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Biophysical Chemistry G4170: Introduction to Molecular Dynamics

Biophysical Chemistry G4170: Introduction to Molecular Dynamics. Ruhong Zhou. IBM Thomas Watson Research Center Yorktown Heights, NY 10598. Contents. Overview Force Fields Solvation Models Molecular Dynamics Sampling and Advanced Topics. NMR or X-ray structure refinements

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Biophysical Chemistry G4170: Introduction to Molecular Dynamics

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  1. Biophysical Chemistry G4170: Introduction to Molecular Dynamics Ruhong Zhou IBM Thomas Watson Research Center Yorktown Heights, NY 10598

  2. Contents • Overview • Force Fields • Solvation Models • Molecular Dynamics • Sampling and Advanced Topics

  3. NMR or X-ray structure refinements Protein structure prediction Protein folding kinetics and mechanics Conformational dynamics Global optimization DNA/RNA simulations Membrane proteins/lipid layers simulations Molecular Simulations

  4. Anti-Microbial Peptide Simulation

  5. Challenges Sampling Solvation Force Fields

  6. I. Force Fields

  7. What is a Force Field? • Force field is a collection of parameters for a potential energy function • Parameters might come from fitting against experimental data or quantum mechanics calculations

  8. Various Types of Force Fields • Lattice models • Off-lattice models • United-atom force fields (OPLS, MM, AMBER) • All-atom force fields (OPLSAA, AMBER94, CHARMM22) • Next generation force fields: Polarizable Force Fields (Polarizable OPLSAA, AMBER2002, TINKER PFF)

  9. Origin of Force Fields Quantum Mechanics The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation. -- Dirac, 1929

  10. Born-Oppenheimer Approximation • Time-dependent Schrödinger Equation • Time-independent Schrödinger Equation (stationery state) • Born-Oppenheimer approximation: separate the nucleus’ motion from electrons’

  11. Force Fields: Typical Energy Functions Bond stretches Angle bending Torsional rotation Improper torsion (sp2) Electrostatic interaction Lennard-Jones interaction

  12. Bonding Terms: bond stretch • Most often Harmonic • Morse Potential for dissociation studies r0 D Two new parameters: D: dissociation energy a: width of the potential well r0

  13. Bonding Terms: angle bending • Most often Harmonic • CHARMM force field’s Urey-Bradley angle term: q0 This UB term is only found in CHARMM force field to optimize the fit to vibrational spectra. s: the 1,3-distance. Mackerell et al. J. Phys. Chem. B 102, 3586, 1998

  14. Bonding Terms: Torsions • Torsion energy: rotation about a bond (dihedral angles) i k f j l i-j-k-l Vn: force constant n: periodicity of the angle ( determines how many peaks and wells in the potential, often from 1-6 ) d: phase of the angle (often 0º or 180º)

  15. Bonding Terms: Improper Torsions • Improper torsion is not a regular torsion angle. It is used to describe the energy of out-of-plane motions. It is often necessary for planar groups, such as sp2 hybridized carbons in carbonyl groups and in aromatic rings, because the normal torsion terms described above is not sufficient to maintain the planarity (w~0). j w k i l or i-j-k-l

  16. Non-bonded Terms • Electrostatic interactions (Coulomb’s Law) • Lennard-Jones interactions • Combination Rules for LJ ~1/r (OPLSAA)

  17. 1-4 Non-bonded Interactions l • Non-bonded exclusions • 1-2 and 1-3 interactions excluded • 1-4 interactions partially excluded • Partly because they are included in bonded terms already, and partly because they would be huge to cause stability problem if included • 1-4 interaction scalings • OPLSAA scales by 0.5 for both electrostatic and LJ • AMBER94 scales 0.5 for LJ and 1/1.2 for electrostatic interaction • CHARMM22 has special 1,4-terms 1-4 1-3 i k 1-2 j Even though they are non-bonded interactions, 1-4 terms are often calculated along with bonded terms. Question: is the number of 1-4 terms the same as the number of torsion terms?

  18. Gradients and Hessians The first and second derivatives of the energy function are often needed Gradient Hessian

  19. What do these FF parameters look like?

  20. Atom types (AMBER)

  21. Bond Parameters

  22. Angle Parameters

  23. Torsion Parameters

  24. Improper Torsions

  25. Van der Waals (LJ) Parameters

  26. Atomic Partial Charges(ESP fitting)

  27. Where do these parameters come from?

  28. Force Field Parameterization • Equilibrium bond distances and angles: X-ray crystallography • Bond and angle force constants: vibrational spectra, normal mode calculations with QM • Dihedral angle parameters: difficult to measure directly experimentally; fit to QM calculations for rotations around a bond with other motions fixed • Atom charges: fit to experimental liquid properties, ESP charge fitting to reproduce electrostatic potentials of high level QM, X-ray crystallographic electron density • Lennard-Jones parameters: often most difficult to determine, fit to experimental liquid properties, intermolecular energy fitting

  29. Applications • NMR or X-ray structure refinement • Protein structure prediction • Protein folding kinetics and mechanics • Conformational dynamics • Global optimization • DNA/RNA simulations • Membrane proteins/lipid layers simulations

  30. Protein Structure Prediction and Protein Folding Fundamental Questions • What is the structure of this protein? • Can be experimentally determined, today we know the structure of ~18,000 proteins • Can be predicted for some proteins, usually in ~1 day on today's computers Protein Structure Prediction • How does this protein form this structure? • The process or mechanism of folding • Limited experimental characterization • Why does this protein form this structure? • Why not some other fold? • Why so quickly? -> Levinthal's Paradox: As there are an astronomical number of conformations possible, an unbiased search would take too long for a protein to fold. Yet most proteins fold in less than a second! Protein Folding

  31. Strategies for Protein Structure Prediction Comparative Modeling Fold Recognition Ab Initio Method 1. Identify sequence homologs as templates 2. Use sequence alignment to generate model 3. Fill in unaligned regions 4. Improves with data 1. Fold classification 2 3D-Profiles 3. Improves with data 1. Representation 2. Force field 3. Global Optimization 4. Structure at global minimum 5. Can discover new folds Caveats 1. Requires > 25% sequence identity 2. Loops and sidechain conformations are critical 1. Needs good number of proteins in each fold 2. Critically dependent on scoring function 1. Computationally intensive 2. Physical modeling Resolution < 3 A 3 - 7 A > 5 A Time to Compute < Day ~ Day >> Day

  32. Protein Folding: Fast Folders Time Scale: • Trp-cage, designed mini-protein (20 aa): 4ms • b-hairpin of C-terminus of protein G (16 aa) : 6ms • Engrailed homeodomain (En-HD) (61 aa): ~27ms • WW domains (38-44 aa): >24ms • Fe(II) cytochrome b562 (106 aa): extrapolated ~5ms • B domain of protein A (58 aa): extrapolated ~8ms 80’s 90’s 00’s 00’s 90’s 80’s ps ns ms ms ms sec Folding Experiments Folding MD Simulations

  33. Example: Trp-cage Folding • Newly designed 20-residue mini-protein called Trp-cage • Residue Trp6 is caged • Folds in about 4ms • Well defined two-state folder • Up to 80-90% population at low temperature Trp-cage

  34. Example: Trp-cage Folding J. Neidigh, R. Fesinmeyer, and N. Andersen, Nature Struc. Bio. 9, 425, 2002

  35. Example: Trp-cage Folding • Folds in 4ms at 300K • Well defined two state folder • Very high population at low T L. Qiu, S. Pabit, A. Roitberg, and S. Hagen, JACS 124, 12952, 2002

  36. Example: Trp-cage Structure Blue: MD simulation Grey: NMR structure 0.97 A Ca RMSD 1.4 A RMSD heavy atoms • AMBER99 Force Field • Continuum Solvent GBSA • NVT ensemble C. Simmerling, B. Strockbine, A. Roitberg, JACS 124, 11258, 2002

  37. Example: Trp-cage Folding Kinetics • OPLS united atom Force Field • Continuum Solvent GBSA • Langevin dynamics • Water viscosity g=91/ps B: MD simulation C: NMR structure 2.1 A Ca RMSD Folding time 1.5ms (3.0 A cutoff) to 8.7 ms (2.5 A cutoff) M. Snow, B. Zagrovic, V. Pande, JACS 124, 14548, 2002

  38. Example: Trp-cage Folding Mechanism Arg16 Asp9 R. Zhou, Proc. Natl. Acad. Sci., 100, 13280-13285, 2003

  39. Force Field Comparison • CHARMM22, AMBER94, OPLSAA • TIP3P explicit water • PME for electrostatics • SHAKE, time step 2fs • 2ns NVT MD simulation D. Price, C. Brooks, J. Comput. Chem. 23, 1045, 2002

  40. Force Field Comparison • Ca RMSD, radius of gyration, SASA, are all comparable for three FF • Radius gyration and SASA slightly larger than experimental values (structures opened up a bit) • Average structures from three FF are very similar (small RMSDs). The differences are comparable to two independent trajectories with the same CHARMM force field.

  41. Force Field Comparison

  42. Force Field Comparison • Backbone order parameters (S2) • NMR order parameters for these residues are 0.85, 0.90, 0.81 for Calbindin, IL4 and GPILA respectively • Fluctuations are small in these regions S2 is plateau value of the autocorrelation function of the 2nd-order Legendre polynomial of N-H vector

  43. Solvation Free Energy Comparison M. Shirt, J. Pitera, W. Swope, V. Pande, J. Phys. Chem. 2003

  44. Relative Solvation Free Energy: Ala-> X mutation

  45. b-hairpin Folding in Various Models R. Zhou, et al, PNAS 98, 2001 R. Zhou, and B. Berne, PNAS 99, 2002

  46. Lowest free energy structures • Erroneous salt-bridges exist in all continuum solvent models • Overly strongly salt-bridge effects expelled F50 out of the hydrophobic core in SGB • AMBER94/GBSA and AMBER99/GBSA turned beta-hairpin into an alpha-helix • Only AMBER96/GBSA gives a reasonable lowest free energy structure

  47. Which Force Field to Use? • Most popular force fields: CHARMM, AMBER and OPLSAA • OPLSAA(2000): Probably the best available force field for condensed-phase simulation of peptides. Work to develop parameterization that will include broader classes of drug-like molecules is ongoing. GB/SA solvation energies are good. • MMFF: An excellent force field for biopolymers and many drug-like organic molecules that do not have parameters in other force fields. • AMBER*/OPLS*: Good force fields for biopolymers and carbohydrates; many parameters were added in MacroModel which extend the scope of this force field to a number of important organic functional groups. GB/SA solvation energies range from moderate (AMBER*) to good (OPLS*). • AMBER94: An excellent force field for proteins and nucleic acids. However, there are no extensions for non-standard residues or organic molecules, also there is a alpha-helix tendency for proteins. AMBER99 fixes this helix problem to some degree, but not completely. • MM2*/MM3*: Excellent force fields for hydrocarbons and molecules with single or remotely spaced functional groups. GB/SA solvation energies tend to be poor relative to those calculated with other force fields. • CHARMM22: Good general purpose force field for proteins and nucleic acids. A bit weak for drug-like organic molecules. • GROMOS96: Good general purpose force field for proteins, particularly good for free energy perturbations due to soft-core potentials. Weak for reproducing solvation free energies of organic molecules and small peptides. http://www.schrodinger.com/docs/mm7.1/html/faqs/which_ffield.html

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