DNA: Structure, Dynamics DNA: Structure, Dynamics and Recognitionand Recognition

Les Houches 2004

L3: DNA dynamics

STRUCTURAL DATABASES

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)

RSCB

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An example - chymotrypsin

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PDB file header

NDB -http://ndbserver.rutgers.edu/

NDB - atlas

NDB - atlas

CCDC - 1965

http://www.ccdc.cam.ac.uk/

CSD – small molecules

CCDC products

TRANSFAC - http://www.gene-regulation.com/

HELICAL PARAMETERS

Helical symmetry

- move between residues by translation along and rotation around the helical axis

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

Curved helical axis ?

Cambridge convention

5’

3’

3’

5’

Dickerson et al. J. Mol. Biol. 205, 1989, 787

Helical parameters

Translation Rotation

Helicoidal parameters

Local Global

Extreme global solutions

Keep linear helicalaxis

Keep monomer orientations

CURVES

R. Lavery and H. Sklenar J. Biomol. Struct. Dyn. 6, 1989, 655

Base reference system

Axis reference system

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)

Curves helical axis

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

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

B-DNA - 2ns dynamic trajectory

"LONG" MD SIMULATIONS

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

Periodic boundary conditions

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

MD snapshots

MD time series- sugar phase- groove width

MD time series- base pair Hbonds

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

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

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

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

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)

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

ACGT trajectory

B-DNA

A-DNA

Last ns

Helical parameters

Translation Rotation

ACGT helical parameters - instantaneous

SYMMETRY?

Each oligomer contains ≥2 "identical" tetramers

G-D-ABCD-ABCD-ABCD-G

ACGT helical parameters - histograms

C6pG7

C10pG11

GCGC helical parameters - histograms

C4pG5

C6pG7

C8pG9

C10pG11

GCGC helical parameters

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

CGCG backbone parameters

G7pC8

G11pC12

C6pG7

C10pG11

g-/g+ g+/t

transition

- G11pC12

- G11pC12

g-

g+

g+

t

impact on twist

- G11pC12

- G11pC12

g-

g+

g+

t

SEQUENCE DEPENDENT STRUCTURE?

CpG translational parameters

CpG rotational parameters

IONS AROUND DNA

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

Volume sampled by ions during 50ns simulation time

Na+

K+

Most frequently visited zones

Na+ K+

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+

Minor groove width at C8 level

Na+

K+

/ transitions in Na+ dynamics

redgreen

/ transitions in K+ dynamics

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