Chromosomal dynamics

predicted by an elastic network model

explains genome-wide accessibility and long-range couplings

1

Bahar Lab

She (John) Zhang

Kingsford Lab

Natalie Sauerwald

She Zhang

Gaussian Network Model GNM

Collective motions

Eigenvalue decomposition of Kirchhoff/Laplacianmatrix

Bahar et al. (2010) Global Dynamics of Proteins: Bridging Between Structure and Function Annu Rev Biophys 39: 23-42

Based on theory of elasticity for polymer networks by Flory, 1976

GNM: Bahar et al Fold & Des 1996; Haliloglu et al. Phys Rev Lett1997 ANM: Doruker et al. Proteins 2000; Atilgan et al, Biophys J 2001

L1tRNA translocation

L7/L12

Wang et al JSB (2004)

Contact map (M) determined by

experiments (n × n)Mi,j = # reads mapped to locus i and j= # interactions between locus i and j

Loci (50kb)

Loci

(50

kb)

Chromosome 17

Reference genome

Locus i Locus j

Chromosome Conformation Capture (e.g. Hi-C)

Rao, S. S., … Aiden, E. L. (2014). A 3D map of the human genome at kilobase resolution reveals principles of chromatin looping. Cell, 159(7), 1665–1680.

Zhang and Wolynes(2015)

Umbarger et al. (2011)

Dixon et al. (2012)

Carl’s Lab: Filippova et al. (2014)

Loci (50kb)

Loci

(50

kb)

Chromosome 17

Chromosome Conformation Capture (e.g. Hi-C)

Eigen decomposition

Loci

Diagonal

Eigenvectors and eigenvalues

…

Squ

are

flu

ctu

atio

ns

Method Pipeline

6

Chromosome 17

Locus Index (5kb)

Mob

ility

/Acc

essib

ility

ChromosomesC

orre

lati

ons

with

exp

erim

entsOpen regions can be

accessed by enzymes

Open Chromatin(High Mobility)

Buenrostro JD et al. (2013) Transposition of native chromatin for fast and sensitive epigenomic profiling of open chromatin, DNA-binding proteins and nucleosome position. Nat Methods 10(12):1213-+.

Square fluctuations vs chromatin accessibility

7Covariance

Freq

uen

cy

ChIA-PET

Background

Locus Index (5kb)

ChIA-PET

Background Background

Chromatin Interaction Analysis by Paired-End Tag Sequencing

“Long range” (~100 kBp)

interactions identified by

ChIA-PET were found to

show higher covariance in

their movement calculated

by GNM than the

background pairs.

Dynamical coupling consistent with ChIA-PET measurements

8

Locus Index (5kb)

GNM Domains

Cross-Correlated Distal Domains (CCDDs)

Hinge sites

Rigid PartsMode 1:

Collective GNM domains can be identified by combining hinge sites from different modes

Structural Domains Identified by GNM modes

GNM domains agree with Lieberman-Aiden compartments. The loci-correlation matrix is computed by Lieberman-Aiden et al. Red and bluerepresents positive and negative correlations respectively. White lines denotes the GNM domains.

GNM Domain

Lieberman-Aiden E, et al. (2009) Comprehensive Mapping of Long-Range Interactions Reveals Folding Principles of the Human Genome. Science 326(5950):289-293.

Structural Domains Identified by GNM modes

10

0-25M bp 25-50M bp

50-75M bp 75-100M bp

Pearson expression correlation

No

rma

lize

d g

ene

pa

ir c

ou

nts

Genes located in the high value region of the covariance matrix arefound to be co-expressed. Yellow: expression correlations of dynamicallycoupled gene-pairs identified by GNM. Blue: those of background gene-pairs.

Distal domains with strong cross-correlations are co-expressed