Modeling the functions of condensin in chromosome shaping and segregation

<div><p>The mechanistic details underlying the assembly of rod-shaped chromosomes during mitosis and how they segregate from each other to act as individually mobile units remain largely unknown. Here, we construct a coarse-grained physical model of chromosomal DNA and condensins, a class of large protein complexes that plays key roles in these processes. We assume that condensins have two molecular activities: consecutive loop formation in DNA and inter-condensin attractions. Our simulation demonstrates that both of these activities and their balancing acts are essential for the efficient shaping and segregation of mitotic chromosomes. Our results also demonstrate that the shaping and segregation processes are strongly correlated, implying their mechanistic coupling during mitotic chromosome assembly. Our results highlight the functional importance of inter-condensin attractions in chromosome shaping and segregation.</p></div

Modeling the functions of condensin in chromosome shaping and segregation - Fig 3

<p>(<i>A</i>) Time-course evolution of the asphericity, overlap, and trans-attraction. Configurations of the two chromosomes and distribution of condensins at <i>t</i> = 0.0 (<i>B</i>), 0.2 (<i>C</i>), and 1.0 (<i>D</i>). The blue and green lines represent two different chromosomes. The red and purple points are condensins bound to the blue and green chromosomes, respectively. The corresponding dynamics are shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006152#pcbi.1006152.s005" target="_blank">S1 Movie</a>. Each chromosome has 5000 monomers and 100 loops. (<i>F</i>_cond, Δ, <i>F</i>_loop) = (1.0, 1.0, 1.0).</p

Modeling the functions of condensin in chromosome shaping and segregation - Fig 4

<p>(<i>A</i>) Segregation speed as a function of the strength <i>F</i>_cond and threshold distance Δ of inter-condensin attractions. <i>F</i>_loop = 1.0. (<i>B</i>) Segregation speed as a function of the loop-holding force <i>F</i>_loop under three pairs of different parameters of inter-condensin attractions. (<i>C</i>) Segregation speed and the decay speed of trans-attractions as a function of Δ for <i>F</i>_cond = <i>F</i>_loop = 1.0. (<i>D–G</i>) Example of configurations observed at the end of the simulations at each point of D–G shown in panel <i>A</i>. Each chromosome in all simulations has 5000 monomers and 100 loops.</p

Schematic of the deterministic loop extrusion process.

<p>The blue monomers and connecting springs represent a chromosome chain, and the red particles represent individual condensins. The arrows represent the time direction. The inset shows a series of processes that cross in a loop.</p

Modeling the functions of condensin in chromosome shaping and segregation - Fig 6

<p>Configuration of chromosomes (blue and green lines) and distribution of condensins (red and purple points) at (<i>F</i>_cond, Δ, <i>F</i>_loop) = (1.0, 2.0, 1.0) (<i>A</i>), (1.0, 1.0, 1.0) (<i>B</i>), and (1.0, 2.0, 0.2) (<i>C</i>). (<i>D</i>) Distribution of condensins on the plane perpendicular to the chromosome axis. The distributions are normalized at the origin. The other parameters are fixed to <i>F</i>_cond = <i>F</i>_loop = 1.0.</p

The radius of gyration, <i>R</i>_<i>g</i>, asphericity and overlap at initial configuration with each parameter set.

<p>The radius of gyration, <i>R</i>_<i>g</i>, asphericity and overlap at initial configuration with each parameter set.</p

Correlation between the asphericity and segregation speed for various parameter sets of (<i>F</i>_cond, Δ, <i>F</i>_loop).

<p>The red plus symbols are the results for Δ < 2.5 and the blue crosses are the results for Δ > 2.5 (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006152#pcbi.1006152.s004" target="_blank">S1 Table</a> in supplementary data for sets of detail parameter values).</p

Modeling the functions of condensin in chromosome shaping and segregation - Fig 2

<p>(<i>A</i>) Asphericity as a function of the strength <i>F</i>_cond and the threshold distance Δ of inter-condensin attractions, with . (<i>B</i>) Asphericity as a function of the loop-holding force <i>F</i>_loop under three pairs of different parameters of the attractions. (<i>C</i>) Chromosome monomer density as a function of the distance from condensin at the points <i>D</i> and <i>E</i> shown in panel <i>A</i>. (<i>D–G</i>) Example of the configurations observed at the end of the simulations at each point of <i>D–G</i> shown in panel <i>A</i>. The blue line is the chromosome and the red points are condensins. All simulations are performed employing a single chromosome condition with the number of monomers <i>N</i> = 5000 and the number of loops <i>M</i> = 100.</p

Modeling the functions of condensin in chromosome shaping and segregation - Fig 1

<p>(<i>A</i>) Parts of two different chromosome chains (blue and green). (<i>B</i>) Enlarged view around the the bases of the loops. Condensins (red and purple points) connect the bases of the loops (dashed lines) and attract each other in cis or in trans (dotted lines). The inter-condensin attraction is controlled by two parameters, <i>F</i>_cond and Δ, whereas the looping is controlled by <i>F</i>_loop. (<i>C</i>) Example of initial configurations, where two chromosome chains (blue and green) are intermingled with each other. (<i>D</i>) Part of the initial configuration shown in panel <i>C</i>.</p