedure of the converged rMD structures (Baleja et cd., 19906) with this as a basis
has been proposed recently. A promising technique, yet computationally demanding, incorporates comparison of calculated and experimental NOE intensities into the rMD trajectory calculations (Yip & Case, 1989). The present study continues our investigation of the structural qualities of alternating purine-pyrimidine sequences and A + T-rich sequences in particular. The TATA-motif is frequently found in promoter regions of genes’and has been the subject of several structural studies in solution (Assa-Munt & Kearns, 1984; Sklenar et al., 1989; Suzuki et al., 1986) as well as in the solid state (Yoon et al., 1988; Drew & Dickerson, 1982; Arnott et al., 1983). Our early studies on [d(AT),], (Suzuki et al., 1986) and [d(GGTATATACC)], (Zhou et al., 1987) comparing 2D NOE cross-peak intensities of experimental and theoretical spectra calculated using the program CORMA (Borgias et al., 1987, 1989) suggested that a wrinkled D structure best accounted for the spectral data of the TATA segments compared with other canonical DNA structures. Remarkable features of this type of structure include a narrower minor groove, alternating torsion angle values at A-T and T-A steps and a pronounced propeller twist. Recent investigations have demonstrated that an improved method of distance constraint generation, using the MARDIGRAS algorithm (Borgias & James, 1989, 1999), in conjunction with rMD calculations leads to a more sophisticated structural analysis (Gochin & James, 1999; Kerwood et al., 1991). constraints for Here, a set of distance [d(GTATATAC)], is generated with MARDIGRAS and employed in subsequent rMD simulations. Comparison with the results of an independent sugar pucker analysis on this oligomer (Schmitz et al., 1999) allows a further assessment of the performance of MARDIGRAS and our protocol for carrying out rMD simulations. To examine the role of the starting structures in the conformational search, three different models are chosen; two of them are relatively similar to each other. Differences among the three converged structures must be related to their initial models. Even if sufficient convergence from different starting structures has been achieved, the final conformation might be dependent on the constraint set employed. To elucidate this methodological limitation, hardly acknowledged in the literature, the rMD simulations were carried out with two slightly different constraint sets. Both of the resulting structures are analyzed and discussed to determine further the uniqueness of MD structures deduced with NOE constraints. Furthermore, our previous sugar pucker analysis provided evidence for conformational averaging for all residues, which was most pronounced for the terminal guanine residues (Schmitz et cd., 1996). Since rMD simulations generally must interpret constraints in terms of one conformer only, it will be interesting to identify any averaging effects in the resulting rMD structures.
n.m.r. Structure of (d(GTATATAC)]
2.
Materials and Methods (a) Sample preparation
purification of the octamer Synthesis and [d(GTATATAC)], has been described (Schmitz et al., 1990). The sample used for the 2D NOE experiments was dissolved in 99996% ‘H,O to give a final concentration of 17 mM in duplex, buffered with boric acid at pH 8 (50 m&f-borate, 100 mM-E&l, 0.2 mM-EGTA). (b) n.m.r. experiments Acquisition and processing of the n.m.r. spectra have been described (Schmitz et al., 1990). Here, pure absorption 2D NOE spectra were obtained using a pulse sequence (Jeener et al., 1979) with alternate block accumulation and phase cycling (States et al., 1982) for 4 mixing times: 50, 100, 250 and 400 ms. All spectra were acquired with 16 scans at each of 400 t,-values and a repetition rate of 10 s. Apodization with strong Gaussian-Lorentzian filters and zero-filling in both dimensions was used to obtain 4000 x 1000 datasets with a digital resolution of 69 Hz/point in oz and 39 Hz/point in the wi-dimension. Baseline correction was applied in both dimensions after the final Fourier transform. 2D NOE cross-peak integration was carried out with a modified version of the program CONTOUR (part of the local University of California, San Francisco, n.m.r. processing software package), allowing semi-automatic deconvolution of peaks in overlapped regions by simulating peak-envelopes in Z- and y-dimensions taking into account the involved protons’ linewidths as specified by the user. Quantification of the cross-peak intensities was achieved by summing the signal inside a contour level that was chosen as close to the noise level as possible. Typically, about 50 data points defined a single peak. A discussion of this technique, beyond the scope of this study, has been published elsewhere (Gochin et al., 1990). (c) Distance constraint generation from 20 NOE intensities Interproton distances were generated using the program MARDIGRAS (Borgias & James, 1989, 1990). For all 4 mixing time intensity sets, a complete 2D NOE relaxation matrix was set up using the geometry of a starting structure to account for all those interproton NOES not available from an experimental dataset. Starting models were standard A-DNA (Arnott & Hukins, 1972) standard B-DNA (Arnott t Hukins, 1973) and wrinkled D-DNA (Arnott et al., 1983). Assuming isotropic motion, a single correlation time was used for the whole molecule (r, = 5 ns), derived from the relation between spin-lattice relaxation time (Ti) and spin-spin relaxation time (T’) (Gochin et aZ., 1990). The complete NOE matrix is calculated for a particular starting structure using CORMA (Borgias et al., 1987, 1989; Borgias & James, 1988). The resulting intensities were used to construct a hybrid intensity matrix, combining with the experimental intensities. MARDIGRAS replaces elements of the relaxation matrix iteratively until either no changes result from each iteration cycle or the recalculated intensities meet the convergence criterion:
where a, and a, are the observed and the calculated intensities, respectively, and 0903 is designed to reflect
273
z
the noise level conservatively. MARDIGRAS calculates upper and lower bounds on distances corresponding to experimentally measured cross-peaks, depending on agreement between the experimental and the converged MARDIGRAS cross-peak intensity as well as signal-tonoise (Borgias & James, 1990). (d) Model building The co-ordinates for the canonical DNA structures (A- and B-DNA) were generated with the NUCGEN module of the AMBER program package (Weiner & Kollman, 1981; P. K. Weiner et al., 1984). The wrinkled D-DNA mode1 was generated from the co-ordinates of Arnott et al. (1983) swapping nucleotides with the aid of the graphics program MIDASPLUS (Huang et al., 1985, 1989) on an Iris workstation. The BDB mode1 of [d(GTATATAC)], was created by docking terminal G 1C base-pairs with B-DNA co-ordinates to a [d(TATATA)J, hexamer duplex possessing wrinkled D-DNA co-ordinates, using MIDASPLUS, and subsequent energy minimization of the ultimate and penultimate base-pairs using AMBER. Hydrogen atoms were added according to standard bond lengths and bond angles with the EDIT module of AMBER. In order to mimic solvent and counlarge sodium ions (hexahydrated terion effects, radius = 5 A; 1 A = 61 nm) were added according to the “implicit” solvent model (Rao et al., 1986; Singh et al., 1985). Prior to minimizations or dynamics, the sodium ions were placed along the PO; bisector, 624 A apart from the phosphorus atom. They were subsequently free were displayed with All structures :ID:%JS. (e) Restrained molecular dynamics The restrained molecular dynamics calculations were performed using a specially modified version of AMBER Version 3.OA (Singh et al., 1986, 1989; Pearlman, 1990) on a Cray Y-MP computer at the Pittsburgh Supercomputing Center. The force-fields used here have been reported previously (S. J. Weiner et al., 1984). Our modified version of AMBER includes 2 new features, which are important for the work presented here. First, the pseudo-energy term for the NOE-derived distance constraints has the form of a flat well with parabolic sides within a defined distance from the flat part and continues linearly beyond these margins: E c0nstr=
kl(r--%)* 0 k2P-rd2
1 4k2(r-rs)
when r2 > r whenr,>r>r, when r3 > r when r > r,; r4--rj = 2 A,
where r2 and r3 define the lower and the upper bounds of the flat part of the potential, corresponding to the distance bounds derived from MARDIGRAS (tide apra), and k, and k, are the force constants that can be selected for each constraint individually. (Note, that having 2 force constants enables different treatment of the 2 parabolic sides.) Since the width of the flat part arises from the accuracy of the MARDIGRAS results for each individual cross-peak with a11its inherent uncertainties, larger force constants were designated for the better defined distances. Four categories of flat well widths (090 to 925 A, 925 to 050 A, 050 to 190 A. and greater than 190 A) were respectively assigned force constants lOO%, 70%, 40% and 25% of the maximum during each stage of the rMD protocol (wide in&). The 4 categories comprised 190, 21, 10 and 2 restraints, respectively. Additionally, 36 constraints were included to guarantee
274
17. Schmitt
maintenance of Watson-Crick hydrogen bonds throughout the calculations. For the G. C base-pairs, lower and upper margins were set to 281 to 301 A (G-O, to C-X$), 2.85 to 3.05 A (G-N, to C-N,) and 276 to 2.96 A (G-N, to C-O,); for A.T base-pairs, values were 2.72 to 292 A (A-N, to T-N,) and 285 to 3.05 A (A-N, to T-O,) according to the literature (Saenger, 1984). The range for the upper parabolic part of the hydrogen bond constraints was 62 A, and the force constants were 10 kcal/mol-A2 (1 cal = 4 184 J). The range for the hydrogen bond angles was set to 170” to 190” with force constants of 5 kcal/mol-A’. The 2nd new pertinent feature of our version of AMBER enables gradual changes in the relative weights of force constants and temperature within a specific run of restrained molecular dynamics. In the past, it has been necessary to perform the calculations in separate pieces, each with fixed values for k and temperature (see also Fig. 5(a)). All rMD runs consisted of 30,000 steps in 0001 pa increments. All atoms within a 30 A radius were included in non-bonded interactions. SHAKE (Ryckaert et al., 1977) was used to constrain all bonds, and translational and rotational motions were removed every 100 steps. Starting points were steepest descent energy-minimized co-ordinates of A-DNA, B-DNA and the BDB-DNA model obtained from the all-atom version of AMBER. Initial velocities were taken from a Maxwellian distribution at 62 K. The system was then heated gradually from 100 K to 600 K during the 1st 3000 steps and maintained at this temperature for 12,000 steps, to avoid becoming trapped in a local energy minimum. From step 15,000 to step 18,000, the temperature was decreased to the final value of 300 K for the remainder of the rMD calculation. Temperatures were maintained through coupling with a thermal bath with a time constant of 94 pa. The weights of the NOE constraints were modulated by multiplying the force constants with a scaling factor. During the heating period, constraints were virtually turned off. From step 2021 to 6041, the force constants k, and k, for the best-defined constraints’ category were increased gradually from 65 kcal/mol-A* to 50 kcal/mol-A2 or 100 kcal/mol-A2 and kept constant to step 18,000, the end of the cooling period. During the subsequent 2000 steps the force constants were reduced to a maximum of 10 kcal/mol-A2 or 20 kcal/mol-A2 as a final value for the remaining 10,000 steps. For each run of 30 pa of rMD, coordinate sets were recorded each 0.2 ps. The last 50 coordinate sets, arising from the last 10 pa, were averaged and subjected to a final restrained energy minimization. (f ) Molecular mechanics All co-ordinates that arose from averaging over a rMD time period or from averaging individual structures from different rMD runs were subjected to restrained energy minimization using the modified version of AMBER 3.OA allowing the application of the flat well potential described above. In all cases the highest force constants for the NOE constraints were set to 10 kcal/mol-A’. During energy minimization, hydrogen bonds did not need to be restrained. (g) Structural parameters Sugar pucker and torsion angles were analyzed with the ANAL module of AMBER 3.OA. Calculation of all helical parameters was carried out with the program CURVES (Lavery & Sklenar, 1990), which is especially well suited
et al. for the characterization of irregular DNA features (Lavery & Sklenar, 1988, 1989).
structural
3. Results and Discussion (a) Proton assignments
and peak integration
The peak assignment procedure has been described previously; for chemical shifts, please refer to Table 1 of Schmitz et al. (1990). The numbering scheme used is: 14345678
5’-GlTZA3T4AST6A7C8-3’ 3’-CSAIIT6AST4A3TZG1-5 16 15 14 13 12 11 10 9
Since no part of the 21) NOE data obtained from 2H20 solution has been shown before, Figure 1 gives representative portions of the 250 milliseconds 2D NOE spectrum. The degree of peak overlap appears to be quite different for the individual protons. Most cross-peaks involving protons H6 and Hl’ of residue T4 and T6, and Hl’ of residue A5 and A7 could be analyzed only using a previously described deconvolution procedure (Gochin et al.. 1990), imposing an additional error onto the intensities’ accuracy by up to 10% compared to isolated peaks. The amount of peaks taken from overlapped regions varied from 23% to 30%, depending upon the dataset. We employ a high, time-consuming repetition rate of ten seconds to allow for sufficient relaxation of all protons, thus enabling extraction of accurate peak intensities. This is especially important, since we wanted to include all quantifiable cross-strand cross-peaks, which arise from the adenine H2 protons, exhibiting the longest spinlattice relaxation time of 3.5 to 3.6 seconds (Schmitz et al., 1990). In the course of the present study, it became apparent that cross-strand constraints play an important role in establishing the structure of an In the past, additional oligonucleotide (vide in&a). quantified cross-strand peak information has been extracted from imino 21) NOE data obtained from H,O solution (Clore et aE., 1988; Baleja et al, 1990a). However, these intensities are prone to large errors, since it is difficult to account for water exchange and non-linear excitation profiles. For the present study. we refrained from using any quantitative information for exchangeable protons. (b) Generation of distance constraints (MARDIGRAS calculation) Recent studies have demonstrated how NOE-based distances, calculated with the algorithm MARDIGRAS, can be used for structure determination of oligonucleotides (Gochin & James, 1990; Kerwood et al., 1991) and proteins (Thomas et al.. 1991). The latter investigation made use of a theoretical NOE intensity set corresponding to a crystal structure and showed that MARDIGRAS is strikingly robust in generating a largely correct unbiased distance set independent of the starting model. However, results improved with better initial
n.m.r. Structure of [d(GTATATAC)],
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Figure time:
1. Representative 250 ma).
portions
of the 2D NOE
spectrum
obtained
4.76
49
4G5
for [d(GTATATAC)],
f
4.00
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U. Schmitz et al.
276
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4.0
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(d)
(c)
Figure 2. Comparison between interproton distances: (a) for canonical A- and B-DPU’Astructures and (c) for B-DPr’A and BDB-DNA; and (b) for corresponding MARDIGRAS-derived distances using A-DNA or B-DKA for the 400 ms dataset; and (d) MARDIGRAS-distances derived from BDB-DNA and B-DNA for the 100 ms dataset.
models. Although the program is designed to take spin-diffusion into account, distance sets derived from shorter mixing times (e.g. 100 ms rather than 409 ms) are in better agreement with the original structure, indicating that MARDIGRAS cannot make up for loss of information at higher mixing times due to severe spin-diffusion (Borgias et al., 1999; Thomas et al., 1991). Furthermore, the accuracy of the distances obtained is improved with fraction of experimental cross-peaks included and by enhanced signal-to-noise ratio. For the present study, all four 2D NOE intensity sets were subjected to MARDIGRAS refinement, employing three different canonical DNA structures as initial models (A-DNA, B-DNA and BDB-DNA). In all 12 MARDIGRAS runs, convergence occurred after four to seven cycles to produce similar distance sets. In general, B-DNA and BDB-DNA as initial models led to more similar distance sets for a given intensity set, when compared with the distance set
for A-DNA
as starting model. A closer convergence of the resulting distances occurs also for the two longer mixing time 2D NOE intensity sets, presumably due to the larger number of cross-peaks. Comparison of distances obtained for the same starting structure and different intensity sets revealed some significant differences between shorter and longer mixing time data sets. The fact that distances associated with HS protons of the adenine- and guanine residues showed less agreement than those associated with other base protons suggested a non-negligible H/D exchange of the purine H8 protons. Since the 2D NOE spectra for the two lower mixing times were obtained immediately after preparing the sample and the other ones ten weeks later without removing the solvent for storage, the distances derived from the “fresh sample” should be more reliable. A comparison of interproton distances for different initial models and MARDIGRAS-derived distance sets (Fig. 2) gives
n.m.r. Structure of [d(GTATATAC)]
277
2
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2
3
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4
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6
7
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Residue
number
Figure 3. Deoxyribose Hl’H4’ distances obtained from MARDIGRAS
(A-DNA as starting structure, open symbols; BDB-DNA as starting structure, filled symbols); 50 ms dataset (A, A), 100 ms (0, ?? ), and 250 ms (0, ?? ) and from 2&F-COSY cross-peak simulation (represented as error bars).
an impression of the degree of agreement achieved. Clearly, however, the distances derived via MARDIGRAS are generally in agreement regardless of starting structure employed or intensity set analyzed. Another problem arose from distances associated with methyl protons. Some methyl deoxyribose distances were slightly inconsistent with the related H6/H8 distances to the same sugar protons. Until recently, MARDIGRAS treated unresolved equivalent spins as pseudoatoms, assuming the same motional model for all protons. However, methyl rotation is considerably faster than the overall tumbling rate, expressed by a correlation time of five nanoseconds. But even reducing the effective isotropic correlation time for all of the methyl pseudoatoms to one nanosecond did not alleviate the discordance completely. Since distances associated with methyl groups do not define additional parts of the molecule compared to distances associated with the pertinent base protons, only the latter were used as constraints for rMD calculations, as they are calculated correctly by MARDIGRAS (our unpublished data). MARDIGRAS’ capability of handling internal motions has been improved recently. Some short distances, inconsistent with any of the common helical DNA structures were obtained for three cross-strand interproton interactions at the terminal base-pair. This is probably due to fraying and has been observed for other oligonucleotides in our laboratory as well. The rMD procedure employed treats the molecule as fully base-paired and is not geared to simulate fraying effects approthese short cross-strand priately. Ultimately, distances, afflicting the terminal residues were not used in the final constraint set.
Some calculated distances relate directly to sugar pucker, especially the Hl’H4’-distance. An independent determination of sugar pucker (Schmitz et al., 1990) using simulation of 2&F-COSY cross-peaks thus allows comparison with the appropriate MARDIGRAS distances. Figure 3 shows the deoxyribose Hl’H4’ distances derived from MARDIGRAS for three different datasets (50, 166, 250 ms) and two initial models (A-DNA, BDB-DNA) in comparison with Hl’H4’ distances derived for the major conformer from the ZQF-COSY simulation results. A-DNA as an initial model yielded slightly larger distances, but nevertheless, all data fit surprisingly well except for residue C8, whose sugar pucker was assigned only tentatively in the 2&F-COSY simulation study. For residues T4 and T6, the pertinent 2D NOE cross-peaks were not available due to severe overlap. Instead, for these residues, we used the Hl’H4’ distances from the 2&F-COSY analysis with conservative bounds. Usually, alternating A-T-sequences exhibit medium-sized cross-peaks between the adenine H2 protons on opposite strands in the core of the helix. Two cross-peaks, A3-H2 A7-H2 and A3-H2 A5-H2, account for four distances, since we are dealing with a self-complementary structure. For the same reason, the cross-peak between the two isochronous A5-H2 protons of the different strands is not observable. Since missing constraints can produce structural artefacts (Gochin & James, 1990), we used other n.m.r. data to restrain the A5-H2 proton distance. MARDIGRAS yielded a shorter distance (2.79 to 2.93 A) for A3-H2 A7-H2 and a longer one (3.44 to 3.63 A) for A3-H2 A5-H2. Following the scheme of an alternating structure, previously suggested by 31P n.m.r. results (Schmitz et al.,
U. Schmitz et al.
278
Table 1 Number of constraints for denoted residues Cross-strand constraints Residue Cl T2 A3 T4 A5 T6 A7 CS
Intraresidue 15 11 14 9 9 8 I1 4
Interresidue (i to if 1) 5 4 5 3 6 4 6
NOES
Hydrogen bonds 6 4 4 4 4 4 4 6
2 B 1
1990), the cross-strand A&H2 A&H2 distance is expected to be short as well. Consequently, we carried out rMD calculations with and without restraining the A&H2 proton distance to 2.79 to 2.93 A in order to understand the impact of this slightly modified constraint set on the resulting rMD structures. Finally, the shortest and the longest of the four MARDIGRAS distances for each proton-proton interaction, calculated for BDB-DNA and B-DNA as starting structures and the two shorter mixing time 2D NOE intensity sets, were assembled into an upper and lower bound constraint set comprising a total of 233 entries with a r.m.s. value of 024 8. Table 1 lists the distribution of constraints over the molecule. (c) The restrained molecular dynamics
strategy
To gauge some of the boundaries of the constraint set, a series of restrained energy izations (rMIN) was carried out using relative weights for the restraint term, and
present minimvarious starting
Force constants
with either one of the presumably converged rMI> structures, or with the corresponding starting model, minimized B-DNA. These restraints all lead basically to the same result (Fig. 4). Increasing distance restraint force constants should improve the fit with the experimental data, decreasing the average constraint deviation. From Figure 4, which shows the energy minimization results for the rMD struct’ure, it becomes evident that an improvement in the average constraint deviation is indeed achieved with force fields up to approximately 40 to 50 kcal/mol-A’. Any further increase in force constants is of little avail; the average constraint deviation asymptotically approaches a value of -0.12 A, which is half of the r.m.s. difference between upper and lower bounds of the constraint set. The flattening of the constraint, energy curve at higher force fields also indicates that the maximum agreement with the experimental data is reached Unfortunately, an improved with 40 kcal/mol-AZ. fit to experimental data is associated with a deterioration in total energy. However, a point of inflection for the &,-curve indicates, that the system has to pay less of a penalty for total energy, but thus reduction of the average constraint deviation is steepest> at force fields below approximately 20 to 30 kcal/mol-AZ; restriction to such small force constants would not allow an average constraint deviation of less than 0.2 A. These model calculations do suggest that we can expect total energies of less than -600 kcal and average constraint deviations of better than 0.25 A for structures successfully converged from different starting models. WC note that it was impossible to achieve even a rough fit of A-DNA as a starting model to the distance constraints by means of restrained energy minimization alone. Relatively mild conditions, 30 picoseconds at
(kcal/mol-8’)
Figure 4. Average constraint deviation (.- + -.), total energy ( - ??-), and constraint violation energy ( - 0 - ) for restrained energy minimizations of previously energy-minimized B-DNA using various force constants for the NOE constraint term.
1z.m.r. Structure of [d(GTATATAC)]
- 600
(a)
4’
0
I....~....~....I....~....~....l 5 IO
15
rMD simulation
20
25
30
time (ps)
(b)
Figure 5. (a) Temperature (---) and maximum NOE
constraints force constants (---) used during the final restrained molecular dynamics procedure. (b) Evolution of the average constraint deviation during 30 ps of restrained molecular dynamics for 3 different starting structures. The protocol for the rMD simulations are shown in (a) with the exception that for the A-DNA calculation, a final value of 20 kcal/mol-A2 was employed.
300 K and force fields of 10 kcal/mol-A2, force B-DNA and BDB-DNA as starting structures into roughly the same conformation exhibiting an average constraint violation of 926 A compared to initial values of 640 A and 0.36 A. For the final ten picoseconds, no drifting in total energy or average constraints deviation was observed, indicating that the conformation is fluctuating in an energy minimum well. In fact, much more drastic conditions have to be employed to propel A-DNA as a starting model (initial average constraint deviation of 1.01 A) into the same structural realm. The system had to be heated up to 600 K, and force fields of up to 100 kcal/mol-A2 had to be.applied for an intermediate period of 12 picoseconds in order to facilitate the conformational changes. Subsequent cooling to 300 K and lowering the constraints’ maximum force constants to 10 kcal/mol-A2 yielded a structure not showing any drifts in total energy and average constraint deviation with the desired values. For all starting models, force constants of 20 kcal/mol-A2, instead of 10 kcal/mol-A2, for the last ten picoseconds enhance the tit with the experimental data from 0.26( +@l) A to @22( +@l) A as illustrated in Figure 5(b). However, this improvement did not produce significant changes in total
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energy and average constraint violation after restrained minimization of the resulting rMD structures, indicating that the applied force fields keep the conformation essentially in the same potential well. This protocol, necessary to enable successful convergence for A-DNA as a starting model, was consequently applied to B-DNA and BDB-DNA as well. It was possible to deduce the appropriate parameters for our rMD calculations largely without comparing atomic r.m.s. differences of the resulting structures as is done most commonly. r.m.s. differences between resulting rMD structures of less than 1 A are usually considered to be indicative of successful convergence (Kerwood et al., 1991). This threshold, however, seems to depend to a great extent upon the individual system, and it was interesting to see how well our rMD protocol would provide convergence in terms of r.m.s. differences. An insufficient number of constraints can drive the molecule from different starting structures into different local energy minima, indicated by an increased r.m.s. difference when using higher constraint force constants (Gochin & James, 1990). Another problem arises from inconsistencies within a constraint set, as these NOE-based distances genuinely reflect time-average structures and yet are expected to be accommodated by a single rMD structure. Thus, some constraints might not be easily compatible with a physically reasonable structure. For the more problematic cases, it is necessary to ascertain the corresponding randomness of a system before the r.m.s. criterion can be used to assess the convergence of different rMD runs. Therefore, we used different random number seeds to produce different sets of starting velocities, and ran three simulations using 10 kcal/mol-A2 restraints and two using 20 kcal/mol-A2 restraints for all three different starting models. The larger force constants did not produce more similar structures within a set derived from one starting structure. In such a structure family, the smallest r.m.s. differences occurred between structures that had been generated from trajectories using the same initial velocities, but differing restraint weights. The average r.m.s. difference among the resulting five members of the family with A-DNA as starting structure was higher (1*07( kO.25) A) than the value for the B-DNA family (095( +@22) A), and smallest for the set of BDB-DNA structures (079( kO.16) A). These results imply that one cannot expect r.m.s. differences between structures converged from different initial structures to be smaller than N 1.1 A. The combination of three structures, each taken from one of the three starting structure families, giving the lowest average r.m.s. deviation yields a value of 1.09 A. The average r.m.s. difference among all 15 converged structures was 1.22( +630) A. This value agrees well with the results of a “distance geometry” study (Pardi et al., theoretical 1988) in which a representative constraint set (precision: +0605 A) was employed to generate a family of ten distance geometry struc-
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tures exhibiting an average r.m.s. deviation of 1.29( &007) L%compared to the target structure. To extract a structure that reflects the conformational commonalities of the 15 resulting conformations, the “final structure”, all co-ordinate sets were superimposed with a least-squares fit, averaged and subsequently subjected to restrained energy minimization (rMD-finall). To locate structural deviations arising from different starting models, the five coordinate sets belonging to each starting structure family were similarly treated to give rMD-A, rMD-B and rMD-BDB. This averaging procedure guarantees that only structural features associated with low energy structures are extracted, as opposed to averaging the structural parameters themselves. This turned out, to be more important for torsion angles than for helix parameters, since the latter seem to be less “quantized”. In the case of averaging two physically reasonable torsion angle values, -gauche and +gauche for example, numerical averaging would produce the energetically unfavornot at all describing a able syn conformation, feature of the molecule. Energy minimization of the averaged co-ordinates enforces an energetically reasonable conformation, generally one of two (or sometimes 3) energetically feasible conformations. Consequently, torsion angles were analyzed for each strand separately, although we are dealing with a self-complementary sequence; the MD trajectory of corresponding residues on the two strands is independent and may lead to different conformations for the two residues in spite of identical constraint terms. Another series of six rMD runs (starting models: A-, B- and BDB-DNA; force fields: 10 kcal/mol-A2 and 20 kcal/mol-82 for the final 10 ps) emanated from a modified constraint set. where just one crossstrand distance (A&H2 A&HZ) has been omitted. The heterogeneity of the set of resulting structures is surprisingly increased, indicated by an average r.m.s. difference of 1*46(+0*35) 8. Furthermore, large r.m.s. differences in comparison with the set of 15 (up to 2.4 A) suggested that we had found another suitable energy minimum with omission of a single critical constraint. The above averaging procedure was applied to this set as well to yield the co-ordinate set for rMD-final2. (d) Characterization
of the converged structures
Before assessing conformational details of all the averaged structures, a more global comparison in terms of r.m.s. deviations, energies and especially matching the original experimental data helped to assess the quality of the experimental structures. Table 2 lists the energy terms and the average constraint deviations for the energy-minimized starting models and the resulting averaged rMD structures. For comparison, structure rMIN-B has been added; rMIN-B results from the introductory model calculations (restrained energy minimization of energy-minimized B-DNA with full constraint set, using maximum NOE force constants of
n.m.r. Structure of [d(CTATATAC)]
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Table 3 Atomic r.m.s. differences (A)
between starting models and structures obtained by restrained molecular dynamics and restrained energy minimization
Structures A-DNA B-DNA BDB-DNA
B-DNA
BDB-DNA
rMD-A
rMD-S
459 ****
672 284 ****
360 210 418
304 2.58 473
****
1.36 ****
rMD-A rMD-U rMD-13DU
rMD-SDI)
rMD-final1
rMD-final2
rMIN-13
3.80 1.76 382
354 1.97 407
261 2.83 500
4.55 0.97 2%7
1.06 1.32 ****
@98 1.01 055
1.84 1.36 1.81
1.81 2.26 1.34
****
1.55 ****
1.59 2.59
rMD-final1 rMD-final2
10 kcal/mol-A2 maximum). All energy terms of the listed calculated structures are strikingly similar. The NOE constraint deviations and constraint energies are considerably improved compared to the starting models, without significant deterioration of total energies. Moreover, all experimental structures have smaller total energies than A-DNA. It is noteworthy that our averaging strategy in general produces total energies and NOE constraint energies that are improved compared to the numerical values for the associated individual structures. rMD-final1 has a lower constraint energy than all other averaged structures. The total energies of all rMD structures listed in Table 2 are close to the best values of any of the individual structures before averaging. However, energy terms do not allow more than crude discrimination between structures. The relationship between structures becomes more evident from the atomic r.m.s. deviations in Table 3. rMD-A and rMD-BDB exhibit the smallest r.m.s.
deviation
(1.06 A) among
the
features remain the same for the two structures being compared. The acid test for all calculated structures obtained by any method should entail the experi-
five-structure
averages, although they arose from the two starting models with the largest r.m.s. deviation (672 A), A-DNA and BDB-DNA. It is interesting to note that rMD-finall, the average of all 15 structures, strongly resembles rMD-BDB, which was obtained from the starting structure with wrinkled D co-ordinates. Analysis of r.m.s. deviations becomes more powerful with information broken down into individual values for each residue. Figure 6 depicts the r.m.s. difference-per-residue analysis for a few selected examples. Typically, r.m.s. deviations for rMD structures are distributed fairly equally over the whole molecule with a tendency to be higher toward the termini, as shown for the comparison among rMD-A, rMD-B and rMD-BDB. Comparison between rMD-final1 and rMD-final2 indicates less smooth deviations. A pronounced r.m.s. difference for residue T4, base-paired with A5, reveals a significant change with removal of the A5-H2 A5-H2 constraint. The difference between rMDfinal1 and rMIN-B is most pronounced for residues closest to the termini, whereas the deviations for the inner residues are in the range similar to those of the five-structure averages. Of course, r.m.s. deviations will increase with distance from the site of any global structural change even if all local structural
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(a) with rMD-final1 (0) ver.susrMD-final2, and rMDfinal1 versusrMIN-B (0).
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mental data. Here, this evaluation was carried out on two levels: (1) with the original NOE cross-peak intensities, and (2) with the distance restraints. For the latter, the constraint energies were extracted for each residue, averaged for the two strands, and further divided into intra- and interresidue contributions, assuming that interresidue constraints contribute more to the overall appearance of a DNA-conformation than the intraresidue ones, which generally establish sugar puckering and the deoxyribose-base geometry. The intraresidue NOE constraint energies did not show any substantial differences among the calculated structures. The interresidue constraint energies, however, allow discrimination between the two rMD structures and rMIN-B, the latter exhibiting significantly larger violations for all residues. Comparing the sums of these individual values reveals that the entire difference in the NOE constraint energy term (Table 2) between rMD-final1 and rMIN-B (11.9 kcal/mol) arises from interresidue effects. On the other hand, the intraresidue constraints contribute 60 to 70% of the constraints’ energy, and thus constitute the major driving force in our calculations. It could be concluded that restrained energy minimization alone may not be capable of adequately manipulating a starting model, even if it is assumed to be in the same family as the structure corresponding to the distance restraint set. Hence, rMIN-B cannot be valid for considered a “final structure” [d(GTATATAC)], and will not be subjected to the structural scrutiny in the next section. We have found it useful for some time now to evaluate DNA structures by comparing their theoretical 2D NOE intensities with the experimental data (Broido et al., 1985; Suzuki et al., 1986); this approach has gained broad acceptance (Boelens et al., 1989; Baleja et al., 199Ob; Nerdal et al., 1988).
Different figures of merit have been used to express the overall fit of data, such as an average difference index (Suzuki et al., 1986; Zhou et al., 1987) and most commonly a residual index similar to the crystallographic R-value (Gupta et al., 1989; Baleja et al., 1999a; Gochin & James, 1999). Since 2D NOE intensities are spread over several orders of magnitude, the “crystallographic R-value” is heavily dominated by strong cross-peaks associated with short distances ( ~2.5 A), changing its meaning considerably compared to its application in X-ray diffraction analysis. However, utilizing the sixthroot relationship between NOE intensities and pertaining distances enables appropriate weighting of the weaker cross-peaks. The sixth-root residual index: 1 l@,)!‘6 - (%P61
is capable of ranking structures most closely to atomic r.m.s. deviation compared with other figures of merit (Thomas et al., 1991). Figure 7 shows residual indices R;, calculated with the program CORMA, for all three starting models, the final rMD structures, and rMIN-B. The two shorter mixing time data sets generally provide the smallest residual indices, especially the 100 millisecond data. Spin-diffusion seems to affect the larger mixing time data sets considerably as R’;-values for all structures become gradually indistinguishable. The starting models satisfy the experimental data to a very- different degree, with BDB-DNA exhibiting the smallest value. All three rMD structures fit the experimental data equally well, so overall residual indices unfortunately cannot be used to favor one of them. Analysis of
n.m.r. Structure of [d(GTATATAC)]
12345676 Residuq
Figure 8. Intra- and interresidue Gth-root residual indices
rMD-final1 (-O-),
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R;-values evaluated residue by residue, however, revealed interesting details as shown for the 100 millisecond data set in Figure 8. For residue C8, only a few intraresidue constraints were extractable due to the isochronicity of protons H2’ and H2”. Nevertheless, CORMA is capable of calculating R-factors for intensities corresponding to a CS-methylene-pseudoatom; accordingly an extremely high R;-value is not surprising. The only significant differences among the interresidue R:-values pertain to the connectivity between T4 and A5, i.e. those residues involved in the particular cross-strand constraint employed only for rMDfinall, which manifests a better match with the experimental data than rMD-final2 and rMIN-B. The overall RT-values in Figure 7 indicate a better fit for intraresidue cross-peaks; Figure 8 reveals that the first three residues might be the reason for the worse fit of the interresidue data. These particularly high R;-values presumably stem from the inappropriate representation of the fraying ends in our rMD simulations. While the constraints reflect the timeaveraged conformational mixture, which may include base-paired helix and opened ends for limited time spans, the imposed hydrogen bond constraints impose continuous “ties” for the terminal base-pairs that are necessary for the successful performance of the calculation but might introduce artefacts for the terminal residues. Due to limited conformational possibilities within a residue, this is more likely to influence interresidue Rt-values. Clearly, the interresidue restraint set is more sensitive than the intraresidue set to conformational fit. This suggests that increased weighting of the interresidue distance constraints during refinement could be an improvement. In addition to permitting a calculation of RT, CORMA calculation of 2D NOE intensities for a structure enables a search for intensities predicted but not found experimentally. We found no instance of significant intensity predicted but not observed for any of the resulting rMD structures.
number
R; for individual residues of the resulting structures:
(e) Conform4ztional features of the final structure Before describing the structural details of our rMD structures, it is important to recall that DNA structure is not completely defined by NOE-derived distance information. A distance geometry study (Pardi et al., 1988) revealed that the backbone, especially the phosphodiester moiety, is less defined than the bases. Sugar pucker and some helix parameters such as tilt and twist, appeared to be best defined; the glycosidic angle and he!ix rise and roll were defined to a lesser degree, but propeller twist and dislocation were found to be ill determined. A more sophisticated theoretical study (Lane, 1990) assessing the impact of independently changed NOE intensities of specific groups of cross-peaks on structural parameters confirms most of these results. Furthermore, helix rise showed a strong dependence on interstrand imino cross-peaks, but helix roll did not seem to be defined at all. A recent distance geometry study showed that sequence-dependent fluctuations in the helical parameters cannot be reliably determined (Metzler et al, 1990). But we must bear in mind that structures obtained from restrained molecular dynamics do not depend solely upon the distance constraints but also on the energy criterion. The extent of the influence of either contribution is not easy to determine and has been the subject of much controversy. Nevertheless, the energy criterion chiefly maintains near- perfect stereochemistry and non-bonded interactions (Gronenborn & Clore, 1989). Our structural analysis focuses on (1) differences between the rMD structures derived from one starting structure and (2) differences between the two final structures with respect to the omission of one crucial constraint. Figure 9 depicts a superposition of rMD-A, rMD-B, rMD-BDB, and rMD-final1 structures and demonstrates the convergence of the rMD structures obtained with the full distance constraint set. The geometry of the inner six base-pairs is virtually
284
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Figure 9. Superposition of the rMD structures separated into a backbone view (left) and a base-pair view (right) for clarity: (red) rMD-A, (green) rMD-B, (cyan) rMD-BDB, and (black) rMD-finall.
identical. For the backbone, rMD-A and rMD-B exhibit slightly more pronounced deviations from rMD-finall, which is strikingly similar to rMDBDB. A detailed comparison of the individual values for torsion angles and sugar pucker is given in Figure 10. For most torsion angles, one of the three rMD structures possesses residues exhibiting a value different from the other two, indicating that there is more than one energetically feasible possibility. All of these outlying values have been observed for DNA but are less common (Saenger, 1984). The smallest range is found for the glycosidic angle x and 6, which is associated with sugar pucker. With our averaging strategy, rMD-final1 exhibits torsion angle values identical with those found for two of the three substructures and does not manifest geometrical averages. Less-common values occur only for rMD-A and rMD-B and do not reflect the initial geometry of the starting structure. Structural characteristics of rMD-A, rMD-B, rMDBDB, and rMD-final1 appear even closer upon evaluating the helix parameters in Figure 11, although the similarity of helix parameters for rMDBDB and rMD-final1 is less striking than for the torsion angles. The right panels of Figure 10 compare between rMD-final1 with rMD-final2 torsion angle values and elucidate their relationship to canonical A-, Band wrinkled D-DNA. In general, torsion angle values are rather similar for the final structures. Significant deviations occur mostly for torsion angles of A5 and T4 base-pairs, i.e. those associated with‘the critical A5-H2 A5-H2 constraint missing in
calculations leading to rMD-final2. Most torsion angle values (LX,/?, y, E) are between the typical values for B- and wrinkled D-DNA. For 6 and glycosidic angle x, where there is hardly a difference between the two B-family structures, the values tend toward the region for A-DNA, more pronounced for residues A7 and CS. c( and [, defining the P-O diester bond. are predominantly found in gauche regions ( -SC). A rare conformation for the phosphate group connecting residues T2 and A3 in the second strand, +sc for c1 and [, introduces the strongest deviation from ideal &-symmetry in the whole molecule. The values for c( are alternating and strongly resemble those of wrinkled D-DNA. The conformations of the C--O ester bonds are trans ( + ap), with few exceptions for E, where gauche values ( +sc and -SC) are found as well. For rMD-finall, B in residue A5 and E in T4. deviate from the other residues to exhibit values similar to wrinkled D-DNA. For y, almost all values indicate a gauche conformation (+sc) with the exception of terminal Gl and residue A3 of the second strand, which exhibits -SC and - ap conformations, respectively. A very narrow range is found for the glycosidic angle x, with values close to those of B- and wrinkled D-DNA. For rMD-finall, the inner six nucleotides of both strands exhibit essentially the same value (x z 110”) whereas rMD-final2 shows some fluctuations especially for residues A5 and T4. 6, directly related to the sugar pucker, appears to be the best-defined torsion angle with values in the gauche-tram range (+ac). Among all parameters defining the backbone,
n.m.r. Structure of [d(GTATATAC)]
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sugar pucker is best-defined and appears to be very symmetrical for the two strands, as expected for a self-complementary sequence. All values except for residue C8 are located in the S-range, close to the lower values of the alternating pucker of wrinkled D-DNA. At this point, a comparison with our previous study (Schmitz et al., 1990) is most appropriate. From simulation of 2&F-COSY cross-peaks, explicit determination of sugar pucker was achieved for residues Gl and T2, suggesting dynamic mixtures of the S/N-type with 60 : 40 and 80 : 20 ratios, respectively. A pseudorotation phase angle of 162” (C-2’-endo) for Gl and 144” for T2 resulted for the major conformer. Minor deviations between the ZQF-COSY cross-peaks of T2 and residues A3 through A7 suggested a very similar sugar pucker with a slightly increased contribution of the
assuming a three-state S-conformer. However, mixture with two S-conformers with pseudorotation phase angles of 162” and 126”, based on published MD results (Rao & Kollman, 1990), provided an equally good description of the deoxyribose conformation for non-terminal residues. Pseudorotation phase angles of residues Gl through T6 in our final rMD structures, especially rMD-finall, are strikingly similar to those of the major conformers of our simulation analysis. Since rMD searches for a single best conformation accommodating the distance restraints, dynamical averaging could give rise to artefacts. Our findings, however, do not indicate this to be a serious problem for the deoxyribose conformations and even suggest that the final rMD structures strongly reflect the major deoxyribose conformer of an equilibrium. The sugar pucker of
U. Schmitt et al.
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the 3’-terminal residues differs significantly from all other residues, which is unexpected at least for A7. Although differences in sugar conformation between the final structures do not seem to be substantial, except for A5, rMD-final2 agrees less with our previous sugar pucker analysis. With regard to the backbone, differences between rMD-final1 and rMD-final2 appear mostly as a structural perturbation pertaining to residues A5 and T4. However, there are general differences that become clearer upon examining the helix parameters. The helix analysis program CURVES (Lavery & Sklenar, 1990) calculates a global helix axis and
provides four groups of parameters: (1) axis-basepair, (2) intra-base-pair, (3) inter-base-pair, and (4) axis junction parameters (Lavery & Sklenar, 1989). Since the definition of group (1 ), (3) and (4) parameters (Diekman, 1989) is dependent upon a global helix axis, we included the canonical DNA structures in our analysis as well. (We note that group (3) parameters may differ from values calculated with other helix analysis programs due to differences in defining the global helix axis.) Figure 11 displays the helix parameters of group (1). (2), and (3) necessary for discriminating between final strurtures. Some results (Fig. I I(c)) are also shown for the substructures rMD-A, rMD-B and rMD-BDB.
287
n.m.r. Structure of [d(GTATATAC)],
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proving that good convergence was also achieved for helix parameters. The graphic module of CURVES, MACB, enables an easy visualization of the global helix axis. Figure 12 presents different perspectives of the two final structures with superposition of global helix axes. In the side view, rMDfinal1 and rMD-final2 are hardly distinguishable; yet, to the eye, the latter seems to be shorter and slightly curved. Examination of the helix axis, however, indicates that neither final structure has an overall curvature. A regular alternation occurs for the helix axis segments of rMD-finall, but rMDfinal2 exhibits a local disturbance in the vicinity of the inner two base-pairs. From the view down the helix axis, it becomes evident that rMD-final1 assumes a leaner helix than does the other structure, which seems to be wound less tightly around its helix axis. A more detailed examination of some of the axis-base-pair parameters in Figure 11(a) confirms these findings, revealing a larger X displacement and inclination for rMD-final2. Among the intra-base-pair parameters, shear and stretch
are minimal for both final structures, although both parameters suggest some similarity to wrinkled D-DNA, more pronounced for the stretch of rMDfinall. Large negative values for the propeller twist, found for both structures, are reminiscent of the wrinkled D model. The inner four base-pairs assume slightly different values for propeller twist and stagger than the two at the termini. Most of the intra-base-pair parameters, however, suggest that the two central base-pairs differ from the others, most obviously for opening and buckle. The absolute opening values are small, but nevertheless, the similarity to wrinkled D-DNA is strongest for these central base-pairs. Increasing buckle values toward the termini are found for both structures. rMDfinal1 shows no buckle for the central two basefor pairs, rMD-final2 assumes values typical wrinkled D-DNA. For the inter-base-pair parameters (Fig. 11(c)), regular structures are indicated by zero values for roll, slide, tilt and shift. Indeed, shift and tilt (not shown) are practically zero for all structures. Slide
U. Schmitz et al.
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Residue
number
number
Cc)
Figure 11. Selected helix parameters for the restrained molecular dynamics structures and the starting structures: (a) axis base-pair parameters, (b) intrabase-pair parameters, and (c) interbase-pair parameters: rMD-final1 ( - 0 - ). rMD-final2 (-0 -), A-DNA (=), B-DPU‘A(---), and BDB-DNA (----). The left panels in (c) compare the 5-struct’ure averages rMD-A ( -A - ), rMD-B ( - 0 - ), rMD-BDB ( - ?? - ) with the average of all 15 structures rMD-final1
t-0-j a pattern that, along with similar results for rise and twist, highlights the structural peculiarity of the central two base-pairs, e.g. the twist of the central base-step in rMD-final1 exceeds all other values by more than 10”. Slide and rise of rMD-finall, however, suggest that the inner four base-pairs assume wrinkled D features. rMD-final2 exhibits slightly alternating values for rise and roll, consistent with wrinkled D-DNA only for the latter one. The roll parameter, which is most strongly associated with the orientation of the global helix axis segments, indicates a deviation from a regular structure only for the T-A steps in rMD-final1 with an alternating direction and zero values for A-T steps. Another differentiation between our final structures arises from examination of the minor groove width, a parameter that is substantially reduced for wrinkled D-DNA. Indeed, for the inner region of rMD-finall, the minor groove is somewhat compressed, whereas rMD-final2 does not deviate from the typical picture for B-DNA. Differences between our two final structures are and roll show
most prominent in the region of the critical distance constraint, compelling us to examine the actual distances between the adenine H2 protons. Among these five distances, the only difference between rMD-final1 and rMD-final2 occurs for the A&H2 protons. Consequently, the proton environment for A5-H2 in rMD-final1 and rMD-final2 differs substantially with two close protons (30 A and 3.6 A) for the former but a close and a more remote one (3.6 A and 45 A) for the latter. A3-H2 and A7-H2 both exhibit a proton environment (3.3 A and 3.6 A) similar to that of A&H2 in rMD-finall. Since the relaxation behavior is dominated by dipole-dipole interactions, the differences in the proton environment should affect the relaxation parameters of the adenine H2 protons. In fact, spinlattice (!Pr) relaxation measurements, reported in our previous study (Schmitz et al., 19!90), do not give any evidence for different proton environments of A5-H2 relative to A3-H2 and A7-H2. This finding encourages us to consider rMD-final1 as the best of the two final structures, although most of its helix
rMD-final2
Figure 12. Stereo views of the final rMD structures rMD-final1 (left) and rMD-final2 (right) including their global helix axis: (top) view into minor groove (residue G1 at, bottom back); (bottom) view down the glohal helix axis.
rMD-final1
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parameters presented a strong discontinuity in the center of the helix. Finally, it is interesting to note, that the solution structure of [d(GTACGTAC)], recently reported in an rMD study (Baleja et al., 1990b) exhibits similar characteristics regarding the uniqueness of the central base-step. In that case, where there were no adenine H2 contacts, the structural features must be attributed to sequencespecific effects. 4. Conclusion demonstrates present study how The MARDIGRAS-derived distances in conjunction with restrained molecular dynamics can be used to establish many features in the solution structure of oligonucleotides even if the sequence is self-complementary and fairly repetitive. MARDIGRAS enables a better representation of distances in a constraint set, since it is based on a complete relaxation matrix analysis and is virtually free of structural biases. Distances obtained for different, data sets and starting models define upper and lower bounds of the constraints in order to reflect their accuracy conservatively. Although most accurate NOE-derived distance constraints do not define DNA structure completely, the empirical force fields of our restrained molecular dynamics approach enabled successful convergence from three different starting models to essentially the same structure. Several steps of averaging the resultant co-ordinates, followed by restrained energy minimization, improved the total energies of structures and the fit with the experimental distances. The structural deviations between the three five-structure averages obtained for A-, Band BDB-DNA as starting models do not reflect the geometry of the initial models; the two more similar starting structures (B- and BDB-DNA) did not produce the most similar rMD structures. The final structure, obtained from the average of all 15 individual structures, and the five-structure averages exhibit quite similar values, even for the least NOE-dependent structural parameters, for torsion angles and most of the helix parameters. One of the biggest methodological limitations seems to be imposed by the paucity of NOE data, most pronounced for interresidue information, especially for cross-strand connections. Such converged rMD structures are usually interpreted as a unique “final structure”. In our study, however, removal of one critical constraint out of 233 led to substantial structural changes in the final structure. Conformational analysis of the two “final structures” obtained with and without the critical A&H2 A&H2 cross-strand constraint revealed that, although the structural deviations are mostly associated with the two central base-pairs involving the cross-strand constraint, some overall structural features, i.e. X displacement’ and inclination, appeared to be significantly different. This leads to the idea that some distance constraints, especially those defining the geometry between the strands, are more important in defining the overall helical
appearance than for example the ample intraresidue ones. Convergence from different starting points to the energy minimum resulting from rMD simulations in vacw does not necessarily mean that the same situation would be found using more or different cross-strand restraints. Advances in our ability to determine these cross-strand restraints better and more accurately will certainly improve the quality of DNA solution structures. Residual indices calculated for both of our final struct,ures with respect to the original NOE data were comparable and considerably better than any starting structure. However, other n.m.r. experiments (proton spin-lattice relaxation measurements, 3 ‘P n.m.r. data) strongly imply that the struct,urr resulting from the constraint set with the indirect cross-strand constraint is a better, but by no means perfect, representation of the time-average solution structure of [d(GTATATAC)],. The inner four to six base-pairs, depending on the parameters, exhibited different structural features than the terminal ones suggesting that fraying influences some structural features of the penultimate as well as the terminal base-pairs. Helix analysis revealed some alternat,ion throughout the whole oligonucleotide, pointing out the different nature of A-T versus T-A steps. A compressed minor groove for the inner region. twist large values for roll, twist and propeller certainly emphasize a wrinkled D-like structure. However. our detailed analysis is not supportive of a canonical wrinkled D structure: rather, most parameters are somewhere between H- and wrinkled D-DNA. The accuracy of sugar pucker determination is likely to be affected by conformational avrraging, since an independent, scalar-coupling-based analysis yielded t,ypical S/N-mixtures with variable pseudorotation angles for the S-conformer (Schmitz et al., 1990). The sugar pucker deduced for the rM 1) structures in the present study is virtually identicbal with that of the major conformers in our previous 2&F-COSY analysis of the octanucleotide duplex. Co-ordinates of all resulting restrained molecular dynamics structures and a list, of NOE rest’raints have been deposited at, the Protein Data Hank. Rrookhaven National Laboratory. I:pton N.Y. 11973, I’.S.A., under accession number: lD42. This work was supported by Kational InstitutPa ot Health grants GM 39247, CA 27343. and RR 01695. Wr thank Dr Richard Lavery for providing the program CURVES. We gratefully acknowledge the use of the [Jniversity of Califorma. San Francisco, Computer Graphics Laboratory (supported by NlH grant RR01081). We also gratefully acknowledge use of the supercomputer at the Pittsburgh Gray-YMP Supercomputing Center, which was supported by a grant Rrsourcaes from the NTH Division of Research Cooperative Agreement U41RR04154 and a grant from the National Science Foundation Cooperative Agreement ASC-8500650.
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by P. E. Wright
Solution Structure of [d(GTATATAC)], via Restrained Molecular Dynamics Simulations with Nuclear Magnetic Resonance Constraints Derived from Relaxation Matrix Analysis of Two-dimensional Nuclear Overhauser Effect Experiments Uli Schmitz, David A. Pearlman and Thomas L. James-f Departments
of Pharmaceutical Chemistry and Radiology University of California San Francisco, CA 94143-0446, U.S.A.
(Received 18 January
1991; accepted 17 April
1991)
Two-dimensional nuclear Overhauser effect (2D NOE) spectra have been used as the experimental basis for determining the solution structure of the duplex [d(GTATATAC)], employing restrained molecular dynamics (rMD) simulations. The MARDIGRAS algorithm has been employed to construct a set of 233 interproton distance constraints via iterative complete relaxation matrix analysis utilizing the peak intensities from the 2D NOE spectra obtained for different mixing times and model structures, The upper and lower bounds for each of the constraints, defining size of a flat-well potential function term used in the rMD simulations, were conservatively chosen as the largest or smallest value calculated by MARDIGRAS. Three different starting models were utilized in several rMD calculations: energy-minimized A-DNA, B-DNA, and a structure containing wrinkled D-DNA in the interior. Considerable effort was made to define the appropriate force constants to be employed with the NOE terms in the AMBER force field, using as criteria the average constraints deviation, the constraints violation energy and the total energy. Of the 233 constraints, one was generated indirectly, but proved to be crucial in defining the structure: the cross-strand A&H2 A5-H2 distance. As those two protons resonate isochronously for the self-complementary duplex, the distance cannot be determined directly. However, the general pattern of 2D NOE peak intensities, spin-lattice relaxation time (T,) values, and 31P nuclear magnetic resonance spectra lead to use of the A3-H2 AT-H2 distance for A5-H2 A5-H2 as well. Five rMD runs, with different random number seeds, were made for each of the three starting structures with the full distance constraint set. The average structure from all 15 runs and the five-structure averages from each starting structure were all quite similar. Two rMD runs for each starting structure were made with the A5-H2 A5-H2 constraint missing. The average of these six rMD runs revealed differences in structure, compared to that with the full set of constraints, primarily for the middle two base-pairs involving the missing cross-strand constraint but global deviations also were found. Conformational analysis of the resulting structures revealed that the inner four to six basepairs differed in structure from the termini. Furthermore, an alternating structure was suggested with features alternating for the A-T and T-A steps. Keywords: 2D n.m.r. of DNA; molecular dynamics; alternating A-T sequences; NOE restraints; complete relaxation matrix analysis
1. Introduction Recently,
$ Abbreviations used: n&r., nuclear magnetic resonance; 2D NOE, two-dimensional nuclear
techniques based on nuclear magnetic (n.m.r.1) have become the method of
resonance choice for solution
structure
determination
Overhauser effect; 2&F-COSY, double-quantum-filtered correlated spectroscopy; ISPA, isolated spin-pair approximation; rMD, restrained molecular dynamics; r.m.s., root-mean-square; rMIN, restrained energyminimization; EGTA, [ethylenebis(oxyethylenenitrilo)]tetra-acetic acid.
of pro-
7 Author to whom all correspondence should be addressed. 0022~2836/91/170271-22
$03.00/O
271
0
1991 Academic Press Limited
272
U. Schmitz et al.
teins, oligosaccharides and oligonucleotides. In general, interproton distance information extractable from two-dimensional nuclear Overhauser effect (2D NOE) spectra and, to a smaller degree, torsion angle information deduced from various COSY experiments, are used in conjunction with the distance geometry algorithm (Crippen & Havel, 1988) and restrained molecular dynamics (rMD) (van Gunsteren et al., 1983) to establish high-resolution structures. Several reviews have been published recently (Scheek et al., 1989; Clore & Gronenborn, 1989; Gippert et al., 1996; Karplus & Petsko, 1996), but no standard procedure for determination of solution structures has been agreed upon. Duplex oligonucleotide analysis encounters a broader methodological range, since the general structural motif, i.e. base-paired helix, is a prerequisite and some of the subtle structural features of interest might not be deducible solely from n.m.r. data (Lane, 1996; Pardi et al., 1988). One major obstacle to establishing accurate oligonucleotide structures is the extraction of a sufficiently large number of accurate interproton distances from 2D NOE cross-peak intensities due to the nature of NOE-based distances and peak overlap, especially for highly repetitive sequences. The commonly applied method for converting intensities into distances, the isolated spin-pair approximation (ISPA), imposes another limitation, since it genuinely cannot account for spin-diffusion, which was shown to affect 2D NOE experiments obtained even for short mixing times (Keepers & James, 1984; Borgias & James, 1988, 1989). A complete relaxation matrix analysis, employed in MARDIGRAS (Borg& & James, 1989, 1996), IRMA (Boelens et al., 1988) and MORASS (Post et al., 1990) algorithms, augments the accuracy of the distance information derived, especially for longer distances accessible via the NOE. Nevertheless, several strategies have been proposed (Nilges et al., 1987a; Pieters et al., 1996; Baleja et al., 1996o) describing how the inaccurate distances derived from ISPA can be implemented as the initial constraints in molecular dynamics simulations. Restrained molecular dynamics (rMD) simulations allow conformational space to be searched for structures that simultaneously satisfy the NOE-derived restraints and correspond to a reasonable potential energy. However, an optimal set of parameters that appropriately balances the influences of potential energy and experimental restraints’ violations, has not yet been established. A major drawback of almost all (Torda et al., 1999) the refinement strategies currently employed is the bias inherent in interpreting n.m.r.-based constraints in terms of only one rigid conformer, which may be contradictory to the dynamic nature of DNA molecules (Pearlman & Kollman, 1991). Comparison of 2D NOE intensities calculated for the resultant rMD structures with the original experimental intensities seems to be a prudent final step. A refinement procedure of the converged rMD structures (Baleja et cd., 19906) with this as a basis
has been proposed recently. A promising technique, yet computationally demanding, incorporates comparison of calculated and experimental NOE intensities into the rMD trajectory calculations (Yip & Case, 1989). The present study continues our investigation of the structural qualities of alternating purine-pyrimidine sequences and A + T-rich sequences in particular. The TATA-motif is frequently found in promoter regions of genes’and has been the subject of several structural studies in solution (Assa-Munt & Kearns, 1984; Sklenar et al., 1989; Suzuki et al., 1986) as well as in the solid state (Yoon et al., 1988; Drew & Dickerson, 1982; Arnott et al., 1983). Our early studies on [d(AT),], (Suzuki et al., 1986) and [d(GGTATATACC)], (Zhou et al., 1987) comparing 2D NOE cross-peak intensities of experimental and theoretical spectra calculated using the program CORMA (Borgias et al., 1987, 1989) suggested that a wrinkled D structure best accounted for the spectral data of the TATA segments compared with other canonical DNA structures. Remarkable features of this type of structure include a narrower minor groove, alternating torsion angle values at A-T and T-A steps and a pronounced propeller twist. Recent investigations have demonstrated that an improved method of distance constraint generation, using the MARDIGRAS algorithm (Borgias & James, 1989, 1999), in conjunction with rMD calculations leads to a more sophisticated structural analysis (Gochin & James, 1999; Kerwood et al., 1991). constraints for Here, a set of distance [d(GTATATAC)], is generated with MARDIGRAS and employed in subsequent rMD simulations. Comparison with the results of an independent sugar pucker analysis on this oligomer (Schmitz et al., 1999) allows a further assessment of the performance of MARDIGRAS and our protocol for carrying out rMD simulations. To examine the role of the starting structures in the conformational search, three different models are chosen; two of them are relatively similar to each other. Differences among the three converged structures must be related to their initial models. Even if sufficient convergence from different starting structures has been achieved, the final conformation might be dependent on the constraint set employed. To elucidate this methodological limitation, hardly acknowledged in the literature, the rMD simulations were carried out with two slightly different constraint sets. Both of the resulting structures are analyzed and discussed to determine further the uniqueness of MD structures deduced with NOE constraints. Furthermore, our previous sugar pucker analysis provided evidence for conformational averaging for all residues, which was most pronounced for the terminal guanine residues (Schmitz et cd., 1996). Since rMD simulations generally must interpret constraints in terms of one conformer only, it will be interesting to identify any averaging effects in the resulting rMD structures.
n.m.r. Structure of (d(GTATATAC)]
2.
Materials and Methods (a) Sample preparation
purification of the octamer Synthesis and [d(GTATATAC)], has been described (Schmitz et al., 1990). The sample used for the 2D NOE experiments was dissolved in 99996% ‘H,O to give a final concentration of 17 mM in duplex, buffered with boric acid at pH 8 (50 m&f-borate, 100 mM-E&l, 0.2 mM-EGTA). (b) n.m.r. experiments Acquisition and processing of the n.m.r. spectra have been described (Schmitz et al., 1990). Here, pure absorption 2D NOE spectra were obtained using a pulse sequence (Jeener et al., 1979) with alternate block accumulation and phase cycling (States et al., 1982) for 4 mixing times: 50, 100, 250 and 400 ms. All spectra were acquired with 16 scans at each of 400 t,-values and a repetition rate of 10 s. Apodization with strong Gaussian-Lorentzian filters and zero-filling in both dimensions was used to obtain 4000 x 1000 datasets with a digital resolution of 69 Hz/point in oz and 39 Hz/point in the wi-dimension. Baseline correction was applied in both dimensions after the final Fourier transform. 2D NOE cross-peak integration was carried out with a modified version of the program CONTOUR (part of the local University of California, San Francisco, n.m.r. processing software package), allowing semi-automatic deconvolution of peaks in overlapped regions by simulating peak-envelopes in Z- and y-dimensions taking into account the involved protons’ linewidths as specified by the user. Quantification of the cross-peak intensities was achieved by summing the signal inside a contour level that was chosen as close to the noise level as possible. Typically, about 50 data points defined a single peak. A discussion of this technique, beyond the scope of this study, has been published elsewhere (Gochin et al., 1990). (c) Distance constraint generation from 20 NOE intensities Interproton distances were generated using the program MARDIGRAS (Borgias & James, 1989, 1990). For all 4 mixing time intensity sets, a complete 2D NOE relaxation matrix was set up using the geometry of a starting structure to account for all those interproton NOES not available from an experimental dataset. Starting models were standard A-DNA (Arnott & Hukins, 1972) standard B-DNA (Arnott t Hukins, 1973) and wrinkled D-DNA (Arnott et al., 1983). Assuming isotropic motion, a single correlation time was used for the whole molecule (r, = 5 ns), derived from the relation between spin-lattice relaxation time (Ti) and spin-spin relaxation time (T’) (Gochin et aZ., 1990). The complete NOE matrix is calculated for a particular starting structure using CORMA (Borgias et al., 1987, 1989; Borgias & James, 1988). The resulting intensities were used to construct a hybrid intensity matrix, combining with the experimental intensities. MARDIGRAS replaces elements of the relaxation matrix iteratively until either no changes result from each iteration cycle or the recalculated intensities meet the convergence criterion:
where a, and a, are the observed and the calculated intensities, respectively, and 0903 is designed to reflect
273
z
the noise level conservatively. MARDIGRAS calculates upper and lower bounds on distances corresponding to experimentally measured cross-peaks, depending on agreement between the experimental and the converged MARDIGRAS cross-peak intensity as well as signal-tonoise (Borgias & James, 1990). (d) Model building The co-ordinates for the canonical DNA structures (A- and B-DNA) were generated with the NUCGEN module of the AMBER program package (Weiner & Kollman, 1981; P. K. Weiner et al., 1984). The wrinkled D-DNA mode1 was generated from the co-ordinates of Arnott et al. (1983) swapping nucleotides with the aid of the graphics program MIDASPLUS (Huang et al., 1985, 1989) on an Iris workstation. The BDB mode1 of [d(GTATATAC)], was created by docking terminal G 1C base-pairs with B-DNA co-ordinates to a [d(TATATA)J, hexamer duplex possessing wrinkled D-DNA co-ordinates, using MIDASPLUS, and subsequent energy minimization of the ultimate and penultimate base-pairs using AMBER. Hydrogen atoms were added according to standard bond lengths and bond angles with the EDIT module of AMBER. In order to mimic solvent and counlarge sodium ions (hexahydrated terion effects, radius = 5 A; 1 A = 61 nm) were added according to the “implicit” solvent model (Rao et al., 1986; Singh et al., 1985). Prior to minimizations or dynamics, the sodium ions were placed along the PO; bisector, 624 A apart from the phosphorus atom. They were subsequently free were displayed with All structures :ID:%JS. (e) Restrained molecular dynamics The restrained molecular dynamics calculations were performed using a specially modified version of AMBER Version 3.OA (Singh et al., 1986, 1989; Pearlman, 1990) on a Cray Y-MP computer at the Pittsburgh Supercomputing Center. The force-fields used here have been reported previously (S. J. Weiner et al., 1984). Our modified version of AMBER includes 2 new features, which are important for the work presented here. First, the pseudo-energy term for the NOE-derived distance constraints has the form of a flat well with parabolic sides within a defined distance from the flat part and continues linearly beyond these margins: E c0nstr=
kl(r--%)* 0 k2P-rd2
1 4k2(r-rs)
when r2 > r whenr,>r>r, when r3 > r when r > r,; r4--rj = 2 A,
where r2 and r3 define the lower and the upper bounds of the flat part of the potential, corresponding to the distance bounds derived from MARDIGRAS (tide apra), and k, and k, are the force constants that can be selected for each constraint individually. (Note, that having 2 force constants enables different treatment of the 2 parabolic sides.) Since the width of the flat part arises from the accuracy of the MARDIGRAS results for each individual cross-peak with a11its inherent uncertainties, larger force constants were designated for the better defined distances. Four categories of flat well widths (090 to 925 A, 925 to 050 A, 050 to 190 A. and greater than 190 A) were respectively assigned force constants lOO%, 70%, 40% and 25% of the maximum during each stage of the rMD protocol (wide in&). The 4 categories comprised 190, 21, 10 and 2 restraints, respectively. Additionally, 36 constraints were included to guarantee
274
17. Schmitt
maintenance of Watson-Crick hydrogen bonds throughout the calculations. For the G. C base-pairs, lower and upper margins were set to 281 to 301 A (G-O, to C-X$), 2.85 to 3.05 A (G-N, to C-N,) and 276 to 2.96 A (G-N, to C-O,); for A.T base-pairs, values were 2.72 to 292 A (A-N, to T-N,) and 285 to 3.05 A (A-N, to T-O,) according to the literature (Saenger, 1984). The range for the upper parabolic part of the hydrogen bond constraints was 62 A, and the force constants were 10 kcal/mol-A2 (1 cal = 4 184 J). The range for the hydrogen bond angles was set to 170” to 190” with force constants of 5 kcal/mol-A’. The 2nd new pertinent feature of our version of AMBER enables gradual changes in the relative weights of force constants and temperature within a specific run of restrained molecular dynamics. In the past, it has been necessary to perform the calculations in separate pieces, each with fixed values for k and temperature (see also Fig. 5(a)). All rMD runs consisted of 30,000 steps in 0001 pa increments. All atoms within a 30 A radius were included in non-bonded interactions. SHAKE (Ryckaert et al., 1977) was used to constrain all bonds, and translational and rotational motions were removed every 100 steps. Starting points were steepest descent energy-minimized co-ordinates of A-DNA, B-DNA and the BDB-DNA model obtained from the all-atom version of AMBER. Initial velocities were taken from a Maxwellian distribution at 62 K. The system was then heated gradually from 100 K to 600 K during the 1st 3000 steps and maintained at this temperature for 12,000 steps, to avoid becoming trapped in a local energy minimum. From step 15,000 to step 18,000, the temperature was decreased to the final value of 300 K for the remainder of the rMD calculation. Temperatures were maintained through coupling with a thermal bath with a time constant of 94 pa. The weights of the NOE constraints were modulated by multiplying the force constants with a scaling factor. During the heating period, constraints were virtually turned off. From step 2021 to 6041, the force constants k, and k, for the best-defined constraints’ category were increased gradually from 65 kcal/mol-A* to 50 kcal/mol-A2 or 100 kcal/mol-A2 and kept constant to step 18,000, the end of the cooling period. During the subsequent 2000 steps the force constants were reduced to a maximum of 10 kcal/mol-A2 or 20 kcal/mol-A2 as a final value for the remaining 10,000 steps. For each run of 30 pa of rMD, coordinate sets were recorded each 0.2 ps. The last 50 coordinate sets, arising from the last 10 pa, were averaged and subjected to a final restrained energy minimization. (f ) Molecular mechanics All co-ordinates that arose from averaging over a rMD time period or from averaging individual structures from different rMD runs were subjected to restrained energy minimization using the modified version of AMBER 3.OA allowing the application of the flat well potential described above. In all cases the highest force constants for the NOE constraints were set to 10 kcal/mol-A’. During energy minimization, hydrogen bonds did not need to be restrained. (g) Structural parameters Sugar pucker and torsion angles were analyzed with the ANAL module of AMBER 3.OA. Calculation of all helical parameters was carried out with the program CURVES (Lavery & Sklenar, 1990), which is especially well suited
et al. for the characterization of irregular DNA features (Lavery & Sklenar, 1988, 1989).
structural
3. Results and Discussion (a) Proton assignments
and peak integration
The peak assignment procedure has been described previously; for chemical shifts, please refer to Table 1 of Schmitz et al. (1990). The numbering scheme used is: 14345678
5’-GlTZA3T4AST6A7C8-3’ 3’-CSAIIT6AST4A3TZG1-5 16 15 14 13 12 11 10 9
Since no part of the 21) NOE data obtained from 2H20 solution has been shown before, Figure 1 gives representative portions of the 250 milliseconds 2D NOE spectrum. The degree of peak overlap appears to be quite different for the individual protons. Most cross-peaks involving protons H6 and Hl’ of residue T4 and T6, and Hl’ of residue A5 and A7 could be analyzed only using a previously described deconvolution procedure (Gochin et al.. 1990), imposing an additional error onto the intensities’ accuracy by up to 10% compared to isolated peaks. The amount of peaks taken from overlapped regions varied from 23% to 30%, depending upon the dataset. We employ a high, time-consuming repetition rate of ten seconds to allow for sufficient relaxation of all protons, thus enabling extraction of accurate peak intensities. This is especially important, since we wanted to include all quantifiable cross-strand cross-peaks, which arise from the adenine H2 protons, exhibiting the longest spinlattice relaxation time of 3.5 to 3.6 seconds (Schmitz et al., 1990). In the course of the present study, it became apparent that cross-strand constraints play an important role in establishing the structure of an In the past, additional oligonucleotide (vide in&a). quantified cross-strand peak information has been extracted from imino 21) NOE data obtained from H,O solution (Clore et aE., 1988; Baleja et al, 1990a). However, these intensities are prone to large errors, since it is difficult to account for water exchange and non-linear excitation profiles. For the present study. we refrained from using any quantitative information for exchangeable protons. (b) Generation of distance constraints (MARDIGRAS calculation) Recent studies have demonstrated how NOE-based distances, calculated with the algorithm MARDIGRAS, can be used for structure determination of oligonucleotides (Gochin & James, 1990; Kerwood et al., 1991) and proteins (Thomas et al.. 1991). The latter investigation made use of a theoretical NOE intensity set corresponding to a crystal structure and showed that MARDIGRAS is strikingly robust in generating a largely correct unbiased distance set independent of the starting model. However, results improved with better initial
n.m.r. Structure of [d(GTATATAC)],
_._~
s-70
970
+I ;r
5.60
t
540
b A7
Gl
A5
I T2
5*90
,: 0
I
t
s.10
5+6
T4 T6
6-W
6.20
~-
275
6ao
0"
6'10
1
C8
A3
6.20
S-30
1
2: 3
640
1 ,,,.,,,,,,,,,.,,,,,,,,.,,,,,,
6.30
640
6.30 6.20 6.10 660
5.60
4.76
CSO
5.66 SM 4.26
560
460
3.75
+::;::::::::::::::I:::~::::
COO
Figure time:
1. Representative 250 ma).
portions
of the 2D NOE
spectrum
obtained
4.76
49
4G5
for [d(GTATATAC)],
f
4.00
3.7s
in ‘H,O
solution
(mixing
U. Schmitz et al.
276
0 0*
0
O
B G
e0
1.t:
I....,..-
_,_ _.., _.__, _ .,.,_ *
c2 I-5
2.0
2.5
3.0
395
HH distances
4.0
(b)),
4.5
5
I.5
in
2.0
2.5
MARDldRAS
A-DNA
(a) ‘G
5.0
:
4.5
:
3.5
3.5
40 (81,
4.5
5-O
hl -DNA
(b)
z
40:
3-O distances
k
0
0 : 0
-
~~~*80%8 # 0
3-O 2.5 2.0
ao
O@
0
0 0
0
oog 0 00
00
00
0
0
O0 0
I.5 4
I.5
2.0
2.5
30
HH distances
3.5 (81,
4.0
45
I.5
5,
BOB-DNA
2.0
MARDIGRAS
2.5
3.0 distances
3.5 (8),
4.0
45
5.0
BOB-DNA
(d)
(c)
Figure 2. Comparison between interproton distances: (a) for canonical A- and B-DPU’Astructures and (c) for B-DPr’A and BDB-DNA; and (b) for corresponding MARDIGRAS-derived distances using A-DNA or B-DKA for the 400 ms dataset; and (d) MARDIGRAS-distances derived from BDB-DNA and B-DNA for the 100 ms dataset.
models. Although the program is designed to take spin-diffusion into account, distance sets derived from shorter mixing times (e.g. 100 ms rather than 409 ms) are in better agreement with the original structure, indicating that MARDIGRAS cannot make up for loss of information at higher mixing times due to severe spin-diffusion (Borgias et al., 1999; Thomas et al., 1991). Furthermore, the accuracy of the distances obtained is improved with fraction of experimental cross-peaks included and by enhanced signal-to-noise ratio. For the present study, all four 2D NOE intensity sets were subjected to MARDIGRAS refinement, employing three different canonical DNA structures as initial models (A-DNA, B-DNA and BDB-DNA). In all 12 MARDIGRAS runs, convergence occurred after four to seven cycles to produce similar distance sets. In general, B-DNA and BDB-DNA as initial models led to more similar distance sets for a given intensity set, when compared with the distance set
for A-DNA
as starting model. A closer convergence of the resulting distances occurs also for the two longer mixing time 2D NOE intensity sets, presumably due to the larger number of cross-peaks. Comparison of distances obtained for the same starting structure and different intensity sets revealed some significant differences between shorter and longer mixing time data sets. The fact that distances associated with HS protons of the adenine- and guanine residues showed less agreement than those associated with other base protons suggested a non-negligible H/D exchange of the purine H8 protons. Since the 2D NOE spectra for the two lower mixing times were obtained immediately after preparing the sample and the other ones ten weeks later without removing the solvent for storage, the distances derived from the “fresh sample” should be more reliable. A comparison of interproton distances for different initial models and MARDIGRAS-derived distance sets (Fig. 2) gives
n.m.r. Structure of [d(GTATATAC)]
277
2
4.0
t r
A
P 0
t 8
B
.e
‘, %
o
2.5
2.0
,
I I
2
3
I
I
I
I
I
4
5
6
7
6
Residue
number
Figure 3. Deoxyribose Hl’H4’ distances obtained from MARDIGRAS
(A-DNA as starting structure, open symbols; BDB-DNA as starting structure, filled symbols); 50 ms dataset (A, A), 100 ms (0, ?? ), and 250 ms (0, ?? ) and from 2&F-COSY cross-peak simulation (represented as error bars).
an impression of the degree of agreement achieved. Clearly, however, the distances derived via MARDIGRAS are generally in agreement regardless of starting structure employed or intensity set analyzed. Another problem arose from distances associated with methyl protons. Some methyl deoxyribose distances were slightly inconsistent with the related H6/H8 distances to the same sugar protons. Until recently, MARDIGRAS treated unresolved equivalent spins as pseudoatoms, assuming the same motional model for all protons. However, methyl rotation is considerably faster than the overall tumbling rate, expressed by a correlation time of five nanoseconds. But even reducing the effective isotropic correlation time for all of the methyl pseudoatoms to one nanosecond did not alleviate the discordance completely. Since distances associated with methyl groups do not define additional parts of the molecule compared to distances associated with the pertinent base protons, only the latter were used as constraints for rMD calculations, as they are calculated correctly by MARDIGRAS (our unpublished data). MARDIGRAS’ capability of handling internal motions has been improved recently. Some short distances, inconsistent with any of the common helical DNA structures were obtained for three cross-strand interproton interactions at the terminal base-pair. This is probably due to fraying and has been observed for other oligonucleotides in our laboratory as well. The rMD procedure employed treats the molecule as fully base-paired and is not geared to simulate fraying effects approthese short cross-strand priately. Ultimately, distances, afflicting the terminal residues were not used in the final constraint set.
Some calculated distances relate directly to sugar pucker, especially the Hl’H4’-distance. An independent determination of sugar pucker (Schmitz et al., 1990) using simulation of 2&F-COSY cross-peaks thus allows comparison with the appropriate MARDIGRAS distances. Figure 3 shows the deoxyribose Hl’H4’ distances derived from MARDIGRAS for three different datasets (50, 166, 250 ms) and two initial models (A-DNA, BDB-DNA) in comparison with Hl’H4’ distances derived for the major conformer from the ZQF-COSY simulation results. A-DNA as an initial model yielded slightly larger distances, but nevertheless, all data fit surprisingly well except for residue C8, whose sugar pucker was assigned only tentatively in the 2&F-COSY simulation study. For residues T4 and T6, the pertinent 2D NOE cross-peaks were not available due to severe overlap. Instead, for these residues, we used the Hl’H4’ distances from the 2&F-COSY analysis with conservative bounds. Usually, alternating A-T-sequences exhibit medium-sized cross-peaks between the adenine H2 protons on opposite strands in the core of the helix. Two cross-peaks, A3-H2 A7-H2 and A3-H2 A5-H2, account for four distances, since we are dealing with a self-complementary structure. For the same reason, the cross-peak between the two isochronous A5-H2 protons of the different strands is not observable. Since missing constraints can produce structural artefacts (Gochin & James, 1990), we used other n.m.r. data to restrain the A5-H2 proton distance. MARDIGRAS yielded a shorter distance (2.79 to 2.93 A) for A3-H2 A7-H2 and a longer one (3.44 to 3.63 A) for A3-H2 A5-H2. Following the scheme of an alternating structure, previously suggested by 31P n.m.r. results (Schmitz et al.,
U. Schmitz et al.
278
Table 1 Number of constraints for denoted residues Cross-strand constraints Residue Cl T2 A3 T4 A5 T6 A7 CS
Intraresidue 15 11 14 9 9 8 I1 4
Interresidue (i to if 1) 5 4 5 3 6 4 6
NOES
Hydrogen bonds 6 4 4 4 4 4 4 6
2 B 1
1990), the cross-strand A&H2 A&H2 distance is expected to be short as well. Consequently, we carried out rMD calculations with and without restraining the A&H2 proton distance to 2.79 to 2.93 A in order to understand the impact of this slightly modified constraint set on the resulting rMD structures. Finally, the shortest and the longest of the four MARDIGRAS distances for each proton-proton interaction, calculated for BDB-DNA and B-DNA as starting structures and the two shorter mixing time 2D NOE intensity sets, were assembled into an upper and lower bound constraint set comprising a total of 233 entries with a r.m.s. value of 024 8. Table 1 lists the distribution of constraints over the molecule. (c) The restrained molecular dynamics
strategy
To gauge some of the boundaries of the constraint set, a series of restrained energy izations (rMIN) was carried out using relative weights for the restraint term, and
present minimvarious starting
Force constants
with either one of the presumably converged rMI> structures, or with the corresponding starting model, minimized B-DNA. These restraints all lead basically to the same result (Fig. 4). Increasing distance restraint force constants should improve the fit with the experimental data, decreasing the average constraint deviation. From Figure 4, which shows the energy minimization results for the rMD struct’ure, it becomes evident that an improvement in the average constraint deviation is indeed achieved with force fields up to approximately 40 to 50 kcal/mol-A’. Any further increase in force constants is of little avail; the average constraint deviation asymptotically approaches a value of -0.12 A, which is half of the r.m.s. difference between upper and lower bounds of the constraint set. The flattening of the constraint, energy curve at higher force fields also indicates that the maximum agreement with the experimental data is reached Unfortunately, an improved with 40 kcal/mol-AZ. fit to experimental data is associated with a deterioration in total energy. However, a point of inflection for the &,-curve indicates, that the system has to pay less of a penalty for total energy, but thus reduction of the average constraint deviation is steepest> at force fields below approximately 20 to 30 kcal/mol-AZ; restriction to such small force constants would not allow an average constraint deviation of less than 0.2 A. These model calculations do suggest that we can expect total energies of less than -600 kcal and average constraint deviations of better than 0.25 A for structures successfully converged from different starting models. WC note that it was impossible to achieve even a rough fit of A-DNA as a starting model to the distance constraints by means of restrained energy minimization alone. Relatively mild conditions, 30 picoseconds at
(kcal/mol-8’)
Figure 4. Average constraint deviation (.- + -.), total energy ( - ??-), and constraint violation energy ( - 0 - ) for restrained energy minimizations of previously energy-minimized B-DNA using various force constants for the NOE constraint term.
1z.m.r. Structure of [d(GTATATAC)]
- 600
(a)
4’
0
I....~....~....I....~....~....l 5 IO
15
rMD simulation
20
25
30
time (ps)
(b)
Figure 5. (a) Temperature (---) and maximum NOE
constraints force constants (---) used during the final restrained molecular dynamics procedure. (b) Evolution of the average constraint deviation during 30 ps of restrained molecular dynamics for 3 different starting structures. The protocol for the rMD simulations are shown in (a) with the exception that for the A-DNA calculation, a final value of 20 kcal/mol-A2 was employed.
300 K and force fields of 10 kcal/mol-A2, force B-DNA and BDB-DNA as starting structures into roughly the same conformation exhibiting an average constraint violation of 926 A compared to initial values of 640 A and 0.36 A. For the final ten picoseconds, no drifting in total energy or average constraints deviation was observed, indicating that the conformation is fluctuating in an energy minimum well. In fact, much more drastic conditions have to be employed to propel A-DNA as a starting model (initial average constraint deviation of 1.01 A) into the same structural realm. The system had to be heated up to 600 K, and force fields of up to 100 kcal/mol-A2 had to be.applied for an intermediate period of 12 picoseconds in order to facilitate the conformational changes. Subsequent cooling to 300 K and lowering the constraints’ maximum force constants to 10 kcal/mol-A2 yielded a structure not showing any drifts in total energy and average constraint deviation with the desired values. For all starting models, force constants of 20 kcal/mol-A2, instead of 10 kcal/mol-A2, for the last ten picoseconds enhance the tit with the experimental data from 0.26( +@l) A to @22( +@l) A as illustrated in Figure 5(b). However, this improvement did not produce significant changes in total
z
279
energy and average constraint violation after restrained minimization of the resulting rMD structures, indicating that the applied force fields keep the conformation essentially in the same potential well. This protocol, necessary to enable successful convergence for A-DNA as a starting model, was consequently applied to B-DNA and BDB-DNA as well. It was possible to deduce the appropriate parameters for our rMD calculations largely without comparing atomic r.m.s. differences of the resulting structures as is done most commonly. r.m.s. differences between resulting rMD structures of less than 1 A are usually considered to be indicative of successful convergence (Kerwood et al., 1991). This threshold, however, seems to depend to a great extent upon the individual system, and it was interesting to see how well our rMD protocol would provide convergence in terms of r.m.s. differences. An insufficient number of constraints can drive the molecule from different starting structures into different local energy minima, indicated by an increased r.m.s. difference when using higher constraint force constants (Gochin & James, 1990). Another problem arises from inconsistencies within a constraint set, as these NOE-based distances genuinely reflect time-average structures and yet are expected to be accommodated by a single rMD structure. Thus, some constraints might not be easily compatible with a physically reasonable structure. For the more problematic cases, it is necessary to ascertain the corresponding randomness of a system before the r.m.s. criterion can be used to assess the convergence of different rMD runs. Therefore, we used different random number seeds to produce different sets of starting velocities, and ran three simulations using 10 kcal/mol-A2 restraints and two using 20 kcal/mol-A2 restraints for all three different starting models. The larger force constants did not produce more similar structures within a set derived from one starting structure. In such a structure family, the smallest r.m.s. differences occurred between structures that had been generated from trajectories using the same initial velocities, but differing restraint weights. The average r.m.s. difference among the resulting five members of the family with A-DNA as starting structure was higher (1*07( kO.25) A) than the value for the B-DNA family (095( +@22) A), and smallest for the set of BDB-DNA structures (079( kO.16) A). These results imply that one cannot expect r.m.s. differences between structures converged from different initial structures to be smaller than N 1.1 A. The combination of three structures, each taken from one of the three starting structure families, giving the lowest average r.m.s. deviation yields a value of 1.09 A. The average r.m.s. difference among all 15 converged structures was 1.22( +630) A. This value agrees well with the results of a “distance geometry” study (Pardi et al., theoretical 1988) in which a representative constraint set (precision: +0605 A) was employed to generate a family of ten distance geometry struc-
280
U. Schmitz et al.
tures exhibiting an average r.m.s. deviation of 1.29( &007) L%compared to the target structure. To extract a structure that reflects the conformational commonalities of the 15 resulting conformations, the “final structure”, all co-ordinate sets were superimposed with a least-squares fit, averaged and subsequently subjected to restrained energy minimization (rMD-finall). To locate structural deviations arising from different starting models, the five coordinate sets belonging to each starting structure family were similarly treated to give rMD-A, rMD-B and rMD-BDB. This averaging procedure guarantees that only structural features associated with low energy structures are extracted, as opposed to averaging the structural parameters themselves. This turned out, to be more important for torsion angles than for helix parameters, since the latter seem to be less “quantized”. In the case of averaging two physically reasonable torsion angle values, -gauche and +gauche for example, numerical averaging would produce the energetically unfavornot at all describing a able syn conformation, feature of the molecule. Energy minimization of the averaged co-ordinates enforces an energetically reasonable conformation, generally one of two (or sometimes 3) energetically feasible conformations. Consequently, torsion angles were analyzed for each strand separately, although we are dealing with a self-complementary sequence; the MD trajectory of corresponding residues on the two strands is independent and may lead to different conformations for the two residues in spite of identical constraint terms. Another series of six rMD runs (starting models: A-, B- and BDB-DNA; force fields: 10 kcal/mol-A2 and 20 kcal/mol-82 for the final 10 ps) emanated from a modified constraint set. where just one crossstrand distance (A&H2 A&HZ) has been omitted. The heterogeneity of the set of resulting structures is surprisingly increased, indicated by an average r.m.s. difference of 1*46(+0*35) 8. Furthermore, large r.m.s. differences in comparison with the set of 15 (up to 2.4 A) suggested that we had found another suitable energy minimum with omission of a single critical constraint. The above averaging procedure was applied to this set as well to yield the co-ordinate set for rMD-final2. (d) Characterization
of the converged structures
Before assessing conformational details of all the averaged structures, a more global comparison in terms of r.m.s. deviations, energies and especially matching the original experimental data helped to assess the quality of the experimental structures. Table 2 lists the energy terms and the average constraint deviations for the energy-minimized starting models and the resulting averaged rMD structures. For comparison, structure rMIN-B has been added; rMIN-B results from the introductory model calculations (restrained energy minimization of energy-minimized B-DNA with full constraint set, using maximum NOE force constants of
n.m.r. Structure of [d(CTATATAC)]
z
281
Table 3 Atomic r.m.s. differences (A)
between starting models and structures obtained by restrained molecular dynamics and restrained energy minimization
Structures A-DNA B-DNA BDB-DNA
B-DNA
BDB-DNA
rMD-A
rMD-S
459 ****
672 284 ****
360 210 418
304 2.58 473
****
1.36 ****
rMD-A rMD-U rMD-13DU
rMD-SDI)
rMD-final1
rMD-final2
rMIN-13
3.80 1.76 382
354 1.97 407
261 2.83 500
4.55 0.97 2%7
1.06 1.32 ****
@98 1.01 055
1.84 1.36 1.81
1.81 2.26 1.34
****
1.55 ****
1.59 2.59
rMD-final1 rMD-final2
10 kcal/mol-A2 maximum). All energy terms of the listed calculated structures are strikingly similar. The NOE constraint deviations and constraint energies are considerably improved compared to the starting models, without significant deterioration of total energies. Moreover, all experimental structures have smaller total energies than A-DNA. It is noteworthy that our averaging strategy in general produces total energies and NOE constraint energies that are improved compared to the numerical values for the associated individual structures. rMD-final1 has a lower constraint energy than all other averaged structures. The total energies of all rMD structures listed in Table 2 are close to the best values of any of the individual structures before averaging. However, energy terms do not allow more than crude discrimination between structures. The relationship between structures becomes more evident from the atomic r.m.s. deviations in Table 3. rMD-A and rMD-BDB exhibit the smallest r.m.s.
deviation
(1.06 A) among
the
features remain the same for the two structures being compared. The acid test for all calculated structures obtained by any method should entail the experi-
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averages, although they arose from the two starting models with the largest r.m.s. deviation (672 A), A-DNA and BDB-DNA. It is interesting to note that rMD-finall, the average of all 15 structures, strongly resembles rMD-BDB, which was obtained from the starting structure with wrinkled D co-ordinates. Analysis of r.m.s. deviations becomes more powerful with information broken down into individual values for each residue. Figure 6 depicts the r.m.s. difference-per-residue analysis for a few selected examples. Typically, r.m.s. deviations for rMD structures are distributed fairly equally over the whole molecule with a tendency to be higher toward the termini, as shown for the comparison among rMD-A, rMD-B and rMD-BDB. Comparison between rMD-final1 and rMD-final2 indicates less smooth deviations. A pronounced r.m.s. difference for residue T4, base-paired with A5, reveals a significant change with removal of the A5-H2 A5-H2 constraint. The difference between rMDfinal1 and rMIN-B is most pronounced for residues closest to the termini, whereas the deviations for the inner residues are in the range similar to those of the five-structure averages. Of course, r.m.s. deviations will increase with distance from the site of any global structural change even if all local structural
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(a) with rMD-final1 (0) ver.susrMD-final2, and rMDfinal1 versusrMIN-B (0).
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mental data. Here, this evaluation was carried out on two levels: (1) with the original NOE cross-peak intensities, and (2) with the distance restraints. For the latter, the constraint energies were extracted for each residue, averaged for the two strands, and further divided into intra- and interresidue contributions, assuming that interresidue constraints contribute more to the overall appearance of a DNA-conformation than the intraresidue ones, which generally establish sugar puckering and the deoxyribose-base geometry. The intraresidue NOE constraint energies did not show any substantial differences among the calculated structures. The interresidue constraint energies, however, allow discrimination between the two rMD structures and rMIN-B, the latter exhibiting significantly larger violations for all residues. Comparing the sums of these individual values reveals that the entire difference in the NOE constraint energy term (Table 2) between rMD-final1 and rMIN-B (11.9 kcal/mol) arises from interresidue effects. On the other hand, the intraresidue constraints contribute 60 to 70% of the constraints’ energy, and thus constitute the major driving force in our calculations. It could be concluded that restrained energy minimization alone may not be capable of adequately manipulating a starting model, even if it is assumed to be in the same family as the structure corresponding to the distance restraint set. Hence, rMIN-B cannot be valid for considered a “final structure” [d(GTATATAC)], and will not be subjected to the structural scrutiny in the next section. We have found it useful for some time now to evaluate DNA structures by comparing their theoretical 2D NOE intensities with the experimental data (Broido et al., 1985; Suzuki et al., 1986); this approach has gained broad acceptance (Boelens et al., 1989; Baleja et al., 199Ob; Nerdal et al., 1988).
Different figures of merit have been used to express the overall fit of data, such as an average difference index (Suzuki et al., 1986; Zhou et al., 1987) and most commonly a residual index similar to the crystallographic R-value (Gupta et al., 1989; Baleja et al., 1999a; Gochin & James, 1999). Since 2D NOE intensities are spread over several orders of magnitude, the “crystallographic R-value” is heavily dominated by strong cross-peaks associated with short distances ( ~2.5 A), changing its meaning considerably compared to its application in X-ray diffraction analysis. However, utilizing the sixthroot relationship between NOE intensities and pertaining distances enables appropriate weighting of the weaker cross-peaks. The sixth-root residual index: 1 l@,)!‘6 - (%P61
is capable of ranking structures most closely to atomic r.m.s. deviation compared with other figures of merit (Thomas et al., 1991). Figure 7 shows residual indices R;, calculated with the program CORMA, for all three starting models, the final rMD structures, and rMIN-B. The two shorter mixing time data sets generally provide the smallest residual indices, especially the 100 millisecond data. Spin-diffusion seems to affect the larger mixing time data sets considerably as R’;-values for all structures become gradually indistinguishable. The starting models satisfy the experimental data to a very- different degree, with BDB-DNA exhibiting the smallest value. All three rMD structures fit the experimental data equally well, so overall residual indices unfortunately cannot be used to favor one of them. Analysis of
n.m.r. Structure of [d(GTATATAC)]
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R;-values evaluated residue by residue, however, revealed interesting details as shown for the 100 millisecond data set in Figure 8. For residue C8, only a few intraresidue constraints were extractable due to the isochronicity of protons H2’ and H2”. Nevertheless, CORMA is capable of calculating R-factors for intensities corresponding to a CS-methylene-pseudoatom; accordingly an extremely high R;-value is not surprising. The only significant differences among the interresidue R:-values pertain to the connectivity between T4 and A5, i.e. those residues involved in the particular cross-strand constraint employed only for rMDfinall, which manifests a better match with the experimental data than rMD-final2 and rMIN-B. The overall RT-values in Figure 7 indicate a better fit for intraresidue cross-peaks; Figure 8 reveals that the first three residues might be the reason for the worse fit of the interresidue data. These particularly high R;-values presumably stem from the inappropriate representation of the fraying ends in our rMD simulations. While the constraints reflect the timeaveraged conformational mixture, which may include base-paired helix and opened ends for limited time spans, the imposed hydrogen bond constraints impose continuous “ties” for the terminal base-pairs that are necessary for the successful performance of the calculation but might introduce artefacts for the terminal residues. Due to limited conformational possibilities within a residue, this is more likely to influence interresidue Rt-values. Clearly, the interresidue restraint set is more sensitive than the intraresidue set to conformational fit. This suggests that increased weighting of the interresidue distance constraints during refinement could be an improvement. In addition to permitting a calculation of RT, CORMA calculation of 2D NOE intensities for a structure enables a search for intensities predicted but not found experimentally. We found no instance of significant intensity predicted but not observed for any of the resulting rMD structures.
number
R; for individual residues of the resulting structures:
(e) Conform4ztional features of the final structure Before describing the structural details of our rMD structures, it is important to recall that DNA structure is not completely defined by NOE-derived distance information. A distance geometry study (Pardi et al., 1988) revealed that the backbone, especially the phosphodiester moiety, is less defined than the bases. Sugar pucker and some helix parameters such as tilt and twist, appeared to be best defined; the glycosidic angle and he!ix rise and roll were defined to a lesser degree, but propeller twist and dislocation were found to be ill determined. A more sophisticated theoretical study (Lane, 1990) assessing the impact of independently changed NOE intensities of specific groups of cross-peaks on structural parameters confirms most of these results. Furthermore, helix rise showed a strong dependence on interstrand imino cross-peaks, but helix roll did not seem to be defined at all. A recent distance geometry study showed that sequence-dependent fluctuations in the helical parameters cannot be reliably determined (Metzler et al, 1990). But we must bear in mind that structures obtained from restrained molecular dynamics do not depend solely upon the distance constraints but also on the energy criterion. The extent of the influence of either contribution is not easy to determine and has been the subject of much controversy. Nevertheless, the energy criterion chiefly maintains near- perfect stereochemistry and non-bonded interactions (Gronenborn & Clore, 1989). Our structural analysis focuses on (1) differences between the rMD structures derived from one starting structure and (2) differences between the two final structures with respect to the omission of one crucial constraint. Figure 9 depicts a superposition of rMD-A, rMD-B, rMD-BDB, and rMD-final1 structures and demonstrates the convergence of the rMD structures obtained with the full distance constraint set. The geometry of the inner six base-pairs is virtually
284
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Figure 9. Superposition of the rMD structures separated into a backbone view (left) and a base-pair view (right) for clarity: (red) rMD-A, (green) rMD-B, (cyan) rMD-BDB, and (black) rMD-finall.
identical. For the backbone, rMD-A and rMD-B exhibit slightly more pronounced deviations from rMD-finall, which is strikingly similar to rMDBDB. A detailed comparison of the individual values for torsion angles and sugar pucker is given in Figure 10. For most torsion angles, one of the three rMD structures possesses residues exhibiting a value different from the other two, indicating that there is more than one energetically feasible possibility. All of these outlying values have been observed for DNA but are less common (Saenger, 1984). The smallest range is found for the glycosidic angle x and 6, which is associated with sugar pucker. With our averaging strategy, rMD-final1 exhibits torsion angle values identical with those found for two of the three substructures and does not manifest geometrical averages. Less-common values occur only for rMD-A and rMD-B and do not reflect the initial geometry of the starting structure. Structural characteristics of rMD-A, rMD-B, rMDBDB, and rMD-final1 appear even closer upon evaluating the helix parameters in Figure 11, although the similarity of helix parameters for rMDBDB and rMD-final1 is less striking than for the torsion angles. The right panels of Figure 10 compare between rMD-final1 with rMD-final2 torsion angle values and elucidate their relationship to canonical A-, Band wrinkled D-DNA. In general, torsion angle values are rather similar for the final structures. Significant deviations occur mostly for torsion angles of A5 and T4 base-pairs, i.e. those associated with‘the critical A5-H2 A5-H2 constraint missing in
calculations leading to rMD-final2. Most torsion angle values (LX,/?, y, E) are between the typical values for B- and wrinkled D-DNA. For 6 and glycosidic angle x, where there is hardly a difference between the two B-family structures, the values tend toward the region for A-DNA, more pronounced for residues A7 and CS. c( and [, defining the P-O diester bond. are predominantly found in gauche regions ( -SC). A rare conformation for the phosphate group connecting residues T2 and A3 in the second strand, +sc for c1 and [, introduces the strongest deviation from ideal &-symmetry in the whole molecule. The values for c( are alternating and strongly resemble those of wrinkled D-DNA. The conformations of the C--O ester bonds are trans ( + ap), with few exceptions for E, where gauche values ( +sc and -SC) are found as well. For rMD-finall, B in residue A5 and E in T4. deviate from the other residues to exhibit values similar to wrinkled D-DNA. For y, almost all values indicate a gauche conformation (+sc) with the exception of terminal Gl and residue A3 of the second strand, which exhibits -SC and - ap conformations, respectively. A very narrow range is found for the glycosidic angle x, with values close to those of B- and wrinkled D-DNA. For rMD-finall, the inner six nucleotides of both strands exhibit essentially the same value (x z 110”) whereas rMD-final2 shows some fluctuations especially for residues A5 and T4. 6, directly related to the sugar pucker, appears to be the best-defined torsion angle with values in the gauche-tram range (+ac). Among all parameters defining the backbone,
n.m.r. Structure of [d(GTATATAC)]
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sugar pucker is best-defined and appears to be very symmetrical for the two strands, as expected for a self-complementary sequence. All values except for residue C8 are located in the S-range, close to the lower values of the alternating pucker of wrinkled D-DNA. At this point, a comparison with our previous study (Schmitz et al., 1990) is most appropriate. From simulation of 2&F-COSY cross-peaks, explicit determination of sugar pucker was achieved for residues Gl and T2, suggesting dynamic mixtures of the S/N-type with 60 : 40 and 80 : 20 ratios, respectively. A pseudorotation phase angle of 162” (C-2’-endo) for Gl and 144” for T2 resulted for the major conformer. Minor deviations between the ZQF-COSY cross-peaks of T2 and residues A3 through A7 suggested a very similar sugar pucker with a slightly increased contribution of the
assuming a three-state S-conformer. However, mixture with two S-conformers with pseudorotation phase angles of 162” and 126”, based on published MD results (Rao & Kollman, 1990), provided an equally good description of the deoxyribose conformation for non-terminal residues. Pseudorotation phase angles of residues Gl through T6 in our final rMD structures, especially rMD-finall, are strikingly similar to those of the major conformers of our simulation analysis. Since rMD searches for a single best conformation accommodating the distance restraints, dynamical averaging could give rise to artefacts. Our findings, however, do not indicate this to be a serious problem for the deoxyribose conformations and even suggest that the final rMD structures strongly reflect the major deoxyribose conformer of an equilibrium. The sugar pucker of
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the 3’-terminal residues differs significantly from all other residues, which is unexpected at least for A7. Although differences in sugar conformation between the final structures do not seem to be substantial, except for A5, rMD-final2 agrees less with our previous sugar pucker analysis. With regard to the backbone, differences between rMD-final1 and rMD-final2 appear mostly as a structural perturbation pertaining to residues A5 and T4. However, there are general differences that become clearer upon examining the helix parameters. The helix analysis program CURVES (Lavery & Sklenar, 1990) calculates a global helix axis and
provides four groups of parameters: (1) axis-basepair, (2) intra-base-pair, (3) inter-base-pair, and (4) axis junction parameters (Lavery & Sklenar, 1989). Since the definition of group (1 ), (3) and (4) parameters (Diekman, 1989) is dependent upon a global helix axis, we included the canonical DNA structures in our analysis as well. (We note that group (3) parameters may differ from values calculated with other helix analysis programs due to differences in defining the global helix axis.) Figure 11 displays the helix parameters of group (1). (2), and (3) necessary for discriminating between final strurtures. Some results (Fig. I I(c)) are also shown for the substructures rMD-A, rMD-B and rMD-BDB.
287
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proving that good convergence was also achieved for helix parameters. The graphic module of CURVES, MACB, enables an easy visualization of the global helix axis. Figure 12 presents different perspectives of the two final structures with superposition of global helix axes. In the side view, rMDfinal1 and rMD-final2 are hardly distinguishable; yet, to the eye, the latter seems to be shorter and slightly curved. Examination of the helix axis, however, indicates that neither final structure has an overall curvature. A regular alternation occurs for the helix axis segments of rMD-finall, but rMDfinal2 exhibits a local disturbance in the vicinity of the inner two base-pairs. From the view down the helix axis, it becomes evident that rMD-final1 assumes a leaner helix than does the other structure, which seems to be wound less tightly around its helix axis. A more detailed examination of some of the axis-base-pair parameters in Figure 11(a) confirms these findings, revealing a larger X displacement and inclination for rMD-final2. Among the intra-base-pair parameters, shear and stretch
are minimal for both final structures, although both parameters suggest some similarity to wrinkled D-DNA, more pronounced for the stretch of rMDfinall. Large negative values for the propeller twist, found for both structures, are reminiscent of the wrinkled D model. The inner four base-pairs assume slightly different values for propeller twist and stagger than the two at the termini. Most of the intra-base-pair parameters, however, suggest that the two central base-pairs differ from the others, most obviously for opening and buckle. The absolute opening values are small, but nevertheless, the similarity to wrinkled D-DNA is strongest for these central base-pairs. Increasing buckle values toward the termini are found for both structures. rMDfinal1 shows no buckle for the central two basefor pairs, rMD-final2 assumes values typical wrinkled D-DNA. For the inter-base-pair parameters (Fig. 11(c)), regular structures are indicated by zero values for roll, slide, tilt and shift. Indeed, shift and tilt (not shown) are practically zero for all structures. Slide
U. Schmitz et al.
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t-0-j a pattern that, along with similar results for rise and twist, highlights the structural peculiarity of the central two base-pairs, e.g. the twist of the central base-step in rMD-final1 exceeds all other values by more than 10”. Slide and rise of rMD-finall, however, suggest that the inner four base-pairs assume wrinkled D features. rMD-final2 exhibits slightly alternating values for rise and roll, consistent with wrinkled D-DNA only for the latter one. The roll parameter, which is most strongly associated with the orientation of the global helix axis segments, indicates a deviation from a regular structure only for the T-A steps in rMD-final1 with an alternating direction and zero values for A-T steps. Another differentiation between our final structures arises from examination of the minor groove width, a parameter that is substantially reduced for wrinkled D-DNA. Indeed, for the inner region of rMD-finall, the minor groove is somewhat compressed, whereas rMD-final2 does not deviate from the typical picture for B-DNA. Differences between our two final structures are and roll show
most prominent in the region of the critical distance constraint, compelling us to examine the actual distances between the adenine H2 protons. Among these five distances, the only difference between rMD-final1 and rMD-final2 occurs for the A&H2 protons. Consequently, the proton environment for A5-H2 in rMD-final1 and rMD-final2 differs substantially with two close protons (30 A and 3.6 A) for the former but a close and a more remote one (3.6 A and 45 A) for the latter. A3-H2 and A7-H2 both exhibit a proton environment (3.3 A and 3.6 A) similar to that of A&H2 in rMD-finall. Since the relaxation behavior is dominated by dipole-dipole interactions, the differences in the proton environment should affect the relaxation parameters of the adenine H2 protons. In fact, spinlattice (!Pr) relaxation measurements, reported in our previous study (Schmitz et al., 19!90), do not give any evidence for different proton environments of A5-H2 relative to A3-H2 and A7-H2. This finding encourages us to consider rMD-final1 as the best of the two final structures, although most of its helix
rMD-final2
Figure 12. Stereo views of the final rMD structures rMD-final1 (left) and rMD-final2 (right) including their global helix axis: (top) view into minor groove (residue G1 at, bottom back); (bottom) view down the glohal helix axis.
rMD-final1
17. Schmitz et al.
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parameters presented a strong discontinuity in the center of the helix. Finally, it is interesting to note, that the solution structure of [d(GTACGTAC)], recently reported in an rMD study (Baleja et al., 1990b) exhibits similar characteristics regarding the uniqueness of the central base-step. In that case, where there were no adenine H2 contacts, the structural features must be attributed to sequencespecific effects. 4. Conclusion demonstrates present study how The MARDIGRAS-derived distances in conjunction with restrained molecular dynamics can be used to establish many features in the solution structure of oligonucleotides even if the sequence is self-complementary and fairly repetitive. MARDIGRAS enables a better representation of distances in a constraint set, since it is based on a complete relaxation matrix analysis and is virtually free of structural biases. Distances obtained for different, data sets and starting models define upper and lower bounds of the constraints in order to reflect their accuracy conservatively. Although most accurate NOE-derived distance constraints do not define DNA structure completely, the empirical force fields of our restrained molecular dynamics approach enabled successful convergence from three different starting models to essentially the same structure. Several steps of averaging the resultant co-ordinates, followed by restrained energy minimization, improved the total energies of structures and the fit with the experimental distances. The structural deviations between the three five-structure averages obtained for A-, Band BDB-DNA as starting models do not reflect the geometry of the initial models; the two more similar starting structures (B- and BDB-DNA) did not produce the most similar rMD structures. The final structure, obtained from the average of all 15 individual structures, and the five-structure averages exhibit quite similar values, even for the least NOE-dependent structural parameters, for torsion angles and most of the helix parameters. One of the biggest methodological limitations seems to be imposed by the paucity of NOE data, most pronounced for interresidue information, especially for cross-strand connections. Such converged rMD structures are usually interpreted as a unique “final structure”. In our study, however, removal of one critical constraint out of 233 led to substantial structural changes in the final structure. Conformational analysis of the two “final structures” obtained with and without the critical A&H2 A&H2 cross-strand constraint revealed that, although the structural deviations are mostly associated with the two central base-pairs involving the cross-strand constraint, some overall structural features, i.e. X displacement’ and inclination, appeared to be significantly different. This leads to the idea that some distance constraints, especially those defining the geometry between the strands, are more important in defining the overall helical
appearance than for example the ample intraresidue ones. Convergence from different starting points to the energy minimum resulting from rMD simulations in vacw does not necessarily mean that the same situation would be found using more or different cross-strand restraints. Advances in our ability to determine these cross-strand restraints better and more accurately will certainly improve the quality of DNA solution structures. Residual indices calculated for both of our final struct,ures with respect to the original NOE data were comparable and considerably better than any starting structure. However, other n.m.r. experiments (proton spin-lattice relaxation measurements, 3 ‘P n.m.r. data) strongly imply that the struct,urr resulting from the constraint set with the indirect cross-strand constraint is a better, but by no means perfect, representation of the time-average solution structure of [d(GTATATAC)],. The inner four to six base-pairs, depending on the parameters, exhibited different structural features than the terminal ones suggesting that fraying influences some structural features of the penultimate as well as the terminal base-pairs. Helix analysis revealed some alternat,ion throughout the whole oligonucleotide, pointing out the different nature of A-T versus T-A steps. A compressed minor groove for the inner region. twist large values for roll, twist and propeller certainly emphasize a wrinkled D-like structure. However. our detailed analysis is not supportive of a canonical wrinkled D structure: rather, most parameters are somewhere between H- and wrinkled D-DNA. The accuracy of sugar pucker determination is likely to be affected by conformational avrraging, since an independent, scalar-coupling-based analysis yielded t,ypical S/N-mixtures with variable pseudorotation angles for the S-conformer (Schmitz et al., 1990). The sugar pucker deduced for the rM 1) structures in the present study is virtually identicbal with that of the major conformers in our previous 2&F-COSY analysis of the octanucleotide duplex. Co-ordinates of all resulting restrained molecular dynamics structures and a list, of NOE rest’raints have been deposited at, the Protein Data Hank. Rrookhaven National Laboratory. I:pton N.Y. 11973, I’.S.A., under accession number: lD42. This work was supported by Kational InstitutPa ot Health grants GM 39247, CA 27343. and RR 01695. Wr thank Dr Richard Lavery for providing the program CURVES. We gratefully acknowledge the use of the [Jniversity of Califorma. San Francisco, Computer Graphics Laboratory (supported by NlH grant RR01081). We also gratefully acknowledge use of the supercomputer at the Pittsburgh Gray-YMP Supercomputing Center, which was supported by a grant Rrsourcaes from the NTH Division of Research Cooperative Agreement U41RR04154 and a grant from the National Science Foundation Cooperative Agreement ASC-8500650.
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by P. E. Wright
