Longer Is Not Always Better: Effects of Equilibration Length on Umbrella Sampling Estimations for RNA Hairpin Folding Stabilities

## Summary

This repository contains molecular dynamics (MD) trajectories from umbrella sampling simulations of four RNA hairpins with the following sequences:

* GCG GUGAAA UGC
* GGC CUGGGA GCC
* GGC GUAAUA GCC
* GCG UUAAUU CGC

The corresponding six-nucleotide loop sequences are GUGAAA, CUGGGA, GUAAUA, and UUAAUU, respectively.

The simulations were performed to investigate the effect of umbrella-window equilibration length on estimates of the relative folding stabilities of RNA hairpins. Each system was simulated using two equilibration protocols: 2 ns and 100 ns of equilibration per umbrella window, followed by 600 ns of production sampling per window.

For each hairpin and equilibration protocol, four independent replicates were simulated. The reaction coordinate was defined as the distance between the 5′- and 3′-terminal hydroxyl oxygen atoms. A total of 31 umbrella sampling windows, spanning reaction-coordinate values from 15 Å to 45 Å at 1 Å intervals, were used.

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## File Format

Production trajectories are provided as multi-frame PDB files generated using AMBER `cpptraj`. Water molecules and ions were removed from the deposited trajectories.

Individual trajectory files are compressed as `.tar.gz` archives and grouped according to hairpin loop sequence and equilibration protocol.

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## Dataset Organization

The dataset is organized into eight top-level `.tar.gz` archives, corresponding to the four RNA hairpins and two equilibration protocols:

GUGAAA-2ns.tar.gz
GUGAAA-100ns.tar.gz

CUGGGA-2ns.tar.gz
CUGGGA-100ns.tar.gz

GUAAUA-2ns.tar.gz
GUAAUA-100ns.tar.gz

UUAAUU-2ns.tar.gz
UUAAUU-100ns.tar.gz

Each top-level archive contains the production trajectories for all four independent replicates and 31 umbrella sampling windows for the corresponding hairpin and equilibration protocol, for a total of 124 individual production trajectories per archive.

The complete dataset therefore comprises 992 individual production trajectories:

4 hairpins × 2 equilibration protocols × 4 replicates × 31 windows = 992 trajectories

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## File Naming Convention

Production trajectories corresponding to a given hairpin and equilibration protocol are grouped in archives named:

[loop_sequence]-[equilibration_time].tar.gz

Within each archive, individual trajectories follow the naming convention:

[loop_sequence]-[equilibration_time]-[replicate_id]-[window_id]-imaged.pdb.tar.gz

where:

loop_sequence - six-nucleotide sequence of the corresponding hairpin loop: `GUGAAA`, `CUGGGA`, `GUAAUA`, or `UUAAUU`
equilibration_time - umbrella-window equilibration protocol: `2ns` or `100ns`
replicate_id - independent simulation replicate, numbered `1` through `4`
window_id - umbrella sampling window, numbered `1` through `31`, where the equilibrium position of the restraint in angstrom is window_id+14

### Example

`CUGGGA-2ns-3-10-imaged.pdb.tar.gz`

corresponds to replicate 3 of the CUGGGA hairpin (GGCCUGGGAGCC), using the 2 ns equilibration protocol, for umbrella sampling window 10 (equilibrium position = 24 Å).

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## Simulation Details

Force field: AMBER RNA.OL3
Ionic conditions: 1 M Na⁺
Equilibration protocols: 2 ns or 100 ns per umbrella sampling window
Production sampling: 600 ns per umbrella sampling window
Production sampling per replicate: 18.6 μs
Total production sampling: 595.2 μs
Independent replicates: 4 per hairpin and equilibration protocol
Umbrella sampling windows: 31
Reaction-coordinate range: 15 - 45 Å
Window spacing: 1 Å
Trajectory output frequency: one snapshot every 100 ps
Deposited trajectory format: multi-frame PDB
Water and ions: removed from deposited trajectories
Trajectory processing: AMBER cpptraj