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implicit vs . explicit solvation

implicit vs . explicit solvation. water is only included implicitly as an effective (averaged) interaction with no atomic detail. an explicit representation of water is included at the molecular level. What does solvent do?. implicit vs . explicit solvation.

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implicit vs . explicit solvation

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  1. implicit vs. explicit solvation water is only included implicitly as an effective (averaged) interaction with no atomic detail an explicit representation of water is included at the molecular level What does solvent do?

  2. implicit vs. explicit solvation water is only included implicitly as an effective (averaged) interaction with no atomic detail an explicit representation of water is included at the molecular level • What does solvent do? • viscous damping force • dielectric screening / polarization • hydrophobic effect • structure

  3. implicit or no solvent

  4. U = q q i j e r ij • What does solvent do? • viscous damping force (not important) • dielectric screening  e = 1 gas phase e = 80 liquid phase ? dielectric constant, e = 4pe0e

  5. U = q q i j e r ij • What does solvent do? • viscous damping force (not important) • dielectric screening  e = 1 gas phase e = 80 liquid phase ? This is BULK solvent screening. At short range, no screening… 80 e vs. 1 distance

  6. U = q q i j e r ij • What does solvent do? • viscous damping force (not important) • dielectric screening  Simple approximation: Distance dependent dielectric e = rij or 4rij 80 e 1 distance

  7. U = q q i j e r ij • What does solvent do? • viscous damping force (not important) • dielectric screening  • Simple approximation: • Distance dependent dielectric • = rij or 4rij Better? Sigmoidal dielectric 80 e 1

  8. What does solvent do? • viscous damping force (not important) • dielectric screening • What does solvent do? • viscous damping force (not important) • dielectric screening  • hydrophobic effect

  9. surface area approaches Observation: Gsolvation for the saturated hydrocarbons in water is linearly related to the solvent accessible surface area …the line passing through the nonpolar Ala, Val, Leu and Phe has a slope of 22 cal/Å2 Creighton Proteins (FM Richards, Ann Rev Biophys Bioeng 6, 151-176 (1977))

  10. DGresidue = DsiAi atoms,i surface area approaches exposed solvent accessible surface area (SASA) Observation: Gsolvation for the saturated hydrocarbons in water is linearly related to the solvent accessible surface area Problems: • sensitive to si’s, parameterization, surface area and change in conformation • in dynamics you need derivatives of SASA • what about polarization effects? free energy of interaction of a solute with water atomic solvation parameters based on free energies of transfer

  11. what is the effective solvent polarization?(solve Poisson equation) Born: isolated point charge (q) in a spherical cavity of radius r immersed in a dielectric continuum with dielectric constant e ? r einside eoutside q

  12. what is the effective solvent polarization?(solve Poisson equation) Born: isolated point charge (q) in a spherical cavity of radius r immersed in a dielectric continuum with dielectric constant e

  13. what is the effective solvent polarization?(solve Poisson equation) Born: isolated point charge (q) in a spherical cavity of radius r immersed in a dielectric continuum with dielectric constant e Onsager: neutral system with dipole m

  14. { GBSA: generalized Born surface area approach SASA term Gsolvation = Gcavity + Gvdw + Gpolarization ? m q qi qj

  15. e-kfGB 1 -(1-)qiqj/fGB e 2 { GBSA: generalized Born surface area approach SASA term Gsolvation = Gcavity + Gvdw + Gpolarization e: dielectric constant, qi’s: charges, rij: distance between atom pairs. ai: Born radii; calculated numerically for each charged atom in solute; values change as calculation proceeds. k: modification to incorporate salt effects at low salt via a Debye-Huckel term fGB = (r2ij + a2ije-Dij)1/2 aij = (aiaj)1/2 Dij = r2ij/ 2a2ij

  16. e-kfGB 1 -(1-)qiqj/fGB e 2 { GBSA: generalized Born surface area approach SASA term Gsolvation = Gcavity + Gvdw + Gpolarization e: dielectric constant, qi’s: charges, rij: distance between atom pairs. ai: Born radii; calculated numerically for each charged atom in solute; values change as calculation proceeds. k: modification to incorporate salt effects at low salt via a Debye-Huckel term “this expression gives the Born equation for superimposed charges when rij = 0, the Onsager reaction field within 10% for a dipole in a spherical cavity when rij < 0.1 aij, and the Born plus Coulomb dielectric polarization energy within 1% for two charged spheres when rij > 2.5 aij.” (Still et al., 1990). fGB = (r2ij + a2ije-Dij)1/2 aij = (aiaj)1/2 Dij = r2ij/ 2a2ij

  17. GBSA: generalized Born surface area approach • Excellent agreement to FEP for neutral small molecules with only ~2-4x overhead compared to gas phase dynamics • Implemented in MacroModel, AMSOL, AMBER and CHARMM. [Recent resurgence in interest! Stable MD simulation / folding !!!] • Can give stable trajectories of proteins and nucleic acids; ~2-5x cost of in-vacuo simulations.

  18. Poisson-Boltzmann electrostatics • treats the solute as a low (fixed) dielectric medium containing atomic charges surrounded by a molecular surface immersed in a dielectric continuum • electrostatic component from solution of PB equations; most often done numerically by finite difference • hydrophobic/cavity term from surface area • gives reasonable free energies of solvation • can include salt effects through solution of non-linear PB Fixed, low dielectric in interior. Charges located at atomic positions. Surface (or dielectric discontinuity) is defined by SASA or vdw surface or … Dielectric continuum

  19. Poisson-Boltzmann electrostatics • treats the solute as a low (fixed) dielectric medium containing atomic charges surrounded by a molecular surface immersed in a dielectric continuum • electrostatic component from solution of PB equations; most often done numerically by finite difference • hydrophobic/cavity term from surface area • gives reasonable free energies of solvation • can include salt effects through solution of non-linear PB Issues: • no microscopic detail • strong dependence on radii • time consuming in MD • sensitivity to grid • sensitivity to interior/exterior dielectric Programs: DELPHI (Honig/Sharp), MEAD (Bashford), UHBD (McCammon), GRASP (Nicholls), APBS, ...

  20. METHODS: modified dielectric functions “surface area” methods “continuum” or Poisson-Boltzmann generalized Born methods [reaction field, integral equation methods] BENEFITS: Averaging is implicit; gives free energy of solvation Conformational sampling is “faster” implicit

  21. METHODS: modified dielectric functions “surface area” methods “continuum” or Poisson-Boltzmann generalized Born methods [reaction field, integral equation methods] BENEFITS: Averaging is implicit; gives free energy of solvation Conformational sampling is “faster” • CURSE: • cannot represent “specific” (direct) structural water interaction • the computational cost is still large • force field balance / parameterization • methods still under development (i.e. in flux) implicit

  22. explicit solvation viscous damping dielectric screening hydrophobicity, …, ? • ISSUES: • water model • sampling • boundary conditions (periodic or non-) • long range forces, cutoff methods/effects • METHODS: • [Langevin dipole] • TIP3P and other models (SHAKE)

  23. explicit solvation • what water model to use? • what representation or boundary conditions? • how to make the calculation tractable? • how much water to add?

  24. Explicit water models • flexible water models: few are in general use… • (see Levitt et al., 1995; Ferguson, 1995; Mizan et al., 1994, etc.) • rigid water models: • require SHAKE/RATTLE to constrain bonds and angles • TIP3P: method of choice with Cornell et al. force field • [well balanced with 6-31 G* charges since prepolarized through larger fixed dipole] • TIP4P/TIP5P: supported within LEaP (and PLEP) • SPC/E: works as well as TIP3P (or better), not supported by default in AMBER. • TIP3P, TIP4P: Jorgensen et al., 1983 • SPC/E: Berendsen et al., 1987 TIP: r(OH) = 0.9572 Å, >HOH = 104.52º SPC/E: r(OH) = 1.0 Å, >HOH = 109.47122 º

  25. rigid water models: how do they perform? • “reasonable” density, interaction energies and 1st peak radial distribution function occupancies • 3 site models underestimate compressibility • TIP3P has too little structure beyond the 1st peak; less tetrahedrality than TIP4P and tends to diffuse too rapidly • TIP4P has excellent density and proper oxygen structure however hydrogens are somewhat misplaced • In simulations of nucleic acids, TIP3P and SPC/E lead to roughly equivalent hydration patterns

  26. explicit solvation • what water model to use? • what representation or boundary conditions? • how to make the calculation tractable? • how much water to add?

  27. explicit water boundary conditions • finite vs. infinite • surrounding? (vacuum, continuum, ...) • size and shape (sphere, orthorhombic, truncated octahedral)

  28. explicit water boundary conditions “blob” or cap truly periodic or Ewald

  29. vacuum boundary conditions spherical shell of atoms around the site of interest Problems: - surface tension leads to high pressure - reduced fluctuations - vacuum interface, waters can drift... “blob” or cap

  30. vacuum boundary conditions spherical shell of atoms around the site of interest Problems: - surface tension leads to high pressure - reduced fluctuations - vacuum interface, waters can drift... “blob” or cap alternatives: stochastic boundary … Langevin forces on “near” surface waters surface waters held fixed at “bulk” density

  31. vacuum boundary conditions spherical shell of atoms around the site of interest Problems: - surface tension leads to high pressure - reduced fluctuations - vacuum interface, waters can drift... “blob” or cap alternatives: solvent boundary potentials how to develop??? +

  32. vacuum boundary conditions spherical shell of atoms around the site of interest Problems: - surface tension leads to high pressure - reduced fluctuations - vacuum interface, waters can drift... “blob” or cap alternatives: reaction field or dielectric continuum What happens to waters that leave? (explicit to implicit conversion?)

  33. explicit water boundary conditions truly periodic or Ewald

  34. explicit solvation • what water model to use? • what representation or boundary conditions? • how to make the calculation tractable? • how much water to add?

  35. nonbonded interactions Can we speed up the calculations by limiting the number of pair interactions?

  36. CUTOFFS x x minimum image spherical • reorientational motion slowed! • Roberts & Schnitker, 1995

  37. nonbonded interactions

  38. nonbonded interactions

  39. 10.0 kcal at 10 Å!

  40. nonbonded interactions

  41. Can we avoid artifacts due to the cutoff of pair interactions? • Avoid minimum image • Don’t split dipoles: charge group neutrality (AMBER) • Use two cutoffs: CUT2ND>CUT • Do not ignore long ranged electrostatic interactions • Ewald (Ewald, 1921), particle mesh Ewald (Essman et al., 1995; Darden & Sagui, 2000), particle-particle particle-mesh Ewald (Luty & van Gunsteren, 1996) • Fast multipole method (Greengard & Rokhlin, 1989; Board et al., 1992; Lambert et al., 1996) • Cell multipole (Ding et al., 1992) outer interactions are updated less frequently x

  42. shift improving cutoffs? switch shift/switch the energy or force discontinuity

  43. improving cutoffs? shift/switch the energy or force discontinuity • Better to use longer cutoff than worry about details of switch/shift • Best cutoff method is atom-based force shift • Switch is not-advised for electrostatics • Truncation may lead to “heating” due to dipole reorientation near the cutoff shift switch

  44. …but what about artifacts from the cutoff? • Examples of the deleterious effects of the cutoff • DNA falls apart (Cheatham et al., 1995) • electrostatic potential (Pettitt & Smith, 1991) • anomalous water transport (Feller et al., 1996) • alpha helical peptides(Schreiber & Steinhauser, 1992) • attractive ion PMF (Bader & Chandler, 1992)

  45. d[CCAACGTTGG]2 overall extension of duplex, middle base pairs fray terminal base pairs fray, duplex bends 120 ps, 12 Å cutoff 50 ps, 16 Å cutoff (group based truncation)

  46. Smith & Pettitt J. Chem. Phys. 95, 8430-8441 (1991) Coulombic potential atom switch group switch Ewald

  47. S. E. Feller, R. W. Pastor, A. Rojnuckarin, S. Bogusz, B. R. Brooks, “Effect of electrostatic force truncation on interfacial and transport properties of water.”J. Phys. Chem.100, 17011-17020 (1996). density weighted water polarization profile Electrostatic potential profile across vapor/water/vapor interface Ewald Ewald (solid) 12 Å shift 12 Å force shift 10-12 Å force switch

  48. Biochemistry31, 5856-5860

  49. + + J. Phys. Chem. 96, 6423-6427 (1992) W(R): PMF of two ions Fe2+-Fe3+ CUTOFF Fe2.5+-Fe2.5+ EWALD Ewald cutoff non-integral charge to avoid dipole correction; leads to same structure and energetics • not cutoff spline dependent! • Artifact is > 8 kBT!!! • in simulation with cutoffs, two like charged ions moved closer together… dielectric continuum

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