Controlling chromosome segrega0on dynamics by the shapes Yuji Sakai (RIKEN iTHES) Masashi Tachikawa (RIKEN), Atsushi Mochizuki (RIKEN)
Yuji Sakai 1/18 Chromosome Condensa,on in mitosis Before cell division, distributed chromosomes in nucleus take condensed rod-shapes. In the condensa0on, entanglement of chromosomes is solved. cell Chromosomes condense by 10,000 0mes in length. cell division
Yuji Sakai 2/18 Chromosomes conserve the diameters ? Chromosomes have the similar diameters, despite large differences of the genomic and physical length. For chromosomes of many species, ������� the diameters are almost same, while the length is different. ��������������������� chromosomes of some species human chromosomes species D [μm] L [μm] ������ human 0.6 5 - 7 barley 0.9 10 - 14 pine 1.0 14 - 21 T. cristatus 1.1 11 - 36 N. viridescens 1.0 10 - 20 @MBoC J. R. Daban, J. R. Soc. Interface 11 (2015) ��������������������
Yuji Sakai 3/18 Chromosome shapes are related to segrega,on ? During development, chromosomes decrease the length and increase the diameters, 480 the segrega0on 0me increases along with them. Furthermore, shorter and thicker chromosomes take longer segrega0on 0me. @ embryo (segrega0on 0me 0.5hrs.) @ soma0c (segrega0on 0me 1-2hrs.) 480 G. Micheli, et. al., Chromosoma 1993 Fig. 1 a, b. Metaphase plates from Xenopus laevis embryos. Chromosomes were prepared by squashing in the absence of drugs inducing metaphase block, a Blastula, stage 7-9 (Nieuwkoop and Faber 1967); b swimming larva. Bar represents 10 gm for both a and b observed frequencies falls between 95% and 97.5% for swimming larva, ranging from the minimal larval values to the maximal blastular ones. The shape of the histo- blastulae and between 97.5% and 99% for swimming larvae. This implies that from blastula to swimming lar- grams in Fig. 2b-d appears rather 'stage specific. None va all chromosomes shorten by the same ratio. shows good fitting to the corresponding reference curve. Though no attempt has been made to quantify the Quantitative analysis of chromosome length values at stages intermediate between blastula and swimming shortening of each specific chromosome, our observa- larva (Fig. 2b-d) shows that the average chromosome tions allow us to exclude the idea that shortening of length (Table 1) decreases from ll.02gm (gastrula), all individual chromosomes occurs gradually in the whole embryo. Length reduction is likely to occur through 9.15 gm (neurula), to 7.96 gm (tail bud). The dispersion of length data is higher than at blastula and asynchronously in different embryonic cells but simulta- Fig. 1 a, b. Metaphase plates from Xenopus laevis embryos. Chromosomes were prepared by squashing in the absence of drugs inducing metaphase block, a Blastula, stage 7-9 (Nieuwkoop and Faber 1967); b swimming larva. Bar represents 10 gm for both a and b swimming larva, ranging from the minimal larval values observed frequencies falls between 95% and 97.5% for blastulae and between 97.5% and 99% for swimming to the maximal blastular ones. The shape of the histo- larvae. This implies that from blastula to swimming lar- grams in Fig. 2b-d appears rather 'stage specific. None shows good fitting to the corresponding reference curve. va all chromosomes shorten by the same ratio. Quantitative analysis of chromosome length values Though no attempt has been made to quantify the shortening of each specific chromosome, our observa- at stages intermediate between blastula and swimming larva (Fig. 2b-d) shows that the average chromosome tions allow us to exclude the idea that shortening of all individual chromosomes occurs gradually in the length (Table 1) decreases from ll.02gm (gastrula), through 9.15 gm (neurula), to 7.96 gm (tail bud). The whole embryo. Length reduction is likely to occur asynchronously in different embryonic cells but simulta- dispersion of length data is higher than at blastula and
Yuji Sakai 4/18 Strategy We inves0gate rela0on between chromosome shapes and the segrega0on. For this purpose, we use MD Simula0on of a simple coarse-grained polymer model. We calculate segrega0on dynamics of polymers with various shapes. L D
Yuji Sakai 5/18 Biological concept for chromosome condensa,on Chromosome condensa0on is achieved by condensin proteins. looping gathering condensin chromosome Entanglement of chromosomes is solved by topo-II proteins. chromosome 1 chromosome 2 chromosome 1 pass release chromosome 1 catch chromosome 1 through chromosome 2 and reseal chromosome 2 and cut chromosome 2 chromosome 1
Yuji Sakai 6/18 Coarse-grained polymer model chromosome polymer à rigid beads + phantom springs U beads + U springs 4 2 3 1 0 5 condensin à loop interac0on 6 7 topo-II à phantom spring U loop 8 14 11 12 13 9 10 15 23 17 22 19 18 24 16 25 21 20 Polymers can pass through springs. 33 34 26 35 So the entanglement can be solved. 29 32 27 31 36 28 30 38 37 39 43 44 42 40 45 53 54 41 46 55 52 47 51 50 56 49 48 58 59 57 60
Yuji Sakai 7/18 Loop interac,on makes polymer shapes The loop interac0on makes a long chain condensed. By changing the loop interac0on, various polymer shapes are obtained. gather loops ; beads concentra0on N loop C loop ; polymer diameter ; polymer length N pole N pole = 2 rod-shape N loop = 10 , C loop = 10 spherical-shape length L N bead = 1000 ∼ 5000 diameter D D
Yuji Sakai 8/18 MD simula,on For each polymers with various shapes, we calculate segrega0on 0mes from overlapping state. We obtain rela0on between shapes and segrega0on dynamics. Langevin dynamics of beads √ m i ˙ v i = ~ v i + T ⌘ ( t ) ~ F i − �~ snapshot overlap=1.0 overlap=0.5 overlap=0.0 ini0al final 0me
Yuji Sakai 9/18 Spherical Shape Polymer Segrega0on overlap=1 overlap=0.5 overlap=0 D Time evolu0on
Yuji Sakai 10/18 Two step processes for segrega,on 1.4 o v CM distance ∆ r CM 1.2 induc0on extract two 0me t i , t s 1 b y fifng a linear func0on segrega0on 0.8 o v = 1 − ( t − t i ) /t s 0.6 0.4 overlap o v t i t s 0.2 0 0 0.2 0.4 0.6 0.8 1 time step (x 10 3 )
Yuji Sakai 11/18 Rela,on of shape to segrega,on Segrega0on 0mes are scaled by the polymer shapes. 1.4 o v ∆ r CM 1.2 1 0.8 0.6 0.4 D t i t s 0.2 c 0 0 0.2 0.4 0.6 0.8 1 time step (x 10 3 ) N bead = 500 ∼ 5000 2 4 induc0on segrega0on t i t s 1.5 3 t s ∼ D/c t i ∼ D 3 1 2 0.5 1 0 0 4 6 8 10 12 14 16 18 0 10 20 30 40 D/c D
1.4 o v ∆ r CM 1.2 induc,on 1 0.8 0.6 0.4 t i t s 0.2 0 0 0.2 0.4 0.6 0.8 1 time step (x 10 3 ) In the ini0al overlapped stage, beads collide with each other randomly. This is like diffusion process. t i ∼ D 2 /µ v µ v ∼ D − 1 mobility D → t i ∼ D 2 /µ v ∼ D 3 strong dependence on the diameter CM distance b/w polymers 2 t i 10 ∆ r CM 1.5 1 1 0.1 0.5 ∆ r CM ∼ t 1 / 2 D t 0.01 0 0.01 0.1 1 10 4 6 8 10 12 14 16 18 time (x 10 3 )
1.4 o v ∆ r CM 1.2 ac,ve segrega,on 1 0.8 0.6 0.4 t i t s 0.2 0 0 0.2 0.4 0.6 0.8 1 time step (x 10 3 ) Driving force of the segrega0on is repulsion between rigid beads. The repulsive force is propor0onal to the beads concentra0on c . v seg v seg ∼ F seg ∼ c D t s ∼ D/v seg ∼ D/c 4 t s 3 2 1 D/c 0 0 10 20 30 40
Yuji Sakai 14/18 Rod Shape Polymer Segrega0on overlap=1 overlap=0.5 overlap=0.2 overlap=0 L D Time evolu0on
Yuji Sakai 15/18 Elonga,on effect on segrega,on Polymer length does not affect on the segrega0on dynamics, while the diameter and the concentra0on affect on the segrega0on. L changing L under fixed D and c spherical overlap c=9.2, D=4.5, α =1 α =2 1 D α =3 elonga0on α = L/D α =4 α =5 0.8 The segrega0on occur on the plane 0.6 perpendicular to the length axis. 0.4 0.2 L 0 0 0.2 0.4 0.6 0.8 1 D time step ( × 10 3 ) MD step [K]
Yuji Sakai 16/18 Rela,on of shape to segrega,on The segrega0on 0mes are on the same func0ons 1.4 as the spherical shape polymer case. o v ∆ r CM 1.2 1 0.8 0.6 0.4 t i t s 0.2 0 0 0.2 0.4 0.6 0.8 1 time step (x 10 3 ) 0.5 0.7 induc0on segrega0on t i t s 0.6 0.4 0.5 t i ∼ D 3 0.3 0.4 0.3 0.2 t s ∼ D/c 0.2 0.1 0.1 0 0 6 7 8 9 3 4 5 6 7 8 D/c D
Yuji Sakai 17/18 Summary We model the chromosome condensa0on and the segrega0on. We inves0gate rela0on b/w the shapes and the segrega0on dynamics by using the MD simula0on. We show that the segrega0on dynamics can be divided into two steps, the induc0on and the segrega0on. Both the segrega0on 0mes strongly depend on the polymer diameters, but not depend on the length.
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