A Coarse-Grained Model of DNA with Almost Atomic Resolution

Transcription

1 A Coarse-Grained Model of DNA with Almost Atomic Resolution Pablo D. Dans Puiggròs, PhD Joint CRG-BSC-IRB Program on Computational Biology Molecular Modelling & Bioinformatics Group Institute for Research in Biomedicine Barcelona, Spain

2 The Coarse Grain Concept As illustrated by Las Meninas Diego Velázquez 1656 Pablo Picasso 1957

3 Biomolecular Simulations A matter of size Macromolecular complexes ~ to ~ atoms Small peptides ~ atoms Bacteria/cells? 7e+9 carbon atoms Virus several millions of atoms

4 Biomolecular Simulations A matter of size and time! fs 100 fs - ps ms ms Electronic exitations Vibrations Rotations Conformational Transitions Macromolecular complexes ~ to ~ atoms Small molecules ~ atoms ps e-tranfer reactions ns Peptide folding Enzymatic reactions ms DNA melting ms - s Protein folding Virus several millions of atoms Bacteria/cells? 7e+9 carbon atoms

5 Biomolecular simulations Molecular Dynamics: limitations How long should I simulate? = What do I want to see? How much should I wait if I expect to see: A rainy day in March? One week A hurricane? One year A glaciation? Hundreds of years In the atomic world: Werner et al. Adv Drug Deliv Rev. 2012, 64: 323.

6 Two Basic Approaches for Modelling Biomolecules Schrödinger and Newton: like cat and dog! Theoretical approaches (Atomic and molecular scales) Based on equations that represent the molecular interactions and allow to extract physical and nonphysical observables (Physicochemical properties) CLASSICAL Newton s equations 1666 Two possible ways QUANTUM Schrödinger s equation 1927 Give rise to two different models (nuclear detail vs electronic detail) Structure at the nuclei level Dynamics / Reactivity Structure at the electronic level Reactivity / Dynamics

7 Models for the Simulation of Biomolecules Dealing with size, time and the answer we want! Quantum Mechanics Dozens to hundreds of atoms Few ps QM/MM Dozens to thousands of atoms Dozens of ps Molecular Mechanics Thousands to (if) few millions of atoms Hundreds of ns to few ms MM/CG few millions of atoms Hundreds of ms to (if) few ms Coarse Grained Several millions of atoms Dozens of ms to ms

8 The Classical Approach How to obtain a coarse-grained Hamiltonian?

9 Review Coarse-grain models: different philosophies Bottom-up The coarse-grained (CG) Hamiltonian is chosen and further parameterized using all-atom (AA) simulations as a reference, based on matching CG and AA partition functions. Top-down The force-field is chosen based on either a structural intuition or trial and error simulations. Afterward, the undetermined parameters are fitted using the available experimental data.

10 Review Coarse-grain models: different approaches Elastic Networks Discrete Molecular Dynamics Orellana L., Rueda M., Ferrer-Costa C., López-Blanco J.R., Chacón P. and Orozco M. Approaching Elastic Network Models to Molecular Dynamics Flexibility J. Chem. Theory Comput. (2010), 6, Go-like models Emperador A., Meyer T. and Orozco M. Protein flexibility from discrete molecular dynamic simulation using quasi - Physical potentials. Proteins: Structure, Function and Bioinformatics. (2010), 78, Hills R. D. Jr, Brooks C. L. III. Int. J. Mol. Sci. (2009), 10,

11 Review Coarse-grain models of DNA The model of Mergell et al: It is composed of one rigid ellipsoid per base pair with an internal energy derived from the Gay-Berne potential. This resolution allows the study of phase transition from B- to S-DNA upon stretching. [Mergell, B. Phys. Rev. E. 2003] Generic model for double-helix molecules in solution: first model in solution that achieve spontaneous helix formation. Molecular recognition between strands is neglected. Lack of correspondence with the atomistic model. [Tepper, H. L.; Voth, G. A. J. Chem. Phys. 2005] From rigid base pairs to semiflexible polymers: Wormlike chain description of DNA. Sequencedependent elastic potentials are obtained from MD. Molecular specifity between the DNA strands is also neglected. [Becker, N. B.; Everaers, R. Phys. Rev. 2007]

12 Review Coarse-grain models of DNA Wevalet-base multi-scale coarse graining approach for DNA: Based on distribution functions between centers of mass and homogenized coarse-scale effective potential functions between superatoms. Loss of the chemical sense and the correspondence with the all-atoms model. [Chen, J.-S.; Teng, H.; Nakano, A. Finite Elem. Anal. Design 2007] Coarse-grained model of DNA by Knotts et al: Explicit electrostatic for phosphate groups. Simulation with implicit solvation. The proposed parametrization is not consisting with the most popular force-fields used to simulated DNA. [Knotts, T. A.; Rathore, N.; Schwartz, D. C.; de Pablo, J. J. J. Chem. Phys. 2007]

13 Review Coarse-grain models of DNA Polymer chain models of DNA to simulate chromatin: Wrapping of a 200-bp DNA on the histone core / Simulation of a DNA fiber consisting of 100 nucleosomes. Solenoid or zig-zag models are discussed. Specific recognition at the molecular level is not present. [Langowski, J. Eur. Phys. J. E 2006] Simulation of genome packing: Molecular dynamics in implicit solvent. One centroid for each base pair. Suggest that packing does not proceed in the deterministic fashion but rather is stochastic in character. [Forrey, C. et al. Biophys. J. 2006] DNA - Protein docking: Coarse grain model specifically dedicated to protein-dna docking. 11 beads per complementary nucleotides. [Poulain, P. et al. J. Comput. Chem. 2008]

14 General Overview A multiscale model for the simulation of B-DNA in implicit and explicit solvent Presentation of the different CG models to deal with DNA, solvent and ions. Implementation and main features. Full CG simulations in explicit solvent at nearly physiological conditions. DNA ions interaction. Full CG simulations in implicit solvent. Breathing, fraying, partial melting, rehybridization, bending and kinking. Multiscale model. Hybrid allatom/coarse-grained simulations in implicit and explicit solvent.

15 General Overview A multiscale model for the simulation of B-DNA in implicit and explicit solvent Presentation of the different CG models to deal with DNA, solvent and ions. Implementation and main features. Full CG simulations in explicit solvent at nearly physiological conditions. DNA ions interaction. Full CG simulations in implicit solvent. Breathing, fraying, partial melting, rehybridization, bending and kinking. Multiscale model. Hybrid allatom/coarse-grained simulations in implicit and explicit solvent.

16 Coarse Grain Scheme A model for simulating B-DNA with 6 beads per nucleic acid residue Dans, Zeida, Machado, Pantano, J. Chem. Theory Comput. 2010, 6, % size reduction

17 Biomolecular Simulations Number of atoms Moore s law in molecular Biology mb.au.dk ns ms Vendruscolo, Dobson, Curr. Biol. 2011, 21, R68. The computational power needed to carry out a simulation increases, at least in the most straightforward approaches, linearly with the simulation time (so that doubling the length of a simulation requires twice the power) and with the square of the number of atoms involved (so that doubling the size of a system quadruples the power required to simulate it). Therefore, from the increase in the accessible timescales (blue line), it is possible to infer the corresponding increase in the accessible system sizes (blue line).

18 Coarse Grain Scheme A coarse-grain model of DNA fully back-mappable Home made fortran 90 code Mapping Back-Mapping Minimization RMSD Fitting Sugar pucker distribution: C2 n = 80% C3 x = 20% e / z distribution: BI = 100% a / g distribution: g-/g+ = 100%

19 Coarse Grain Scheme Explicit solvent and ions CG Ions Head-Gordon, Hura. Chem. Rev. 2002, 102, CG solvent WT4 Na+ K+ Cl- NaW KW ClW Darre, Machado, Dans, et al. J. Chem. Theory Comput. 2010, 6, 3793.

20 A Painless Way to Transferability and Compatibility A plug & play force field using a standard Hamiltonian Very easy to parameterize (all bonds and angles have the same force constant) Very hard (reproduce the behavior of stateof-the-art all-atom force-field, parmbsc0) T >4.0 Å 500 ns 20ºC 100 ns Hard Fairly easy (compatible with all-atom force-fields) 3 ms Dans, Zeida, Machado, Pantano, J. Chem. Theory Comput. 2010, 6, 1711.

21 Review Major groove Minor groove Coarse-grain models of DNA: Sirah force field 30 atoms 6 beads Reducción of 80% Some characteristics of the model Run 2400 time faster than all-atom simulations Reproduce Watson-Crick hbonds Reproduce base stacking Capture sequence dependent effects Fully back-mappeable Explicit electrostatic Dans, Zeida, Machado et al. J Chem Theory Comput. 2010, 6:1711. Darré, Machado et al. J Chem Theory Comput. 2010, 6:3793. Machado et al. Phys Chem Chem Phys. 2011, 13: Zeida, Machado et al. Phys Rev E. 2012, Aceptado.

22 Full Coarse Grain Description B-DNA in explicit solvent at nearly physiological conditions

23 General Overview A multiscale model for the simulation of B-DNA in implicit and explicit solvent Presentation of the different CG models to deal with DNA, solvent and ions. Implementation and main features. Full CG simulations in explicit solvent at nearly physiological conditions. DNA ions interaction. Full CG simulations in implicit solvent. Breathing, fraying, partial melting, rehybridization, bending and kinking. Multiscale model. Hybrid allatom/coarse-grained simulations in implicit and explicit solvent.

24 CG-DNA with explicit solvation: WT4 Ion induced minor groove widening in the ms timescale Shui, et al. Biochemistry 1998, 37, Manning s counterion condensation theory ms Na+ and K+ binding events ns Na+ binding events Ponomarev, Thayer, Beveridge. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, Pérez, Luque, Orozco. J. Am. Chem. Soc. 2007, 129,

25 CG-DNA with explicit solvation: WT4 Reversible electrostatic collapse and the minor groove widening Shui, et al. Biochemistry 1998, 37, ions = 0.98 nm agw 6 ions = 0.94 nm agw

26 CG-DNA with explicit solvation: WT4 Ions and solvation sites in fused hexagon motif Experimentally the structure is organized in four layers of solvent/ions sites 3D occupancy map of WT4, NaW and KW around the minor groove of the AT-track Shui, et al. Biochemistry 1998, 37, Darre, Machado, Dans, et al. J. Chem. Theory Comput. 2010, 6, 3793.

27 General Overview A multiscale model for the simulation of B-DNA in implicit and explicit solvent Presentation of the different CG models to deal with DNA, solvent and ions. Implementation and main features. Full CG simulations in explicit solvent at nearly physiological conditions. DNA ions interaction. Full CG simulations in implicit solvent. Breathing, fraying, partial melting, rehybridization, bending and kinking. Multiscale model. Hybrid allatom/coarse-grained simulations in implicit and explicit solvent.

28 Experimental ways to measure the time of structural events Measured over eight orders of magnitude Small conformational changes ps timescale 1. Time-resolved Stokes shifts (TRSS) spectroscopy using coumarin. Helix fraying occurs in a few ps time scale. Base pair opening in the multi-ps time scale. Andreatta et al. J. Am. Chem. Soc. 2006, 128, Moderate conformational changes ns timescale Large? conformational changes ms timescale 2. 1 H NMR measurement of imino-proton/water exchange. According to this methodology the rate for the closing of an unbounded base pair is from hundreds of ps to dozens of ns. Deva Priyakumar, MacKerell Jr. J. Am. Chem. Soc. 2006, 128, Fluorescence spectroscopy, using fluorophore and quenchers. The dynamics of bubble formation triggers a life time of 20 to 100 ms. Altan-Bonnet, Libchaber, Krichevsky. Phys. Rev. Letters 2003, 90,

29 CG-DNA in Implicit Solvent Breathing dynamics and timescale >4.0 Å Multiexponential kinetics inferred from fluorescence relaxation times = open states of many sizes are formed (2 to 10 bp) From ps to ms time scale Altan-Bonnet, Libchaber, Krichevsky. Phys. Rev. Letters 2003, 90, Time

30 CG-DNA in Implicit Solvent bubbles? ~50 microseconds fluorophore and quenchers Strong bending Kinks few microseconds? Breathing ps to ns Time-resolved Stokes shifts & imino-proton Partial melting / rehybridization multi-microseconds fluorophore and quenchers End fraying picoseconds Time-resolved Stokes shifts

31 CG-DNA in Implicit Solvent Breathing dynamics and timescale Zeida, Dans, Pantano, submit 2011

32 The Sampling Problem What s the moral of the story? The woman, the cow or both??????????????

33 The Sampling Problem What s the moral of the story? The woman, the cow or both

34 The Sampling Problem What s the moral of the story? The woman, the cow or both

35 The Sampling Problem The woman and the cow: hybrid AA/CG models +

36 General Overview A multiscale model for the simulation of B-DNA in implicit and explicit solvent Presentation of the different CG models to deal with DNA, solvent and ions. Implementation and main features. Full CG simulations in explicit solvent at nearly physiological conditions. DNA ions interaction. Full CG simulations in implicit solvent. Breathing, fraying, partial melting, rehybridization, bending and kinking. Multiscale model. Hybrid allatom/coarse-grained simulations in implicit and explicit solvent.

37 Hybrid All-Atom / Coarse-Grained Simulations Which are the advantages of a multiscale approach? Residue modifications / Non-WC interactions DNA-Protein interaction Ligand binding 3N4O 2IVH 2V3L 2XRO

38 Hybrid All-Atom / Coarse-Grained Simulations Which are the advantages of a multiscale approach? Structural representation of the hybrid model (Hydrogen atoms are omitted for clarity) Machado, Dans, Pantano, Phys. Chem. Chem. Phys. 2011, 13,18134

39 Hybrid All-Atom / Coarse-Grained Simulations Helical parameters Technical details: SOFTWARE: AMBER RUN: 100ns production TIMESTEP: 2fs (+SHAKE) TEMP: 298K SOLVENT: GB model SALT: 0.15M CUTOFF: 18Å ANALYSIS: Curves+ Nucleic Acids Res. (2009) 37: 5917.

40 Hybrid All-Atom / Coarse-Grained Simulations Electrostatic balance Difference in electrostatic potential grids between hybrid and AA systems Dipole moments APBS calculations parm99 charmm97 CG

41 Perspectives A multiscale model including explicit solvent All Together Now System composition: 20-mer DNA 6 AA residues 14 CG residues Ions 8 Na+ 30 NaW (CG ion) Water 783 SPC 2024 WT4 (~22264 SPC)

42 Perspectives A multiscale model including explicit solvent and now PROTEINS!!! Thank you!