Figure 2.
Quantifying bridging-mediated chromosome compaction. (A) Schematic showing the definition of gyration radius, Rg, and acylindricity, Ac. (B) Analysis of bridging-induced folding of mitotic chromosomes with fixed loop size. The time t = 0 corresponds to the instant at which condensin bridge binding is switched on. (i and ii) Temporal evolution of the gyration radius for simulations with fixed topoisomerase II activity strength A and variable loop size Lloop (panel i) and for simulations with fixed loop size and variable topoisomerase activity (panel ii). The values of A and Lloop are indicated in the figure. (iii and iv) Time evolution of the acylindricity for simulations with fixed A and variable Lloop (panel iii) and for simulations with fixed Lloop and variable A (panel iv). The decrease in loop length or increase in topoisomerase activity results in the acylindricity curves getting closer to zero, which indicates a more cylindrical shape. (v) Schematics of the coarse-graining procedure used to compute the tangent–tangent correlation of the chromatin fiber backbone. (vi) Resulting plots for a BBP and a SAC configuration (Lloop = 80 kbp, A = 10 kBT). The x axis measures the distance along the backbone. Curves correspond to coarse-graining the backbones (as shown in the schematics in panel v) such that either 1 bead in 5 or 1 bead in 10 is considered (“5 loops” and “10 loops” curves). The coarse-graining does not much affect the results for BBP configurations, where the backbone is sufficiently smooth, but it has an effect for SAC configurations, as the backbone is locally crumpled in places—here coarse-graining is necessary to get a better estimate of the large-scale backbone bending. The negative dip for BBP structures is statistically significant (a two-sided Student test to see whether the minimum can be compatible with 0 returns a P value 0.002). The insets show snapshots of a BBP structure (left) and of a SAC structure (right). (C) Analysis of bridging-induced folding for mitotic chromosomes with variable size of condensin loops. Again, t = 0 corresponds to the instant when condesin bridge binding is switched on. (i and ii) Temporal evolution of the gyration radius for simulations with fixed topoisomerase II activity A (panel i) and for simulations with fixed loop size Lloop (panel ii). (iii and iv) Temporal evolution of the acylindricity for simulations with fixed A (panel iii) and fixed Lloop (panel iv). (v and vi) Experimental (panel v) and simulated (panel vi) contact probability between pairs of beads along the chromatin fiber versus genomic separation. Experimental curves refer to two different HeLa S3 mitotic chromosomes and are adapted from Naumova et al. (2013). The two simulation curves correspond to (Lloop, A) = (80 kbp, 1 kBT) (purple curve) and to (Lloop, A) = (80 kbp, 10 kBT) (blue curve). Once a couple of parameters (Lloop, A) was fixed, all simulation curves in panels B and C were obtained by averaging over 10 independent simulations.

Quantifying bridging-mediated chromosome compaction. (A) Schematic showing the definition of gyration radius, Rg, and acylindricity, Ac. (B) Analysis of bridging-induced folding of mitotic chromosomes with fixed loop size. The time t = 0 corresponds to the instant at which condensin bridge binding is switched on. (i and ii) Temporal evolution of the gyration radius for simulations with fixed topoisomerase II activity strength A and variable loop size Lloop (panel i) and for simulations with fixed loop size and variable topoisomerase activity (panel ii). The values of A and Lloop are indicated in the figure. (iii and iv) Time evolution of the acylindricity for simulations with fixed A and variable Lloop (panel iii) and for simulations with fixed Lloop and variable A (panel iv). The decrease in loop length or increase in topoisomerase activity results in the acylindricity curves getting closer to zero, which indicates a more cylindrical shape. (v) Schematics of the coarse-graining procedure used to compute the tangent–tangent correlation of the chromatin fiber backbone. (vi) Resulting plots for a BBP and a SAC configuration (Lloop = 80 kbp, A = 10 kBT). The x axis measures the distance along the backbone. Curves correspond to coarse-graining the backbones (as shown in the schematics in panel v) such that either 1 bead in 5 or 1 bead in 10 is considered (“5 loops” and “10 loops” curves). The coarse-graining does not much affect the results for BBP configurations, where the backbone is sufficiently smooth, but it has an effect for SAC configurations, as the backbone is locally crumpled in places—here coarse-graining is necessary to get a better estimate of the large-scale backbone bending. The negative dip for BBP structures is statistically significant (a two-sided Student test to see whether the minimum can be compatible with 0 returns a P value 0.002). The insets show snapshots of a BBP structure (left) and of a SAC structure (right). (C) Analysis of bridging-induced folding for mitotic chromosomes with variable size of condensin loops. Again, t = 0 corresponds to the instant when condesin bridge binding is switched on. (i and ii) Temporal evolution of the gyration radius for simulations with fixed topoisomerase II activity A (panel i) and for simulations with fixed loop size Lloop (panel ii). (iii and iv) Temporal evolution of the acylindricity for simulations with fixed A (panel iii) and fixed Lloop (panel iv). (v and vi) Experimental (panel v) and simulated (panel vi) contact probability between pairs of beads along the chromatin fiber versus genomic separation. Experimental curves refer to two different HeLa S3 mitotic chromosomes and are adapted from Naumova et al. (2013). The two simulation curves correspond to (Lloop, A) = (80 kbp, 1 kBT) (purple curve) and to (Lloop, A) = (80 kbp, 10 kBT) (blue curve). Once a couple of parameters (Lloop, A) was fixed, all simulation curves in panels B and C were obtained by averaging over 10 independent simulations.

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