EXTENDING THE BOUNDARIES OF STRUCTURAL MODELING EPIGENETIC EFFECTS ON NUCLEOSOME POSITIONING

Transcription

1 EXTENDING THE BOUNDARIES OF STRUCTURAL MODELING EPIGENETIC EFFECTS ON NUCLEOSOME POSITIONING Peter Minary Computational Structural Biology Group Stanford University Stanford, CA 94305

2 ~ 0.3 nm TO MODEL ATOMIC EFFECTS THAT ARE MAGNIFIED IN THE CONTEXT OF LARGE ASSEMBLIES ~ 1.3 nm OBJECTIVE!? SOLUTION BY JUMPING FROM ATOMIC TO MESO SCALE AND KEEPING THE RESOLUTION ~ 10 nm ~ 50 nm

3 THE PROBLEM

4 OBSTACLES TO MESO SCALE ALL ATOM MODELING Energy Surface Problem: Rough Guiding Potential on Each Scale V(u) V(x) V ref (x) x u[x] = x 0 + exp{ β V ref [y] } dy x 0 Chandler et al. Minary et al. SIAM J. Sci. Comp (2008). REPSWA Dimensionality Problem: Large Number of Degrees Of Freedom N DOFs = 6000 N atm = 2000 N res = 100 N a/r = 10 Bottom Line 6000 vs 6 SOLUTION: MOSAICS (Methodologies for Optimization and SAmling In Computational Studies) 4

5 OBSTACLES TO MESO SCALE ALL ATOM MODELING Energy Surface Problem: Rough Guiding Potential on Each Scale Chandler et al. Dimensionality Problem: Large Number of Degrees Of Freedom N DOFs = 6000 N atm = 2000 N res = 100 N a/r = 10 Bottom Line 6000 vs 6? SOLUTION: MOSAICS (Methodologies for Optimization and SAmling In Computational Studies) 5

6 THE OUTLINE Natural Move Monte Carlo, Basic Concepts & the Algorithm In Silico Epigenetics, Nucleosome Positioning / Methylation Algorithmic Benchmarks or Hierarchical Natural Move MC 6 6

7 NATURAL MOVE MONTE CARLO Minary, P., Levitt, M. Conformational Optimization with Natural Degrees of Freedom: A Novel Stochastic Chain Closure Algorithm. Journal of Computational Biology 17(8), (2010).

8 NATURAL DEGREES OF FREEDOM FOR NUCLEIC ACIDS D x D y D z Shift Slide Rise τ Tilt ρ Roll ω Twist S x S y S z Shear Stretch Stagger κ Buckle π Propeller σ Opening D x y D y y D z y y y y τ ρ ω z z z z z z x x x x x x O3 S x y y y S y S z D x D y D z τ ρ ω z z z C4 RC 1 N S x S y S z κ π σ x x x C5 O1 O5 P y y y dof: 10 (4+12x½) κ π σ z z z O3 Moves break the chain! x x x 8

9 NATURAL DEGREES OF FREEDOM FOR PROTEINS S x S y S z Shear Stretch Stagger S x y z x κ π σ Buckle Propeller Opening Moves break the chain! 9

10 RECURSIVE STOCHASTIC CLOSURE 1 cycle of RSC = DFC[ SPC[ SPC[ SPC[ ] ] ] ] Molten zone 1 st cycle One SPC step Restores 4-5, breaks 3-4 DFC Multiple SPC steps Propagates the chain brake Narrows closure gap AC = O(N cd ) 2 << O(f NP (N cd )) 1 N cd = 2 N m + 5 m cycles Molten zone (1) Dodd et al. Mol. Phys (1993). (2) Minary, P., Levitt, M. J. Comp. Biol. 17(8) (2010). 10

11 < P acc > NATURAL MOVE MONTE CARLO USING RSC DFC RSC (m = 1) RSC (m = 5) log 10 [σ trans (Å)] Force Field: amber99-bs0, System: E2 binding DNA site, 5 -ACCGAATTCGGT-3 11

12 APPLICATIONS 12

13 NUCLEOSOME POSITIONING Minary, P., Levitt, M. Ab Initio Nucleosome Positioning and Epigenetics. Nature XXX, xxxxx-xxxxx (2012). In Review. 13

14 NUCLEOSOME POSITIONING E(i) O(i) THE COMPUTATIONAL PIPELINE Threading S n Q i = n Template Sequence Structure S(i) NUCLEOSOME FORMATION ENERGY S j E = E ( ) E ( ) T k Q T j O i / O k ~ exp( β ΔE jk ) S k 14

15 ( E n E l )( i ) CC x ( i ) YEAST CHROMOSOME 14 In Vitro NUCLEOSOME POSITIONING NUCLEOSOME FORMATION ENERGY CC 2000 CC P( CC x ) E n : E nucleosome E l : E linear E n E l InVitro CC = Sequence Position (i) E n E l 15

16 YEAST CHROMOSOME 14 NUCLEOSOME POSITIONING CONTROL CALCULATIONS P(i) in vitro ab initio AMBER99-bs0 ab initio AMBER99 ab initio CHARMM27 P(i) in vitro 300 K No Solvent 300 K 1200 K 1500 K 2500 K P(i) in vitro DNA template 1kx5 DNA template ideal P Minary Sequence Position (i) 16

17 NUCLEOSOME POSITIONING EPIGENETIC EFFECTS Small Atomic Changes (5Me-C, 5hMe-C, HXXxx, ) Atomic Large Meso-Scale Assemblies (Nucleosome, Hetero/EuChromatin) Meso Haifa

18 YEAST CHROMOSOME 14 In Vitro NUCLEOSOME POSITIONING DNA METHYLATION, G C 5Me CC = Percentage GC ΔΔE me NOT ADDITIVE ΔE nme ADDITIVE ΔE lme ADDITIVE CC = CC = CC = ΔΔE me ΔE nme ΔE lme Percentage GC Percentage GC Percentage GC 18

19 YEAST CHROMOSOME 14 Energy NUCLEOSOME POSITIONING DNA METHYLATION, G C 5Me E n E l E nme E lme ΔΔE me Sequence Position (i) ΔΔE me MODERATES THE SEQUENCE DEPENDENCE OF NUCLEOSOME BINDING CC = CC = CC = ΔΔE me ΔE nme ΔE lme E n E l E n E l E n E l 19

20 NUCLEOSOME POSITIONING MAIN MESSAGE Binding energy correlates to in vitro nucleosome occupancy. 5MeCyt modulates bending energy, nucleosome occupancy. Methylation is not additive with respect to G+C concentration. There is no need for specific DNA nucleosome interactions. AMBER-99bs0 & implicit electrostatics works sufficiently well

21 ALGORITHMIC BENCHMARKS OR HIERARCHICAL NATURAL MOVE MC Sim, A. S. L., Levitt, M., Minary, P. Modeling and Design by Hierarchical Natural Moves. PNAS 109: (2012). 21

22 HIERARCHICAL NATURAL MOVE MC RNA 4-WAY JUNCTION 22

23 SYMMETRICAL FRACTAL RNA εrror(i) HIERARCHICAL NATURAL MOVE MC BENCHMARK TO THEORY i x 10 4 L 1 L 7 i<j i, j εrror(i) 23

24 RNA NANOTECHNOLOGY HIERARCHICAL NATURAL MOVE MC BENCHMARK TO EXPERIMENT WT MT? WET LAB IN SILICO PREDICTION WT <θ> ~90 MT <θ> ~60 24

25 FUTURE DIRECTIONS Further Applications of (Hierarchical) Natural Move Monte Carlo Epigenetics & Nucleosome Positioning 5-Me-C, 5-MeOH-C 5-CO-C, 5-COOH-C HXXxx,. 2D Image Driven Cryo-EM Refinement 3WJ FAS RIB Modeling RNA Nanomedicine & rrna Methodologies for Optimization and SAmpling In Computational Studies MOSAICS, MOSAICS-EM: FURTHER RELEASES: MOSAICS-NMR, MOSAICS-X, MOSAICS-FRET 25

26 ACKNOWLEDGEMENTS Michael Levitt (Stanford) Mark Tuckerman (NYU) Glenn Martyna (IBM) Past & Present Jernei Ule (Cambridge) Peter Lukavsky (ETH) Michael Kiebler (UVienna) RNA Roger Kornberg (Stanford) Yahli Kornberg (Stanford) Jody Puglisi (Stanford) Chromatin Wah Chiu (Baylor) Timothy Richmond (ETH) Junjie Zhang (Biophysics) Gaurav Chopra (Math/ME) Adelene Sim (Physics) MOSAICS Applications Steve Ludtke (Baylor) Cryo-EM Workshop 26

27 MOSAICS-EM Workshop 3WJ 3WJ 3WJ 27

28 MONTE CARLO RECURSIVE STOCHASTIC CLOSURE Monte Carlo Minimization (1) is Monte Carlo (MC) guided by E( X ) min E( X ) X E E Monte Carlo Recursive Stochastic Closure (2) is guided by E (X i X d ) min E(X X i X d ) d (1) Wales, D. J., Scheraga, H. A. Science (1999). (2) Minary, P., Levitt, M. J. Comp. Biol. 17(8) (2010). 28

29 NATURAL MOVE vs LOOP TORSIONAL MC NM-6 (1) (1) N cd = 19 NMMC (2) SCOP id: d1div_2, 55 residue domain (1) Minary, P., Levitt, M. J. Comp. Biol. 17(8) (2010). (2) Minary, P., Levitt, M. J. Mol. Biol (2008). 29

30 HIERARCHICAL NATURAL MOVE MC TESTING METHOD-SOFTWARE NM-MOSAICS FA-MCSym FA-Rosetta HNM-MOSAICS L 1 L 1 - L 4 Distance Distributions Canonical Trajectory L 1 - L 4 30

31 HIERARCHICAL NATURAL MOVE MC THE METHOD 31

32 TRANSFORMATION OF VARIABLES Minary P., Tuckerman, M. E., Martyna, G. J. Dynamical Spatial Warping: A Novel Method for the Conformational Sampling of Biophysical Structure. SIAM J. Sci. Comp (2008).

33 TRANSFORMATION OF VARIABLES Q X dxexp V (x) U Q duexp V% eff (x(u)) V (x) 1 ln J(u[x]) % Veff (x[u]) x u[x] dy exp V ref ( y) x 0 J(u[x]) dx du exp V (x[u]) ref % V eff (x[u]) V(x) V ref (x[u]) REPSWA 33

34 Φ 200 (X[U]) Φ 200 (U[X]) X MCMC BENCHMARKS U 10 6 fold speedup x analytical MCMC β = kt E = 10 kt x analytical MCMC steps (10 3 ) P(x) X[U] -1 1 x U[X] steps (10 3 ) P(x) 10 6 fold speedup steps (10 3 ) steps (10 3 ) Φ(X[U]) Φ(U[X]) steps (10 3 ) C 400 H 802 steps (10 3 ) 34 34