Polymer physics of chromosome large-scale 3D organization
نویسندگان
چکیده
In the String & Binders Switch (SBS) model 1,2 a chromatin filament is represented as a self-avoiding (SAW) polymer chain, composed by N beads. Each bead of the chain interacts with diffusing Brownian particles (binders) having a molar concentration c. The scale of their binding energy to a cognate polymer bead is named í µí°¸!"#. The beads of the chain and the binders are subject to Brownian motion, so each particle of the system (bead or binder) obeys the Langevin equation 3. The friction coefficient of a particle, í µí¼, in the Langevin equation is related to the viscosity of the solvent í µí¼ according to Stokes equation í µí¼ = 6í µí¼í µí¼í µí± , where í µí± is the radius of the particle. For sake of simplicity, in our simulations we set the diameter of polymer beads and of binders equal to σ, and take it as the unit of lengths. In our simulations we also set the mass of beads and binders equal, and use it as the reference mass unit, m=1. We checked that by changing the ratio of the masses our general results remain unchanged, apart from a shift in the time constants of the dynamics. We use the detailed particle interaction potential developed in classical studies of polymer physics simulations 4. The potential energy, V(x), of a particle at a position, x, has three components. Between any two consecutive beads along the polymer chain there is a potential modeling a finitely extensible spring, the FENE potential 4. We set the FENE length constant í µí± ! equal to 1.6σ and K, the strength of the FENE spring, equal to 30k B T/σ 2 (Ref. 4). To account for excluded volume effects between any two particles there is also a purely repulsive, shifted Lennard-Jones (LJ) potential 4 , the so called Weeks-Chandler-Andersen potential, having σ as the length scale unit and ε = k B T as the energy scale unit, in the notation used in Ref. 4. A bead of the polymer interacts with its cognate binders through a short-ranged, attractive Lennard-Jones potential í µí± !"#
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