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-Yang Institute of Theoretical Physics Chinese Academy of Sciences Beijing ,

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 decade Physical 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 protein mechanics with single molecules. [4] J. T. Perkins, D. E. Smith, R. G. Larson, S. Chu, Science 268 (1995) [5] S. B. Smith, L. Finzi, C. Bustamantl, Science 258 (1992) [6] S. B. Smith, Y. Cui, C. Bustmantl, Science 271 (1996) [7] P. Cluzel et al., Science 271 (1996) [8] M. Rief, H. C.-Schauman, H. E. Gaub, Nat. Struct. Biol. 6 (1999) [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

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 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 Mechanics-Inspired Bioinformatics.

4 types of nucleotides: Adenine, Guanine, Thymine, Cytosine Watson-Crick base pair: A-T, G-C Intrinsic right-handed helix (torsional state) B-DNA: uniform, sequence-independent 4-letter text: …ATTTTAATGTCATGATAAAGTTACT TCCTTTTTTTTTAAGTTACTTCTATAAT ATATGTAAATTACTTTTAATCTCTACT GAAATTACTTTTATATATCTAAGAAGT ATTTAGTGAAATCTAAAAGTAATTTA GATATAATATAAAAGTAATTTGTATTT TTTTCATCAAAATATAATCATGTGAGA CCTTGTTATAAAGATTTAA… 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 Force: Secondary Structures

Sequence 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 Bioinformatics An 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 Assembly Chromatin 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: 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-DNA  Lk : linking number, number of helical turns when DNA is imposed in planar conformation  Lk 0 : linking number of relaxed ds-DNA. Lk 0 = 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 – Lk 0 )/ Lk 0 σ 0, positive supercoiling  For eukaryotes, σ ~  σ* Lk 0 = Lk – Lk 0 = △ 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~ (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 corresponding to σ ( ~ ) ?

Bubble Formation is Sequence Dependent Benham Model Bauer WR, Benham CJ., J Mol Biol. 1993, 234(4): N configurations {… …} local bubble a : initiation energy of bubble formation = 0 … base paried = 1 … base unparied : rewinding angle of the denatured region : base unparing energy A : 10.5 bp per helical turn of B-DNA : superhelical density σ 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  total energy

Base-stacking Energy form:

Stress-induced melting profile

H （ n ）, H j （ n ） calculated by transfer matrix method (e.g., circular DNA) Constrains on specific sites can be realized as following ： (s k = 0) s j =0s j =1

Different unpairing energy The following calculation is indeed insensitive to the parameters except the difference between b AT and b GC

Unpairing Probability Profile Benham Model M. Li, Z.C. Ou-Yang, Thin Solid Film, 499: (2006) Unpairing Probability for any base pair

M.Li, Z.C. Ou-Yang, Jphys: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 Gene Cluster 5- —H3—H4—H2A—H2B—H1— -3 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  Lk 0 : linking number of relaxed ds-DNA. Lk 0 = 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 – Lk 0 )/ Lk 0 σ 0, positive supercoiling  For eukaryotes, σ ~  σ* Lk 0 = Lk – Lk 0 = △ Tw (r, r’) + △ Wr (r)

DNA Topology : Ribbon Model 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 DNA topoisomerases: why so many? Journal of Biological Chemistry 266:

Some geometrical parameters to characterize ds-DNA The double-helical DNA taken as a flexible ladder with rigid rungs of fixed length 2R. Central axis R 0 (s), its arc length denoted as s. The tangent vector of R 0 (s) denoted as t The two strands R 1 (s), R 2 (s). The tangent vector of R 1 (s), R 2 (s) denoted as t 1, t 2. The distance between nearest rungs: along R 1 (s) or R 2 (s): r 0, fixed and along R 0 (s): U, variable The folding angle between t and t1 (or t2): .  ~ 57 o for standard B- DNA

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:

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