the mechanics of dna looping and the influence of intrinsic curvature
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
THE MECHANICS OF DNA LOOPING AND
THE INFLUENCE OF INTRINSIC CURVATURE
EngineeringSachin GoyalSachin GoyalTodd Lillian Todd Lillian Noel PerkinsNoel PerkinsEdgar MeyhoferEdgar Meyhofer
Seth BlumbergSeth BlumbergDavid WilsonDavid WilsonChris MeinersChris MeinersAlexei Tkachenko Alexei Tkachenko Ioan Andricioaei Ioan Andricioaei
NSF, LLNLNSF, 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
OutlineOutline
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 Model2. Computational Rod Model
ChallengesChallenges
Nonlinearity (large bending & torsion)
Non-isotropy
Non-homogeneity
Non-trivial stress-free shapes
Self-contact / Excluded volume
Structural ModelingStructural Modeling Multi-Physical InteractionsMulti-Physical Interactions
Elasticity
Hydrodynamics( Drag / Coupling )
Thermal Kinetics
Electrostatics
),( tsai
),( tsR
Computational Rod ModelComputational Rod ModelGoyal et al., Goyal et al., Comp. PhysicsComp. Physics, 2005, 2005
( , ) ( , )q s t s t
moment/curvature relation
internal force
internal moment
f
q
velocity
angular velocity
v
0( , ) ( )[ ( , ) ( )]q s t B s s t s example constitutive law
)(00
0)(0
00)(
)( 2
1
sC
sA
sA
sB
1
2
( ) 0 0
( ) 0 ( ) 0
0 0 ( )
A s
B s A s
C s
intrinsic or stress-free curvature
Computational Rod Model
c c
f vf A v F
s t
Linear Momentum
3( )q
q I I f as t
Angular Momentum
s t
Compatibility Condition
3
vv a
s
Inextensibility Constraint
Field Variables: {v, ω, f, κ}
0( , ) ( )[ ( , ) ( )]q s t B s s t s
Constitutive Law
1
2
( ) 0 0
( ) 0 ( ) 0
0 0 ( )
A s
B s A s
C s
3. Quick Example3. Quick ExamplePlectoneme FormationPlectoneme Formation
EnergyEnergy
Work
Elastic Energy
Torsional Energy
Bending Energy
En
erg
y
1
2
3
4
Twist Tw
0 5 10 15 20 25 30 350
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Time, t(s)
LinkingNumber,
Lk
Twist,Tw
Writhe,Wr
Linking NumberLinking Number
Wr
Tw
, Wr,
Lk
Tw
Time
1
2
3
4
L k
Known Lac crystal structure (loop boundary conditions)
Courtesy: Courtesy: http://www.ks.uiuc.edu/Research/pro_DNA/elastic
4. Protein-Mediated Looping of DNA4. Protein-Mediated Looping of DNA(LacR protein - regulating expression of LacZ,Y,A in (LacR protein - regulating expression of LacZ,Y,A in E. coliE. coli))
Highly Curved SequencesHighly Curved SequencesJ. Kahn, Univ. MarylandJ. Kahn, Univ. Maryland
J. Mol. Biol., 1999
plstraight ‘linker’
straight ‘linker’
curved A-tract
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]
Unbent Control
11C12
9C14
7C1670°
11C12
9C14
7C16
Unbent Control
Highly Curved SequencesHighly Curved SequencesJ. Kahn, Univ. MarylandJ. Kahn, Univ. Maryland
J. Mol. Biol., 1999
(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’
(d) Output: Topology and energetics of loop formation
Simulate Dynamic Kirchhoff Rod Model
LacR
(c) Input 2: DNA-Operator Crystal Structure
Oid Oid
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 TopologiesMultiple Binding Topologies(Multiple Boundary Conditions)(Multiple Boundary Conditions)
Most “Compact” Loop
Example Calculation
Minimum Energy Conformations
Control
11C12
7C16
9C14
E=12kTR=8.4nm
E=7.5kTR=8.0nm
E=8.5kTR=7.5nm
E=11kTR=7.7nm
A2F
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-FRETMorgan, 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 FRETEdelman, 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 EnergyMehta and Kahn, J. Mol. Bio., 1999.,
Least Stable Sequence(3.8% labeled remaining)
Control
E=12kTGreatest Energy
E=7.4kTLeast 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 SizeMehta and Kahn, J. Mol. Bio., 1999.,
Control
11C12
slowest
fastest
9C14
7C16
8.4
8.0
7.5
7.7
largest
smallest
gR
5. Looking Forward - New Hypotheses5. Looking Forward - New Hypotheses
1bp
2bp
Phasing of A-tract determined by: &1bp 2bp
Possible Minimum Loop Energies Possible Minimum Loop Energies and Preferred Binding Topologiesand Preferred Binding Topologies
1bp1bp
2bp 2bp
10
5
12
5
5
Energy kT
Possible Loop Sizes and Topologies (*)Possible Loop Sizes and Topologies (*)
1bp1bp
2bp 2bp
(*) See cyclization assays in Mehta and Kahn, J. Mol. Bio., 1999.,
Radius of Gyration Change in Link
ConclusionsConclusions
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)