Hydrogen-5

Initial helical conformations were defined as all amino acids having (φ, ψ)=(−60°, −40°). Initial extended conformations were defined as all (φ, ψ)=(180°, 180°). Native conformations, as appropriate, were defined for each system as below. Explicit solvation was achieved with truncated octahedra of TIP3P water¹⁶ with a minimum 8.0 Å buffer between solute atoms and box boundary. All structures were built via the LEaP module of Ambertools. Except where otherwise indicated, equilibration was performed with a weak-coupling (Berendsen) thermostat³³ and barostat targeted to 1 bar with isotropic position scaling as follows. With 100 kcal mol⁻¹ Å⁻² positional restraints on protein heavy atoms, structures were minimized for up to 10000 cycles and then heated at constant volume from 100 K to 300 K over 100 ps, followed by another 100 ps at 300 K. The pressure was equilibrated for 100 ps and then 250 ps with time constants of 100 fs and then 500 fs on coupling of pressure and temperature to 1 bar and 300 K, and 100 kcal mol⁻¹ Å⁻² and then 10 kcal mol⁻¹ Å⁻² Cartesian positional restraints on protein heavy atoms. The system was again minimized, with 10 kcal mol⁻¹ Å⁻² force constant Cartesian restraints on only the protein main chain N, C_α, and C for up to 10000 cycles. Three 100 ps simulations with temperature and pressure time constants of 500 fs were performed, with backbone restraints of 10 kcal mol⁻¹ Å⁻², 1 kcal mol⁻¹ Å⁻², and then 0.1 kcal mol⁻¹ Å⁻². Finally, the system was simulated unrestrained with pressure and temperature time constants of 1 ps for 500 ps with a 2 fs time step, removing center-of-mass translation and rotation every picosecond.
SHAKE³⁴ was performed on all bonds including hydrogen with the AMBER default tolerance of 10⁻⁵ Å for NVT and 10⁻⁶ Å for NVE. Non-bonded interactions were calculated directly up to 8 Å. Beyond 8 Å, electrostatic interactions were treated with cubic spline switching and the particle-mesh Ewald approximation³⁵ in explicit solvent, with direct sum tolerances of 10⁻⁵ for NVT or 10⁻⁶ for NVE. A continuum model correction for energy and pressure was applied to long-range van der Waals interactions. The production timesteps were 2 fs for NVT and 1 fs for NVE.

Four canonical 44 (link)–47 (link) and nine non-canonical RNA structures
48 (link)–56 (link) obtained from the protein databank and one
computationally-modeled canonical RNA structure 57 (link) were considered for the force field assessment (Table 1). MD simulations and analysis were done
using the CHARMM58 (link) or NAMD59 (link) programs using the published CHARMM27 all-atom
additive nucleic acid force field parameters25 ,26 with subsequent
revisions associated with changes the 2′-hydroxyl parameters as part of
the present work (Table SI1 of
the supporting information). After the addition of missing hydrogen
atoms to the crystallographic coordinates using the Hbuild 60 (link) facility in CHARMM, the RNAs were immersed in a
pre-equilibrated truncated octahedron shaped water box (1MSY, 1UUU, and 1Y26) or
a cubic shaped water box (all additional RNA molecules). The length of each box
was extended approximately 9 Å beyond all dimensions defined by the RNA
non-hydrogen atoms. Overlapping water molecules with their oxygen atoms within
1.9 Å of the non-hydrogen RNA atoms were deleted. Sodium ions or
potassium ions (Tables SI2 and
SI3 of the supporting information) were randomly placed in the water
box to make the system electrically neutral except in the riboswitch (1Y26),
where Mg²⁺ ions were used in addition to the
Mg²⁺ ions identified in the crystal structure. The
resultant configurations for each of the RNAs in solution were used as the
initial structures for further minimizations and MD simulations.
For the minimizations and MD simulations, the CRYSTAL utility in CHARMM
was used to implement periodic boundary conditions, and the particle mesh Ewald
summation method 61 (link),62 was used for the calculation of electrostatic
interactions. Lennard-Jones (LJ) interactions were truncated at 12 Å,
with a force switch smoothing function from 8 to 12 Å. The non-bonded
interaction lists were updated heuristically, and similar to LJ interactions,
the real space electrostatic interactions were also truncated at 12 Å.
Other than the SHAKE algorithm 63 that
was employed to constrain all the covalent bonds involving hydrogen atoms, the
production simulations did not involve any other constraints or restraints.
Initially, the systems underwent a 500-step adopted basis Newton-Raphson
minimization followed by a 200 ps MD simulation in the NPT ensemble with mass
weighted restraints with force constant 5 kcal/mol/Ų on all
RNA non-hydrogen atoms. This enabled the equilibration of the solvent molecules
and ions around the RNAs, filling any voids created by deleting the water
molecules. The resultant structures were used as the initial structures for the
production MD simulations.
Overall, 50 ns of production simulation, unless noted, was performed on
each system in the NPT ensemble employing the Leapfrog integrator for CHARMM
simulations and MTS algorithm integrator for NAMD simulations. All the
simulations used an integration time step of 2 fs and coordinates were saved
every 2 ps for analysis. The Langevin piston algorithm64 was used for maintaining the pressure at 1 atm and
Hoover chains were employed to maintain the temperature at 298 K. On 1Y26, the
presented results from CHARMM27 are from a previously reported simulation of 40
ns where the frequency of saving the coordinates was 5 ps 23 (link). The double-stranded 18-mer RNA (SEQ4 from
Faustino et. al.57 (link)) was simulated in the NVE ensemble
using CHARMM with the CHARMM27 and CHARMM27d parameter sets using spherical
force-shift cutoff scheme with a 12 Å cutoff 65 –67 ,
and with PME in a rhombic dodecahedron (58.8 Å distance across)
containing 34 Na⁺ and 4481 TIP3P water molecules. Nonbonded
interactions were evaluated using fast lookup tables. 68 (link) For parameter set CHARMM27d, four independent
simulations were performed, two with (50 ns) and two without (100 ns) PME (Table SI3 of the supporting
information).