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

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

Outline 1.Background 2.Computational Rod Model 3.Quick Example - Plectoneme Formation 4.Looping of Highly Curved DNA (Kahn’s Sequences) 5.Looking Forward - New Hypotheses

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

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

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

3. Quick Example Plectoneme Formation

Energy Work Elastic Energy Torsional Energy Bending Energy Energy

Twist Tw Linking Number Wr Tw, Wr, Lk Tw Time L k

Known Lac crystal structure (loop boundary conditions) Courtesy: Courtesy: 4. Protein-Mediated Looping of DNA (LacR protein - regulating expression of LacZ,Y,A in E. coli)

Highly Curved Sequences J. Kahn, Univ. Maryland Highly Curved Sequences J. Kahn, Univ. Maryland J. Mol. Biol., 1999 straight ‘linker’ curved A-tract

PDB files for sequences (zero temperature in aqueous solution) generated by webtool: [Gabrielian and Pongor FEBS Letters, 1996] Unbent Control 11C12 9C14 7C16 70° 11C12 9C14 7C16 Unbent Control Highly Curved Sequences J. Kahn, Univ. Maryland Highly Curved Sequences J. Kahn, Univ. Maryland J. Mol. Biol., 1999

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

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

Example Calculation

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

11C12 Unbent Control Intrinsic Curvature Lowers Energetic Cost of Looping kT/bp

A Survey of the Experimental Data for the Highly Curved Sequences

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) Lowest 11kT P1F Second 11.5kT P1R

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

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

Gel Mobility Assays & Loop Size Mehta and Kahn, J. Mol. Bio., 1999., Control 11C12 slowest fastest 9C14 7C largest smallest g R

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

Possible Minimum Loop Energies and Preferred Binding Topologies Energy kT

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

Conclusions 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) Intrinsic Curvature May Have a Pronounced Effect on  Preferred Binding Topology  Loop Elastic Energy  Loop Size  Loop Topology (Tw, Wr, Lk)