The ABCs of molecular dynamics simulations on B-DNA, circa 2012

Abstract

This article provides a retrospective on the ABC initiative in the area of all-atom molecular dynamics (MD) simulations including explicit solvent on all tetranucleotide steps of duplex B-form DNA duplex, ca. 2012. The ABC consortium has completed two phases of simulations, the most current being a set of 50–100 trajectories based on the AMBER ff99 force field together with the parmbsc0 modification. Some general perspectives on the field of MD on DNA and sequence effects on DNA structure are provided, followed by an overview our MD results, including a detailed comparison of the ff99/parmbsc0 results with crystal and NMR structures available for d(CGCGAATTCGCG). Some projects inspired by or related to the ABC initiative and database are also reviewed, including methods for the trajectory analyses, informatics of dealing with the large database of results, compressions of trajectories for efficacy of distribution, DNA solvation by water and ions, parameterization of coarse-grained models with applications and gene finding and genome annotation

1. Introduction

This article is a review of the progress made in the area of all-atom molecular dynamics (MD) computer simulations including solvent on duplex B-form DNA over the last 10 years by an international alliance of research groups known as the Ascona B-DNA Consortium (ABC). The original objective of this project was to produce a database of state-of-the-art MD on DNA in which all 136 unique tetranucleotide steps are represented, a sizable undertaking at the time (ca. 2001). The idea was to provide a comprehensive documentation of the performance of all-atom MD on DNA based on the best current nucleic acid force fields, and to obtain information for the comprehensive study and improved understanding of base pair sequence effects on structure and dynamics. Detailed knowledge of the effect of sequence on DNA structure is necessary for a general understanding of the sequence specificity of DNA–protein and DNA–ligand interactions as well as the role of DNA shape, flexibility, bending and bendability in mechanisms of action. In the course of this project, it has also been necessary to address critically some issues fundamental to the general application on MD to DNA, such as the parameterization of force fields, MD simulation protocols, the stability and convergence of MD simulations and methods for the analysis and validation of results. These topics are also reviewed.

The ABC initiative began in June 2001 at an informal lunchtime discussion during a workshop/conference on Atomistic to Continuum Models for Long Molecules in Ascona, Switzerland (http://lcvmwww.epfl.ch/~lcvm/ascona2001/index.html), and involved a number of those working on methods and applications of MD simulations to nucleic acids. There was specific interest in basic knowledge of the structure and motions of duplex B-form DNA, the predominant DNA conformation in vivo and the effect of base pair sequence on structure. Earlier studies of sequence effects in DNA had been carried out at the dinucleotide step level, but the influence of base pairs adjacent to dinucleotide steps was likely to be an important factor. In this case, at least a tetranucleotide model would be required to be able to fully understand sequence effects. Although the available experimental data for unbound DNA structures at the dinucleotide step level had been compiled (Berman et al. 1992) and analysed in detail (Olson et al. 1998; Zhurkin et al. 2005; Olson et al. 2006), sufficient statistical sampling of all tetranucleotide steps is not yet available.

At this point the idea was broached that the tetranucleotide database could be created using all-atom MD simulations. With the latest developments in nucleic acid force fields and access to high-performance computing, all-atom MD on DNA including explicit solvent was coming into its own and producing computational models of DNA for specific sequences that showed improved agreement with experiment (Beveridge and McConnell 2000; Cheatham 3rd and Kollman 2000). However, MD simulation projects described at this meeting typically dealt with one or just a few sequences, most at the dodecamer level of sequence length, with ~5 ns trajectories. Anticipating further advances in computer power, taking on a full set of tetranucleotide simulations at a meaningful level was estimated to require at least ~15 ns trajectories. At that time, a project of this magnitude was beyond the immediate capability of any one research group, but the idea that we could do this collectively with a ‘divide and conquer’ strategy was intriguing. The feasibility of such collaboration was influenced strongly by the ever-increasing capabilities of the Internet for ease of communication amongst participants and transferring data files. The proposed modus operandi was to parcel out the tetranucleotide sequences to various research groups willing and able to commit resources, and have each group perform the MD on their own computers using a commonly-agreed-upon force field and simulation protocols. Each of the potential participants was a user of the AMBER suite of programs for molecular simulations developed in the laboratory of our late colleague Peter A Kollman (Pearlman et al. 1995; Kollman et al. 2002; Case et al. 2005), and AMBER was thus adopted as our simulation engine. We recognized that not only getting the simulations done but the analysis of such a large database of results was going to be a considerable challenge in informatics. From the outset, our intention was to make the trajectories generally available to the field for further studies once they were completed.

We began the ABC initiative with limited expectations about whether it would actually get done, especially since everyone already had a full platter of other projects and commitments to various funding agencies to fulfill. The issue of obtaining funding for ABC was discussed, but we decided that in such a rapidly developing field it was better to just work on the project any way we could rather that commit the time (1–2 years, even if successful) to obtain a grant and then go from there. In summary, the consortium members found a quite viable way to work together, and simulations were set up and carried out over the course of the next ~2 years. To discuss preliminary results, informal gatherings of as many of the consortium members as possible were convened in conjunction with scheduled international symposia and CECAM Workshops. MD trajectories of 15 ns that comprise what we now call ‘phase I’ (ABC I) were completed on in a reasonable time frame, and are described in papers published in 2004 (Beveridge et al. 2004) and 2005 (Dixit et al. 2005). While interesting results were obtained, there turned out to be an ergodic problem in the MD force field that only materialized in longer trajectories beginning with canonical B-DNA. Specifically, transitions in the DNA backbone of the γ backbone torsion angle to trans, transitions that should be reversible (Varnai et al. 2002), were found to accumulate and eventually degrade the duplex structure. Considerable effort was required to correct this problem properly (Perez et al. 2007a, b; Svozil et al. 2008) and the whole set of simulations was rerun, this time at the level of 50 ns trajectories. This is referred to as ABC II and is described in an article that appeared in 2010 (Lavery et al. 2010). An ABC III initiative pushing simulations to the microsecond timescale is currently in progress, and future problems involving MD on DNA that require cooperation of laboratories and sharing of resources are being discussed amongst the active participants.

This article provides a retrospective on the ABC initiative circa 2012. A full list of those who contributed to the various phases of the ABC is provided in the papers published so far (Beveridge et al. 2004; Dixit et al. 2005; Lavery et al. 2009). Some projects that came about all or in part as a consequence of ABC or because of general public access to the database are also reviewed. Specifically, the focus in this article is (a) limited to the ABC project, (b) concerns only B-form DNA and (c) is AMBER-centric. A number of reviews with a broader purview of the field of MD on DNA during the time frame of ABC I and II are available in the recent literature (Beveridge and McConnell 2000; Cheatham 3rd and Young 2001; Giudice and Lavery 2002; Reddy et al. 2003; Mackerell Jr and Nilsson 2008; Orozco et al. 2008; Laughton and Harris 2011; Perez et al. 2012)

2. Background

JD Watson and Francis Crick in 1953 reported the discovery of the structure of DNA as a double helix of intertwined single-stranded polynucleotides interacting via complementary hydrogen bonds between nucleotide bases (Watson and Crick 1953). Some of the data they worked from were obtained from diffraction experiments on fibres (Franklin and Gosling 1953), which led to a duplex structure now known as the right-handed B-form of DNA. From this structure, models for how DNA self-replicates and codes for proteins were deduced. Subsequently, higher-resolution fibre diffraction structures were obtained that have served to define all-atom models of the canonical form of B-DNA (Arnott et al. 1976). The first X-ray crystal structure of B-form DNA at molecular resolution was reported in 1980 by Dickerson and coworkers (Wing et al. 1980) and was generally consistent with the structure proposed by Watson and Crick. However, the higher resolution revealed sequence-dependent helix bending, conformational irregularities and hydration patterns. Dickerson (Dickerson 1983) recognized that a code for the sequence-specific interactions may be found not only in the patterns of donor and acceptor sites in the major and minor grooves but also in sequence-dependent shape and structure of DNA. The role of dynamics as well as structure should also be considered (Pastor and Weinstein 2001). These ideas have generally stood the test of time, and have become essential elements of core knowledge in the field.

Since these pioneering studies, the techniques for obtaining high-resolution models based on X-ray diffraction of DNA in crystals and more recently NMR spectroscopy on DNA in solution have been considerably refined. The field of purely computational modelling of DNA using molecular simulation techniques has developed in parallel (Beveridge and McConnell 2000; Cheatham 3rd et al. 2001; Cheatham 3rd and Young 2001; Perez et al. 2012). The method of choice in the ABC initiative is MD, which produces a time series of individual structures that define the MD model structure and motions. Molecular structures of DNA can be analysed in terms of the derived parameters shown in figure 1. The first MD on DNA was reported in 1983 (Levitt 1983; Tidor et al. 1983), following the first MD on a protein by several years (McCammon et al. 1977). The time step for numerical integration in MD is typically 1–2 fs, and early simulations were carried out on a picosecond time frame. In these early simulations, solvent was not considered explicitly, but introduced via a distance-dependent dielectric screening function. However, the early MD on DNA produced highly distorted and unreasonable conformations when the simulations were extended without unphysical approximations, i.e. neglecting electrostatic repulsions and other adjustments or constraints. MD on DNA was expected to present challenging problems to simulation due to the polyelectrolyte character of the system. Also, with solvent water and ions already well known to be an integral part of DNA stability (Saenger 1984), a molecular model for water was likely to be required for accurate simulations.

Figure 1.

Definition of (a) conformational and (b) helicoidal parameters describing DNA structures (Lu and Olson 2003).

The computer power to perform MD on DNA including explicit solvent became available circa 1990, but the force fields were still not up to the task. Breakthroughs in the field of MD on DNA using AMBER came with the development of the ‘second generation’ force field ff94 (originally referred to as parm94) designed specifically for simulations including explicit solvent (Cornell et al. 1995), the availability of high-performance parallel computing compatible versions of the code, and implementation of fast Ewald methods (Essmann et al. 1995). All-atom MD on DNA including explicit solvent using the ff94 force field produced the first MD models of stable B-form DNA in solution on nanosecond timescales (McConnell et al. 1994; Cheatham 3rd et al. 1995; Young et al. 1997a, b). Detailed comparisons of MD on DNA were carried out on crystal structures (Young et al. 1995) and on NMR structures, some comparing calculated and observed NOESY peak volumes (Arthanari et al. 2003). Even though the MDs were ~5 ns and thus short by the standards of 2012, stable results were obtained and showed overall reasonable agreement between MD calculated and observed results, especially considering the complexity of the problem. However, some specific differences were also noted, particularly a general tendency in the MD models based on ff94 to form under-twisted structures (Cheatham 3rd and Kollman 1997a, b, 1998; Cheatham 3rd et al. 1999) and an ergodic problem with the ff94/ff98/ff99 force fields, discussed in detail below. A limitation of all-atom MD then and now is that only the relatively fast motions of a system are accessible to study, whereas many phenomena of biological interest occur on the milliseconds to seconds time frame and beyond. Thus, there has been and will be a continuing emphasis on extending MD on DNA to longer time scales to gain direct access to biological problems.

By the time of the 2001 Ascona meeting, successful MD simulations on DNA were being carried out in several laboratories with generally encouraging results (Miller et al. 1999; Cheatham 3rd and Kollman 2000), including a theoretical account of the hydration dependent A- to B-DNA transition (Cheatham 3rd and Kollman 1996, 1997a,b; Sprous et al. 1998). This system has also been the subject of a number of subsequent studies (Knee et al. 2008). The calculated distribution functions for mobile counterions provided a description of the ion atmosphere of DNA in remarkable agreement with Manning's counterion condensation theory (Manning 1978; Young et al. 1997a, b), and introduced the provocative idea that fractional occupation of ions in the grooves of DNA, i.e. that the minor groove spine of hydration reported in crystal structures may not all be water (Young et al. 1997a, b; McConnell and Beveridge 2000; Hamelberg et al. 2001). This point has been addressed further in a number of subsequent papers (Ponomarev et al. 2004; Rueda et al. 2004). The consensus MD view is now that the ions, as expected, preferentially sample electronegative sites around the DNA, but direct ion association with nucleotide bases in the grooves are found in only ≤ 10% of the time (Rueda et al. 2004). In any case, with a reasonable MD model of DNA available, a number of questions about sequence effects on structure were addressed over the next few years, including the structure of A-tracts (~ straight helix axis) (Sherer et al. 1999; McConnell and Beveridge 2001; Madhumalar and Bansal 2003; Lankas et al. 2010), an account of augmented DNA bending in sequences with A-tracts phased by a full helix turn (bending locus often at CpG steps) (Lefebvre et al. 1995; Young and Beveridge 1998; Lankas et al. 2010) and an explanation of the relative bending in sequence of phased A₄T₄ (bent) compared with phased T₄A₄ (~straight) (Sprous et al. 1999). More details on the dynamics of DNA bending are available in recent reviews (Beveridge et al. 2004; Zhurkin et al. 2005).

As the crystal structures of more and more oligonucleotides became available, information on patterns in DNA sequence effects accumulated (El Hassan and Calladine 1995; Suzuki et al. 1997; Olson et al. 1998). Classification of steps as either purine-pyrimidine (RY), purine-purine (RR) or pyrimidine-purine (YR) is useful to classify many of the observed conformational variations. YR steps (CA/TG, CG, TA) tend to have positive values of roll and higher than average twist, RY steps (AC/ GT, AT, GC) tend to have negative roll and lower than average twist, and RR steps (AA/TT, AG/ CT, GA/TC and GG/CC) are intermediate between these two groups. Dinucleotide steps also display sequence-dependent flexibility and deformability (bendability) (Ulyanov and Zhurkin 1984). Further evidence for the flexibility of CA/TG steps was noted early on from studies using empirical energy functions (Zhurkin 1985; Olson et al. 1998) A pattern with three rigid steps, AA/TT, AT and GA/TC, was noted (El Hassan and Calladine 1997), with the remaining more flexible steps further subdivided into bistable (all homogenous GpC steps) and flexible (CA/TG and TA). Mining the protein–DNA crystal structures further elucidated trends in sequence effects and correlations in the structural parameters (Olson et al. 1998, 2006), and provided further evidence that YR steps show the greatest flexibility, especially CA/TG. The subject of intrinsic flexibility of DNA and the ligand-induced bendability has been a subject of active interest due to the role these properties play in binding mechanisms (Olson and Zhurkin 2000; Lankas et al. 2004; Noy et al. 2004).

Ideas about the origins of sequence effects on DNA were first based on the steric clashes between purine and pyrimidine bases (Calladine 1982) and the variation in twist (Ulyanov and Zhurkin 1984). Further development of the steric effects view of sequence on structure was described by Suzuki et al. (1997) An alternative view based on base pair stacking interactions was subsequently advanced (Packer et al. 2000; Farwer et al. 2006). Normal mode analysis of oligonucleotide DNA using knowledge-based potentials obtained from mining the crystal structures successfully accounted for the bending persistence length and stretching modulus of DNA and indicated a sensitivity of twisting force constants to the base pair sequence (Matsumoto and Olson 2002). An MD study of two 18-base-pair DNA oligomers was reported in which all 10 unique dinucleotide base pair steps are represented (Lankas et al. 2003) and showed a trend in relative flexibility in roll, YR>RR>RY. The YR steps were also found to be the most flexible in tilt and partially in twist, supporting previous results. Slide–rise, twist–roll and twist–slide elastic couplings of various degrees were observed and a correlation of motions on a length scale of 2–3 base pairs was noted, which falls in the neighbourhood of first neighbour context effects. A number of subsequent studies of MD on DNA flexibility have extended and refined this account. (Lankas et al. 2000; Olson and Zhurkin 2000; Lankas et al. 2003, 2004; Noy et al. 2004).

With respect to the ABC initiative, it had by this point become clear that the issue of sequence effects on DNA the tetranucleotide level was only one of questions of interest. More fundamental was the issue of convergence and validation of the simulations – what length of trajectories were required to obtain stable results and how accurate are they over a broad range of sequences? One can envisage future use of good-quality computational models of DNA in diverse ways in problems ranging from structural biology to systems biology. Other questions had to do with the identification of thermally accessible sub-states, the nature of correlations within and between the conformational and helicoidal parameter sets, principal component and flexibility analysis of results, and sequence effects on DNA solvation. Another of the original motivations for doing the ABC project was to use ABC trajectories as a basis for choosing parameters for coarse-grained energy functions that could be used in calculations that predict structures for longer oligonucleotide sequences and for statistical mechanics partition functions. The progress in each of these areas related to the ABC simulations is also reviewed below.

3. Calculations

The effect of base pair sequence on structure can be conveniently expressed in terms of parameters derived from the Cartesian coordinates of model DNA structures (figure 1). The minimum structural unit that carries information on the three-dimensional structure of DNA is the dinucleotide base pair step, 5′-dXY-3′, where X and Y may be A, T, G or C. The four alternatives lead to 16 permutations, of which 10 are unique. The tetranucleotide problem arises since dinucleotide steps structures may depend on their nearest neighbours. In this case, the minimum structural unit necessary to study would be 4 base pair steps, of which there are 136 unique permutations.

A novel research design for ABC was proposed by Richard Lavery (Beveridge et al. 2004) and adopted for all phases of the project to date. Instead of running 136 different MD trajectories with one tetrad per oligomer embedded as the central 4 base pairs of a dodecamer, Lavery's idea was to pack repeating tetranucleotide sequences (WXYZWXYZWXYZ...), where W, X, Y and Z are any of the four nucleotide bases, A, T, G or C, within a single longer sequence. In this way, each oligomer can contain up to four distinct tetranucleotides, WXYZ, XYZW, YZWX and ZWXY. This strategy enables all 136 tetranucleotides to be studied using only 39 oligomers. Oligomers of 13 base pairs were used in ABC I and of 18 base pairs in ABC II. The ends of each oligomer were capped with a single GC pair (13-mers) and two GC pairs (18-mers) to avoid fraying. Thus, a given 18-base-pair oligomer contains 3 tetranucleotide repeats 5′-GC- YZ- WXYZ-WXYZ-WXYZ-GC-3′ and a four base pair repeating sequence, WXYZ, which occurs 3.5 times. Having multiple copies of each sequence is advantageous for statistics, and comparison of several different examples of any given sequence serves as a test for convergence.

Each oligomer was constructed as a canonical B-form DNA to begin with. All MD simulations were carried out with periodic boundary conditions on a truncated octahedral cell (figure 2) using the AMBER suite of programs (Case et al. 2006) using ff94 (Cornell et al. 1995) in ABC phase I and ff99 (Cheatham 3rd et al. 1999) with the modifications of parmbsc0 (Perez et al. 2007a, b) in ABC phase II. The water model used was SPC/E (Berendsen et al. 1987) ion parameters were those of Aqvist (Aqvist 1990) in ABC I and Smith and Dang (Dang 1995) in ABC II. (Note: improved parameters for ions are now available) (Joung and Cheatham 3rd 2009). Long-range electrostatic interactions were treated using the particle mesh Ewald method (Cheatham et al. 1995). A standard protocol of minimization, heating and equilibration was applied. Production simulations were carried out using an NPT ensemble with bonds to hydrogen atoms were restrained, allowing for stable simulations with a 2 fs time step. Centre-of-mass motion was removed every 5000 steps to avoid kinetic energy building up in translational motion (Harvey et al. 1998) and to keep the solute centered in the simulation cell.

Figure 2.

An image of the truncated octahedral cell used in MD simulations on DNA under periodic boundary conditions in the ABC project (Lavery et al. 2010). The environment of the DNA includes water molecules represented as small blue spheres and ions represented by the larger yellow spheres.

4. Results

4.1 ABC Phase I (Beveridge et al. 2004; Dixit et al. 2005)

The MD simulations in ABC I provided a database of the trajectories and structural parameters for all tetranucleotide steps based on 15 ns trajectories. The dinucleotide steps present clear differences with respect to YR, RY and RR/YY steps. The YR and GG steps present large positive roll towards the major groove. The average twist values for the YR steps are in general lower than the RR and RY steps, and the difference is even more pronounced. The YR steps present relatively large and positive roll values, i.e. a local bending towards the major groove. The GC and GA steps exhibit the highest average twist values in our MD simulations, and the CG, GG, and AG the lowest. This result is in good accord with the high-twist profile (HTP) and low-twist profiles (LTP) classification in a previous analysis of crystal structures (Yanagi et al. 1991). The range of MD calculated values for rise, slide and shift are relatively narrow: 0.4 Å for rise, 0.7 Å in slide and 0.2 Å in shift, with standard deviations in the range of 0.1–0.2 Å. However, average values in the database indicate anti-correlated changes in rise and slide values trending as YR<RY<RR for rise and RR<RY<YR for slide.

Some conformational transitions to structures distinct from the canonical B-form such as BI/ BII and α/γ flips (see below) were found. There are strong correlations between the backbone conformational angles and the helicoidal properties such as twist, rise and slide. The calculated mean lifetimes of BI and BII in ABC I are 918 ps and 180 ps, respectively. Although YR steps are intrinsically flexible, they are also least affected by the neighbouring base pairs. Conversely, these steps have a significant structural impact when adjacent to a RR or RY step, which are intrinsically more rigid than YR.

Notably, a parallel study of all tetranucleotide steps based on 136 separate 10 ns MD simulations in dodecamer sequences was reported by Fujii et al. (2007), also based the AMBER ff99 force field. Their results support that WATX tetramers show the most rigidity and the WYRX steps show the largest flexibility. Here, MD results were compared with data compiled from 239 protein–DNA complexes and agree with the experimental data quite well (Olson et al. 2006). The sequence dependent deformability was analysed on the basis of conformational entropy to study indirect readout and nucleosome positioning.

4.2 The α/γ flip problem

The AMBER force fields ff94 (Cornell et al. 1995), ff98 (Cheatham 3rd et al. 1999) and ff99 (Wang et al. 2000) were parameterized when ‘state-of-the-art’ simulations were on the 1 ns timescale and ab initio quantum mechanical calculations were limited to small model systems and to moderate levels of theory. Starting MD from a canonical B or a B-form crystal structure, both of these force fields performed well in simulations on DNA in the 5–10 ns range, a typical trajectory length circa 2004. However, a then recently published MD on DNA extended to 50 ns showed a number of irreversible α/γ transitions from the canonical to a non-canonical sub-state, accompanied by severe distortions of the structure (Varnai and Zakrzewska 2004). Likewise, persistent α/γ transitions to this non-canonical state began to appear in ABC I. One would expect such transitions, but they should only occur infrequently, i.e. they should be short-lived and reversible. This turned out to be a general sequence-independent ergodic problem in the ff94 and ff99 force fields and was causing an unphysical artifact to appear in long simulation times.

In response, a re-examination of the α/γ torsional behaviour in ff99 was carried out based on refined quantum chemical studies of the relevant part of the DNA backbone, resulting in the modification to ff99 now known as parmbsc0 (Perez et al. 2007a, b; Svozil et al. 2008). This was a non-trivial undertaking, since not only the behaviour of the α/γ torsional needs to be corrected but extensive testing is required to make sure other errors were not inadvertently introduced. The ff99/parmbsc0 force field for DNA has now been shown to produce stable MD on DNA on a ~1 μs timescale. Notably, the α/γ flip problem has not yet been seen in shorter (10 ns or less) simulations starting from canonical B-form DNA, and so this does not necessarily invalidate earlier all-atom MD studies prior to ABC. However, this artefact is expected to be more common in longer MD runs, and the ABC participants decided to rerun the entire set of 39 sequences using the parmbsc0 force field modification. By this time, the gold standard for MD trajectories had increased to ~100 ns (Ponomarev et al. 2004; Varnai and Zakrzewska 2004). Thus, an ABC phase II round of simulations was set in motion with a target of generating MD on DNA for all tetranucleotide steps at the 50–100 ns level. This phase of the ABC initiative was carried out over the next 4 years

4.3 ABC Phase II (Lavery et al. 2010) – Sequence averaged results

Mean values averaged over all sequences considered describe a model that clearly belongs to the B-DNA family. Base pairs show relatively small average deformations, excepting a propeller which has an average deviation of 11°. There is a weak positive average inclination to the helical axis (6.8°) and moderate shift towards the major groove (1.4 Å). The inter-base pair parameters show an average rise of 3.32 Å and a twist of 32.6°. The calculated value for average twist is improved over that found with the AMBER ff94 or ff99 force fields without the recent bsc0 modifications to the backbone parameters. Shift and tilt are on the average quite small, but there is an overall tendency to negative slide (0.44 Å) and positive roll (3.6°). Rise and twist show large ranges (~ 4.5 Å and ~76°, respectively), reflecting large fluctuations in base pair steps where local axis bending can reach 20°. The axis bending averages 20° with a 12° standard deviation, although fluctuations up to 40–50° are not uncommon.

The MD calculated groove widths show values consistent with B-form DNA, with a narrow minor groove (6.4 Å) and a wide major groove (12.3 Å), with average depths of 4.7 Å and 6.2 Å respectively. The groove widths have considerably large thermal dispersion. The major groove depth fluctuates twice as much as that of the minor groove, with standard deviations of 2 Å and 0.8 Å, respectively. Large fluctuations in groove geometries result in backbone distortions over several base pairs. The thermal dispersion of both grooves covers a range from completely closed to 2.5 times their normal widths. This has significant implications with respect to ligand-induced changes in DNA structure, since apparent sequence-dependent changes in groove widths may not be statistically significant.

Backbone angles show that conventional states dominate for α/γ = gauche⁻/gauche⁺, with ε/ζ = trans/gauche (BI) and 15% of ε/ζ = gauche⁻/trans (BII). Averaging over the entire dataset shows only 1% of non-canonical α/γ states, which supports that the repair of the α/γ flip problem has been successful, if not over-corrected. The average sugar pucker φ has a phase of 137° (C1′-exo, but near to the line with C2′-endo and an amplitude of 40°. All parameters show occasional, large deviations from their average values, often connected with incipient base pair opening. Backbone torsions show generally very large and polymodal fluctuations, but canonical α/γ and ε/ζ sub-states dominate on average.

4.4 Results averaged over flanking sequences

The averages and standard deviations of base pair step parameters averaged over all flanking sequences are shown in figure 3. Sequence effects at this level are seen to be relatively small overall, with statistically significant variations limited to a few steps. In particular, the YR steps show low rise, low twist and high positive roll. These steps also show much lower proportion of BII states in either strand, whereas RR steps have significant amounts (25–50%) of BII in the Watson strand and RY steps have more BII in the Crick strand. Negative rolls (bending towards the minor groove) occur for GC, GT, AT and AA. The AA and GA steps have the largest values of twist, with averages of 35.3°. Thermal fluctuations in all of the base pair steps are also quite similar, although the more flexible twist and rise of YR steps stand out somewhat. However, the difference between average values of the inter-base pair parameters for the 10 base pair steps and sequence-averaged values is not statistically significant. A set of distribution functions for base pair step parameters is shown in figure 4. Most are close to normal, but slide and twist show bimodal distributions at several steps and there is some evidence of shoulders. Bimodal distributions in twist are found for all RY steps (TG, TA, and CG). Twist is broad in GG, and GA shows a shoulder. CG essentially favours a low twist in CCGA and a high twist in ACGT, whereas ACGA is in equilibrium between these two states. These differences are linked to BI/BII transitions of the 3′ nucleotides. A bimodal distribution of base pair slide was found for RR steps.

Figure 3.

Average values and standard deviations for base pair step parameters from ABC II (Lavery et al. 2010).

Figure 4.

Distribution functions of base pair step parameters from ABC II for RR (black), YR (red) and RY (blue) (Lavery et al. 2010).

4.5 Analysis of tetranucleotide steps

First nearest-neighbour sequence effects on dinucleotide steps are revealed in the analysis of tetranucleotide fragments. Tilt and roll are hardly affected, but shift and slide both show variations of up to 1 Å, but the changes occur mainly for RR steps. Rise and twist show changes of up to 0.7 Å and 18° in YR steps, especially TG and CG. The absence of a significant fraction of BII states for YR steps holds in all sequence environments. However, the presence of BII for RR and RY steps depends strongly on the flanking bases. Thus, for example, AA steps have 50–80% BII in the Watson strand if the 5′-neighbour is a pyrimidine, but less than 20% if it is a purine. Similar patterns are seen for GG and AG, although in these cases a 5′ adenine suppresses BII despite a 3′ pyrimidine. For RY steps, GT shows 40–80% BII in the Crick strand if the 3′ neighbour is a purine and a comparable percentage in the Watson strand in CGCG. GT has even more specific effects, with significant BII in the Crick strand only for AGTA, AGTG, GGTA and GGTG sequences. With respect to fluctuations, the effects are relatively small for rise, tilt and roll, but more significant for shift and slide, where given environments can modify standard deviations by 60–70%. The standard deviations of twist values can double with respect to flanking sequence. A 5′-C and a 3′-A leads to high twist fluctuations for all RR and RY steps (except TG), while a 5′-T and a 3′-G leads to high twist fluctuations only for the AA step.

4.6 Beyond tetranucleotide steps

In ABC II, there is data on four pentanucleotide environments around all trinucleotide sequences, namely CXYZC, AXYZA, GXYZG and TXYZT. The results show that in each case the central nucleotide pair changes conformation significantly as a function of the next-nearest neighbours. A full description and understanding of this requires a more elaborate research design, but clearly next-nearest-neighbour effects on nucleotide pair conformations may be significant.

4.7 Comparison with experimentally observed structures

Direct comparison with experimental data is essential to validation of any MD on DNA. There is crystal structure and NMR data on some sequences containing tetrameric steps, but quantities directly comparable with ABC results are few and not sufficient for establishing a comprehensive vantage point (Olson et al. 2006). However, there are now refined X-ray and NMR structures for the Dickerson's sequence d (CGCGAATTCGCG), and all-atom MD trajectories on d (CGCGAATTCGCG) using same force field as used in ABC II are available for trajectories from 100 ns up to 1.2 μs. Selected comparisons of observed and calculated helicoidal parameters as a function of sequence are shown in figure 5. Here the experimentally observed and MD calculated parmbsc0 results for the helical parameters roll, tilt, twist, shift slide and rise agree at >95% confidence level, which provides a good validation of the force field used in ABC II on this prototype case. Overlays of MD structures for d(CGCGAATTCGCG) shown in figure 6 convey the ensemble nature of the dynamical structure and flexibility of DNA even at the 12-mer level. Further direct comparison of ABC results and MD on DNA in general with experiment will need to be an objective of future studies in the field.

Figure 5.

A comparison of base pair step parameters calculated from MD simulations on duplex d(CGCGAATTCGCG) based on parm99/parmbsc0 force field with corresponding experimentally observed crystal structure values from PDB file #1bna. Values for a canonical B-form structure are indicated by dotted lines. Triangles: PDB #1bna; squares: 100 ns MD trajectory; circles: 1 μsec MD trajectory (Perez et al. 2007).

Figure 6.

Superposition of MD structures from a 100 ns trajectory on d(CGCGAATTCGCG) including solvent.

4.8 ABC Phase III

During the time frame of phase II of the ABC initiative, MD trajectories on d(CGCGAATTCGCG) in the range of 1 μs were reported (Perez et al. 2007a, b). In addition, longer sequences had become accessible to MD study including a DNA minicircle (Lankas et al. 2006). Thus it became feasible to consider running MD on tetranucleotide sequences at the microsecond time frame, which is adopted for ABC III. We can envisage that MD on much longer time frames will be necessary in studies of biological phenomena, and so the issue of the performance of MD on DNA simulation capabilities upon access each new decade of time will likely be necessary. It is interesting to note the similarity between the results on base pair step parameters at 100 ns and 1 μs, but this may not hold for all sequences. The Cheatham lab has now pushed MD on DNA beyond the 10 μs timescale for several sequences, using an AMBER implemented on the Anton machine at the Pittsburgh Supercomputing Center. The results show reversible base pair opening on microsecond timescales and convergence of structural properties in 2–3 μs. A full account of these results will be forthcoming.

5. ABC-enabled and related projects

5.1 New programs for analysis of MD on DNA

The analysis of the results of MD simulations on DNA involves the calculation of all the conformational, helicoidal and morphological (major and minor groove widths, axis bending and persistence length) properties of each snapshot in each the trajectory. The ABC initiative coincided with the development of a new and improved version of the analysis program Curves by Lavery and coworkers called Curves+(Lavery et al. 2009). In addition, a new program called Canal was created that reads Curves+analysis of an MD trajectory and organizes further analysis including statistics due to thermal dispersions. The programs are described in detail in a corresponding publication (Lavery et al. 2009) and are available as a Web server at http://gbio-pbil.ibcp.fr/cgi/Curves_plus/ (Blanchet et al. 2011).

5.2 Informatics

MD carried out for ABC sequences involve running a number of simulations simultaneously. MANYJOBS, a python-based tool for managing this task on widely distributed computing resources, has been created by Bishop and coworkers and has been implemented on a number of supercomputing resources. The code is available able for distribution and can be obtained at http://dna.engr.latech.edu/.

For ease of sharing results, a suite of programs has been developed to compress MD trajectories using principal component analysis (PCA) and can be downloaded at http://mmb.pcb.ub.es/software/pcasuite/pcasuite.html. This technique offers a trade-off of compression ratio at the expense of losing some precision in the trajectory. PCA involves a linear transformation into modes that can be ordered with respect to the amount of motional variance. The idea here is to back transform with only the PC modes that have a significant effect on the overall dynamics. This makes a significant difference in the size of the data set. The ABC II results compressed by this method are available at http://holmes.cancres.nottingham.ac.uk/~charlie/ABC2.

Analysis of the large ABC datasets requires efficient methods of data management and distribution. A Web-based SQL database and a server for interactive analysis and structure prediction was developed for ABC I (Dixit and Beveridge 2006). Results from the structural analysis of all the trajectories using Curves and also the 3DNA program (Lu and Olson 2003) were stored in the database, indexed with respect to nucleotide position, the time step in the simulation, the sequence composition such as dinucleo-tide step, tetranucleotide step and accessible analysis via a structured query language. Assuming the individual bases to be planar and rigid, the helicoidal parameters can be employed to predict the average structure of a DNA sequence of any length. Some examples of some structure predictions are shown in figure 7. These account for some key features of sequence-dependent DNA bending noted in section 2. While this original server is no longer active, an alternative server for DNA structure prediction based on ABC II results as well as other dinucleotide models is available at www.wesleyan.edu/bendna (Liu and Beveridge 2001).

Figure 7.

DNA structures for several oligonucleotide sequences predicted from ABC parameters using the server www.wesleyan.edu/bendna. This view is (a) perpendicular to the helix axis in the top set of structures, and (b) the same structures looking down the helix axis.

5.3 Statistical significance of sequence effects

The derived parameters calculated from MD on DNA come out as distribution functions that describe the thermal fluctuations of structures that comprise the MD ensemble. Since DNA has notable flexibility, the fluctuations may be relatively large, and thus in studies comparing MD results with experiment or investigating sequence effects within and MD simulations, it is important to consider not only the differences but also the statistical significance of the differences as well. A particular problem case arises when two means are quite different in magnitude, but the difference is not statistically significant. A number of situations like this have been identified in an MD on d(CGCGAATTCGCG) (Lee et al. unpublished). The mean groove widths in a DNA sequence vary by~± 1 Å, and sequence effects here are particularly vulnerable to misinterpretation. The output from a Canal analysis of a MD trajectory on DNA provides all the information necessary for means testing as long the distributions are normal or nearly so. Non-normal, bimodal or polymodal distributions, of course, require special consideration.

5.4 Base pair sequence effects on DNA solvation

The ABC I dataset of was used by Dixit et al. (2012) for detailed analyses of the sequence-dependent hydration and ion atmosphere of DNA for all the 136 unique tetranucleotide steps. Proximity analysis (Mehrotra and Beveridge 1980; Mezei and Beveridge 1986; Makarov and Pettitt 2002) was employed to obtain sequence-dependent differences. Significant sequence effects on solvation and ion localization are indicated by these simulations. A representative MD-calculated hydration density for DNA is shown in figure 8. Energetic analysis of solute–solvent interactions based on proximity analysis of solvent reveals that the GC or CG base pairs interact more strongly with water molecules in the minor groove of DNA that the A-T or T-A base pairs, while the interactions of the A-T or T-A pairs in the major groove are stronger than the G-C or C-G pairs. The MD results for DNA–cation distribution functions show a structured (condensed) region of mobile ions within a radius of 10 Å from the DNA surface. This is dominated by interactions with the DNA anionic phosphates, and is thus essentially independent of sequence. However, The G-C and C-G pairs tend to associate with cations in the major groove of the DNA structure to a greater extent than the A-T and T-A pairs. Cation association is more frequent in the minor groove of A-T than the G-C pairs. However, as noted above, the fraction of counterions in the grooves is relatively low. The contribution this might make to the thermodynamics of counterion release on ligand binding to the grooves remains to be established. A comparison of solvent-accessible surface areas of the nucleotide units with results derived from analysis of crystallographic structures was found to be quite good. Time-resolved Stokes-shift experiments measure the dynamics of DNA and solvent on sub-nanosecond time scales, and MD was used as an aid in interpreting the results (Sen et al. 2009). The simulations were found to account for the magnitude and unusual power-law dynamics of the Stokes shift. Water is found to have the largest contribution to power-law dynamics, with counterions having a smaller but non-negligible contribution. The contribution to the signal of the DNA itself is only minor.

Figure 8.

An example of a MD calculated hydration density (poly-A) DNA (Dixit et al. 2012).

5.5 Using ABC for parameterization of coarse-grained models

The set of ABC MD trajectories contains a full complement of details about the time evolution of the structure and energetics for each sequence. The MD model in ABC simulations is an all-atom representation of the DNA and includes explicit consideration of solvent water, counterions and co-ions. In many instances, such a detailed model is not necessary for the interpretation of a particular experiment or explanation of a phenomenon. Thus, quite a range of models for DNA have been devised that are based on a reduced representation or coarse-grained model of the system (DeMille et al. 2011). As in MD, these models typically involve functions with adjustable parameters chosen with respect to experimental data or calculations on small prototypes, and the problem then is how to choose the parameters. Thus, the ABC database can serve as a basis for parameterizing coarse-grained models. We review below several instances from the recent literature in which the ABC data has been used in this manner. Note also that a force field based on crystal structure results on DNA and protein DNA complexes has been constructed and used for normal mode calculations on DNA (Olson et al. 1998).

A general approach to parameterization of sequence-dependent rigid base and rigid base pair models of DNA from MD has been described (Gonzalez and Maddocks 2001; Lankas et al. 2009). This method treats the internal energy as a quadratic function of internal coordinates, with sequence-dependent shape, stiffness and mass parameters. What is unique about this method is incorporation of the kinetic energy as a quadratic function of the linear and angular velocities, which permits construction of a coarse-grained model for use in statistical mechanics on the full phase space of the system. An implementation of the method was parameterized on the basis of the parm94 force field and a demonstration case on the sequence G(TA)₇C was provided. A parameterization of this method based on ABC is in progress.

5.6 Genome annotation

A coarse-grained trinucleotide model was used for the characterization of the physicochemical properties of DNA codons from ABC results (Singhal et al. 2008). In this study, the hydrogen bonding involved in DNA base pairing and the base pair step stacking energies were parsed from the energetics of the ABC phase I sequences. These two datasets referred to the base pair level plus a third parameter assigned based on the conjugate rule previously proposed to account for the wobble hypothesis with respect to degeneracies in the genetic code (Crick 1966; Young et al. 1997a, b). The third parameter values were found to correlate well with ab initio MD-calculated solvation energies and flexibility of codon sequences. Assignment of these three parameters enables the calculation of the magnitude and orientation of a ‘j-vector’ for each codon and a cumulative ‘J-vector’ for a DNA sequence of any length in each of the six genomic reading frames. Analysis of 372 genomes comprising 350,000 genes using this method (figure 9) shows that the orientations of the gene and non-gene vectors were found to be well differentiated. Thus, a method based on parameters derived from the ABC database results in a clear distinction between gene and non-gene sequences comparable to knowledge-based methods for gene finding (Singhal et al. 2008).

Figure 9.

Results of prokaryotic gene finding based on MD on DNA (Singhal et al. 2008): Cumulative physicochemical codon vectors projected onto a unit sphere for 4250 genes (blue) and equal number of frame-shifted non-genes (red) in E. Coli.

5.7 Partition functions and free energies from ABC parameters

Energy parameters were obtained from ABC I to construct statistical mechanics partition functions and calculate thermodynamic properties of DNA sequences (Khandelwal et al. unpublished). The methodology derives from and parallels closely the COREX method used extensively by Hilser et al. (2006) to study the statistical thermodynamics of proteins. In this approach, called GAREX, individual base pairs are presumed to assume either of two states: a ‘closed’ Watson Crick paired form or an open state. The microstates of a DNA sequence are formed in terms of blocks of base pairs that are themselves fully closed or open. This gives rise to a finite set of ‘bubble-like’ microstates, which are fully enumerable in the calculation of a partition function. From the GAREX partition function, thermodynamic properties can be calculated for DNA sequences of any composition and length. The method has been found to describe the thermodynamic stability of oligonucleotides with a correlation coefficient of .95 over a sample of 93 cases for which melting data is available.

The GAREX method was designed to be extensible, and has now been used the hypothesis that genes, introns and exons differ in their thermodynamic stability. Nucleotide stability constants are calculated for genomic sequences by a moving window average over 75 base pair sequences. Some preliminary results from a more comprehensive study are shown in figure 10, which shows that (a) promoter sequences in stretches of the E. coli K-12 genome exhibit lower stabilities than their corresponding genes, and (b) the introns in granule-bound starch sythetase genes exhibit lower stabilities than exons. This idea that genes are the most thermodynamically stable of the sequence elements has significant implications with respect to evolutionary genomics.

Figure 10.

Genome Stability profiles based on GAREX parameterized with MD results (Khandelwal et al. unpublished): (a) Nucleotide stability profile for a stretch of 641 bases of Escherichia coli K-12 genome, encompassing betT promoter and betT gene regions along with the preceding betI region. (b) Nucleotide stability profile for Granule Bound Starch Synthase I gene of Oryza sativa comprising 13 exons and 12 introns.

6. Summary and conclusions

The ABC consortium has completed two phases of MD on DNA. The latest being a set of 50–100 ns MD simulations on all tetranucleotide steps based on the AMBER ff99 force field with the parmbsc0 modification. The general characteristics of the simulations are described in the context of the literature on experimental and computational modeling studies of sequence effects on DNA structure. The ABC project and database has inspired or enabled related research on analysis of MD trajectories, informatics, compression of trajectories for efficacy of distribution, DNA solvation by water and ions, parameterization of coarse-grained models as well as gene finding and genome annotation. A future phase of ABC is in progress, and involves producing MD trajectories of at least 1 μs for sequences containing all tetranucleotide steps.