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Scaling in Biomolecular Solvation Are Proteins Large?

Scaling in Biomolecular Solvation Are Proteins Large?. Ray Luo Molecular Biology and Biochemistry University of California, Irvine. Different levels of abstraction: Approximations in Biomolecules. Quantum description: electronic & covalent structure

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Scaling in Biomolecular Solvation Are Proteins Large?

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  1. Scaling in Biomolecular SolvationAre Proteins Large? Ray Luo Molecular Biology and Biochemistry University of California, Irvine

  2. Different levels of abstraction: Approximations in Biomolecules • Quantum description: electronic & covalent structure • Atom-based description: non-covalent interactions • Residue-based/coarse-grained description: overall motion/properties of a biomolecule

  3. Challenges in biomolecular simulations Mathematical models should be as realistic as possible • Every atom is represented as a classical particle. • Potential energy is in a pairwise form only.

  4. Challenges in biomolecular simulations:Atomistic representation • Realistic water environment • Long-range interactions • Periodic boundary • How to avoid O(n2)?

  5. Challenges in biomolecular simulations:Time scales are in the 109 time steps Multiple trajectories, often as many as 10s to 100s, are needed

  6. Explicit solvent and implicit solvent:Removing solvent degrees of freedom ru: solute coordinates; rv: solvent coordinates

  7. Biomolecules in implicit solvents Mathematical models should be as realistic as possible • Solute biomolecule is still in all-atom representation. • Solvent molecules are now in continuum representation. • There is an interface between solute and solvent.

  8. Continuum solvationapproximations • Homogenous structureless solvent distribution • Solute geometry (shape/size) influence in solvent density is weak in solvation free energy calculation • Solvation free energy can be decomposed into different components

  9. Implicit electrostatic solvent Dielectric constant Charge density - ep Charge of salt ion in solution + - - Electrostatic potential + + + - s

  10. Implicit nonpolar solvents Wrep: Estimated with surface (SES/SAS) or volume (SEV/SAV) Watt: Approximated by (D. Chandler and R. Levy)

  11. Implicit solvents: pros and cons Computational efficiency for alanine dipeptide Are structureless implicit solvents sufficient?

  12. Does size matter in biomolecular solvation? D. Chandler, Nature, 437, 640-647, 2005

  13. 310 Helix αHelix π Helix How consistent are implicit and explicit solvents on conformation dependent energetics? Tan et al, JPC-B, 110, 18680-18687, 2006

  14. Electrostatic Solvation

  15. Explicit solvent (TI) • TIP3P water model. Periodical Boundary Condition. Particle Mesh Ewald, real space cutoff 9Å. • NPT ensemble, 300K, 1bar. Pre-equilibrium runs at least 4 ns and until running potential energy shows no systematic drift. • All atoms restrained to compare with PB calculations on static structures • 25 λ’s with simulation length doubled until free energies change less than 0.25kcal/mol (up to 320ps equilibration/production per λ needed). • Thermodynamic Integration:

  16. Implicit solvent (PB) • Final grid spacing 0.25 Å. Two-level focusing was used. Convergence to 10-4. • Solvent excluded surface. Harmonic dielectric smoothing was applied at dielectric boundary. • Charging free energies were computed with induced surface charges. • (110+110 snapshots) × 27 random grid origins were used. • Cavity radii were refitted before comparison ε= 80 Linearized Poisson-Boltzmann Equation: where

  17. Accurate Atomic Radii:Basis of Quantitative Studies Atomic cavity radii are responsible for the desolvation penalties of amino acids and nucleotides. Different cavity radii for PB solvents will result in different agreements with explicit solvent.

  18. Quality of radius refit Correlation Coefficient: 0.99995 Root Mean Square Deviation: 0.33 kcal/mol AMBER/TIP3P Error (wrt Expt): 1.06 kcal/mol AMBER/PB Error (wrt Expt): 0.97 kcal/mol (neutral side chain analogs) Tan et al, JPC-B, 110, 18680-18687, 2006

  19. Conformation dependencePeptide reaction field energies • Three helical conformations 310 helix α helix π helix • Ten beta-strand conformations 5 Parallel 5 Anti-parallel • Peptides with salt bridge HD3 HD4 HD5 Tan et al, JPC-B, 110, 18680-18687, 2006

  20. Peptide reaction field energies Correlation Coefficient: 0.997 RMSD: 2.90 kcal/mol TI statistical uncertainties less than 0.6 kcal/mol.

  21. Size dependenceSalt-bridge charging free energies • Tested salt bridge with atom ids. • PEPenh, a 16mer helix from1enh. • ENH, (1enh, ~50 aa). • P53a, (1tsr, ~200 aa) • ARG154-GLU76 on p53. • P53b, ARG178-GLU190 on p53. Tan and Luo, In Prep.

  22. Salt-bridge charging free energies Tan and Luo, In Prep

  23. Electrostatic solvation • Conformation dependent energetics is consistent between PB and TI. • PB correlate very well with TI from short peptides up to proteins of typical sizes.

  24. Nonpolar Solvation

  25. Explicit solvent (TI) • TIP3P water model. Periodical Boundary Condition. Particle Mesh Ewald, real space cutoff 9Å. • NPT ensemble, 300K, 1bar. Pre-equilibrium runs with neutral molecules for at least 8 ns and until running potential energy shows no systematic drift. • All atoms restrained to compare with single-snapshot calculations in implicit solvent. • Thermodynamic Integration: • 60 λ’s with simulation length doubled until free energies change less than 0.25kcal/mol (160ps equilibration or production per λ needed). Tan et al, JPC-B, 111, In Press, 2007

  26. Nonpolar repulsive free energies • SES • CC: 0.997 • RMSD: 0.30kcal/mol RMS Rel Dev: 0.026 • (B) SEV • CC: 0.985. • RMSD: 0.69kcal/mol RMS Rel Dev: 0.082 • (C) SAS • CC: 0.997 • RMSD: 0.30kcal/mol RMS Rel Dev: 0.026 • (D) SAV • CC: 0.998. • RMSD: 0.27kcal/mol RMS Rel Dev: 0.022 Tan et al, JPC-B, 111, In Press, 2007

  27. Nonpolar attractive free energies CC: 0.9995 RMSD: 0.16kcal/mol RMS Rel Dev: 0.01 Tan et al, JPC-B, 111, In Press, 2007 Error bars too small to be seen

  28. Total nonpolar free energies • SES • CC: 0.981 • RMSD: 0.33kcal/mol • (B) SEV • CC: 0.891 • RMSD: 0.67kcal/mol • (C) SAS • CC: 0.984 • RMSD: 0.31kcal/mol • (D) SAV • CC: 0.986 • RMSD: 0.28kcal/mol Tan et al, JPC-B, 111, In Press, 2007

  29. Conformation and size dependenceNonpolar free energies of TYR • Tested side chain with atom ids. • PEPα, a 17mer helix from 1pgb. • PEPβ, a 16mer hairpin from 1pgb. • PGB, 1pgb, ~50 aa. • P53, 1tsr, ~200 aa. Tan and Luo, In Prep.

  30. Nonpolar attractive free energies CC: 0.983 RMSD: 0.29 kcal/mol RMS Rel Dev: 0.035 Tan and Luo, In Prep. Error bars too small to be seen

  31. Nonpolar repulsive free energies • SAS • CC: 0.975 • RMSD: 2.42kcal/mol. • RMS Rel Dev: 0.55 • (B) SAV • CC: 0.984 • RMSD: 0.53kcal/mol • RMS Rel Dev: 0.053 Tan and Luo, In Prep.

  32. Behavior of Two Estimators for TYR Side-Chain Conformations SAS SAV Tan and Luo, In Prep.

  33. Nonpolar solvation • Both attractive and repulsive nonpolar component works well from tested peptides to proteins of different scales if the volume estimator is used. • Conformation dependent energetics is consistent between implicit and explicit solvents.

  34. Acknowledgements Jun Wang, Siang Yip Chuck Tan, Yuhong Tan Qiang Lu, MJ Hsieh Gabe Ozorowski, Seema D’Souza Morris Chen, Emmanuel Chanco NIH/GMS

  35. How does implicit solvents perform in dynamics?

  36. PMEMD simulations at 450K • 10 independent trajectories for at least 8ns in NVT at 450K • Pre-equilibrated for 2ns in NPT at 300K • Simulation parameters: • TIP3P water • Truncated octahedron box with a buffer of 11Å • Real space cutoff 9Å • Continuum van der Waals energy correction beyond cutoff • Berendsen heat bath

  37. PBMD simulations at 450K • P3M treatment of electrostatics • Modified VDW surface for dielectrics • Nonpolar contributions reweighted after MD simulations (C, Tan et al. JPC, 2007 ) • Simulation parameters: • Solvent probe radius: 0.6Å (C, Tan et al. JPC, 2006 ) • Finite difference solver grid spacing: 0.5Å • Finite difference solver tolerance: 0.0001 • Cutoff for PM electrostatic interaction: 7.0Å • No VDW cutoff • Langevin heat bath Lu and Luo, JCP, 119, 11035-11047, 2003

  38. PME PB ARG GLU (Φ,Ψ) Free Energy Landscape

  39. PME PB LEU GLN (Φ,Ψ) Free Energy Landscape

  40. Alpha content (Hu et al. PROTEINS, 2003)

  41. PBMD • No systematic bias in secondary structure propensities in PBMD for the tested dipeptides • More challenging tests: • HD4 Alpha Helix : AAAAAHAAADAAAAAA • HPN Beta hairpin: GEWTYNDATKTFTVKQ • Observables: secondary structures, salt bridges, Hydrophobic contacts, and free energy landscapes

  42. Beta content (Hu et al. PROTEINS, 2003)

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