Mathematical Model for Structure and Dynamics of Chromatin

An explicit formulation of the configuration-dependent potential energy function and the Brownian Dynamics (BD) algorithm used to simulate the chromatin polymer is detailed. For the readers’ convenience, this document provides a complete description of our methodology, and thus some of the material is redundant with that found in the Material and Methods section of Beard & Schlick (Structure with Folding and Design ??:??–??, 2000). Model Geometry The model structure is illustrated in Figure 1. Each core particle disk is connected to one or two linker DNA segments (see Figure 1, top panel). In Figure 1, denotes the position of the center of a core disk, while , , and , denote positions of linker DNA beads. The orientation of the core disk is specified by a local coordinate system , , where the unit vectors and lie in the plane of the flat surface of the disk, and . The attatchment of the linker DNA to the core particle is illustrated in the lower panel of Figure 1. The linker DNA enters the core particle at the position ! #"%$ & "('*)+$ -,-.0/1 and exits at position 2 3 2 3/1 . The scalar parameters , /1 , and $ are determined by the geometry of the wrapped DNA supercoil. Based on the crystal structure [1], we set the values of these parameters as follows: 547698 nm, /1 ;:<698 nm, $ >=<?#@ (see Table 1). A local coordinate system 2A , A , A is also associated with each linker bead position, A , and is used to calculate the local torsion on the linker beads. We define the sets BDC and BDE to be, respectively, the set of core beads and the set of linker DNA beads. The vectors for FHGIBDE are directed in the direction of the linker DNA segment: