a fast and accurate computational approach to protein ionization: combining the generalized born...

A fast and accurate computational approach to protein ionization: combining the Generalized Born model with an iterative mobile cluster method

Velin Z Spassov, Accelrys

© 2008 Accelrys, Inc. 2

Outline

• Introduction

• Background/theory

• Results/validation

• Conclusions


INTRODUCTION

Protein Ionization and pKScientific Needs• To provide a fast and convenient way to study the effects

of the pH changes on a wide range of important mechanism such as enzyme catalysis, ligand binding and protein stability.

• In protein modeling, a correct assignment of protonation states and hydrogen atom positions are critical for:

» Accurate docking of small molecules to receptors» Accurate protein-protein docking» Stable, convergent molecular dynamics simulations


IntroductionCalculate Protein Ionization and Residue pKA new Discovery Studio computational protocol to calculate the pH dependent electrostatic effects in protein molecules*.

Calculates:– the titration curves and pK1/2 of the titratible residues.– the electrostatic contribution to the protein free energy as a function of pH.– the pH dependency of the folding energy of the protein and the pH optimum

of protein stability.– pI of the protein.

Optimizes the positions of all hydrogen atoms and – automatically sets the protonation state of each residue at a given pH, based

on the calculated pK1/2 .– finds the optimal proton binding sites for tautomeric ASP, GLU and HIS

residues.– flips the O and N atoms of ASN and GLN residue to find an optimal

conformation.

*Spassov, V.Z. and Yan, L. (2008) Protein Science,17,1955-1969.


Protein Ionization and pK: Background

• Titratable residues: exist in protonated and deprotonated forms

• A titration curve gives the fractional protonation of a titratable group as a function of pH

Titratable Groups in Proteins

B:ASP30

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14 16

B:ASP30

pK1/2 = 3.9

Deprotonated Protonated Deprotonated Protonated

Arg Lys

Asp

N-terCys

Glu

Tyr His

C-terpH = pKa + log10{[A-]/[HA]}

HA + H2O H3O+ + A-

H+

H+


Extended GB/IM2,3,4,5 instead of grid based PB solvers

THEORYCalculate Protein Ionization and Residue pK

( ) ∑∑ +−=ji

jiij

N

iiintri xxWpKpHxRTpHG

,, ),(2/13.2),(X

]/),(exp[

]/),(exp[),(2

1RTpHG

RTpHGpHN

ll

ll

∑=

−

−=

X

XXρ

[ ]),(),()303.2( 1modint MMHGPPHGRTpKpK r ∆∆−∆∆+= −

IMC6 instead of Monte Carlo

CHARMM force-field

Library of pentapeptide model compounds and pKmod data7

instead of monopeptides

Ionization Model1

1Bashford D, Karplus M. (1990) Biochemistry, 29, 10219-10225.2Still, W.C. et al. (1990)J. Am. Chem. Soc. 1990, 112, 6127-61293Dominy, B.N.,Brooks III, C.L. (1999) J. Phys. Chem. B 103, 3765-3773.4 Onufriev A. et al. (2000) J. Phys. Chem. B 2000, 104, 3712-3720.

5Spassov VZ et al. (2002) J. Phys. Chem B106:8762-8738.6Spassov V.Z., Bashford, D. (1999) J..Comput. Chem.,20,1091-1111.7Thurlkill et al. 2006. Protein Science,15,1214-1218.

CHARMm-based Protocol for Preliminary Optimization


Protein Ionization and pK: Solution

1. Spassov, et al, Protein Sci. 2008, 17, 1955-1969)

• New method1 to ‘Calculate Protein Ionization and pK’– Predicts pK1/2 and titration curves for each titratable residue using 3D environment of protein– Automatically protonates the residues at a given pH according to predicted pK1/2.

• For HIS, ASP, and GLU residues the hydrogens are added to yield the lowest CHARMm energy• The N and O atoms on the side-chain of ASN and GLN residues are flipped if necessary to give the lower

energy conformation – Calculates the following as a function of pH

• Electrostatic contribution to the free energy• Estimate of relative folding energy (electrostatic contribution)• Total charge of system

– Based on CHARMm Generalized-Born methods

• Strength of Solution– More accurate and rigorous than rule-based methods– Faster and more accurate than existing Poison-Boltzmann/Monte Carlo methods– Consistent CHARMm force field used throughout

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14

*:GLU23*:GLU38*:GLU77*:GLU97*:GLU104*:GLU107*:GLU119*:GLU129*:GLU133*:GLU135*:GLU140*:GLU145*:GLU165*:GLU183*:GLU186*:GLU219*:GLU239


Model Compounds

MEAD, UHBD and othersStructure: MonopeptidepK data: standard setNozaki Y, Tanford C. 1967. Examination of titration behavior. Methods Enzymol 11:715–734.

DS Protein IonizationStructure: Blocked PentapeptidesAla-Ala-X-Ala-AlapK data:Thurlkill et al. 2006. Protein Science,15,1214-1218.


IMC (Iterative Mobile Clustering) ApproachSpassov V.Z., Bashford, D. (1999) J..Comput. Chem.,20,1091-1111

)|','()|,()(),( kxcfkxcfkfXC outg Γ=ρ

Mean-field approach to protein ionization:One site/Single conformer Tanford C., Roxby R (1972),11,2192-2198.Clustering/distance criterion/single conformerYang A.S. et al. (1993) Proteins,15,252-265.Gilson M.K. (1993) Proteins,15,266-282.Clustering/energy criterion/single or multiple conformersSpassov & Bashford (1999)

IMC: Ntot(cluster) = Nglobal 3Nclstr2Nclstr


Protein Ionization and pK: Method

• Electrostatic interaction energies are calculated using an implementation of Generalized Born solvation model in CHARMm

– atomic parameters from either CHARMm or CHARMM polar hydrogen forcefields

• The energies of the protonated and deprotonated states are calculated and the percentage of protonation of each residue is predicted at given pH based on Boltzmann distribution

• Relative folding energy estimated based on energy of protonation of the protein and the protonation energy of the model compounds

• Current implementation treats protein as a single conformer embedded in a dielectric medium

– A dielectric constant of 10-11 for the protein interior gives the lowest RMSD compared to experimentally obtained pK data.

– This dielectric constant is the only parametrized variable in the method


Parameterization of the model

∑∑∑∑−+

−−=∆> i j jiijjiij

ji

slv

ji

mi ij jim

jielec

rr

qqIDrqq

G)4/exp(

)),,(1(166332

22, ααααε

ααεε

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

dielectric constant

RMSD

pK1/2 Residue Experimental* CHARMM

polar H CHARMM

LYS1_NTR 7.9 7.81 8.00 LYS1 10.6 10.01 10.01 GLU7 2.9 3.17 3.39 LYS13 10.3 10.49 10.56 HIS15 5.4 6.20 5.87 ASP18 2.7 2.87 3.11 TYR20 10.3 10.85 11.18 TYR23 9.8 10.16 10.87 LYS33 10.4 10.58 10.79 GLU35 6.2 5.05 5.90 ASP48 2.5 2.96 2.91 ASP52 3.7 4.32 4.67 TYR53 >12 11.71 >12 ASP66 <2.0 2.15 2.87 ASP87 2.1 2.43 2.97 LYS96 10.7 11.18 11.42 LYS97 10.1 10.79 10.85 ASP101 4.1 3.89 3.92 LYS116 10.2 10.12 10.09 ASP119 3.2 3.08 3.28

LEU129_CTR 2.8 2.73 2.83 rmsd 0.45 0.57

Hen-egg lyzozyme 2lzt.pdb

* Bartik et al., 1994, Kuramitsu and Hamaguchi 1980.

In contrast to some popular pK prediction programs based on multi-parameter empirical models, the only fitting parameter in our method is the value of intra-molecular dielectric constant, εm, while all other parameters are kept at their standard CHARMm force-field values.


Results: pK Prediction of Selected Proteins

• Comparison of experimental pK1/2 with calculated values for select PDB files

• All computations about 1 minute per system on a single CPU

PDB code

Sites with experimantal pK data

CHARMm

polar hydrogens

CHARMm

all hydrogens

PROPKA

MCCE ε = 8

1 4pti 14 0.36 0.36 0.6 0.47 2 2lzt 21 0.45 0.57 0.66 0.74 3 2rn2 25 0.59 0.68 0.72 0.87 4 3rn3 16 0.47 0.71 0.67 0.66 5 1pga 15 0.50 0.57 0.72 0.63 6 3icb 10 0.33 0.35 0.9 0.38 7 1hng 14 0.55 0.53 0.83 0.76 8 1a2p 12 0.60 0.49 0.68 0.89 9 1omu 15 0.64 0.70 0.44 1.10 10 9rnt 14 0.54 0.65 1.51 11 1bi6-heavy chain 18 0.54 0.53 0.56 12 1bi6-light chain 4 0.18 0.27 0.38 13 1rgg 24 0.84 0.89 0.97 14 1igd 16 0.35 0.36 0.62 15 135l 11 0.63 0.65 0.66 16 1div 6 0.26 0.32 0.74 17 1xnb* 13 0.70 1.09 0.62 18 1kxi 3 0.57 0.50 0.66 19 1beo 10 0.46 0.56 0.98 20 1trs 17 0.88 0.86 0.94 21 1qbs 16 0.34 0.34 0.78 22 1de3 25 0.66 0.70 1.33 23 2bus 4 0.46 0.49 0.23 24 1egf 9 0.49 0.53 0.49 Total sites 331 331 331 331 141

Average RMSD

0.508

0.548 0.742

0.720

PROPKA: Li et al. (2005) Proteins,61, 704-721.

MCCE: Georgescu et al. (2002) Biophysical Journal, 83, 1731-1748.


Results: pK Prediction of Selected Proteins

• Predicted results well correlate with the experimental measurements

• Computation time scales roughly linearly with residue number

• Most systems take about 1 to 2 minutes on a single CPU

0

1

2

3

4

5

6

0 100 200 300 400 500 600 700 800

residues

Tim

e [m

in]

Intel Pentium4 3.0 GHz machine

y = 0.9868x + 0.0282R2 = 0.9672

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14pK exp

pK

calc


The Comparison of the accuracy of pK predictions with other methods

sites

GB/IMC

MCCE Const. pH FD/DH SCP

PROPKA

4pti 14 0.36 0.47 NA 0.35 0.33 0.6

2lzt 21 0.45 0.76 0.6 0.47 0.49 0.66

2rn2 25 0.59 0.87 0.9 1.17 0.57 0.72

3rn3 16 0.44 0.66 1.2 0.87 0.55 0.94

1pga 15 0.42 0.63 NA 0.80 0.59 0.72

3icb 10 0.33 0.38 NA 0.37 0.39 0.9

3rnt 4 0.28 0.54 NA NA 0.41 NA

Average 0.41 0.63 - 0.67 0.49 0.76


pK1/2 Prediction – Applications

• Application 1: Optimize the protonation state of proteins and hydrogen coordinates– Prepare the protein for other calculations, such as more stable Molecular Dynamics

simulations

• Application 2: Estimate maximum stability by studying the pH dependent folding energy of proteins

• Application 3: Calculate the electrostatic component of protein-ligand binding energies or protein-protein binding energy

• Application 4: Use unusual tritation curves to find relevant functional residues • Application 5: Estimate the effect of mutation

– pK and titration curve changes on other titratible sites when a residues is mutated– Shift of the stability of the protein to different pH when a residue is mutated

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14

*:HIS26*:HIS95*:HIS100*:HIS115*:HIS185*:HIS195*:HIS224*:HIS248

His 95


Rubredoxin from Pyrococcus Furiosus at pH 8; 1vcx.pdbComparison of the predicted hydrogen positions with neutron diffraction structure

Application – Protonation and Hydrogen Coordinates



Comparison between the predicted protonation state of HEWL and neutron diffraction data at pH 4.7 File: 1lzn.pdb protonation pK1.2

Residue Neutron diffraction

Predicted

Experimental NMR*

Calculated

LYS1_NTR P P 7.9 8.172 LYS1 P P 10.6 10.840 GLU7 P D 2.9 3.701 LYS13 P P 10.3 11.120 HIS15 P P 5.4 7.380 ASP18 D D 2.7 3.674 TYR20 P P 10.3 11.271 TYR23 P P 9.8 10.886 LYS33 P P 10.4 11.669 GLU35 P P 6.2 5.691 ASP48 D D 2.5 2.818 ASP52 D D 3.7 4.604 TYR53 P P >12 12.000 ASP66 D D <2.0 3.526 ASP87 D D 2.1 3.389 LYS96 P P 10.7 11.456 LYS97 P P 10.1 10.933 ASP101 D D 4.1 3.916 LYS116 P P 10.2 10.220 ASP119 D D 3.2 3.456

LEU129_CTR D D 2.8 2.984

* Bartik et al., 1994, Kuramitsu and Hamaguchi 1980.

• Protonation state of HEWL: Comparison with neutron diffraction data at pH 4.7

• Asn and Gln flips:13 sucessfully predicted out 17 residues in the structure (77%)


A B

Myoglobin 1l2k.pdb: Neutron Diffraction Structure at pH 6.8

The protonation and tautomeric states of histidine residues.

A. Predicted structure. B. Neutron-diffraction structure


1lzn, pH 4.7

1l2k, pH 6.8

2gve, pH 8.0

6rsa, pH 6.6

ASP18

3.66 0.13 D

NTR1

7.30 0.75 NA

NTR1

7.6 0.30 P*

NTR1

7.40 0.86 P

ASP48

2.80 0.03 D

HIS12

6.76 0.48 D

HIS49

6.17 0.02 D

HIS12

6.86 0.62 P

ASP52

4.54 0.47 D

HIS24

6.69 0.47 D

HIS54

7.6 0.30 P*

HIS48

8.70 0.99 P

ASP66

3.67 0.13 D

HIS36

7.19 0.69 P

HIS71

7.03 0.11 D

HIS105

6.95 0.68 P

ASP87

3.33 0.07 D

HIS48

6.22 0.22 P**

HIS96

5.13 0.03 D

HIS119

6.50 0.43

P*

ASP101

3.90 0.18 D

HIS64

4.47 0.02 D

HIS198

6.64 0.06 P**

1vcx, pH 8

ASP119

3.45 0.08 D

HIS81

6.37 0.31 NA

HIS220

7.08 0.15 P**

NTR1

9.22 0.94 P

GLU7

3.70 0.13 P**

HIS82

6.41 0.33 D

HIS230

6.67 0.06 P**

GLU35

5.67 0.89 P

HIS97

6.28 0.26 D

HIS243

6.40 0.07 D

HIS15

7.50 0.99 P

HIS113

5.60 0.10 NA

HIS285

9.35 0.93 P

CTR129

2.90 0.03 D

HIS116

6.71 0.46 NA

HIS382

7.54 0.29 P*

HIS119

4.94 0.19 D

Comparison between calculated and experimental protonation states in neutron-diffraction structures. First row - computed pKhalf values; second row – the fractional protonations of residues. P – residue protonated in crystal structure; D – deprotonated; NA –more than one polar hydrogen is missing. In bold – accurately predicted structures; ** -completely incorrect prediction; * - underpredicted, but close.



Application - Optimized Protonation for Stable Molecular Dynamics • HIV Protease dimer has two Asp 25

residues in binding pocket

• Run CHARMm MD (100pS, GBSW solvent model) on two forms of the protein (PDB ID 1kzk)

– Protein with default protonation– Protein with pK-optimized protonation

(Asp 25 B protonated)Optimized-protonation of Asp 25’s in

HIV protease leads to more stable MD trajectories

RMSD of select residues to starting conformation, default protonation of Asp 25’s

RMSD of select residues to starting conformation, optimized protonation

© 2008 Accelrys, Inc. 21Todd et al. (1998) J Mol Biol,283,475-488

Zero model∆G(unfld) = - (Relative Folding Energy)

∆G(unfld) = ∆G0 – ∆G(fld)

∆G0: pKint,I = pKmod

Wij = 0

Application – Unfolding Energy

1HHP- predicted unfolding energy

6

7

8

9

10

11

12

13

14

15

2 3 4 5 6pH

∆G

(unf

old)

• HIV Protease apo form; 1hhp.pdb• Folding energy calculated using zero

model and beta-modelβ-model

Extendedconformation

Unfolding in urea


Application – Ligand Binding Energy

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12

pH

Ener

gy [k

cal/m

ol]

Energy of binding of KNI-272 to HIV-1 protease – 1hpx.pdb

The association constant is maximal between pH 5 and pH 6

Velazquez-Campoy et al. (2007) Protein Science, 9,1801-1809.

Calculated pH optimum of binding at pH ~ 5.0


pK1/2

Calculated GBIM

Calculated without membrane

Calculated using MEAD with PB and membrane2

Experiment

ARG82 > 14 >14 >15 >13.8

ASP85 2.96 7.1 1.7 2.6

ASP96 8.80 8.7 >15 >12

ASP115 6.54 8.1 8.4 >9.5

GLU194 9.69 8.6 > 15 Proton releasegroup

keeps one proton

GLU204 3.35 8.7 < 0

ASP212 <0.00 7.1 <0 <2.5

Schiff base216

> 14 12.1 >15 >12

1Luecke et al. (1999) J. Mol.Biol.,291,899-911.2Spassov et al. (2001) J. Mol.Biol.,312,203-219

MEMBRANE PROTEINS

Bacteriorhodopsin: 1c3w.pdb1


β2-adrenergic G Protein-coupled Receptor: 2rh1.pdb1

antagonist: carazololagonist: epinephrine (adrenaline,a cateholeamine)

MEMBRANE PROTEINS

Calculated pK1/2

carazolol adrenaline

residue unbound bound unbound bound

Asp 113 9.4 2.6 9.4 2.4

Asp 79 8.2 8.4 8.2 8.2

Glu 122 11.0 10.5 11.0 10.8

ligand: -NH2- 9.0 12.7 8.9 13.

Ligand: catehol -OH 10.4 14.


β2-adrenergic G Protein-coupled Receptor: Electrostatic contribution to the free energy of ligand binding.

MEMBRANE PROTEINS

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

0 2 4 6 8 10 12 14 16

∆∆

G b

indi

ng

pH

carazolol

adrenaline


MD simulation of β2-adrenergic G Protein-coupled Receptor – adrenaline complex.

MEMBRANE PROTEINS

Selected parameters of the production run :Production Steps 500000

Production Time Step 0.002

Production Target Temperature 300.0

Implicit Solvent ModelGeneralized Born with Implicit Membrane (GBIM)

Dielectric Constant 2

Implicit Solvent Dielectric Constant

80

Minimum Hydrogen Radius 1.0

Use Non-polar Surface Area True

Non-polar Surface Constant 0

Non-polar Surface Coefficient 0.00542

Nonbond List Radius 12.0

Nonbond Higher Cutoff Distance 11.0

Nonbond Lower Cutoff Distance 11.0

Dynamics Integrator Leapfrog Verlet

Apply SHAKE Constraint False

Random Number Seed 314159

Number of Processors 1

Preliminary preparation of the structure before MD simulations.

1. Use the Discovery Studio Create and Edit Membrane tool to add a membrane object to the input protein structure.

2. Run the Discovery Studio Calculate Protein Ionization and Residue pK protocol to assign the protonation state of all acidic and basic titratable groups at a selected pH.

3. Run Add Membrane and Orient Molecule protocol for a preliminary optimization of the position of the protein relative to membrane.

Steps 2 and 3 could be critical for the success of the MD simulations: Whenusing the default state of protonation, the simulation on 2rh1 structurewas compromised in a early phase, because of a significant overheatingof the system.


A 1 ns MD simulation of β2-adrenergic G Protein-coupled Receptor complex with adrenaline.

RMSD values of CA atoms along the MD trajectory.

all CA atoms CA atoms inside membrane (helix 1 excluded)

MEMBRANE PROTEINS

The low dielectric environment of membrane stabilizes the structure of transmembrane helices.


• The combination of the GB calculations with IMC approach increases dramatically the speed of calculations and makes it possible to treat very large structures of arbitrary shape which are difficult to calculate using methods based on grid techniques to solve Poisson-Boltzmann equation and Monte-Carlo sampling schemes.

• The results of the tests indicate that the method returns very accurate pK values, comparable to the best results previously reported in the literature.

• Compared to crystallographic data at given pH, the tests show a high accuracy of the predicted protonation and hydrogen coordinates.

• The use of the GBIM CHARMm module makes it possible to study not only water soluble proteins but also protein-membrane complexes.

• The Discovery Studio implementation provides an easy way to integrate the protein ionization calculations with many other molecular modeling protocols, such as pH-dependent MD simulations, ligand docking, protein docking, ion binding. It also made it easy to study the pH dependent protein stability and the effect of mutation on protein stability.

Conclusions


Acknowledgments

Lisa YanPaul FlookDon Bashford

a fast and accurate computational approach to protein ionization: combining the generalized born...

Technology

protein science

protein molecules

protein modeling

ph optimumof protein

protein free energy

ph rt x

d environment of protein

given ph