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Effective Potentials for Protein Folding and Binding

With Thermodynamic Constraints

Effective potential

Important coordinates

- The AGBNP effective solvation potential
- Optimization for structure prediction
- Free energy surfaces for b-hairpin and a-helical peptide folding
- Dynamics and kinetics

Roadmap to GB/NP Effective Potential Models for Solvation

- Electrostatic Component
- Dielectric Continuum approximation. Generalized Born models
- Parameterization (atomic radii) against FEP explicit solvent
- calculations with OPLS-AA force field

- Non-Polar Component
- Novel non-polar estimator from FEP explicit solvent studies
- Parameterization against experimental gas solubilities of small molecules
- Parameterization for macromolecules: binding, folding

R.M. Levy, L. Y. Zhang, E. Gallicchio, and A.K. Felts, JACS, 125, 9523 (2003)

E. Gallicchio, L. Y. Zhang, and R.M. Levy, JCC, 23, 517, (2002)

E. Gallicchio, M. Kubo, and R.M. Levy, JPC, 104, 6271 (2000)

The AGBNP Implicit Solvent Model

AGBNP: Analytical Generalized Born + Non-Polar

Requirements:

- Applicable to small ligands and large biomolecules, many different functional groups
- Applicable to study small and large conformational changes: sensitive to molecular geometry.
- Analytical with analytical gradients: MD sampling

E. Gallicchio, R. Levy, J. Comp. Chem., 25, 479-499 (2004)

AGBNP

- Novel pairwise descreening Generalized Born model.
- Separate models for cavity free energy and solute-solvent van der Waals interaction energy.
- Fully analytical.
- Sensitive to conformational change.
- Equally applicable to small molecules and macromolecules.

Generalized Born

Surface area model

Born radius-based estimator

Charging Free Energy in linear dielectric medium:

Bi is the Born radius of atom i defined by:

AGBNP: Pairwise Descreening Scheme

Born radii: rescaled pairwise descreening approximation:

j

i

Rescale according to self-volume of j:

Self-volume of j (Poincarè formula, ca. 1880):

Hawkins, Cramer, and Truhlar, JPC 1996

Schaefer and Karplus, JPC 1996

Qiu, Shenkin, Hollinger, and Still, JPC 1997

E. Gallicchio, R. Levy, J. Comp. Chem. (2004)

Non-Polar Hydration Free Energy

Non-polar hydration free energy estimator:

: Surface area of atom i

: Estimator based on Born radius

: Surface tension and van der Waals adjustable parameters

R.M. Levy, L. Y. Zhang, E. Gallicchio, and A.K. Felts, JACS, 125, 9523 (2003)

E. Gallicchio, M. Kubo, and R.M. Levy, JPC, 104, 6271 (2000)

Enthalpy-Entropy and Cavity Decomposition of Alkane Hydration Free Energies: Numerical Results and Implications for Theories of Hydrophobic Solvation

Emilio Gallicchio, Masahito Kubo, Ronald Levy, J. Phys. Chem., 104, 6271 (2000)

Solute-Solvent van der Waals Energy of Proteins: Comparison of Surface Area and Continuum Solvent Models

(A)

(B)

UvdW (kcal/mol)

SASA (A2)

SASA (A2)

Figure: Continuum solvent solute-solvent van der Waals interaction energies of various peptides and proteins conformations plotted against their accessible surface area. (A) Data with accessible surface area between 3000 and 12000 A2. Filled circles denote 98 native peptide and protein conformations, open triangles denote 12 extended protein conformations, and filled triangles denote 273 decoy conformations of 4 native proteins. (B) Data with accessible surface area between 6000 and 10000 A2. Filled triangles denote decoy conformations of of protein lz1 (the native conformation of lz1 is circled).The lines are the linear least square fit to all native and extended protein conformations examined, respectively.

Optimization of the AGBNP Effective Potential for Structure Prediction with thermodynamic constraints

Geff = Uint + GAGB + Gnp

Gnp = i k Ai + k(16ii6 / 3Bi3)

where k indicates atomtype of atom i

Z-score: Zn = ave(GiGn)/d

Maximize: Zn2

Protein Loops Modeling

Prediction of native loop conformation using the

OPLS/AGBNP effective energy function

7RSA (13-24)

AGBNP: Applications

- Protein Folding
- Peptides.
- Protein Decoys.

- Structure Prediction
- Protein Loop Modeling.

- Ligand binding
- Binding Mode Prediction.
- Binding Free Energy Prediction.

The b-Hairpin of B1 Domain of Protein G

The hydrophobic sidechains are in green.

Pande, PNAS, 1999

Nussinov, JMB, 2000

Garcia et al., Proteins, 2001

Zhou & Berne, PNAS, 2002

Dinner, Lazaridis, Karplus, PNAS, 1999

Pande et al., JMB, 2001

Zhou & Berne, PNAS, 2002

Replica Exchange Sampling for b-hairpin Folding

• Replica exchange sampling* is a method to effectively sample rough energy

landscapes which have high dimensionality - the b-hairpin has 768 degrees of

freedom

•~20 MD simulations of the b-hairpin run in parallel over the temperature range

270 K -690 K.

• Every 50 MD steps MC replica exchange moves are attempted

• Total sampling time: 20 processors x 4 x 106 step/processor = 80 x 106 steps

Time series of the temperature for one replica

Time series of the replicas for one Temp., T = 442 K

* Y. Sugita, and Y. Okamoto, Chem. Phys. Let., 314, 141 (1999)

The b-Hairpin of B1 Domain of Protein G

AGB-NP with Scharged=0.5

Simple nonpolar model.

The potential of mean force of the capped peptide.

A Felts, Y. Harano, E. Gallicchio, and R. Levy, Proteins, 56, 000 (2004)

The b-Hairpin of B1 Domain of Protein G

AGB-NP with Scharged=0.5

Simple nonpolar model.

The potential of mean force of the capped peptide.

A Felts, Y. Harano, E. Gallicchio, and R. Levy, Proteins, 56, 000 (2004)

Estimated b-Hairpin and a-Helical Populations(native peptide from protein G, T=298K)

b-hairpin > 90%

a-helix < 10%

DG ~ 2 kcal/mol

T-WHAM: PMF contains information from high temperature walkers

No WHAM

T-WHAM

DGmax=5 kcal/mol

DGmax=10 kcal/mol

T-WHAM

- A way to combine data from simulations at various temperatures to obtain properties at one given temperature.

Solve for (E) and insert into expression for P(E;Ti).

Energy distribution:

- Given P(Ej;T0) can predict histogram of energies n(Ej;Ti) at any temperature.

- Select P(Ej;T0) that best reproduces observed histograms (maximum likelihood solution assuming multinomial-distributed counts).

{

WHAM equations:

Same derivation for joint probability P(x,E;T).

Alternative Coordinates for the b-Hairpin

Projections onto the first four principal components

Free Energy Surface of the Protein G b-Hairpin With Respect to the (1,4) Principle Components

T-WHAM

In Silico Mutation Study of the protein Gb-Hairpin Sequence

Sequence b a coil

native GEWTYDDATKTFTVTE 88% 8% 4%

W43S mutant GESTYDDATKTFTVTE 42% 40% 18%

Y45S mutant GEWTSDDATKTFTVTE 23% 71% 6%

W43S, Y45S GESTSDDATKTFTVTE 0.1% 83% 17%

44% homol* GEQVAREALKHFAETE 0% 95% 5%

random #1 VTGADFTKYTTEDWTE 35% 4% 61%

random #2 VYEWDGTTKTEFADTT 31% 13% 56%

*C-terminal a-helix of 1b6g: 44% BLAST homology with sequence from protein G

Free Energy Surfaces Generated with REM and OPLS-AA/AGBNP

b-Hairpin of C-terminus

of B1 domain of protein G

a-Helix of C-peptide

of ribonuclease A

GEWTYDDATKTFTVTE

KETAAAKFERQHM

Effective Potentials for Protein Folding and Binding

With Thermodynamic Constraints

Effective potential

Important coordinates

- The AGBNP effective solvation potential
- Emilio Gallicchio, Tony Felts
- Optimization for structure prediction
- Emilio Gallicchio, Tony Felts
- Free energy surfaces for b-hairpin and a-helical peptide folding
- Yuichi Harano, Tony Felts, Emilio Gallicchio, M. Andrec
- Dynamics and kinetics
- Dimitriy Chekmarev, Tateki Ishida, Michael Andrec

Effective Potentials for Protein Folding and Binding

With Thermodynamic Constraints

Effective potential

Important coordinates

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