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Mathematics of Materials and Macromolecules: Multiple Scales, Disorder, and Singularities, September 2004 - June 2005

Abstracts

IMA Workshop:

Modeling Sequence-Dependent DNA Dynamics: The Third ABC Debriefing

May 7-8, 2005

Talk Materials

David L. Beveridge (Chemistry Department and Molecular Biophysics Program, Wesleyan University, Middletown, CT 06459)

Molecular Dynamics Simulations of the 136 Unique Tetranucleotide Sequences of DNA Oligonucleotides. II. Sequence Context effects on the Dynamical Structures of the 10 unique Dinucleotide Steps

Joint work with Surjit B. Dixit .

Molecular dynamics (MD) simulations including water and counterions on B-DNA oligomers containing all 136 unique tetranucleotide base pair steps are reported. The objective is to obtain the calculated dynamical structure for at least two copies of each case, and use the results to examine outstanding issues with regard to methods and protocols in MD on DNA, convergence and dynamical stability, and to determine the significance of sequence context effects on all unique dinucleotide steps. This information is essential to understanding sequence effects on DNA structure and has implications on diverse problems in the structural biology of DNA. Calculations were carried out on the 136 cases imbedded in 39 DNA oligomers with repeating tetranucleotide sequences, capped on both ends by GC pairs and each having a total length of 15 nucleotide pairs. All simulations were carried out using a well-defined state-of-the-art MD protocol, the AMBER suite of programs, and the parm94 force field. In a previous article (Biophysical Journal 87, 3799-3813), the research design, details of the simulation protocol, and informatics issues were described. Preliminary results from 15 ns MD trajectories were presented for the d(CpG) step in all ten unique sequence contexts. The results indicated the sequence context effects to be small for this step, but revealed that MD on DNA at this length of trajectory is subject to surprisingly persistent cooperative transitions of the sugar-phosphate backbone torsion angles a and g. Here, we report detailed analysis of the entire trajectory database. In particular, we present results on the occurrence of various conformational substates in the light of related experimental observation and discuss their impact on studies of context effects in DNA. At the tetranucleotide level, we observe that in many cases the difference in mean of the individual base pair step helicoidal parameter distributions with different flanking sequence differs by as much as 1 standard deviation, implying that the sequence effects could be significant. We present a novel analysis based on 2D-RMS data for studying the differences in structure and flexibility and employ it to analyze the flexibility of the dinucleotide steps and the effect of the base pair flanking the dinucleotide in the tetra-nucleotide sequences. We observe that the presence of pyrimidine-purine (YpR) steps, esp. the CpG and CpA steps greatly increases the flexibility of DNA while the purine-purine step (YpY/RpR) has a rigidifying effect. The neighboring base pair steps act cooperatively in such a way that the flexible steps tend to dominate the nature of the DNA sequence, there by leading to greater flexibility of the YpY steps in the neighborhood of YpR steps. Further, we observe that the effect of flexible YpR steps extends beyond its place as the first neighbor.

Dave Case (Scripps Research Institute)

Generalized Born studies of ABC DNA sequences

It is often useful in computer simulations to use a simple description of solvation effects, instead of explicitly representing the individual solvent molecules. Continuum dielectric models often work well in describing the thermodynamic aspects of aqueous solvation, and approximations to such models that avoid the need to solve the Poisson equation are attractive because of their computational efficiency. The generalized Born model is simple and fast enough to be used for molecular dynamics simulations of proteins and nucleic acids.

I will describe two applications of this methodology to the study of DNA duplex oligomers taken from the ABC sequence set. The first uses molecular dynamics simulations to look at mean structures, fluctuations and conformational transitions, with an eye towards explicit solvent simulations already carried out. The second application uses normal mode analysis (as a function of sequence length) to analyze low frequency distortion modes, and to prepare for a parameterization of a low-resolution model that could be used for much large pieces of DNA.

Thomas E. Cheatham, III (Departments of Medicinal Chemistry and of Pharmaceutics and Pharmaceutical Chemistry University of Utah)

Do longer or bigger simulations of DNA actually teach us anything new?

This past decade may rightly be called the "10 nanosecond era" (hopefully not "error") in relation to molecular dynamic simulation applied to nucleic acids. Computational power (and time) previously limited calculations to small solvated systems (< 25 base pairs) in single sets of simulation on a 1-10ns time scale. Over this time, little advance in the force fields has emerged (with many of the "good" force fields now ~10 years old!). So far, only anecdotal evidence of "failure" has been forthcoming. Usually this is manifest as a structural bias (such as towards A-form structures with the 2005 Gromos force field, low twist with Cornell et al. or wide minor grooves with the CHARMM a27 force field) with sampled structures. It has also become rather clear that there are significant sampling limitations across multiple time and size scales. Examples include the long times needed to relax the counterion atmosphere (~500 ns) and the backbone substates. A concern is that as we push into larger size and longer time scales, previously hidden (and perhaps unrealistic) conformational substates may emerge. We have seen this in simulation of the hairpin loops bridging strands in G-DNA quadruplexes; we are starting to see this, randomly, in simulations pushing 25-50 ns of DNA duplexes. One way to investigate this is to take a set of simulations that appears to be stable on a 5-10 ns time scale and run then for ~500 ns. This has been performed with the d(CGCGAATTCGCG)2 sequence with DAPI bound in two different binding modes in a set of four distinct simulations. What we find is that anomalous backbone states tend to emerge (outside the drug binding region). Another serious concern, often raised by reviewers (and structural biologists), is end-effects (due to finite sequence) in simulations of small DNA helices. To address this question, we have performed a series of simulations of d(GG)n and d(GC)n from n=1 to 18 (i.e. up to 36 base pairs). For some of the small duplexes, such as d(GCGC)2 we see clear biases emerging in the backbone conformational substates. For even smaller duplexes, dissociation (as is expected) is observed. There is good news and bad news: Yes, sometimes there are artifacts (which we hope to find and overcome), however in a large series of simulations of phased A-tracts, nucleosome pro- and anti-positioning sequences and a variety of RNA structures on a 25-75 ns time scale, these artifacts appear minimal (or at haven't been exposed yet). The same is true for even larger DNA and RNA structures including a series of DNA minicircles of 94-106 base pairs and of RNA tRNAlys anticodon stem loop - Aloop interactions on a 25-75 ns time scale. After my first DNA grant submission to NIH in 2000, I received the comment: "One has to wonder how many relatively short MD simulations have to be performend on short DNA fragments before what can be learned will have been learned". My answer, one that is likely shared by the ABC colleagues, is a lot more. Hence my title: "Do longer or bigger simulations of DNA actually teach us anything new?" I think the answer is "yes", but it isn't always good news...

[The material discussed in the abstract involves collaborative efforts with a number of different groups and people including: Jiri Sponer, Eva Fadrna, Richard Stefl and Nada Spackova (Czech Acad Sci & Masayrk U), Tom Bishop (Tulane), and Ty Curtis (Utah)].

Richard Lavery (Laboratoire de Biochimie Théorique, Institut de Biologie Physico-Chimique, Paris )

CURVES+

A pared-down, souped-up, groovy, outward-looking, new millennium tool for analyzing nucleic acid conformations.

John H. Maddocks (Institut de Mathématiques Bernoulli (IMB), FSB (School of Basic Sciences), EPFL (Swiss Federal Institute of Technology) http://lcvmsun9.epfl.ch/~jhm/ )

Molecular Dynamics Simulations of DNA minicircles
Slides:   pdf

Joint work with Filip Lankas and Richard Lavery.

Molecular Dynamics simulations of 94bp minicircles in explicit solvent are described. The trajectories are 30 ns in length, and are started from an approximately circular configuration. During approximately the first third of the trajectory the shape oscillates close to its circular shape, then it starts to writhe out of the plane, reaching a highly deformed shape at approximately 20 ns in which there is a straight segment flanked at each end by kinks in the DNA double helix, and a highly deformed S-shaped segment between the two kinks. This shape appears to have stabilized during the 20--30 ns part of the trajectory. The kink formation is in line with suggestions made by Crick and Klug (1975), and offers a potential explanation of the anomolously good cyclization rates of 94 bp minicircles that has been observed experimentally by Cloutier and Widom (2004).

Modesto Orozco (Departments of Biochemistry and Molecular Biology University of Barcelona)

Exploring the flexibility of nucleic acids

Nucleic acids are very flexible structures whose conformation can be adapted in response to chemical and mechanical stress. Such perturbation can be of two types: i) large transitions that lead to helical unfolding and ii) small perturbations that can be fitted to harmonic deformation modes. I will present theoretical studies on both type of distortions, making an special emphasis on harmonic deformations, since these can be well represented by means of the analysis of covariance matrices (Cartersian, mass-weigthed Cartesian or helical) obtained from database analysis or from extended molecular dynamics simulations. I will show how these simple harmonic deformations can explain many physical and even biological properties of nucleic acids.

Rami Osman (Department of Physiology and Biophysics, Mount Sinai School of Medicine, New York, NY 10029)

Quantum Chemistry and Energetics in Pu-p-Pu

Joint work with Elena Rusinova and Emmanuel Giudice.

The occurrence of interconversions in backbone angles present an interesting question as to its origin and frequency. Unlike the rather frequent BI-BII transitions characterized by the combination backbone angles epsilon and zeta, the transition due to an interconversion of the alpha and gamma pair is less frequent and in a simulation time span of 15 ns may occur at most once or twice. Two stable states have been identified – the canonical characterized by alpha/gamma (-g/+g) and the non-canonical with alpha/gamma (+g/t). The energetics and the barrier for the interconversion between these two states are not known.

We have conducted quantum chemical calculations on four Pu-p-Pu pairs using a PCM to represent the effect of the solvent. The canonical conformations are lower than the non-canonical and the barriers for the interconversion are in the range of 7.6 – 11.4 kcal/mol. We will discuss these results in the context of the observed transitions in the ABC simulations.

Jiri Sponer (Institute of Biophysics, Academy of Sciences of the Czech Republic, Kralovopolska 135, 612 65 Brno, Czech Republic)

Molecular dynamics simulations of RNA and noncanonical DNA molecules. Successes and troubles

Since 2000, we have carried out an extensive set of RNA simulations, with cumulative time scale at this moment above 2 microseconds and individual simulations expanded up to 100 ns, with 6 published and ca 5 in preparation papers. The aim of the project is MD analysis of distinct classes of RNA systems, including main rRNA non-Watson-Crick motifs. The studied systems include frameshifting pseudoknot, several RNA kissing complexes and related extended duplexes, wide range of ribosomal kink-turns, 5S rRNA Loop E and its complex with L25 protein, sarcin-ricin loop, hepatitis delta virus ribozyme and some other systems. The simulations appear to provide unique qualitative insights into the RNA dynamics, including role of tightly bound waters (residency times 1-25+ ns), unprecedented cation binding sites with up to 100% occupancy and frequent solute-bulk cation exchange, distinct mechanical properties of various classes of ribosomal RNA that can be related to the function, and others. In response to the recent observations of alpha/gamma transitions in B-DNA, we reanalyzed all our MD data. Since the RNA molecules have often a low resolution and there are many possible substates of backbone in RNA, the analysis is not always straightforward. Nevertheless, until now, we did not identify anything what could be considered as evident backbone pathology. If there are alpha/gamma switches, they are mostly reversible and often can be identified as being between two established RNA backbone conformations. Quality of backbone at the end of the simulations is comparable to the experimental data and there is no degradation of the structures in the course of the simulations. It is also notable that the nature of conformational variability in RNA allows to direct the research in a rather qualitative way, thus modest force field imbalances could often be tolerated. In addition, the simulations appear to very well reproduce many aspects of RNA molecules established by crystallography, including water-mediated dynamics of A-minor type I interaction (the most prominent RNA tertiary motif) in K-turns, correct prediction of topology of bulged out bases subsequently confirmed by crystallography, stability of specific backbone states such as S-turn, correct prediction of mutated structure of spinach chloroplast Loop E independently verified by NMR and others. We do not suggest that the force field is perfect but we can safely claim that it can be used very successfully to study many aspects of RNA structural dynamics. At the same time, we recently reported a large-scale failure of simulations to predict topology of d(GGGGTTTTGGGG)2 quadruplex loops, which halted all our advances in the G-DNA field. It appears to be accompanied by the same backbone alpha/gamma switch as noticed in ABC B-DNA simulations.

Mathematics of Materials and Macromolecules: Multiple Scales, Disorder, and Singularities, September 2004 - June 2005