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P h y s i c s o f b i o l o g i c a l s y s t e ms P H 5 4 9 L E C T U R E 1 2 : c h r o ma t i n p a c k i n g mithun@phy.iitb.ac.in Office: Physics 303 D N A t o c h r o mo s

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SLIDE 1

P h y s i c s

  • f

b i

  • l
  • g

i c a l s y s t e ms – P H 5 4 9

L E C T U R E 1 2 :

c h r

  • ma

t i n p a c k i n g

mithun@phy.iitb.ac.in Office: Physics 303

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SLIDE 2

D N A t

  • c

h r

  • mo

s

  • me

s

Interphase Metaphase Human genome: 3.2x109 bp

  • No. of genes: 20K-25K

Diameter of nucleus: 10µm

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SLIDE 3

T h e H i e r a r c h i c a l mo d e l

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SLIDE 4

H I S T O N E S A N D N U C L E O S O ME

DNA per nucleosome: 150 50 200 bp ( + ) ~

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SLIDE 5

B e a d s

  • n

a s t r i n g – 3 n m f i b e r

ν10 nm ∼ 2.200 50 ∼ 8 bp/nm ν30nm ∼ 100bp/nm νmetaphase ∼ 30,000 bp/nm

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SLIDE 6

C H R O MO S O ME T E R R I T O R I E S

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SLIDE 7

C H R O MO S O ME T E R R I T O R I E S

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SLIDE 8

C H R O MO S O ME s a r e d e n s e l y p a c k e d

Y E A S T N U c l e u s

Diameter of yeast nucleus 2 ~ µm Number of chromosomes in yeast 16 = Total genome size 12 Mb 12000000 bp = = What is the density of chromosomes inside the nucleus? ρvivo ∼ 3 Mb/μ m

3

A verage size of yeast chromosome 12Mb / 16 750 kb ~ ~ Length of single chromosome 750kb/ 8bp/nm 94 ~ ( ) ~ µm Persistence length of 10 nm fiber 30 nm ~ What is the RG of this chromosome ? What is the density of the free yeast chromosome? ρvivo ∼ 200 kb/μ m

3

∼ 1μ m

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SLIDE 9

Heng et. al. JCS, 117, 999 (2004)

F I S h E X P E R I ME N T S

Shopland et. al. JCB, 174, 27 (2006)

Fluoroscence in situ hybridization

➢ Confinement ➢ Tethering ➢ Protein Interactions

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SLIDE 10

L A MI N – C H R O MA T I N i n t e r a c t i

  • n

s

Kind & van Steensel, Nucleus, 5, 124 (2014)

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SLIDE 11

D N A L O O P I N G

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SLIDE 12

Sanborn et. al. PNAS 2015

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SLIDE 13

Representations of the structure and conformations of the cohesin ring (not drawn to scale). aSmc proteins contain a nucleotide binding domain (NBD) at their N- and C- terminal ends and a central “hinge” domain. The protein folds back on itself to form 50 nm long rod-shaped antiparallel coiled coils bringing the N- and C-terminal NBDs together to form an ATP-binding cassette. Interactions between the Smc hinge domains close the ring on one interface, while asymmetric interactions between Scc1 and the Smcs close the other two interfaces. Evidence exists to support both a fully

  • pen and partially open ring structure of cohesin.

Barrington et. al. Chrom. Res. 2017

C O H E S I N

  • a

l

  • p

e x t r u s i

  • n

c

  • mp

l e x

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SLIDE 14
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SLIDE 15

C

  • h

e s i n d i f f u s e s

  • n

D N A

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SLIDE 16

C

  • h

e s i n i s t

  • p
  • l
  • g

i c a l l y b

  • u

n d t

  • D

N A

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SLIDE 17

T h e S i z e

  • f

t h e C

  • h

e s i n p

  • r

e

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SLIDE 18

N u c l e

  • s
  • me

s a s b a r r i e r s

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SLIDE 19
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SLIDE 20

D N A mo t

  • r

p r

  • t

e i n s c a n p u s h c

  • h

e s i n

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SLIDE 21

C H R O MO S O ME C O N F O R MA T I O N C A P T U R E 3 C / 5 C / H i

  • C
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SLIDE 22

C

  • n

t a c t p r

  • b

a b i l i t y

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SLIDE 23

C

  • n

t a c t p r

  • b

a b i l i t y

  • 1

D R W

p0 = prob. of loop formation = No. of looped conformations Total no. of conformations p0 = 1 2

N .

N !

(

N 2 )!( N 2 )! Use Stirling's approximation: N ! =( N e )

N

√2π N

⇒ p0 = √ 2 π N

Cyclization probability p0 ∼ N

−1/2 for 1D RW

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SLIDE 24

C

  • n

t a c t p r

  • b

a b i l i t y

  • 1

D R W

The probability distribution for the end-to-end vector R in 1D is: p1 D(R , N) = 1

√2π N a

2 e −R

2/2 N a 2

pc

1 D = ∫ −δ δ

p1 D(R , N)dR ≈ √ 2 π N ( δ a)

Contact probability pc

1 D ∼ N −1/2 for 1D RW

More generally, the contact probability is defined as the probability for the two segments to approach within some small distance δ of each other, δ≪√ Na

2

For contact, we require, -δ R < < δ

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SLIDE 25

C

  • n

t a c t p r

  • b

a b i l i t y

  • 3

D R W

The probability distribution for the end-to-end vector R in 3D is: p3 D(R , N) = ( 3 2π N a

2) 3/2

e

−3 R

2/2 N a 2

pc

3 D = ∫ δ

4 π R

2 p3 D(R , N)dR ≈ (

3 2π N a

2) 3/2 4 πδ 3

3 ≈ √ 6 π N

3(

δ a)

3

Contact probability pc

3 D ∼ N −3/2 for 3D RW

A simple random walk calculation explains Yeast data! What sort of polymer model would reproduce human data?

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SLIDE 26

C

  • n

t a c t p r

  • b

a b i l i t y

Nicodemi et. al. PNAS, 109, 16173 (2012)

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SLIDE 27

C H R O MO S O ME C O N T A C T MA P S

Chromosome 20 Chromosome 14

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SLIDE 28

C H R O MO S O ME C O N T A C T MA P S

Wang et. al. PloS One, 8, e58793 (2013)

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SLIDE 29

C H R O MO S O ME C O N T A C T MA P S

Neva C. Durand*, James T. Robinson*, Muhammad S. Shamim, Ido Machol, Jill P. Mesirov, Eric S. Lander, and Erez Lieberman Aiden. "Juicebox provides a visualization system for Hi-C contact maps with unlimited zoom." Cell Systems 3(1), 2016.

http://www.aidenlab.org/juicebox/