Dissertation Defense

Thu Zar W. Lwin

Departments of Chemistry and Molecular Biology and Biochemistry

University of California at Irvine

February 22, 2005

Application of Replica Exchange Method in Protein Folding Simulation

20 natural amino acids - polar and non polar Hydrophobic core

Ordered Secondary structures - helix and sheet - 33% in helix, 33% in sheet, - 33% in loops and turns

How are the above structures formed?

Basics of Protein Structure

O

O’

O’-

Structure of Beta Hairpin

G E W T Y D D A T K T F T V T E

- B1 Domain of Protein G in Streptococcal bacteria

- Binds to mammalian IgG

- NMR and X-ray (, ,

- No disulfide bridges => Folding study

- Fragmentation study - Stability in aqueous water - Initiation site for folding

- Computational studies

NC

16 residues

• How does a protein spontaneously fold into its native structure?

• How do we predict a protein’s native structure from its sequence?

Questions about Protein Folding

• How can we design a protein with a specified function?

Replica Exchange Method

old new

Hansmann, UHE (1997) Chem. Phys. Lett., 281:140-150

Efficient sampling of conformational space

Can quickly reach to states available at specified temperature

18 replicas: 270K……………690K

Amber Force Field Model

• Amber• CHARMM• Cedar• Gromos• OPLS

An all atom energy model

Outline

• Influences of solvent models- Explicit solvent vs. implicit

solvent- PB vs. GB

• Influences of force field on secondary structure propensity

• Sampling algorithm - Test on model energy function - Ab initio folding

Motivation to Analyze Solvation Models

Most populated structures Zhou,R. (2003) Proteins, 53:148-161

- These 2 degrees of freedom describe folding landscape

- Rg(core) consists of residues that form hydrophobic core F, W, T, V => describes compactness of hydrophobic core

- No. of H-bonds represent the secondary structure.

(Explicit) (Implicit)

Explicit vs. Implicit Solvent Model

Every atom of solvent molecule is represented

No explicit representation a continuum medium

Explicit Implicit

Implicit Solvent: How do we do it?

Solvation free energy

Components of the Solvation Energy

Polar Solvation Models

Solvent Accessible (SA) Model

1PB/PBSA

2GB/GBSA1Lu, Q. and Luo, R. (2003) J. Chem. Phys. 119:11035-11047 2Onufriev, A. et al. (2004) Proteins 55:383-394

Amber99ci

Poisson-Boltzmann Model

p

+

+-

-+ +

-

-

Attempts to solve the Poisson-Boltzmann equation numerically

s

Dielectric constant

Electrostatic potential

Charge density

Charge of salt ion in solution

Generalized Born Model

=> It is an approximation to the PB equation.

Electrostatic screening effect of salt Effective Born radius

Solvent dielectric constant

Backbone RMSD

(A)

At 282KAre the conformations similar to crystal structure?

Misfolded Salt Bridges

D46

E42

D47E56

K50SA appears to generate more mis-folded salt bridges.

Calculated NOE Distances

34: 5.52 6.21 A35: 4.9 6.3 A

Blanco, FJ. et al., (1994) Struct. Biol. 1:584-590

NOE pair # Type of proton coupling

1 – 10 Intra-residue: HN ….. HCA

11 – 35

11 – 22

23 – 29

30 – 31

32

33, 34

35

Inter-residue: HN, HCA, HCB

(i)HCA ….. (i+1)HN

(i)HN ….. (i+1)HN

HCA ….. HCA ( Y F, W V )

HCA ….. HE2 ( K Y)

HCA, HCB ….. HD2, HE1 ( Y F )

HH2 ….. HCB ( W F )PB models agree NMR data.

In NMR, the distance information for macromolecules can be obtained from Nuclear Overhauser Effect (NOE), transfer of spin polarization between nuclei. Rate of increase in NOE peak intensity Ç

Free Energy Landscape

The problem is specific to GB model.

Native Contacts and Melting Temperatures of -Hairpin

Solvents %Native Contacts (273K)

Melting temperature (K)

PB 81.6 370

PBSA 78.3 400

GB 66.5 320

GBSA 63.0 350

Experiment 80.0 ~300Muñoz, V., et al. (1997) Nature, 390:196-199

Summary

• Performance of polar solvation based on PB is reasonably good.

• The nonpolar interaction needs to be better defined.

Outline

• Influences of solvent models- Explicit solvent vs. implicit

solvent- PB vs. GB

• Influences of secondary structure propensity- Force fields

• Sampling algorithm - Test on model function - Ab initio folding

Why is Force Field Analysis Necessary?

• A Helical peptide can be erroneously folded into a beta-hairpin with Amber96.

Ace – A5 ( AAARA )3 A -- NME

García, AE and Sanbonmatsu, KY (2002) Proc. Natl. Acad. Sci. USA, 99:2782-2787

Folded short (Fs) peptide

AMBER96 vs. QM

RMSD 1.794kcal/mol

kcal/mol

Cond. Phase 300K AMBER96 *Cond. Phase 300K QM/MM

Amber96 QM/MM

Beta 0.86 0.61

Pass 0.02 0.16

Alpha R 0.11 0.26

Alpha L 0.00 0.07

Lu, Q. and Luo, R. ( In preparation)

*H. Hu, et al., (2003) Proteins, 50: 451-463

Amber94 Favors Helical Structures

García, AE and Sanbonmatsu, KY (2001) Proteins, 42:345-354

• Hairpin peptide can be erroneously folded into helix with Amber94.

AMBER94 vs. QM

*Cond. Phase 300K QM/MMCond. Phase 300K AMBER94

RMSD 1.985 kcal/mol

Lu, Q. and Luo, R. ( In preparation)kcal/mol

Amber94 QM/MM

Beta 0.17 0.61

Pass 0.01 0.16

Alpha R 0.82 0.26

Alpha L 0.00 0.07

*H. Hu, et al., (2003) Proteins, 50: 451-463

Spline Fitting vs. QM

Cond. Phase 300K Spline *Cond. Phase 300K QM/MM

RMSD=0.0056kcal/mol kcal/mol

Amber Spline

QM/MM

Beta 0.66 0.61

Pass 0.01 0.16

Alpha R 0.21 0.26

Alpha L 0.10 0.07

Lu, Q. and Luo, R. ( In preparation)

*H. Hu, et al., (2003) Proteins, 50: 451-463

AMBER Force Fields1. Amber03 Duan, Y. et al. (2003) J. Comput. Chem.

24:1999-2012.

2. Amber99ci Lu, Q. and Luo, R. (in preparation).

3. Amber99m2 Wang, J. and Luo, R. (in preparation).

4. Amber99m1 Simmerling, C. et al. (2002) J. A. Chem. Soc. 124:11258-11259.

5. Amber99off García, AE and Sanbonmatsu, KY (2002) Proc. Natl. Acad. Sci. USA 99:2782-2787.

6. Amber94 Cornell, WD, et al. (1995) J. Am. Chem. Soc.

117:5179-5197.

Comparing PME and PB using -Hairpin Peptide

Region PME PBBeta 0.46 (0.10) 0.53 (0.10)Pass 0.02 (0.004) 0.01 (0.008)Helix-R 0.38 (0.09) 0.26 (0.07)Helix-L 0.09 (0.02) 0.19 (0.02)State 4 0.01 (0.007) 0.01 (0.005)

Region PME PBBeta 0.46 (0.10) 0.53 (0.10)Pass 0.02 (0.004) 0.01 (0.008)Helix-R 0.38 (0.09) 0.26 (0.07)Helix-L 0.09 (0.02) 0.19 (0.02)State 4 0.01 (0.007) 0.01 (0.005)

Distribution of / angles from10 residues in sheet (450K)

6 force fields => 14 s

Is PB good enough?

Comparisons

Structure - Crystal structure => Native contact

=> Backbone RMSD - Experimental NOE - Secondary structure propensity

Thermodynamics - Population => Fluorescence => NMR

- Transition temperature

Mechanism - Free energy landscape - Order of hydrogen bonding

Native Contact FractionC – C distance of non-neighboring residue pairs => 6.5 A cut off distance => 21 pairs in crystal structure => Fractional number of pairs found in a conformation

Backbone RMSDThe smaller the RMSD value, the better.

Distribution of Salt Bridges

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

ff99ci ff03 ff99m2 ff99m1 ff99off ff94

Force fields

Popu

latio

n

E42-->K50 D46-->K50 D47-->K50 E56-->K50

E42

E56

K50

D47

D46

NOEff99ci in agreement with all NOE structural data.

Secondary Structure Propensity

Gray: HelixOlive green: Beta-sheetIs there a balance between secondary structures?

Comparisons

Structure - Crystal structure => Native contact

=> Backbone RMSD - Experimental NOE

- Secondary structure propensity

Thermodynamics - Native population => Fluorescence => NMR

- Transition temperature

Mechanism - Free energy landscape - Order of hydrogen bonding

Research group

Type ofExp.

Temperature (Kelvin)

Hairpin population

%

Blanco (1994)

NMR (direct) 278 42

Fesinmeyer (2004)

NMR (mutation) 278 42 43

Fesinmeyer (2004)

NMR (mutation) 298 30

Comparison of Hairpin Populations to NMR

Force field Avg. % Populationat 282 K

ff03 28 %

ff99ci 31 %

ff99m2 4.6 %

ff99m1 8.0 %

ff99off 1.5 %

ff94 0.5 %

Experimental data in aqueous water

Simulations in PB solvent with dielectric 80.0

Comparison of Native Contact Populations to Fluorescence Data

Population% (270 K)

ff03 74.4ff99ci 81.5ff99m2 59.5ff99m1 50.8ff99off 44.5ff94 43.4FluorescenceStudy (273 K) 80.0

Muñoz, V., et al. (1997) Nature, 390:196-199

Transition Temperature

(K)

Muñoz, V., et al. (1997) Nature, 390:196-199

50% of sheet population exits at transition temperature.

TF (K)

ff03 385ff99ci 368ff99m2 368ff99m1 368FluorescenceStudy ~300

Comparisons

Structure - Crystal structure => Native contact

=> Backbone RMSD - Experimental NOE - Secondary structure propensity

Thermodynamics - Population => Fluorescence => NMR

- Transition temperature

Mechanism - Free energy landscape - Order of hydrogen bonding

Free Energy Landscape

Temperature 282K

Hydrogen Bonding Probability

3 > 5 > 4 > 2 4 > 5 > 3 > 2 7 > 4 > 5 > 3

5 > 4 > 3 > 6 7 > 5 > 4 > 6 7 > 6

3 > 5 > 4 > 2 4 > 5 > 3 > 2

Summary

Out of 6 force fields, only the most recent 2 force fields (ff03 and ff99ci) treat the backbone torsion right

Structure => can produce native like conformaitons. => mis-folded salt bridges can form in imperfect force fields.

Thermodynamics => balance between helical and sheet structures

Mechanism => L shaped landscape => Existence of intermediates and their locations depend on force fields.

Outline

• Influences of solvent models- Explicit solvent vs. implicit

solvent- PB vs. GB

• Influences of secondary structure propensity- Force fields

• Sampling algorithm - Test on model function - Ab initio folding

Dill, K. A. and Chan, H. S., (1997) Nature Struct. Biol., 1:10-19.

Residue Model All atom model

Why New Method Necessary?

Dual REM

Model Energy:

Global OptimizationThermodynamic Simulation

Testing Dual REM

-Hairpin Peptide:

Ab Initio Folding

16 residues

G E W T Y D D A T K T F T V T E

300 4390

Instantaneous Energy to Global minimum

Energy Model

Efficiency

3d_2d 14

5d_4d 1

5d_3d 43

5d_2d 49

Distribution of Energy

Comparing Imperfectness across Different Resolution Combinations

_

Simulations

PB REM

18 temps (18 nodes)1 ps MD b/f rep. xch5 replica xch b/f resol. xch

*Lattice REM

9 temps one node100 MC b/f rep. xch 10 replica xch. b/f resol. xch

Simulated Annealing (2.5, 10 anneal step, 200 MC/step)Const. temp lattice run (200 MC)

ReconstructionGas/Min: 500 stepsHeating: 100 steps

Interface (400 trial exchanges)

270 K 0.90295 K 0.98

Single PB REMs:

Extended structure (5ns)Crystal structure (2ns)

Dual REM (2 ns) Interface

*MMTSB

Ab Initio Folding (RMSD)

0 2 4 6 8 10 120.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Pro

babi

lity

RMSD

Dual REM Single REM Crystal REM

Dual REM can fold into native structure (1 to 2 Angstrom)Analysis on last 0.5 ns of simulation

Dual REM 0.2 ns

Single REM > 5.0 ns

Summary• Dual REM is faster than single REM in both testing

scenarios.

• Limitations of this method are:

=> The imperfectness between the two resolutions must be small.

=> We have to use fairly efficient low resolution model.

=> The cost of computation for interface must be low. In our folding simulation, cost of computation for interface is very insignificant.

Future Directions

• Better treatment to the non polar solvation.

• Similar testing on helical peptide in force field analysis.Improvement on ff99ci with condensed phase QM calculations.

• Testing of Ab Initio folding on a protein that contains both kind of secondary structures, such as domain B1 of protein G.

Acknowledgements

Mengjuei HsiehMorris ChenDr. Qiang LuDr. Chuck TanDr. Yu-Hong TanDr. Lijiang Yang

Department of ChemistryChemical and Material Physics Program

UC Regents Dissertation Fellowship

Committee Members:

Professor Ray Luo Professor Douglas J. TobiasProfessor David A. Brant