PAR–FUS

Coarse-grained molecular dynamics code and analysis scripts for studying how poly(ADP-ribose) (PAR) modulates the liquid–liquid phase separation (LLPS) and self-association of the RNA-binding protein FUS (Fused in Sarcoma).

This repository contains everything needed to (1) build the coarse-grained models, (2) run the phase-separation and binding-affinity simulations, and (3) reproduce the analyses and figures.

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1. Overview

FUS is an intrinsically disordered, phase-separating protein central to stress granule biology and ALS. We use a residue-level coarse-grained model to address two quantitative questions:

1. Phase behavior — How does PAR change the propensity of FUS to phase separate? We measure this via the critical temperature (Tc) of a simulated protein/PAR slab, comparing systems with and without PAR.
2. Molecular interactions — Which domain–domain contacts drive self-association, and how strong are they? We compute potentials of mean force (PMFs) and binding affinities for pairs of FUS regions (e.g. PrLD–PrLD, PrLD–CTRR) using umbrella sampling.

Model summary

• Chain topology & disordered regions: each residue is a single bead connected by harmonic bonds.
• Nonbonded interactions: the HPS (hydrophobicity scale) model — a modified Lennard-Jones potential scaled by per-residue hydrophobicity (λ), plus Debye–Hückel electrostatics.
• Folded domains: the RRM (residues 284–367) and zinc finger / ZnF (residues 421–451) are held near their AlphaFold structures with structure-based Gō potentials (bonds, angles, native contacts).
• PAR is modeled as a linear charged polymer (a dedicated PAR bead type with its own mass, charge, σ, λ), 16 beads per chain in the LLPS runs.

Simulations use OpenMM with a Langevin integrator and are run on GPUs via SLURM job arrays.

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2. Repository layout

PAR-FUS/
├── data/                  # Model inputs and force-field parameters
│   ├── seq.toml           # Sequences: FUS + domains (PrLD, RGG3PY, ZnF, CTRR)
│   ├── residues.csv       # Per-residue properties and multiple λ scales
│   ├── params_hps_M1.csv  # HPS force-field parameters used in this work (incl. PAR)
│   ├── FUS_AlphaFold.pdb  # Reference full-length structure
│   ├── RRM/               # RRM domain: AlphaFold structure + Gō-model params/scripts
│   └── ZnF/               # ZnF domain: AlphaFold structure + Gō-model params/scripts
│
├── LLPS/                  # Phase-separation (slab) simulations
│   ├── WT/script/
│   │   ├── functions.py           # Builds the OpenMM System (HPS + elec + Gō + PAR)
│   │   └── llps_equilibration.py  # NPT equilibration of the protein/PAR slab
│   └── script/
│       ├── llps_production.py     # Production runs over a T ladder (380–470 K)
│       ├── utils.py, center.py, contacts.py, density.py, ...  # helpers
│       └── plot_*.py              # Figure generation
│
├── Kd/                    # Binding free-energy / dissociation-constant calculations
│   ├── PrLD-PrLD/script/
│   └── PrLD-CTRR/script/
│       ├── umbrella_sampling.py   # Umbrella windows along COM distance (0–20 nm, 61 windows)
│       ├── analysis_sampling.py   # MBAR reweighting → PMF (uses FastMBAR)
│       └── plot_pmf.py            # PMF comparison figures
│
└── analysis-scripts/      # Post-processing and figure generation
    ├── compute-Tc-density-chunks.py / plot-Tc-errorbar.py  # Critical temperature
    ├── compute-FUS-contacts.py     / plot-FUS-contacts.py  # FUS–FUS contact maps
    ├── compute-FUS-PAR-contacts.py / plot-FUS-PAR-contacts.py
    ├── compute-FUS-Rg.py           / plot-FUS-Rg.py        # Radius of gyration
    ├── compute-FUS-CTRR-dist.py    / plot-FUS-CTRR-dist.py
    ├── center-snapshot-traj.py, make-snapshot-pdb.py       # Snapshots / visualization
    └── arial/             # Fonts bundled for consistent figure typography