International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

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Mechanics Inspired Bioinformatics: Predicting the Function of Eukaryotic Scaffold/Matrix Attachment Region (SMAR) by Single Molecule DNA Mechanics International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijin g, China Zhong-can Ou-Yang Institute of Theoretical Physics Chinese Academy of Sciences Beijing 100080, [email protected]

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Mechanics Inspired Bioinformatics: Predicting the Function of Eukaryotic Scaffold/Matrix Attachment Region (SMAR) by Single Molecule DNA Mechanics. International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China Zhong-can Ou-Yang - PowerPoint PPT Presentation

Transcript of International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Page 1: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Mechanics Inspired Bioinformatics: Predicting the Function of Eukaryotic

Scaffold/Matrix Attachment Region (SMAR) by Single Molecule

DNA Mechanics

International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Zhong-can Ou-YangInstitute of Theoretical Physics Chinese Academy of SciencesBeijing 100080, [email protected]

Page 2: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Outline:

I. Stretching single molecule DNA

II. Mechanics-inspired Bioinformatics :An example S/MARs on Eukaryotic Chromosome, predicting the location and function

Page 3: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

In the past decadePhysical techniques such as hydrodynamic drag [4], magnetic beads [5], optical tweezers [6], glass needles [7] and AFM [8,9] offer the opportunity to study DNA/RNA and p

rotein mechanics with single molecules.

[4] J. T. Perkins, D. E. Smith, R. G. Larson, S. Chu, Science 268 (1995) 83-87

[5] S. B. Smith, L. Finzi, C. Bustamantl, Science 258 (1992) 1122-1126

[6] S. B. Smith, Y. Cui, C. Bustmantl, Science 271 (1996) 795-799

[7] P. Cluzel et al., Science 271 (1996) 792-794

[8] M . Rief, H. C.-Schauman, H. E. Gaub, Nat. Struct. Biol. 6 (1999) 346-349

[9] David J. Brockwell et al., Nat. struct. Biol. 10 (2003) 731

I. Stretching single molecule DNA

Page 4: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Stretching double-stranded DNA can be treated as a uniform polymer

Page 5: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Zhou, Zhang, Ou-Yang, PRL, 82, 4560(1999)

Page 6: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

* Two classical models:

** Freely jointed chain (FJC)

, Kuhn segment 2

coth 1

3 for low force

1 for high force

p

B

B

B

L Nb b l

z L fb K T x x x

bf K T

K T fb

L ff L

** Worm-like chain (WLC)

2

0

2

1

2

1 41

4 1

2 3 for low force

L

B p

B

p

p B

E K Tl k ds

K T zf

l Lz L

z L l K T f

As a Hookian spring with Hooke's constant

5

3 2

10 pN nm 10 m

DNA B pK K T l

L

Page 7: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China
Page 8: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Zhou, Zhang, Ou-Yang, PRL, 82, 4560(1999)

Page 9: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

* Introduction of a new structural parameter, the folding angle .

* Without consideration of force-induced melting and nick.

s

• Our Model

2Rb s

LJU

0r

2R

Page 10: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

• Mathematically

* Two backbones ,

* Central axis ,

1r s 2 1 2r s r Rb s

1 21 2r s r r

t dr ds

11

22

cos sin

cos sin

drt t n

dsdr

t t nds

n b t

• Bending energy2 2 2 2

41 220 0

sin2

L L

b

dt dt dt dE ds ds

ds ds ds ds R

* decomposed into the bending energy of central axis plus folding energy

Page 11: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

* Introduction of a new structural parameter, the folding angle .

* Without consideration of force-induced melting and nick.

s

• Our Model

2Rb s

LJU

0r

2R

Page 12: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

16 base-pair stacking potentials

Page 13: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

* The asymmetric Lennard-Jones potential ensures relaxed DNA in B-form, a right-handed double-helix.

*

* is harmonic in low force/extension regimes. (FJC and WLC)

* strongly prevent right-handed overtwist, weakly so for left-handed one and allow a torque-induced B-to-Z-form transition in dsDNA

thermal energy stable dsDNABK T

Biophys. J. 78(2000) 1979-1987

12 60 0

12 6

0 0

0

cos 2cos , 0

cos cos 2 cos cos , 0

62

U

Page 14: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

• The Potential of External Force F

0

0

0

cos

cos

L

L

f

F fz

R t ds

E F R f t z ds

• The Energy of External Torque

0

00

2

sin

1

t

L

E Lk

z t dt dsds

R z t

T

T

Page 15: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

0

,

b LJ f t

L

e

E E E E E

r s ds r t

2

2e

m dr drA r V r

ds ds

• Total Elasticity Energy

f

,t

i

Particle moves in a field A and a potential V if look s as time t

Page 16: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

• Polymer Dynamics and Path Integral Method

* Partition function:

, ; ,0

1 , Green function is

, ; , exp ,

f f f i i i i

B

r s

er s

Z L dr r G r L r r dr

K T

G r s r s r ds r s

D

* “Schrödinger equation”

2 2

, , ; , ,2 2 2

r r rA A Ar s dr G r s r s s s V

s m m m m

* , Bs t K T i

* z F f

lnBF K T Z* Free energy:

Page 17: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

• Extension/Force of 0T

2 24

0* 2 2 2

cossin

4 4P

P P B B

f lt z

s l t l K T K T R

is Hermitian, it is real Schrödinger Eq.

Extension:

00

2

0 0

0

cos

cos

normalized ground-state eigengfunction

Lz t z ds

L t z dtd

* * ,P B P Bl K T l K T

Page 18: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Extension of Torsionally Relaxed DNA

Zhou, Zhang, Ou-Yang, PRL, 82, 4560(1999)

Page 19: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Distribution of Folding of Backbones

2

0 ,P t dt

Page 20: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Above calculationss are interesting for pure theoretical physicists but not for biologists and IT scientists. Both they are interested in the information and function hided in their sequence (AGCT….). The Bioinformatics is based on pure statistic mathematics, our propose is a Mechanic

s-Inspired Bioinformatics.

Page 21: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

4 types of nucleotides: Adenine, Guanine, Thymine, CytosineWatson-Crick base pair: A-T, G-CIntrinsic right-handed helix (torsional state)B-DNA: uniform, sequence-independent

4-letter text:…ATTTTAATGTCATGATAAAGTTACTTCCTTTTTTTTTAAGTTACTTCTATAATATATGTAAATTACTTTTAATCTCTACTGAAATTACTTTTATATATCTAAGAAGTATTTAGTGAAATCTAAAAGTAATTTAGATATAATATAAAAGTAATTTGTATTTTTTTCATCAAAATATAATCATGTGAGACCTTGTTATAAAGATTTAA…

II. Mechanics-inspired Bioinformatics :An example S/MARs on Eukaryotic Chromosome, predicting the location and function

Page 22: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

DNA: ~ centimeters (human cell 2meters)

DNA in lily cell 30 meters. Nucleus: ~ microns compaction ratio: ~1/8000 DNA must undergo

significant mechanical force in the nucleus

The elastic response is vital for DNA

Elasticity Plays the Key Role… !

Page 23: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

compaction ratio: ~ 1/8000 considerable force exerted

on DNA (stretching,

bending and twisting) S/MARs:

topologically independent

domains

basement of chromatin loops S/MAR(Scaffold/Matrix Attachment Region)

Chromosome AssemblyChromatin Loop Model

Page 24: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Chirality Variable bubble

cruciform

H-Bond Broken

Structure Heterogeneity Induced by Mechanical Structure Heterogeneity Induced by Mechanical Force:Force:

Secondary StructuresSecondary Structures

Page 25: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

How to predict SMAR location and function ? it’s difficult in the framework of conventional

bioinformatics methods because there is very little similarity among SMAR sequences, thus

sequence comparison cannot work well.

Page 26: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

S/MARs have been observed to adopt noncanonical DNA structures, bubble configuration (stress-induced unwound elements * )

* Bode J., et al., Science, 1992, 255: 195-197

Standard B-form DNA

Local bubble

Page 27: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

The unwinding stress can induce the formation of local bubbles

Lk=Wr+Tw, writhing number—axis self-linking number, Tw—inter-winding number of two strands

Page 28: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

topological parameters for ds-DNALk : linking number, number of helical turns when DNA is

imposed in planar conformation

Lk0 : linking number of relaxed ds-DNA. Lk0= N/10.5Tw : twisting number, number of helical turns

Wr : writhing number, coiling times of the central axis

(supercoiling). for planar conformation, Wr = 0

σ: superhelical density, defined as (Lk – Lk0)/ Lk0

σ< 0, negative supercoiling ;σ> 0, positive supercoiling

For eukaryotes, σ~ - 0.06σ* Lk0 = Lk – Lk0 = △Tw (r, r’) + △Wr (r)

Page 29: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Can we make the prediction on bubbles (S/MARs) by taking account of the unwinding stress, i.e., the energy correspond

ing toσ (~ -0.06 ) ?

Page 30: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Bubble Formation is Sequence Dependent Benham Model

Bauer WR, Benham CJ., J Mol Biol. 1993, 234(4):1184-96.

2N configurations{…10111111100…}

local bubble

a : initiation energy of bubble formation

jn = 0 … base paried

jn = 1 … base unparied

j : rewinding angle of the denatured region

ATb GCb : base unparing energy

A : 10.5 bp per helical turn of B-DNA

: superhelical densityσ

N

jjnn

1

N

j

jjn

1 2

A

nTw

total change in twisting turns upon bubble formation

Page 31: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Benham Model

twisting energy of DNA

interwinding energy of the two strands in bubble regions

unpairing energy in bubble (sequence dependent )

initiation energy of bubble formation from the intact helix,The boundary energy between bubble and B-form, interface energy

4321 HHHHH

21

1( )

2 rH K Lk

j

jjnc

H 22 2

j

jjbnH 3

j

jj nnaarH )1( 14

total energy

0 0, :r Lk Lk cLk L onsk Tw Tw t

Page 32: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

1

2

2

n

K

CnLk

N

jjjsbarnC

nnLkKE

1

2

2

2

1

22

1

N

jjj ssr

111=å j

j

n s

Base-stackingEnergy form:

dE/dt=0

Page 33: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

jj

jj psn

Stress-induced melting profile

Page 34: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

H ( n ) , Hj ( n ) calculated by transfer matrix method (e.g., circular DNA)

N

n

nj

N

jiij xnHMMTr

0

1'

N

n

nN

jj xnHMTr

0

1

0

Constrains on specific sites can be realized as following :

(sk= 0)

sj=0 sj=1

Page 35: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

8.10a 1molkcal

58.3c 21 radmolkcal

2350K NRT

255.0ATb 1molkcal

301.1GCb 1molkcal

5.10A

Different unpairing e

nergy

The following calculation is indeed insensitive to the parameters except the difference bet

ween bAT and bGC

Page 36: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Unpairing Probability ProfileBenham Model

M. Li, Z.C. Ou-Yang, Thin Solid Film, 499:207-212 (2006)

{ }

{ }

( 1)Hj

sj H

s

e n

pe

Unpairing Probability for any base pair

Page 37: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

M.Li, Z.C. Ou-Yang, J. Phys:Condens. Matter 17 S2853-S2860

(2005)Nucleosome:

Core of 8 histone molecules:2(H3—H4—H2A—H2B)—link H1

Drosophila melanogaster: Real DNA Sequence: Histone Gen

e Cluster

Page 38: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Drosophila melanogaster: Real DNA Sequence: Histone Gene Cluster

5- —H3—H4—H2A—H2B—H1— -3MAR MAR

Arrow: transcriptional direction

Experimentally find a SMAR for the cluster of the above five geneswith known DNA sequence (X14215, NCBI), calculation with 2 repeats

Page 39: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

The position of the two distinct peaks coincide with the identified S/MARt DB (SM0000037)

S/MAR identified between H1 and H3

The two SMARs define a single structure unit

Result shows nicely: Where Are They ?

Page 40: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Flanking SMARs as barriers to retain the unwinding stress Possible LRAE: SMARs fixation onto the matrix induces unpairing events elsewhere Function Unit:the new unpairing events may play a role in transcriptional termination between H4-(weaker SMAR ?)

5—H3—H4—H2A—H2B—H1—3

Take out Flanking SMARs, find new bubbles: Why They Are There? Long Range Allosteric Effect (LRAE) play the role…

Page 41: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Unwinding stress induces strong bubbles (SMARs) (strong) SMARs may inversely function in gene regulation by protecting the unwinding stress on the chromatin loop chromatin loop as both structure and function unit Mechanics analysis is hopefully a new approach complementary to sequence analysis, especially on the study of DNA function

Summary

Page 42: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Thanks for your

attention !

Page 43: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China
Page 44: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

topological parameters for ds-DNA

Lk : linking number, number of helical turns when DNA is imposed in planar conformation Lk0 : linking number of relaxed ds-DNA. Lk0= N/10.5 Tw : twisting number, number of helical turns Wr : writhing number, coiling times of the central axis (supercoiling). for planar conformation, Wr = 0 σ: superhelical density, defined as (Lk – Lk0)/ Lk0

σ< 0, negative supercoiling ;σ> 0, positive supercoiling

For eukaryotes, σ~ - 0.06 σ* Lk0 = Lk – Lk0 = △Tw (r, r’) + △Wr (r)

Page 45: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

DNA Topology : Ribbon Model

3

1 ( ) ( ) [ ( ) ( )]

4 ( ) ( )

dr s dr s r s r sLk

r s r s

12

( )( )

1]

2

de se s

dsTw ds

3

1 ( ) ( ) [ ( ) ( )]

4 ( ) ( )

dr s dr s r s r sWr

r s r s

Circular dsDNA: topological invariant Lk (r, r’) = Tw (r, r’) + Wr (r)

Central axis of dsDNA

one strand

local frame

Ribbon (r, r’) : central axis + one strand

Page 46: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Adapted from: Wang, J.C. 1991. DNA topoisomerases: why so many? Journal of Biological Chemistry 266:6659-6662.

Page 47: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

Some geometrical parameters to characterize ds-DNA

2Rb s

LJU

0r

2R

The double-helical DNA taken as a flexible ladder with rigid rungs of fixed length 2R. Central axis R0 (s) , its arc length denoted as s. The tangent vector of R0 (s) denoted as t The two strands R1(s), R2 (s). The tangent vector of R1(s), R2(s) denoted as t1 , t2 . The distance between nearest rungs: along R1(s) or R2(s): r0 , fixed and along R0(s): U , variable The folding angle between t and t1 (or t2): . ~ 57o for standard B-DNA

Page 48: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

3

the coiling number of the central axis.

1

4s s

Wr

r s r s r s r sWr dsds

r s r s

0 linking number of natural (standard) B-DNA

interwinding times of the two strands

link number of twisted DNA

Lk

Lk

1 0 0

the times of one strand coiling around the central axis

1 1 sin( , )

2 2

L L

Tw

dbTw r r t b ds ds

ds R

3

1 ( ) ( ) [ ( ) ( )]

4 ( ) ( )

dr s dr s r s r sLk

r s r s

Page 49: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China
Page 50: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

a word about twist: given the link shown below, the twist tells us basically which component ‘wraps  around’ which.                                           

Page 51: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

 We need three vectors to parameterize a surface:- Correspondence vector: pointing from one curve to the other and tracing out the surface between the two curves).- T: unit tangent vector at x- V: unit vector perpendicular to T but lies on the surface defined by correspondence vector.

Now we can define twist more rigorously:

Definition:

                                                     

                                         

( )r s

Page 52: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

the number of Complete Revolutions of one DNA strand about the other

the total number of turns of the DNA duplex itself

total number of turns about the superhelical axis itself

Central axis of dsDNA

one strand

local frame

Central axis of dsDNA

one strand

local frame

Page 53: International Workshop on Continuum Modeling of Biomolecules Sept. 14-16, 2009 in Beijing, China

compaction ratio: ~ 1/8000 considerable force exerted

on DNA (stretching,

bending and twisting) S/MARs:

topologically independent

domains

basement of chromatin loops S/MAR(Scaffold/Matrix Attachment Region)

Chromosome AssemblyChromatin Loop Model