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RNA unrestrained molecular dynamics ensemble improves agreement with experimental NMR data compared to single static structure: a test case

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Abstract

Nuclear magnetic resonance (NMR) provides structural and dynamic information reflecting an average, often non-linear, of multiple solution-state conformations. Therefore, a single optimized structure derived from NMR refinement may be misleading if the NMR data actually result from averaging of distinct conformers. It is hypothesized that a conformational ensemble generated by a valid molecular dynamics (MD) simulation should be able to improve agreement with the NMR data set compared with the single optimized starting structure. Using a model system consisting of two sequence-related self-complementary ribonucleotide octamers for which NMR data was available, 0.3 ns particle mesh Ewald MD simulations were performed in the AMBER force field in the presence of explicit water and counterions. Agreement of the averaged properties of the molecular dynamics ensembles with NMR data such as homonuclear proton nuclear Overhauser effect (NOE)-based distance constraints, homonuclear proton and heteronuclear 1H–31P coupling constant (J) data, and qualitative NMR information on hydrogen bond occupancy, was systematically assessed. Despite the short length of the simulation, the ensemble generated from it agreed with the NMR experimental constraints more completely than the single optimized NMR structure. This suggests that short unrestrained MD simulations may be of utility in interpreting NMR results. As expected, a 0.5 ns simulation utilizing a distance dependent dielectric did not improve agreement with the NMR data, consistent with its inferior exploration of conformational space as assessed by 2-D RMSD plots. Thus, ability to rapidly improve agreement with NMR constraints may be a sensitive diagnostic of the MD methods themselves.

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Abbreviations

RNA:

ribonucleic acid

PME:

particle mesh Ewald

NMR:

nuclear magnetic resonance

NOE:

nuclear Overhauser effect

2D:

two-dimensional

RMSD:

root mean square deviation

ps:

picoseconds

fs:

femtoseconds

Å:

angstroms

K:

Kelvin

°C:

degrees Centigrade

kcal:

kilocalories

mol:

mole

AMBER:

assisted model building with energy refinement

ISPA:

isolated spin pair approximation

IRMA:

iterative relaxation matrix analysis

T 1 :

longitudinal NMR relaxation time

T 2 :

transverse NMR relaxation time

J :

NMR coupling constant

NOESY-JRE:

nuclear Overhauser effect spectroscopy, with jump return excitation

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Acknowledgements

We would like to thank Wendy Cornell and James Dunbar for advice regarding use of AMBER, Mark Duffield for computer system administration, and Donald Emerson, John SantaLucia, Jr., Douglas Turner, and Eric Westhof for helpful discussions. We are also indebted to Drs. SantaLucia and Turner for sharing their NMR data.

Author information

Author notes

  1. Robert A. Beckman

    Present address: Clinical Research & Development, Hematology & Oncology, Centocor, Inc.,, 200 Great Valley Parkway, Malvern, PA, 19355-1307, USA

Authors and Affiliations

  1. Discovery Research Informatics, Computer-Assisted Drug Design, Pfizer Global Research and Development, Ann Arbor, MI, 48105, USA

    Robert A. Beckman, David Moreland, Shirley Louise-May & Christine Humblet

  2. Biophysics Research Division, University of Michigan, Ann Arbor, MI, 48109-1055, USA

    Robert A. Beckman

  3. Division of Pediatric Hematology/Oncology, University of Michigan Medical Center, Ann Arbor, MI, 48109-0238, USA

    Robert A. Beckman

  4. Neurogen Corporation, Branford, CT, 06405, USA

    Shirley Louise-May

  5. Wyeth Research, Princeton, NJ, 08543, USA

    Christine Humblet

Authors
  1. Robert A. Beckman
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  4. Christine Humblet
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Corresponding author

Correspondence to Robert A. Beckman.

Appendix: Simulation Methods

Appendix: Simulation Methods

Force fields

Primary (PME) simulations used the AMBER 4.1 force field [28, 29].

Negative control (DDD) simulations were performed in SYBYL 5.5, 6.1a, and 6.22 in a force field parameterized to be identical to the AMBER 4.1 force field in which the primary (PME) simulations were done [28, 29].

For the sodium counterions, the Lennard-Jones energy parameter ε was calculated at 0.0028 kcal/mol and the van der Waals radius at 1.87 Å [56].

Preparation and minimization of conformers

Primary simulation

Structure preparation was performed using standard methods with the AMBER 4.1 [57] programs PREP, LINK, EDIT, and PARM. Sodium counterions were added to the RNA NMR structures, and the resulting neutral molecule was placed in a box of TIP3P waters [58, 59].

The water molecules were relaxed in SANDER by fixing the RNA and sodium atoms and performing 200 steps of steepest descent minimization. PME [60] was used with the direct sum tolerance set to 0.000001 and the B-spline interpolation order set to 3, with periodic boundary conditions. The periodic box measured 51.9 × 38.9 × 38.5 Å for r(GGCGAGCC)2 and 51.5 × 39.7 × 44.6 Å for r(GCGGACGC)2.

SHAKE [61] was applied to all bonds with a tolerance of 0.0005 Å, and the van der Waals cutoff was 9.0 Å. The minimization was performed using an initial step length of 0.1, a maximum step length of 0.5 and a gradient convergence of 0.001.

Negative control simulation

NMR conformers were subjected to simplex optimization and 100 steps of steepest descents minimization with a gradient termination criterion of 0.1 kcal/mol Å, a distance dependent dielectric constant of 1, a non-bonded cutoff of 8 Å, no periodic boundary conditions, and the AMBER 4.1 charges and force field. The structures were nearly identical to the starting structures, hydrogen bonding geometries were maintained, and the structures improved in terms of bond angles and van der Waals energies.

The molecule was then solvated with TIP3P waters using the Sybyl algorithm Silverware [62]. Sodium atoms were then added by replacing the water molecule closest to each phosphate, neutralizing most of the unfavorable electrostatic interactions. The solvated systems with sodium counterions were then subjected to simplex optimization and 100 steps of steepest descents minimization with RNA atoms fixed, termination criterion gradient 0.1 kcal/mol Å, distant dependent dielectric of 1, non-bonded cutoff of 8 Å, AMBER 4.1 force field and charges, and periodic boundary conditions within cubic periodic boxes 36.1 Å on a side. Nine hundred steps of Powell minimization were then undertaken under the same conditions with RNA atoms fixed.

The minimized, solvated conformers with counterions were then further minimized utilizing a low temperature, constant temperature and volume dynamics protocol under the same conditions, with RNA atoms fixed. Five 1 picosecond (ps) intervals were used with set temperatures of 5, 4, 3, 2, and 1 K. The SHAKE algorithm was applied to all H containing bonds. Finally, 100 steps of Powell minimization were performed with RNA atoms fixed.

Dynamics

Primary simulation

Constant volume and temperature (NVT) molecular dynamics was performed using SANDER (AMBER 5.0) with a time step of 2 fs. The Berendsen algorithm for temperature scaling [63] was used. Electrostatics were evaluated with a constant dielectric of 1.0 using PME. SHAKE was applied to all hydrogen-containing bonds. The van der Waals cutoff was 9 Å. Distance constraints were applied to the three hydrogen bonds (G-NH2:C-O2, G-NH:C-N3, and G-O6:C-NH2) at each of the terminal GC pairs (G1:C16 and G8:C9) with an equilibrium distance of 1.9 Å and a force constant of 10 kcal/mol.

The water molecules were first allowed to relax in a 5-ps run at 298 K with the RNA and sodium atoms fixed and with a temperature-scaling time constant of 0.40 ps. The sodium atoms were then included in the simulation for successive 1-ps runs at 100, 200, and 300 K, with the same temperature scaling time constant.

Finally, all atoms were included in a series of 1-ps runs at 50, 100, 150, 200, and 250 K and a 5-ps run at 298 K with a temperature scaling time constant of 0.20 ps. Atom velocities were re-generated at each different temperature. The data generation run was for 300 ps at 298 K, with a 0.2 ps temperature scaling time constant and data collected every 25 steps (50 fs).

Negative control simulation

NVT molecular dynamics runs (500 ps) were performed in Sybyl 6.1a (for (rGGCGAGCC)2) and Sybyl 6.22 (for (rGCGGACGC)2). The runs consisted of nine 500 fs warming periods at 5, 33, 67, 100, 133, 167, 200, 233, and 267 K, followed by 495.5 ps at 300 K. The initial velocity distribution was Boltzmann for the first period, whereas the previous velocity distribution was carried over for subsequent periods. Integration step size was 1 femtosecond (fs), conformational snapshots were taken every 25 fs, and the temperature coupling constant was 100 fs. The SHAKE algorithm was applied to all H-containing bonds. The force field was that of AMBER 4.1 with a distance dependent dielectric constant of 1, a non-bonded cutoff of 8 Å, and periodic boundary conditions.

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Beckman, R.A., Moreland, D., Louise-May, S. et al. RNA unrestrained molecular dynamics ensemble improves agreement with experimental NMR data compared to single static structure: a test case. J Comput Aided Mol Des 20, 263–279 (2006). https://doi.org/10.1007/s10822-006-9049-z

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  • DOI: https://doi.org/10.1007/s10822-006-9049-z

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