P h y s i c s o f b i o l o g i c a l s y s t - PowerPoint PPT Presentation

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 o me s Human genome: 3.2x10 9 bp No. of genes: 20K-25K Diameter of nucleus: 10 µ m Interphase Metaphase

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

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

B e a d s o n a s t r i n g – 3 0 n m f i b e r ν 10 nm ∼ 2 . 200 ∼ 8 bp/nm 50 ν 30 nm ∼ 100bp/nm ν metaphase ∼ 30,000 bp/nm

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

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

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 µ m = Number of chromosomes in yeast 16 = = Total genome size 12 Mb 12000000 bp What is the density of chromosomes inside the nucleus ? ρ vivo ∼ 3 Mb /μ m 3 ~ ~ A verage size of yeast chromosome 12Mb / 16 750 kb ~ ( ) ~ Length of single chromosome 750kb/ 8bp/nm 94 µ m ~ Persistence length of 10 nm fiber 30 nm ? ∼ 1 μ m What is the R G of this chromosome What is the density of the free yeast chromosome ? 3 ρ vivo ∼ 200 kb /μ m

F I S h E X P E R I ME N T S Fluoroscence in situ hybridization Shopland et. al. JCB, 174, 27 (2006) ➢ Confinement ➢ Tethering ➢ Protein Interactions Heng et. al. JCS, 117, 999 (2004)

L A MI N – C H R O MA T I N i n t e r a c t i o n s Kind & van Steensel, Nucleus, 5, 124 (2014)

D N A L O O P I N G

Sanborn et. al. PNAS 2015

C O H E S I N - a l o o p e x t r u s i o n c o mp l e x 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 open and partially open ring structure of cohesin. Barrington et. al. Chrom. Res. 2017

C o h e s i n d i f f u s e s o n D N A

C o h e s i n i s t o p o l o g i c a l l y b o u n d t o D N A

T h e S i z e o f t h e C o h e s i n p o r e

N u c l e o s o me s a s b a r r i e r s

D N A mo t o r p r o t e i n s c a n p u s h c o h e s i n

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

C o n t a c t p r o b a b i l i t y

C o n t a c t p r o b a b i l i t y - 1 D R W p 0 = prob. of loop formation = No. of looped conformations Total no. of conformations N ! 1 p 0 = N . ( 2 ) ! ( 2 ) ! 2 N N Use Stirling's approximation: N ! = ( e ) N N √ 2 π N ⇒ p 0 = √ 2 π N − 1 / 2 for 1D RW Cyclization probability p 0 ∼ N

C o n t a c t p r o b a b i l i t y - 1 D R W 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 The probability distribution for the end-to-end vector R in 1D is: 1 − R 2 / 2 N a 2 p 1 D ( R , N ) = 2 e √ 2 π N a < < δ For contact, we require, - δ R p 1 D ( R , N ) dR ≈ √ δ 1 D = ∫ 2 π N ( a ) δ p c −δ 1 D ∼ N − 1 / 2 for 1D RW Contact probability p c

C o n t a c t p r o 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: p 3 D ( R , N ) = ( 2 ) 3 / 2 3 2 / 2 N a 2 − 3 R e 2 π N a ≈ √ 2 p 3 D ( R , N ) dR ≈ ( 3 / 2 4 πδ 2 ) δ 3 3 D = ∫ 3 6 3 ( a ) 3 δ 4 π R p c 2 π N a π N 3 0 3 D ∼ N − 3 / 2 for 3D RW Contact probability p c A simple random walk calculation explains Yeast data! What sort of polymer model would reproduce human data ?

C o n t a c t p r o b a b i l i t y Nicodemi et. al. PNAS, 109, 16173 (2012)

C H R O MO S O ME C O N T A C T MA P S Chromosome 20 Chromosome 14

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)

C H R O MO S O ME C O N T A C T MA P S http://www.aidenlab.org/juicebox/ 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.