A Lamin-Associated Chromatin Model for Chromosome Organization

Abstract

We propose a simple model for chromatin organization based on the interaction of the chromatin fibers with lamin proteins along the nuclear membrane. Lamin proteins are known to be a major factor that influences chromatin organization and hence gene expression in the cells. We provide a quantitative understanding of lamin-associated chromatin organization in a crowded macromolecular environment by systematically varying the heteropolymer segment distribution and the strength of the lamin-chromatin attractive interaction. Our minimal polymer model reproduces the formation of lamin-associated-domains and provides an in silico tool for quantifying domain length distributions for different distributions of heteropolymer segments. We show that a Gaussian distribution of heteropolymer segments, coupled with strong lamin-chromatin interactions, can qualitatively reproduce observed length distributions of lamin-associated-domains. Further, lamin-mediated interaction can enhance the formation of chromosome territories as well as the organization of chromatin into tightly packed heterochromatin and the loosely packed gene-rich euchromatin regions.

Figure 1

A schematic representation of a bead-spring polymer model with type-A and type-B beads confined within a sphere (see text). To see this figure in color, go online.

Figure 2

(a) Mean-square-distance $\langle R^2\left(s\right)\rangle$ as a function of the separation s for different binding energies and different volume fractions. (b) The contact probability (p_c(s)) as a function of the separation s for different binding energies and different volume fractions. (c) The volume fraction within spherical shells as a function of the normalized radial distance is shown. (d) The (normalized) number of monomers within a spherical shell as a function of the normalized radial distance is shown. To see this figure in color, go online.

Figure 3

Lamin proximity indices for R = 12 and binding energies (a) E_B = 0 k_BT and (b) E_B = 1 k_BT. Shown are the proximity indices for R = 7 and binding energies (d) E_B = 1 k_BT and (e) E_B = 5 k_BT. (c) and (f) Shown are domain size distributions for different binding energies for R = 12 and R = 7, respectively. To see this figure in color, go online.

Figure 4

(a)The mean-square displacement exponent ν as a function of E_B for a different fraction of binding monomers f. (b) Shown is the contact probability exponent β as a function of E_B for different f. (c) Plots of the radial volume fraction are shown. All results are shown for the random heteropolymer model in a spherical cavity of R = 7. To see this figure in color, go online.

Figure 5

LPI for E_B = 3 k_BT for a sphere with R = 7 for the three heteropolymer models: (a) random heteropolymer, (d) uniform block copolymer, and (g) Gaussian block copolymer. The red lines indicate type-B monomers that are in proximity to the NL, whereas green lines indicate bond-forming type-A monomers. The corresponding distributions of domain sizes is shown for R = 7 in (b, e, and h) and for R = 12 in (c, f, and i). To see this figure in color, go online.

Figure 6

(a) Contact maps and (c) sample configuration for a system of four polymers, none of which interact with lamin proteins. (b) Shown are contact maps and (d) sample configuration for a system of four polymers of which two interact with lamin proteins, whereas the other two do not. To see this figure in color, go online.