Statistical Mechanics of DNA Melting and Related Biological Effects in

Bioinformatics:Predicting the function of eukaryotic

scaffold/matrix attachment region via DNA mechanics

CCP 2006, Aug. 30, Korea

Ming Li and Zhong-can Ou-YangInstitute of Theoretical Physics

Chinese Academy of Sciences

Beijing 100080, oy@itp.ac.cn

Outline:

I. Stretching single molecule DNA/RNA

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

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/RNA

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

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

Stretching RNA:

Optical Tweezer Technique

C. Bustamante et al. Science (2001)

Model and Method

( ) ( ) ( , ) ( )ds ds ss ss ds ssi i i i i i iE G S W x W x n f x x

Continuous Time of Monte Carlo Simulation [1] shows good agreement with exact partition function method [2]

[1] F.Liu, ZC Ou-Yang, Biophys. J. 88 (2005) 76

[2] U. Gerland et al. Biophys. J. 84 (2003) 2831

Stretch-Induced Hairpin-Coil Transitions in poly(dG-dC) or poly(dA-dT) Chains can be treated as hybrid polymer

0 1 1 2 0

A...A B...BA...A B...B............B...Bi j i j j

H.Zhou, Y.Zhang, Z.C. Ou-Yang., Phys. Rev. Lett. 86, 356(2001).

Above Three cases 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.

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

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… !

Chirality Variable bubble

cruciform

H-Bond Broken

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

Secondary StructuresSecondary Structures

Sequence Heterogeneity Sequence Heterogeneity ? ? Structure Heterogeneity Structure Heterogeneity

secondary structures are closely but not specifically associated with the underlying DNA sequence

conventional sequence analysis is not sufficient to predict the secondary structure; the torsional state of double-stranded DNA must be taken into account

Biophysics v.s. Bioinformatics

(Continuous) macromolecule,double-stranded (twistable)

Physical properties: long range allosteric effects, …

Elasticity, thermal melting, …

Statistical physics, …

Structural properties function, even evolution, …

(Discrete) symbolic sequence recoding one strand of DNA chain

Statistical information: sequence heterogeneity, …

String Counting, gene finding, …

Statistics, linguistics, …

Sequence pattern evolution, even function, …

Integrated Approach: sequence-dependent physics

Mechanics-inspired BioinformaticsAn example

S/MARs on Eukaryotic Chromosome:predicting the location and function

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

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.

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

The unwinding stress can induce the formation of local bubbles

DNA segment per nucleosome: ~167 bp

The segment is actually unwound :

1 helical turn unwound per nucleosome.

Large amount of torsional stress is generated on DNA

DNA undergoes unwinding stress in eukaryotic cell

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)

Lk : linking number, number of helical turns Lk0 : linking number of relaxed DNA (uniform B-DNA) Lk0= N/10.5

σ : superhelical density. (Lk – Lk0)/ Lk0 σ< 0, negative supercoiling σ> 0, positive supercoiling

For eukaryotes, DNA is always unwound to a degree σ~ - 0.06 (1/167)

How to characterize the degree of unwinding …

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 ) ?

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

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

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

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:

jj

jj psn

Stress-induced melting profile

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

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

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

M.Li, Z.C. Ou-Yang, Jphys:Condens. Matter 17 S2853-S2860 (20

05)Nucleosome:

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

Drosophila melanogaster: Real DNA Sequence: Histone Gene Cluster

5- —H3—H4—H2A—H2B—H1— -3MAR MAR

Arrow: transcriptional direction

The position of the two distinct peaks coincide with the identified S/MARs

S/MAR identified between H1 and H3

The two SMARs define a single structure unit

Where Are They ?

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(weaker SMAR ?)

5—H3—H4—H2A—H2B—H1—3

Why They Are There? Long Range Allosteric Effect (LRAE) play the role…

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

Thanks for your

attention !

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)

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

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

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

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

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

 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

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