DOI: 10.6084/m9.figshare.29063591
title: <b>Liquid-liquid phase separation of lamin drives altered </b><b>chromatin organisation in cardiomyopathic mutations </b><b>of lamin A</b>

description: # Coarse-Grained Chromatin–Lamin Simulation<br>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).<br>---<br>## 🧬 Coarse-Grained Model of Chromatin and Lamins<br>### Chromatin Model<br>- 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)**<br>Classification is based on **H3K9me3 ChIP-seq** enrichment [[Beyer et al., 2016]](https://doi.org/10.1016/j.celrep.2016.06.081).<br>#### HC Fraction Calculation (`f_HC`)- Chromosome segments were binned into **2140 × 5kb** windows.- A bin is HC if ≥ 50% of it is enriched in H3K9me3.- `f_HC` = fraction of HC beads out of 2140.<br>### Random Block Copolymer Control<br>- Segment = block of 20 consecutive beads.- Beads randomly labeled EC or HC based on `f_HC`.<br>### Lamin Model<br>- Lamins are modeled as coarse-grained particles with: - Diameter: `σ_L = σ / 2` - Total count: **2000 lamin particles**<br>---<br>## 🧱 Simulation Box<br>- Dimensions: `20σ × 20σ × 35σ` (x, y, z)- **Periodic** boundary in `x`, `y`; **fixed** boundary in `z` - Simulates confinement near the **nuclear envelope**<br>### Volume Fractions<br>Chromatin:```V_chromatin / V_box = (2140 × 4πσ³/24) / (14000σ³) ≈ 0.08```<br>Lamin:```V_lamin / V_box = (2000 × 4πσ³/192) / (14000σ³) ≈ 0.01```<br>---<br>## ⚙️ Interaction Potentials<br>The **total energy** of the system is:<br>```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|)```<br>### 1. FENE Spring Potential<br>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`<br>### 2. Nonbonded Interactions<br>Depending on the context, either **Lennard-Jones (LJ)** or **WCA** (purely repulsive LJ) potential is used.<br>#### Lennard-Jones (LJ)<br>```U_LJ(r) = 4ε[(σ/r)^12 - (σ/r)^6], r &lt; 1.8σ 0, r ≥ 1.8σ```<br>#### Weeks-Chandler-Andersen (WCA)<br>```U_WCA(r) = 4ε[(σ/r)^12 - (σ/r)^6] + E_cut, r &lt; 1.12σ 0, r ≥ 1.12σ```<br>Where the shift:```E_cut = -4ε[(σ/r_c)^12 - (σ/r_c)^6], r_c = 1.12σ```<br>---<br>## 🧲 Boundary Interactions<br>- `z = +17.5σ` (upper): **Attractive LJ** interaction (nuclear membrane with lamin)- `z = -17.5σ` (lower): **Completely repulsive** for all particles<br>---<br>## 📋 Table of Interaction Parameters<br>| Interaction Type | Potential Used | Notes ||-------------------------|----------------|-------|| Chromatin–Chromatin | LJ / WCA | EC–EC, HC–HC, HC–EC types || Lamin–Lamin | LJ / WCA | Short-range attraction || Chromatin–Lamin | LJ / WCA | HC-specific attractive interaction || Wall (Top)–Lamin | LJ | Simulates membrane || Wall (Bottom)–All | WCA | No penetration |<br>---<br>## 📚 Reference<br>Beyer, T. A., et al. (2016). *Canonical histone marks are predictive of chromatin architecture*. Cell Reports, 17(2), 307-320. https://doi.org/10.1016/j.celrep.2016.06.081<br>