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DNA: Structure, Dynamics DNA: Structure, Dynamics and Recognitionand Recognition
Les Houches 2004
L3: DNA dynamics
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STRUCTURAL DATABASES
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RSCB-PDB
http://www.rscb.org
H.M. Berman, J. Westbrook, Z. Feng, G. Gilliland,T.N. Bhat, H. Weissig, I.N. Shindyalov, P.E. BourneNucleic Acids Research, 28 pp. 235-242 (2000)
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RSCB
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Full search
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Custom forms
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An example - chymotrypsin
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Display
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PDB file header
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NDB -http://ndbserver.rutgers.edu/
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NDB - atlas
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NDB - atlas
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CCDC - 1965
http://www.ccdc.cam.ac.uk/
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CSD – small molecules
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CCDC products
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TRANSFAC - http://www.gene-regulation.com/
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HELICAL PARAMETERS
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Helical symmetry
- move between residues by translation along and rotation around the helical axis
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Finding a helical axis
(1) Build vectors between helically equivalent atoms
(2) Find plane defined by vectors placed at origin
(3) Draw perpendiculars to chords between heads of vectors
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Curved helical axis ?
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Cambridge convention
5’
3’
3’
5’
Dickerson et al. J. Mol. Biol. 205, 1989, 787
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Helical parameters
Translation Rotation
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Helicoidal parameters
Local Global
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Extreme global solutions
Keep linear helicalaxis
Keep monomer orientations
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CURVES
R. Lavery and H. Sklenar J. Biomol. Struct. Dyn. 6, 1989, 655
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Base reference system
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Axis reference system
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Curves function
A) Bases (X, E) in the same place with respect to the local axis (U, P) ? A1) Rotation
(Ui.Xi - Ui-1.Xi-1)2 - where X = J, K, L
A2) Translation
[(Pi - Ei).Xi - (Pi-1 - Ei-1).Xi-1)2
B) Axis straight and continuous ? B1) Rotation
(Ui - Ui-1)2
B2) Translation
(Qi - Qi-1)2 - where Qi = (Pi - Pi-1) - <U>.[<U>.(Pi - Pi-1)]
Final formula: F (X,Y,I,T) = 10 (A1 + B1) + (A2 + B2)
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Curves helical axis
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Parameter B-DNA A-DNA
Xdisp 0.0 -5.28Ydisp 0.0 0.0Inclination 1.5 20.7 Propeller -13.3 -7.5
G-Slide 0.0 0.0G-Rise 3.38 2.56G-Roll 0.0 0.0G-Twist 36.0 32.7 L-Slide 0.08 -1.92L-Rise 3.38 3.44L-Roll 0.9 11.4L-Twist 35.6 30.7 Phase 155 18Amplitude 40 42
Helical parametersfor B- and A-DNA
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B-DNA structural variation
Value Min. Max. Mean Value Min. Max. Mean
Xdisp -0.6 1.5 0.5 Shift -1.1 1.1 0.0
Inc 11 11 -1 Slide -1.1 1.1 -0.1
Tip -11 11 0 Rise 3.2 4.0 3.4
Buck -11 16 1 Tilt -8 8 0
Prop -24 5 -11 Roll -12 16 2
Open -8 8 1 Twist 22 51 36
-109 -23 -64 90 173 132
112 -159 166 141 -61 -179
-16 104 50 148 -68 -94
Pha 19 206 150 -62 -160 -104
Amp 15 58 39
Hartmann and Lavery Q. Rev. Biophys. 29, 1996, 309
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B-DNA - 2ns dynamic trajectory
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"LONG" MD SIMULATIONS
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Time integration of Newton's equation of motion:
F = ma
-dE/dr = m dr2/dt2
Taylor expansion:
r(t + t) = r(t) + t dr(t)/dt + t2/2 d2r(t)/dt2 + …
Fastest movements: O(10-15 s)
Molecular dynamics
r
t
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Periodic boundary conditions
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Equilibration
0
100
200
300
Temp (K)
Time (ns)
1 2 3
Heat
Equilibrate Production
NPT ensemble
Reassign or rescale velocities
Initially constrain solute
Minimize
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MD snapshots
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MD time series- sugar phase- groove width
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MD time series- base pair Hbonds
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Ascona B-DNA Consortium
USA EUROPE
D. Beveridge, Wesleyan U.
D. Case, Scripps Institute
T. Cheatham, U. Utah
R. Osman, Mount Sinai, NY
M. Young, Berkeley
F. Lankas, Herovsky Inst.Czech Republic EPFL
R. Lavery, IBPCFrance
J. Maddocks, EPFLSwitzerland
H. Sklenar, MDCGermany
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136 unique tetramers
AAAA AAAC AAAG AAAT AAGA AAGC AAGG AAGTAATA AATC AATG AATT ACGA ACGC ACGG ACGTAGAA AGAC AGAG AGAT AGCA AGCC AGCG AGCTAGGA AGGC AGGG AGGT AGTA AGTC AGTG AGTTATAA ATAC ATAG ATAT ATGA ATGC ATGG ATGTCAAA CAAC CAAG CAAT CAGA CAGC CAGG CAGTCATA CATG CCGA CCGG CGAA CGAC CGAG CGATCGCA CGCG CGGA CGGC CGGG CGGT CGTA CGTCCGTG CGTT CTAA CTAG CTGA CTGC CTGG CTGTGAAA GAAC GAAG GAAT GAGA GAGC GAGG GAGTGATA GATC GATG GCGA GCGC GCGG GGAA GGACGGAG GGAT GGCA GGCC GGCC GGGA GGGC GGGGGGGT GGTA GGTC GGTG GGTT GTAA GTAC GTAGGTGA GTGC GTGG GTGT TAAA TAAC TAAG TAATTAGA TAGC TAGG TAGT TATA TCGA TGAA TGACTGAG TGAT TGCA TGGA TGGC TGGG TGGT TGTATGTC TGTG TGTT TTAA TTGA TTGC TTGG TTGT
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ABC oligomers - construction
G-D-ABCD-ABCD-ABCD-G
• 15 base pairs
• Central tetranucleotide repeats
• GC terminal base pairs for stability
• No sampling for i<3 or i>13
• Two copies of each tetranucleotide
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39 oligomer database
GGGGGGGGGGGGG AAAAAAAAAAAAA CGCGCGCGCGCGCTATATATATATAT AGAGAGAGAGAGA TGTGTGTGTGTGTAGGGAGGGAGGGA CGGGCGGGCGGGC TGGGTGGGTGGGTGAAAGAAAGAAAG CAAACAAACAAAC TAAATAAATAAATCGGCCGGCCGGCC AGGAAGGAAGGAA TGGTTGGTTGGTTTAATTAATTAATT CGGACGGACGGAC AGGCAGGCAGGCAAGGTAGGTAGGTA TGGATGGATGGAT CGGTCGGTCGGTCTGGCTGGCTGGCT CAAGCAAGCAAGC GAACGAACGAACGTAACTAACTAACT CAATCAATCAATC TAAGTAAGTAAGTGAATGAATGAATG TGAGTGAGTGAGT CGAGCGAGCGAGCTGCGTGCGTGCGT TAGATAGATAGAT GACAGACAGACAGTACATACATACAT AGCTAGCTAGCTA TGCATGCATGCATCGATCGATCGATC TGACTGACTGACT CGTACGTACGTAC
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Simulation protocol
AMBER program
PARM94 parameters
Truncated octahedral box (~7600 waters)
Neutralising K+ counterions
Particle Mesh Ewald electrostatics
2 fs timestep (SHAKE on X-H)
Careful equilibration, NVTNPT
Save configuration every 1ps
15 ns trajectories (for Phase I)
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ABC dataset – Phase I Finished 5/03
• 150 months of CPU time
• 0.6 s of simulation
(2.2x Vilin folding simulation)
• 600,000 coordinate sets
• 272 tetranucleotide steps
• 400 Gb of data
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ACGT trajectory
B-DNA
A-DNA
Last ns
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Helical parameters
Translation Rotation
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ACGT helical parameters - instantaneous
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SYMMETRY?
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Each oligomer contains ≥2 "identical" tetramers
G-D-ABCD-ABCD-ABCD-G
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ACGT helical parameters - histograms
C6pG7
C10pG11
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GCGC helical parameters - histograms
C4pG5
C6pG7
C8pG9
C10pG11
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GCGC helical parameters
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Backbone torsion angles
: C5’ – C4’ – C3’ – O3’
: O5’ – C5’ – C4’ – C3’
: P – O5’ – C5’ – C4’
: O3’ – P – O5’ – C5’
: C3’ – O3’ – P – O5’
: C4’ – C3’ – O3’ – P
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CGCG backbone parameters
G7pC8
G11pC12
C6pG7
C10pG11
g-/g+ g+/t
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transition
- G11pC12
- G11pC12
g-
g+
g+
t
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impact on twist
- G11pC12
- G11pC12
g-
g+
g+
t
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SEQUENCE DEPENDENT STRUCTURE?
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CpG translational parameters
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CpG rotational parameters
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IONS AROUND DNA
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Diffusion coefficients(10-9 m2sec-1 )
<(xi(t0+dt)-xi(t0))2> = 6D dt
<(x
i(t0
+d
t)-x
i(t0
))2> K+
D= 2.85
Exp=1.96
Na+
D= 1.72
Exp=1.33
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Volume sampled by ions during 50ns simulation time
Na+
K+
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Most frequently visited zones
Na+ K+
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Tight binding
phosphate 2 2 3 2 2 9 5 3 13 2 3
strand 1 C1 C2 A3 T4 G5 C6 G7 C8 T9 G10 A11 C12
groove 1 3 7 12 2 1 5
groove 2 1 2 1 3 8 8,1 6 3
strand 2 G24 G23 T22 A21 C20 G19 C18 G17 A16 C15 T14 G13
phosphate 2 6 3 17 2 4 12 3 8 3 2
phosphate 1 2 2 3 2 5 2 4 3 2 3
strand 1 C1 C2 A3 T4 G5 C6 G7 C8 T9 G10 A11 C12
groove 1 2 7 4 13,3 2 1
groove 2 2 2 1,1 1 3,8 3 11 1,6 1,1 1 2
strand 2 G24 G23 T22 A21 C20 G19 C18 G17 A16 C15 T14 G13
phosphate 2 3 2 3 2 4 3 3 6 1 1
Na+
K+
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Minor groove width at C8 level
Na+
K+
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/ transitions in Na+ dynamics
redgreen
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/ transitions in K+ dynamics
red green