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THE MECHANICS OF DNA LOOPING AND THE INFLUENCE OF INTRINSIC CURVATURE

THE MECHANICS OF DNA LOOPING AND THE INFLUENCE OF INTRINSIC CURVATURE. Engineering Sachin Goyal Todd Lillian Noel Perkins Edgar Meyhofer. Physics/Biophysics & Chemistry – Univ. Michigan. Seth Blumberg David Wilson Chris Meiners Alexei Tkachenko Ioan Andricioaei.

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THE MECHANICS OF DNA LOOPING AND THE INFLUENCE OF INTRINSIC CURVATURE

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  1. THE MECHANICS OF DNA LOOPING ANDTHE INFLUENCE OF INTRINSIC CURVATURE EngineeringSachin GoyalTodd Lillian Noel PerkinsEdgar Meyhofer Physics/Biophysics & Chemistry – Univ. Michigan Seth BlumbergDavid WilsonChris MeinersAlexei Tkachenko Ioan Andricioaei Chemistry Univ. Maryland Jason Kahn NSF, LLNL

  2. Evolution of loops and tangles in cables DNA supercoiling and looping Engineering Structural Mechanics Drs. C.L. Lu, C. Gatti-Bono, S. Goyal

  3. Outline • Background • Computational Rod Model • Quick Example - Plectoneme Formation • Looping of Highly Curved DNA (Kahn’s Sequences) • Looking Forward - New Hypotheses

  4. Challenges 2. Computational Rod Model Multi-Physical Interactions Structural Modeling Nonlinearity (large bending & torsion) Non-isotropy Non-homogeneity Non-trivial stress-free shapes Self-contact / Excluded volume Elasticity Hydrodynamics( Drag / Coupling ) Thermal Kinetics Electrostatics

  5. Computational Rod ModelGoyal et al., Comp. Physics, 2005 moment/curvature relation example constitutive law intrinsic or stress-free curvature internal force velocity angular velocity internal moment

  6. Computational Rod Model Linear Momentum Angular Momentum Compatibility Condition Constitutive Law Inextensibility Constraint Field Variables: {v, ω, f, κ}

  7. 3. Quick ExamplePlectoneme Formation

  8. Energy 1 Work Elastic Energy Torsional Energy Energy 4 2 Bending Energy 3

  9. Linking Number 1 L k Tw Twist Tw 4 Tw, Wr, Lk 2 3 Wr Time

  10. 4. Protein-Mediated Looping of DNA(LacR protein - regulating expression of LacZ,Y,A in E. coli) Known Lac crystal structure (loop boundary conditions) Courtesy: http://www.ks.uiuc.edu/Research/pro_DNA/elastic

  11. straight ‘linker’ straight ‘linker’ curved A-tract Highly Curved SequencesJ. Kahn, Univ. MarylandJ. Mol. Biol., 1999

  12. 11C12 9C14 UnbentControl 7C16 70° 7C16 UnbentControl 11C12 9C14 Highly Curved SequencesJ. Kahn, Univ. MarylandJ. Mol. Biol., 1999 PDB files for sequences (zero temperature in aqueous solution) generated by webtool: http://hydra.icgeb.trieste.it/~kristian/dna/index.html, [Gabrielian and Pongor FEBS Letters, 1996]

  13. (b) Compute Stress-Free Shape Based on Consensus Tri-nucleotide Model (c) Input 2: DNA-Operator Crystal Structure Oid Oid + Input 3: Constitutive Law (e.g., Bending and Torsional Persistence Lengths) (d) Output: Topology and energetics of loop formation Compute Boundary Conditions Simulate Dynamic Kirchhoff Rod Model LacR (a) Input 1: Sequence of Substrate DNA Operator “Oid” at location L1 - - Inter-Operator sequence - - Operator “Oid” at location L2 5’ … GGTAATTGTGAGC-GCTCACAATTAGA … … … … … GCTAATTGTGAGC-GCTCACAATTCGT … 3’ 3’ … ccattaacactcg-cgagtgttaatct … … … … … cgattaacactcg-cgagtgttaagca … 5’

  14. Multiple Binding Topologies(Multiple Boundary Conditions) Most “Compact” Loop

  15. Example Calculation

  16. Control E=12kT R=8.4nm E=7.5kT R=8.0nm A2R A2F E=11kT R=7.7nm E=8.5kT R=7.5nm A2F Minimum Energy Conformations 11C12 9C14 7C16 P1F

  17. Intrinsic Curvature Lowers Energetic Cost of Looping kT/bp

  18. A Survey of the Experimental Data for the Highly Curved Sequences

  19. Lowest 11kT P1F Second 11.5kT P1R Binding Topology of 9C14 via SM-FRET Morgan, et al., Biophysical J., 2005., “The LacI-9C14 loop exists exclusively in a single closed form exhibiting essentially 100% ET” (~3.4 nm)

  20. 8 nm Binding Topology of 11C12 via Bulk FRET Edelman, et al., Biophysical J., 2003., Lowest 7.5kT A2R Second 10.5kT A1R FRET efficiency 10%

  21. Most Stable Sequence (63% labeled remaining) Least Stable Sequence (3.8% labeled remaining) Control 11C12 Competition Assays & Loop Stability and Energy Mehta and Kahn, J. Mol. Bio., 1999., (Labeled looped DNA with a 50-fold concentration of unlabeled DNA) E=7.4kTLeast Energy E=12kTGreatest Energy The relative stability of the two intermediate cases (7C16 and 9C14) are not correctly predicted by the rod elastic energies

  22. slowest R largest g Control 8.4 8.0 11C12 9C14 7.7 7C16 7.5 fastest smallest Gel Mobility Assays & Loop Size Mehta and Kahn, J. Mol. Bio., 1999.,

  23. 5. Looking Forward - New Hypotheses Phasing of A-tract determined by:&

  24. 10 Possible Minimum Loop Energies and Preferred Binding Topologies Energy kT 12 5 5 5

  25. Possible Loop Sizes and Topologies (*) Radius of Gyration Change in Link (*) See cyclization assays in Mehta and Kahn, J. Mol. Bio., 1999.,

  26. Established Predictive Ability of Rod Model for Highly-Curved Sequences Preferred (P1) Binding Topology of 9C14 (SM-FRET) Preferred (A1, A2) Binding Topology of 11C12 (Bulk FRET) Max and Min Loop Stabilities (Competition Assays) Relative Loop Sizes (Gel Mobility Assays) Conclusions Intrinsic Curvature May Have a Pronounced Effect on • Preferred Binding Topology • Loop Elastic Energy • Loop Size • Loop Topology (Tw, Wr, Lk)

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