Scaling in biomolecular solvation are proteins large
Download
1 / 42

Scaling in Biomolecular Solvation Are Proteins Large? - PowerPoint PPT Presentation


  • 76 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Scaling in Biomolecular Solvation Are Proteins Large?' - neila


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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 Biomolecules

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: BiomoleculesAtomistic 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: BiomoleculesTime 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: BiomoleculesRemoving solvent degrees of freedom

ru: solute coordinates; rv: solvent coordinates


Biomolecules in implicit solvents
Biomolecules in implicit solvents Biomolecules

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 solvation Biomoleculesapproximations

  • 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 Biomolecules

Dielectric

constant

Charge density

-

ep

Charge of salt ion in solution

+

-

-

Electrostatic potential

+

+

+

-

s


Implicit nonpolar solvents
Implicit nonpolar solvents Biomolecules

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 Biomolecules

Computational efficiency for alanine dipeptide

Are structureless implicit solvents sufficient?


Does size matter in biomolecular solvation
Does size matter in Biomoleculesbiomolecular solvation?

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


How consistent are implicit and explicit solvents on conformation dependent energetics

3 Biomolecules10 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) Biomolecules

  • 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) Biomolecules

  • 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: BiomoleculesBasis 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 Biomolecules

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 dependence BiomoleculesPeptide 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 Biomolecules

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 dependence BiomoleculesSalt-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.


Salt bridge charging free energies
Salt-bridge charging free energies Biomolecules

Tan and Luo, In Prep


Electrostatic solvation1
Electrostatic solvation Biomolecules

  • Conformation dependent energetics is consistent between PB and TI.

  • PB correlate very well with TI from short peptides up to proteins of typical sizes.


Nonpolar solvation

Nonpolar Solvation Biomolecules


Explicit solvent ti1
Explicit solvent (TI) Biomolecules

  • 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 Biomolecules

  • 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 Biomolecules

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 Biomolecules

  • 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 dependence BiomoleculesNonpolar 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 Biomolecules

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 Biomolecules

  • 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.


Behavior of Two Estimators for BiomoleculesTYR Side-Chain Conformations

SAS

SAV

Tan and Luo, In Prep.


Nonpolar solvation1
Nonpolar solvation Biomolecules

  • 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 Biomolecules

Jun Wang, Siang Yip

Chuck Tan, Yuhong Tan

Qiang Lu, MJ Hsieh

Gabe Ozorowski, Seema D’Souza

Morris Chen, Emmanuel Chanco

NIH/GMS


How does implicit solvents perform in dynamics

How does implicit solvents Biomolecules perform in dynamics?


PMEMD simulations at 450K Biomolecules

  • 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


PBMD simulations at 450K Biomolecules

  • 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


Free energy landscape

PME Biomolecules

PB

ARG

GLU

(Φ,Ψ) Free Energy Landscape


Free energy landscape1

PME Biomolecules

PB

LEU

GLN

(Φ,Ψ) Free Energy Landscape


Alpha content
Alpha content Biomolecules

(Hu et al. PROTEINS, 2003)


PBMD Biomolecules

  • 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 Biomolecules

(Hu et al. PROTEINS, 2003)


ad