Mechanics Inspired Bioinformatics Predicting the Function of Eukaryotic
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 Institute of Theoretical Physics Chinese Academy of Sciences Beijing 100080, oy@itp. ac. cn
Outline: I. Stretching single molecule DNA II. Mechanics-inspired Bioinformatics : An example S/MARs on Eukaryotic Chromosome, predicting the location and function
I. Stretching single molecule DNA 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) 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
Stretching double-stranded DNA can be treated as a uniform polymer
Zhou, Zhang, Ou-Yang, PRL, 82, 4560(1999)
* Two classical models: ** Freely jointed chain (FJC) ** Worm-like chain (WLC) As a Hookian spring with Hooke's constant
Zhou, Zhang, Ou-Yang, PRL, 82, 4560(1999)
• Our Model * Introduction of a new structural parameter, the folding angle. * Without consideration of force-induced melting and nick.
• Mathematically * Two backbones * Central axis , , • Bending energy * decomposed into the bending energy of central axis plus folding energy
• Our Model * Introduction of a new structural parameter, the folding angle. * Without consideration of force-induced melting and nick.
16 base-pair stacking potentials
Biophys. J. 78(2000) 1979 -1987 * 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 ds. DNA
• The Potential of External Force • The Energy of External Torque T
• Total Elasticity Energy Particle moves in a field A and a potential V if look s as time t
• Polymer Dynamics and Path Integral Method * Partition function: * “Schrödinger equation” * * Free energy: *
• Extension/Force of is Hermitian, it is real Schrödinger Eq. Extension:
Extension of Torsionally Relaxed DNA Zhou, Zhang, Ou-Yang, PRL, 82, 4560(1999)
Distribution of Folding of Backbones
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 Mechanics-Inspired Bioinformatics.
II. Mechanics-inspired Bioinformatics : An example S/MARs on Eukaryotic Chromosome, predicting the location and function 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: …ATTTTAATGTCATGATAAAGTTAC TTCCTTTTTAAGTTACTTCTATA ATATATGTAAATTACTTTTAATCTCT ACTGAAATTACTTTTATATATCTAAG AAGTATTTAGTGAAATCTAAAAGTA ATTTAGATATAAAAGTAATT TGTATTTTTTTCATCAAAATATAATC ATGTGAGACCTTGTTATAAAGATTT AA…
Elasticity Plays the Key Role… ! ¡ DNA: ~ centimeters (human ¡ ¡ ¡ cell 2 meters) 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
Chromosome Assembly Chromatin Loop Model ¡ 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)
Structure Heterogeneity Induced by Mechanical Force: Secondary Structures H-Bond Broken Chirality Variable bubble cruciform
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 Lk=Wr+Tw, writhing number—axis self-linking number, Tw—inter-winding number of two strands
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, negative supercoiling ; σ> 0, positive supercoiling ¡For eukaryotes, σ~ - 0. 06 ¡σ* Lk 0 = Lk – Lk 0 = △Tw (r, r’) + △Wr (r)
Can we make the prediction on bubbles (S/MARs) by taking account of the unwinding stress, i. e. , the energy corresponding toσ(~ -0. 06 ) ?
Bubble Formation is Sequence Dependent Benham Model = 0 … base paried = 1 … base unparied 2 N configurations {… 10111111100…} local bubble : base unparing energy : rewinding angle of the denatured region a : initiation energy of bubble formation A : 10. 5 bp per helical turn of B-DNA total change in twisting turns upon bubble formation σ : superhelical density Bauer WR, Benham CJ. , J Mol Biol. 1993, 234(4): 1184 -96.
Benham Model Ø total energy Øtwisting energy of DNA Ø interwinding energy of the two strands in bubble regions Ø unpairing energy in bubble (sequence dependent ) Øinitiation energy of bubble formation from the intact helix, The boundary energy between bubble and B-form, interface energy
d. E/dt=0 Base-stacking Energy form:
Stress-induced melting profile
H（n）, Hj（n） calculated by transfer matrix method (e. g. , circular DNA) sj=0 sj=1 Constrains on specific sites can be realized as following： (sk= 0)
The following calculation is indeed insensitive to the parameters except the difference between b. AT and b. GC Different unpairing energy
Unpairing Probability Profile Benham Model M. Li, Z. C. Ou-Yang, Thin Solid Film, 499: 207 -212 (2006) Unpairing Probability for any base pair
M. Li, Z. C. Ou-Yang, J. Phys: Condens. Matter 17 S 2853 S 2860 (2005) Nucleosome: Core of 8 histone molecules: 2(H 3—H 4 —H 2 A—H 2 B)—link H 1 Drosophila melanogaster: Real DNA Sequence: Histone Gene Cluster
Drosophila melanogaster: Real DNA Sequence: Histone Gene Cluster Arrow: transcriptional direction 5 - —H 3—H 4—H 2 A—H 2 B—H 1— -3 MAR Experimentally find a SMAR for the cluster of the above five genes with known DNA sequence (X 14215, NCBI), calculation with 2 repeats
Result shows nicely: Where Are They ? ¡ The position of the two distinct peaks coincide with the identified S/MARt DB (SM 0000037) ¡ S/MAR identified between H 1 and H 3 ¡ The two SMARs define a single structure unit
Take out Flanking SMARs, find new bubbles: Why They Are There? Long Range Allosteric Effect (LRAE) play the role… n Flanking SMARs as barriers to retain the unwinding stress n Possible LRAE: SMARs fixation onto the matrix induces unpairing events elsewhere n 5—H 3—H 4—H 2 A—H 2 B—H 1— 3 Function Unit: the new unpairing events may play a role in transcriptional termination between H 4(weaker SMAR ? )
Summary ¡ 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
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, negative supercoiling ; σ> 0, positive supercoiling ¡ For eukaryotes, σ~ - 0. 06 ¡ σ* Lk 0 = Lk – Lk 0 = △Tw (r, r’) + △Wr (r)
DNA Topology : Ribbon Model Circular ds. DNA: topological invariant Lk (r, r’) = Tw (r, r’) + Wr (r) Ribbon (r, r’) : central axis + one strand Central axis of ds. DNA one strand local frame
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 n The double-helical DNA taken as a flexible ladder with rigid rungs of fixed length 2 R. n Central axis R (s) , its arc length 0 denoted as s. The tangent vector of R 0 (s) denoted as t n The two strands R (s), R (s). The 1 2 tangent vector of R 1(s), R 2(s) denoted as t 1 , t 2. n The distance between nearest rungs: along R 1(s) or R 2(s): r 0 , fixed and along R 0(s): U , variable n The folding angle between t and t 1 (or t 2): .
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 ds. DNA one strand local frame
Chromosome Assembly Chromatin Loop Model ¡ 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)
- Slides: 53