Agenda: motivation basic knowledge on electrostatics...
Transcript of Agenda: motivation basic knowledge on electrostatics...
Sfb765, 29. January 2009 electrostatic energy computations of complex molecular systems 1
Institute of Chemistry and Biochemistry Freie Universität Berlin Takustrasse 36A14195 Berlin, Germany
email: [email protected]
Computation of electrostatic energies for complex molecular systems
Agenda:
motivation
basic knowledge on electrostatics
Application:
Compute electrostatic energies in proteins to evaluate pKa values
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motivation
Electrostatic interactions are ubiquitous and most relevant not only in all kinds of molecular systems but more general everywhere in the universe where there is not too densely pact matter of low enough energy.In the sun, of course, the most important interactions are gravitation and nuclear interactions. But, already in the earth atmosphere ionic interactions are most important being for instance responsible for aurora borealis.
Electrostatic interactions in chemistry are responsible for van der Waals interactions about 80% of the H-bond interaction energies and consequently they determine melting and boiling points of substances.
They govern the specificity in molecular recognition in: base pairing in DNA and RNA, protein substrate interactions, protein complex formation, immune response and cell-cell interactions. This list is by far not complete.
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motivation
hydrophobicity versus hydrophilicity:
Charged and polar molecular groups are generally considered to be
hydrophilic (i.e. they like water).
Water with its large permanent dipole
interacts strongly with such molecular
groups by reorienting its dipoles around a
charge. Hence, the hydrophilicity is here
governed by electrostatic interactions.
For the same reason bulk water interacts
strongly among each other. On the average it forms 3 of 4 possible
H-bonds per molecule. There are many different H-bond pattern in
bulk water, which vary dynamically on picosecond timescale. That is
why water is a low viscosity liquid. The large number of H-bond
pattern involve a large amount of entropy.
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+
- +
+
-
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-
+
+
- +
+- +-
+
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motivation
hydrophobicity versus hydrophilicity:
What about hydrophobic groups like CH4? They do not strongly
interact with water, but disturb the H-bond structure of bulk water.
Specifically they force water in the neighborhood to be locked in a
rigid H-bond pattern reducing the entropy of bulk water.
Bulk water fights back by pushing these molecules into separate
clusters (the “oil drop in water” phenomenon).
This is the classical hydrophobic effect related to bulk water entropy.
But what about ions?
Are they not disturbing the H-bond structure of bulk water?
Yes, they are, but, the electrostatic effect is stronger and leads to
efficient solvation in spite of the hydrophobic effect.
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basic knowledge on electrostatics
Interaction of point charges:
Coulomb interaction: q1 q2
1 2
1 2
1 2
q qW(| r - r |) =
| r - r |
� �
� �
1r�
2r�
0in a homogeneous dielectric:
1 2
1 2
1 2
q qW(| r - r |) =
| r - r |ε
� �
� �
Interaction of a unit charge
q =1 with a charge cloud ρρρρ’( ): r′� q ρρρρ’( )
r�
r′�
0
ρ (r )(r) = dr
| r - r |
′ ′′ ′φ
′∫
�
� �
� �
φφφφ’ is the electrostatic potential generated by the charge cloud ρρρρ’
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The electrostatic potential is the fundamental quantity of electrostatics to
calculate interaction energies between different charge clouds ρ and ρ’:
Disadvantage: more difficult to evaluate φ
Advantage: allows to consider inhomogeneous dielectrics
as they occur in protein membrane water systems.
An alternative way to calculate the electrostatic potential Φ
induced by a charge cloud ρ is the Poisson equation:
( ) ( ) ( )r r 4 r∇ε ∇φ = − πρ� �� � �
i
where
tf (r) f (r) f (r)
f(r) =x y z, ,
∂ ∂ ∂∇
∂ ∂ ∂
� � �� �
basic knowledge on electrostatics
(r) (r )W = dr (r) (r) = dr dr
| r r |
''′ρρ
′ρ ρ′ρ φ
′∫ ∫ ∫
-
� �
� � � � �
� �
( )rε�
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What is a dielectric medium?
A dielectric considers a material consisting of microscopic dipoles, which
can reorient and are continuously distributed (cloud of dipoles).
These implicit dipoles react on charges: they reorient or in other words
they are polarized.
For molecular systems there are two such contributions:
Nuclear polarization due to permanent dipoles and
Electronic polarization due to distortion of the electronic wave function.
Typical values of the dielectric constant ε are
ε = 2 for electronic polarization (the only contribution for fast processes)
ε > 2 for nuclear polarization (for water ε = 80).
Note that the dielectric constant will be ε = 1, if all components of a
molecular system are considered explicitly, i.e. the Schrödinger
equation is solved in all detail. Whatever is not considered explicitly
can be considered approximately by a dielectric medium.
basic knowledge on electrostatics
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streptococcal protein G
pKa predictions in proteins with pH adapted global conformers
application
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AH A + H+
=
+
A
A HK
AH
( )
= −
∆ → =
A
OA
ApK pH log
AH
G AH A ln10 RT pK− −
− −
= +−
=+
A
A
A
ln10(pH pK )
ln10(pH pK )
xpK pH log
1 x
ex
1 e
( )∆ = − AG(pH,T) ln10 RT pH pK
application pKa, what is it?
Sfb765, 29. January 2009 electrostatic energy computations of complex molecular systems 10
pKA of titratable groups in proteins
ASH AS + H+S
APH AP + H+S
H+
H+
∆GS,P(AH) ∆GS,P(A)
∆GP(AH�A)
∆GS(AH�A)
∆GP(AH�A) = ∆GS(AH�A) + ∆GS,P(A) – ∆GS,P(AH)
∆∆GS,P
∆∆GS,P = ∆∆Gborn + ∆∆Gback + ∆∆Gint
εw=80 εw=80
εp=4 εp=4
application computation of pKa in proteins
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pKA of titratable groups in proteins
∆GP(AH�A) = ∆GS(AH�A) + ∆∆Gborn + ∆∆Gback + ∆∆Gint
( ) ( )
( ) ( )
Φ − Φ
− Φ − Φ
∑
∑
i
i
N
i P i S ii
N
i P i S ii
1Q r,A r,A
2
1Q r,AH r,AH
2
µ µ µ ν µνµ µ ν µ ν= = = ≠
∆ = − + ∆∆∑ ∑ ∑N N N
n n int r n nA,
1 1 1,
g x RT ln10 (pH pK ) x x W
interaction of titratable groupsin protein (enthalpy)
µ
µ
−∆
=
−∆
=
=∑
∑
Nn
Nn
2n g /RT
n 12
g /RT
n 1
x ex
e
application computation of pKa in proteins
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data set of experimental pKA: 15 different proteins in 22 crystals, 199 experimental pKA
B. amyloliquefaciens barnase
- 1A2P, 1B20 (14)
bovine pancreatic trypsin inhibitor
- 4PTI (14)
intestinal bovine Ca2+-binding protein
- 3ICB (19)
T-lymphocyte adhesion glycoprotein
- 1HNG (14)
hen egg-white lysozyme
- 2LZT, 1B0D (19)
turkey ovomucoid inhibitor
- 1PPF, 1CHO, 3SGB (15)
streptococcal B1 IG-binding protein G
- 1PGA (15)
ribonuclease A
- 3RN3, 7RSA (16)
ribonuclease H1RNH, 2RN2, 1RDD (25)
ribonuclease T3RNT (4)
HIV protease- 1HPX (8)
xylanase- 1XNB (10)
experimental pKa in proteins
thioredoxin- 1ERT (17)
cryptogein- 1BEO (3)
ribosomal protein L9- 1DIV (6)
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computed vs. experimental pKA shifts
computed vs. experimental pKa
weak ARG salt bridge (#contacts <=2)
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pKa of residues in salt bridges
salt bridges
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energetics of arginine salt bridges
OD2
OD1
+2
-2
protonation of Asp
deprotonation of Arg
salt bridges
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Including conformational flexibility
µ µ µνµ µ ν= ≠
∆ = − + ∆∆ + ∆∑ ∑N N
n,l n,l int r,l l lA, conf
1
g x RT ln10 (pH pK ) W G
∆ = − = ∆ + ∆∆ + ∆∆l l r l l lconf conf conf hom.elec. S NESG G G G G G
∆ lconfG
∆ lhom.elec.G
∆ rSG ∆ r
NESG ∆ lSG ∆ l
NESG
conformational flexibility
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generation of global conformers – perturbing ion pairs
1. Identify salt bridge on protein surface
- distance cutoff (4.0 Å)
- SASA cutoff (>30 Å2)
2. Generate 30 global conformations by random perturbation of dihedrals & minimization with constraints toward crystal structure
3. Identify lowest energy conformations
- CHARMM22 force field energy including bonded and non-bonded (electrostatic and vdW) energy terms
- vacuum or GBSW
4. Save coordinates & repeat N times with different random seed
- 5-8 conformers used in sampling
streptococcal protein G, 1PGA
conformational flexibility
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generation of global conformers – perturbing ion pairs
1. Identify salt bridge on protein surface
- distance cutoff (4.0 Å)
- SASA cutoff (>30 Å2)
2. Generate 30 global conformations by random perturbation of dihedrals & minimization with constraints toward crystal structure
3. Identify lowest energy conformations
- CHARMM22 force field energy including bonded and non-bonded (electrostatic and vdW) energy terms
- vacuum or GBSW
4. Save coordinates & repeat N times with different random seed
- 5-8 conformers used in sampling
streptococcal protein G, 1PGA
conformational flexibility
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generation of global conformers – self-consistency
PDB
self-consistentPQR
protonation pattern
KarlsbergMonte Carlo
pKint∆∆W
TAPBSelectrostatics
PQR-Hcoordinates, charges, radii
CHARMM
repeat untilprot. patterndoes not change
Rabenstein et al (1998) Eur Biophys J 27: 626-637
conformational flexibility
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generation of global conformers – adapting to pH
PDB
self-consisten t PQR
protonation pattern
Karlsberg
pK int
∆ ∆W
TAPBS
PQR-H
CHARMM
repeat until
prot. patterndoes not change
PDBPDB
self-consisten t PQR
self-consisten t PQR
protonation pattern
Karlsberg
protonation pattern
KarlsbergKarlsbergKarlsberg
pK int
∆ ∆W
TAPBS
pK int
∆ ∆W
pK int
∆ ∆W
pK int
∆ ∆W
TAPBSTAPBS
PQR-H
CHARMM
PQR-HPQR-H
CHARMMCHARMMCHARMM
repeat until
prot. patterndoes not change
repeat until
prot. patterndoes not change
PDB
self-consisten t PQR
protonation pattern
Karlsberg
pK int
∆ ∆W
TAPBS
PQR-H
CHARMM
repeat until
prot. patterndoes not change
PDBPDB
self-consisten t PQR
self-consisten t PQR
protonation pattern
Karlsberg
protonation pattern
KarlsbergKarlsbergKarlsberg
pK int
∆ ∆W
TAPBS
pK int
∆ ∆W
pK int
∆ ∆W
pK int
∆ ∆W
TAPBSTAPBS
PQR-H
CHARMM
PQR-HPQR-H
CHARMMCHARMMCHARMM
repeat until
prot. patterndoes not change
repeat until
prot. patterndoes not change
PDB
self-consisten t PQR
protonation pattern
Karlsberg
pK int
∆ ∆W
TAPBS
PQR-H
CHARMM
repeat until
prot. patterndoes not change
PDBPDB
self-consisten t PQR
self-consisten t PQR
protonation pattern
Karlsberg
protonation pattern
KarlsbergKarlsbergKarlsberg
pK int
∆ ∆W
TAPBS
pK int
∆ ∆W
pK int
∆ ∆W
pK int
∆ ∆W
TAPBSTAPBS
PQR-H
CHARMM
PQR-HPQR-H
CHARMMCHARMMCHARMM
repeat until
prot. patterndoes not change
repeat until
prot. patterndoes not change
self-consistent with respect to pH -8
PDB
5x 5x
1x
self-consistent with respect to pH 7
self-consistent with respect to pH 20
5 global
conformers
5 global
conformers
hydrogenconformer
conformational flexibility
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results – occupancies of 4 different protein conformations
streptococcal protein G, 1PGA
results conformational flexibility
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results – occupancies of 4 different protein conformations
streptococcal protein G, 1PGA
results conformational flexibility
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results – conformer occupancies
barnase, 1A2P
results conformational flexibility
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comparison of results – scatter plots
Tyr53
Asp66
results conformational flexibility
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comparison of results – RMSD
5.903.322.901.959.26
(3.45)
11.51
(4.68)
MAXERR
|pKa|>=1.8
2.491.311.241.052.73
(1.64)
3.85
(2.69)
RMSD
|pKa|>=1.8
5.904.862.903.219.26
(5.25)
11.51
(9.47)
MAXERR
|pKa|>=1.0
1.781.230.991.052.15
(1.81)
3.12
(2.76)
RMSD
|pKa|>=1.0
5.904.864.403.269.26
(8.51)
11.51
(10.86)MAXERR
1.030.911.021.101.84
(1.74)
2.62
(2.51)RMSD
NULLPROPKAbMCCEamc(pH,sb)mc(pH)scpH7
a Georgescu et al., Biophysical Journal 2002, 83, 1731-48. b Li, Robertson, Jensen, Proteins, 2005, 61, 704-721.
comparison with other methods
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comparison of results – PROPKA
results other methods - PROPKA
Li, Robertson, Jensen, Proteins, 2005, 61, 704-721.
Sfb765, 29. January 2009 electrostatic energy computations of complex molecular systems 27
Team: Francesco Bettella, Gernot Kieseritzky, Ane L Gamiz, Artur Galstjan,
Hiroshi Ishikita, Alok Junea, Björn Kleier, Björn Kolbeck, Jorge Numata,
Dr. Björn Rabenstein, Dawid Rasinski, Henning Riedesel,
Tobias Schmidt-Gönner, Marcel Schmidt am Busch
Emmy Noether young researcher group of Dr. Thomas Renger:
Julia Adolphs, Dr. Mohamed El Amine Madjet, Dr. Frank Müh,
Grzegorz Raszewski
Funding: Berlin, Sfb 498, 2 Graduiertenkollegs, DAAD, Studienstiftung