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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

Scaling in Biomolecular SolvationAre Proteins Large?

Ray Luo

Molecular Biology and Biochemistry

University of California, Irvine

different levels of abstraction approximations in biomolecules
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
challenges in biomolecular simulations
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.
challenges in biomolecular simulations atomistic representation
Challenges in biomolecular simulations:Atomistic representation
  • Realistic water environment
  • Long-range interactions
    • Periodic boundary
    • How to avoid O(n2)?
challenges in biomolecular simulations time scales are in the 10 9 time steps
Challenges in biomolecular simulations:Time scales are in the 109 time steps

Multiple trajectories, often as many as 10s to 100s, are needed

explicit solvent and implicit solvent removing solvent degrees of freedom
Explicit solvent and implicit solvent:Removing solvent degrees of freedom

ru: solute coordinates; rv: solvent coordinates

biomolecules in implicit solvents
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.
continuum solvation approximations
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
implicit electrostatic solvent
Implicit electrostatic solvent

Dielectric

constant

Charge density

-

ep

Charge of salt ion in solution

+

-

-

Electrostatic potential

+

+

+

-

s

implicit nonpolar solvents
Implicit nonpolar solvents

Wrep: Estimated with surface (SES/SAS) or volume (SEV/SAV)

Watt: Approximated by (D. Chandler and R. Levy)

implicit solvents pros and cons
Implicit solvents: pros and cons

Computational efficiency for alanine dipeptide

Are structureless implicit solvents sufficient?

does size matter in biomolecular solvation
Does size matter in biomolecular solvation?

D. Chandler, Nature, 437, 640-647, 2005

how consistent are implicit and explicit solvents on conformation dependent energetics

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

explicit solvent ti
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:
implicit solvent pb
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

accurate atomic radii basis of quantitative studies
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.

quality of radius refit
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

conformation dependence peptide reaction field energies
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

peptide reaction field energies
Peptide reaction field energies

Correlation Coefficient:

0.997

RMSD:

2.90 kcal/mol

TI statistical uncertainties less than 0.6 kcal/mol.

size dependence salt bridge charging free energies
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.

electrostatic solvation1
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.
explicit solvent ti1
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

nonpolar repulsive free energies
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

nonpolar attractive free energies
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

total nonpolar free energies
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

conformation and size dependence nonpolar free energies of tyr
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.

nonpolar attractive free energies1
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

nonpolar repulsive free energies1
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.

nonpolar solvation1
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.
acknowledgements
Acknowledgements

Jun Wang, Siang Yip

Chuck Tan, Yuhong Tan

Qiang Lu, MJ Hsieh

Gabe Ozorowski, Seema D’Souza

Morris Chen, Emmanuel Chanco

NIH/GMS

slide36

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
slide37

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

alpha content
Alpha content

(Hu et al. PROTEINS, 2003)

slide41
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
beta content
Beta content

(Hu et al. PROTEINS, 2003)

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