Coarse-Grained Chromatin–Lamin Simulation

This repository describes the setup and simulation details for a coarse-grained model of chromatin and lamin interactions, inspired by experimental data from the mouse C2C12 cell line (GRCm38/mm10).

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🧬 Coarse-Grained Model of Chromatin and Lamins

Chromatin Model

• A 10.7 Mbp region of mouse chromosome 18 was modeled.
• Chromatin is represented as a heteropolymer chain with:
  • 2140 beads
  • Each bead corresponds to 5 kbp of DNA (~25 nucleosomes)
  • Bead diameter: σ
  • Beads are classified as:
    • Euchromatin (EC)
    • Heterochromatin (HC)

Bead classification is based on H3K9me3 ChIP-seq enrichment.

Lamin Model

• Lamins are modeled as coarse-grained particles with:
  • Diameter: σ_L = σ / 2
  • Total count: 2000 lamin particles

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🧱 Simulation Box

• Dimensions: 20σ × 20σ × 35σ (x, y, z)
• Periodic boundary in x, y; fixed boundary in z
  • Simulates confinement near the nuclear envelope

Volume Fractions

Chromatin:

V_chromatin / V_box = (2140 × 4πσ³/24) / (14000σ³) ≈ 0.08

Lamin:

V_lamin / V_box = (2000 × 4πσ³/192) / (14000σ³) ≈ 0.01

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⚙️ Interaction Potentials

The total energy of the system is:

U = Σ_{i=1}^{N-1} U_spring(|r_{i+1}-r_i|) + Σ_{i=1}^{N-1} Σ_{j=i+1}^{N} U_pair(|r_j - r_i|)

1. FENE Spring Potential

Used for polymer backbone connectivity:

U_spring(r) = -½ k R₀² ln[1 - (r / R₀)²]

• k = 30 k_B T / σ²
• R₀ = 1.6σ

2. Nonbonded Interactions

Depending on the context, either Lennard-Jones (LJ) or WCA (purely repulsive LJ) potential is used.

Lennard-Jones (LJ)

U_LJ(r) =
  4ε[(σ/r)^12 - (σ/r)^6],   r < 1.8σ
  0,                       r ≥ 1.8σ

Weeks-Chandler-Andersen (WCA)

U_WCA(r) =
  4ε[(σ/r)^12 - (σ/r)^6] + E_cut,   r < 1.12σ
  0,                               r ≥ 1.12σ

Where the shift:

E_cut = -4ε[(σ/r_c)^12 - (σ/r_c)^6],  r_c = 1.12σ

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🧲 Boundary Interactions

• z = +17.5σ (upper): Attractive LJ interaction (nuclear membrane with lamin)
• z = -17.5σ (lower): Completely repulsive for all particles

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📋 Table of Interaction Parameters

Interaction Type	Potential Used	Notes
Chromatin–Chromatin	LJ / WCA	EC–EC, HC–HC, HC–EC types
Lamin–Lamin	LJ
Chromatin–Lamin	LJ / WCA	HC-Lamin attractive interaction
Wall (Top)–Lamin	LJ / WCA	Simulates membrane
Wall (Bottom)–All	WCA	No penetration

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📚 Reference

Cardiomyopathic mutations of lamin A perturb mutual interactions of lamin, nuclear membrane, and chromatin leading to LLPS Subhradip Nath, Shuvadip Dutta, Shreyasi Dey Sarkar, Duhita Sengupta, Mithun K. Mitra, Kaushik Sengupta bioRxiv 2024.10.07.616979; doi: https://doi.org/10.1101/2024.10.07.616979

License

This repository is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).