Controlling chromosome segrega0on dynamics by the shapes Yuji Sakai - - PowerPoint PPT Presentation

Controlling chromosome segrega0on dynamics by the shapes

Yuji Sakai (RIKEN iTHES)

Masashi Tachikawa (RIKEN), Atsushi Mochizuki (RIKEN)

cell

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 division

Chromosomes condense by 10,000 0mes in length.

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human chromosomes

Chromosomes conserve the diameters ?

Chromosomes have the similar diameters, despite large differences of the genomic and physical length.

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

• For chromosomes of many species,

the diameters are almost same, while the length is different.

chromosomes of some species

• J. R. Daban, J. R. Soc. Interface 11 (2015)

@MBoC

Yuji Sakai 2/18

Chromosome shapes are related to segrega,on ?

During development, chromosomes decrease the length and increase the diameters, the segrega0on 0me increases along with them. Furthermore, shorter and thicker chromosomes take longer segrega0on 0me.

480

• 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
• bserved frequencies falls between 95% and 97.5% for

blastulae and between 97.5% and 99% for swimming

• larvae. This implies that from blastula to swimming lar-

va all chromosomes shorten by the same ratio. Quantitative analysis of chromosome length values at stages intermediate between blastula and swimming larva (Fig. 2b-d) shows that the average chromosome length (Table 1) decreases from ll.02gm (gastrula), through 9.15 gm (neurula), to 7.96 gm (tail bud). The dispersion of length data is higher than at blastula and swimming larva, ranging from the minimal larval values to the maximal blastular ones. The shape of the histo- grams in Fig. 2b-d appears rather 'stage specific. None shows good fitting to the corresponding reference curve. Though no attempt has been made to quantify the shortening of each specific chromosome, our observa- tions allow us to exclude the idea that shortening of all individual chromosomes occurs gradually in the whole embryo. Length reduction is likely to occur asynchronously in different embryonic cells but simulta- 480

• 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
• bserved frequencies falls between 95% and 97.5% for

blastulae and between 97.5% and 99% for swimming

• larvae. This implies that from blastula to swimming lar-

va all chromosomes shorten by the same ratio. Quantitative analysis of chromosome length values at stages intermediate between blastula and swimming larva (Fig. 2b-d) shows that the average chromosome length (Table 1) decreases from ll.02gm (gastrula), through 9.15 gm (neurula), to 7.96 gm (tail bud). The dispersion of length data is higher than at blastula and swimming larva, ranging from the minimal larval values to the maximal blastular ones. The shape of the histo- grams in Fig. 2b-d appears rather 'stage specific. None shows good fitting to the corresponding reference curve. Though no attempt has been made to quantify the shortening of each specific chromosome, our observa- tions allow us to exclude the idea that shortening of all individual chromosomes occurs gradually in the whole embryo. Length reduction is likely to occur asynchronously in different embryonic cells but simulta-

@ embryo (segrega0on 0me 0.5hrs.) @ soma0c (segrega0on 0me 1-2hrs.)

• G. Micheli, et. al., Chromosoma 1993

Yuji Sakai 3/18

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.

Strategy

D

L

Yuji Sakai 4/18

Chromosome condensa0on is achieved by condensin proteins.

looping gathering

Entanglement of chromosomes is solved by topo-II proteins.

catch chromosome 1 and cut chromosome 2 chromosome 1 pass through chromosome 2 release chromosome 1 and reseal chromosome 2 chromosome 2 chromosome 1 chromosome 1

Biological concept for chromosome condensa,on

condensin

chromosome

Yuji Sakai 5/18

chromosome polymer à rigid beads + phantom springs condensin à loop interac0on

Polymers can pass through springs. So the entanglement can be solved.

Coarse-grained polymer model

topo-II à phantom spring

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Ubeads + Usprings

Uloop

Yuji Sakai 6/18

Loop interac,on makes polymer shapes

The loop interac0on makes a long chain condensed. By changing the loop interac0on, various polymer shapes are obtained.

spherical-shape rod-shape

D

L

D

diameter length

gather loops

Nloop = 10, Cloop = 10

Npole = 2

; beads concentra0on ; polymer diameter ; polymer length

Nloop Npole Cloop

Nbead = 1000 ∼ 5000

Yuji Sakai 7/18

MD simula,on

For each polymers with various shapes, we calculate segrega0on 0mes from overlapping state.

snapshot 0me

• verlap=1.0
• verlap=0.5
• verlap=0.0

ini0al final

Langevin dynamics of beads

We obtain rela0on between shapes and segrega0on dynamics.

mi ˙ ~ vi = ~ Fi − ~ vi + √ T⌘(t)

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Spherical Shape Polymer Segrega0on

• verlap=1
• verlap=0.5
• verlap=0

Time evolu0on

D

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Two step processes for segrega,on

extract two 0me by fifng a linear func0on

• v = 1 − (t − ti)/ts

ti, ts

Yuji Sakai 10/18

0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1

time step (x 103 )

• v

∆rCM

• verlap
• v

CM distance induc0on segrega0on

ts ti

1 2 3 4 10 20 30 40 0.5 1 1.5 2 4 6 8 10 12 14 16 18

Segrega0on 0mes are scaled by the polymer shapes.

induc0on segrega0on

D D/c

D

c

Rela,on of shape to segrega,on

ti ts ti ∼ D3 ts ∼ D/c

Nbead = 500 ∼ 5000

Yuji Sakai 11/18

ts ti

0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1

time step (x 103 )

• v

∆rCM

ts ti

time step (x 103 )

• v

0.5 1 1.5 2 4 6 8 10 12 14 16 18

In the ini0al overlapped stage, beads collide with each other randomly. This is like diffusion process.

mobility strong dependence on the diameter

induc,on

D

ti ∼ D2/µv µv ∼ D−1

0.01 0.1 1 10 0.01 0.1 1 10

time (x 103)

CM distance b/w polymers

∆rCM ∼ t1/2

→ ti ∼ D2/µv ∼ D3

D

ti

∆rCM

t

ts ti

time step (x 103 )

• v

1 2 3 4 10 20 30 40

Driving force of the segrega0on is repulsion between rigid beads. The repulsive force is propor0onal to the beads concentra0on c.

D/c

ac,ve segrega,on

D

vseg

ts ts ∼ D/vseg ∼ D/c vseg ∼ Fseg ∼ c

Rod Shape Polymer Segrega0on

• verlap=0.2
• verlap=0.5
• verlap=1
• verlap=0

Time evolu0on D

L

Yuji Sakai 14/18

Polymer length does not affect on the segrega0on dynamics, while the diameter and the concentra0on affect on the segrega0on.

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1

MD step [K]

c=9.2, D=4.5, α=1 α=2 α=3 α=4 α=5

• verlap

L D

D L

α = L/D

spherical

elonga0on

Elonga,on effect on segrega,on

changing L under fixed D and c The segrega0on occur on the plane perpendicular to the length axis.

Yuji Sakai 15/18

time step (×103)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 3 4 5 6 7 8 0.1 0.2 0.3 0.4 0.5 6 7 8 9

induc0on segrega0on

ti ts ti ∼ D3 ts ∼ D/c

The segrega0on 0mes are on the same func0ons as the spherical shape polymer case.

D D/c

Rela,on of shape to segrega,on

Yuji Sakai 16/18

ts ti

0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1

time step (x 103 )

• v

∆rCM

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.

Yuji Sakai 17/18