Osmotic mechanism of the loop extrusion process

The loop extrusion theory assumes that protein factors, such as cohesin rings, act as molecular motors that extrude chromatin loops. However, recent single molecule experiments have shown that cohesin does not show motor activity. To predict the physical mechanism involved in loop extrusion, we here theoretically analyze the dynamics of cohesin rings on a loop, where a cohesin loader is in the middle and unloaders at the ends. Cohesin monomers bind to the loader rather frequently and cohesin dimers bind to this site only occasionally. Our theory predicts that a cohesin dimer extrudes loops by the osmotic pressure of cohesin monomers on the chromatin fiber between the two connected rings. With this mechanism, the frequency of the interactions between chromatin segments depends on the loading and unloading rates of dimers at the corresponding sites.

Figure 1

(a) Chromatin fiber with a loading site for cohesin rings in the middle (magenta) and corresponding unloading sites at the ends (blue). Cohesin rings (green) topologically bind to the fiber as monomers or dimers. The two ends of this fiber stretch feature boundary elements (triangles) beyond which the cohesin rings cannot diffuse. (b) In our model we treat the chromatin fiber as a 1D lattice along which the cohesin monomers and dimers diffuse.

Figure 2

The probability distribution ${\psi }_{\mathrm{d}}\left(z\right)$ of dimers [rescaled by $k_{\mathrm{on}}^{\mathrm{d}}{D}_{\mathrm{c}}/\left(k_{\mathrm{on}}^{\mathrm{m}2}M\right)]$ is shown as a function of the rescaled position $z/M$ for $M{k}_{\mathrm{on}}^{\mathrm{m}}c/D_{\mathrm{c}}=3.4$ (cyan), 150.6 (black), and 1092.0 (magenta). We used $M{k}_{\mathrm{off}}^{\mathrm{d}}/D_{\mathrm{c}}=0.5$ and $M{k}_{\mathrm{off}}^{\mathrm{m}}/D_{\mathrm{c}}=5.0$. The solid and broken curves are derived by using Eq. (5) and Eq. (S12) in the Supplemental Material [8], respectively.

Figure 3

Diagram of states defined by the sign of the factor $\alpha$ [see Eq. (5)] is shown as a function of the rescaled monomer loading rate $k_{\mathrm{on}}^{\mathrm{m}}cM/D_{\mathrm{c}}$ and the rescaled dimer unloading rate $k_{\mathrm{off}}^{\mathrm{d}}M/D_{\mathrm{c}}$. The boundary is shown for the values of the rescaled monomer unloading rate $k_{\mathrm{off}}^{\mathrm{m}}M/D_{\mathrm{c}}=0.5$ (blue), 1.0 (black), and 2.0 (magenta).