Electrostatic Interactions

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Electrostatic Interactions

• Principles and applications

From Coulombs Law to continuum electrostatics
http//www.biochem.oulu.fi/juffer/
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Importance of electrostatics

• Every interaction contains an electrostatic
  component.
• Important for protein folding and binding
• pKas (acid-dissociation constants).
• Salt bridges in protein.
• Protein-membrane associations.
• Protein function
• Enzymatic activity
• Solvent effects, polarization effects.
• Drug design.

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Coulombs Law
High School
Electrostatic force acting on charge qi due to
charge qj
Electric field at qi
qj
qi
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Electrostatic potential
High School
Coulomb potential (vacuum potential)
High School
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Graphical representation
R


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Interaction energy
Electrostatic potental of qj
Electrostatic interactions are long ranged.
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Field and potential of collection of N charges
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2
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Origin
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Protein electrostatics

• Charged groups
• Lys(), Arg(), Glu(-), Asp(-),
• C-term(-), N-term().
• Polar groups
• Ser (OH), Tyr(OH), peptide-bond, .
• His (Imidazol group), free Cys (SH),
• Titrating sites may modify their charge
  distribution as a function of the pH.
• Asymmetric molecular charge distribution
  charges, dipoles, etc..

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Protein in a solvent
pH effects

• Solvent polarization
• Solvent reorientation.
• Ion redistribution.
• Induced dipoles.
• Protein polarization
• Induced dipoles.
• Reorientation of groups.

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Solvent modelling

• Explicit waters and ions (all-atom
  representation)
• Biomolecular simulation techniques, e.g.
  molecular dynamics.
• Semi-microscopic (semi-macroscopic)
• Water as background continuum.
• Explicit ions.
• Langevin dipoles at lattice points.
• Full continuum no atomic detail at all
• Continuum electrostatics.

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Continuum electrostatics

• Rigid protein molecule.
• No analytical solution.

• Macroscopic in nature.

Solvent region
Dielectric boundary
Inverse Debye Length
Protein
Partial charges
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Dielectric constants

• Symbol e.
• Represents the ability of material to be
  polarized.

Solvent
Effective interaction
All atom
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Numerical methods for continuum electrostatics
Finite difference method
Mapping onto a 3D-lattice
Triangulated surface
Boundary element method (BEM)
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Total electrostatic work (1)

• The amount of work Wel to assemble the protein
  charge distribution.
• Electrostatic contribution to solvation free
  energy difference of electrostatic work Wel in a
  solvent and in vacuum (gas).
• The effect of solvent is generally to screen
  electrostatic interactions
• Solvent exposure or charge burial.

Gas
Solution
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Total electrostatic work (2)
Set of point charges
Charge distribution
P polarization (dipole moment per unit volume)
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Multifunctional Enzyme
MFE
SCP-2L
hydratase
dehydrogenase
PTS1
PEX5
lipid-like molecule
TPRs
PEX13
PEX14
Peroxisomal membrane
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Liganded SCP-2L with TPR domain of PEX5
SCP-2L domain

• Binding
• PTS has an inherent ability to bind to TPR
• Electrostatic properties?
• Crucial
• PTS1 most be accessible for binding.

Triton

• TPR-domain
• helix-loop structural elements
• domain has a ring-like structure

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Unliganded SCP-2L with TPR domain of PEX5
SCP-2L domain
Mechanism Lipid-like ligand pushes PTS1 out

• TPR-domain
• helix-loop structural elements
• domain has a ring-like structure

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Electrostatics
TPR (PEX5)
SCP-2L
PTS
PTS binding site
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Acid dissociation constants (1)

• Enzymatic reactions generally depend on the pH
• Changes in average protonation state of reactive
  residues will affect the reaction rate classical
  examples are serine proteases, such as
  chymotrypsin.
• Affinity of ligands for proteins is influenced by
  the pH.
• Stability of folded protein conformation depends
  on the pH unfolding occurs generally below pH5
  and above pH10.

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Acid dissociation constants (2)
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Normal pKa of a His residue is 6.5-7.
pH unfolding of staphylococcal nuclease A
Reaction mechanism of chymotrypsing
Rate depends on pH
Stability depends on pH
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How to define pKa (1)

• The pKa of a titrating site is defined as the pH
  for which the site is 50 occupied, that is
• The pH for which the occupancy q is 0.5.

Deprotonation reaction
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How to define pKa (2)
q is degree of protonation or occupancy Number
of bound protons as a function of pH
Titration curve
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How to define pKa (3)
Protonation state is always an average Change in
pH results in a different ratio of protonated and
deprotonated molecules in solution.
One state transition
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Experimental determination of pKas (1)

• Nuclear Magnetic Resonance (NMR) is the most
  accurate method currently available.
• Determined from the changes in the chemical shift
  (d) as a function of the pH of an NMR-sensitive
  nucleus.
• Data is fitted to a modified Hill equation

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Experimental determination of pKas (2)
Chemical shift of the Ce1 proton of His49 in
Asp49His Rnase T1 as a function of pH in D2O and
and 0.2 M NaCl. The line is based on the
Henderson-Hasselbalch equation with a
pKa7.17?0.02. Taken from Grimsley et al., Prot.
Sci., 8, 1843-1849, 1999.
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Experimental determination of pKas (3)

• Protein may undergo conformational changes.
• Protein may not be stable over full pH range
• How valid are the observed pKas?
• Calculations are required for a full
  understanding of the underlying molecular
  mechanism of the observed changes.

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Calculation method
i
j
Titrating site (Glu, Arg, Lys, )
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pKas are influenced by

• Ionic strength.
• Protein conformation
• Structure relaxation and reorganization.
• Changes in structure very often ignored.
• Presence of ligands, such as bound ions.
• Difference in dielectric properties between
  protein and solvent.

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Effect of proteins dielectric constant
Test case Lysozyme.
Juffer et al., J. Phys. Chem. B, 101, 7664-7673,
1997.
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Test case pKas of calbindin D9k (1)

• Calcium binding protein.
• Minor conformational
• changes upon Ca2
• binding.
• What are the shifts in
• pKa upon Ca2 binding?

• Both X-ray as NMR
• structures were
• employed.

Juffer and Vogel, Proteins, 41, 554-567, 2000
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Test case pKas of calbindin D9k (2)
Shifts of pKas may be either positive or
negative.
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Test case pKas of calbindin D9k (3)
Calbindin Titration curves of ion ligating groups.
No structure relaxation upon ion release.
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Test case pKas of calbindin D9k (4)
Calbindin Titration curves of ion ligating groups.
With structure relaxation upon ion release.
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Protein-ligand affinity calculations

• Protein have the fundamental ability to
  selectively bind to other molecules.
• Important for
• Enzyme function.
• Receptor actions (membrane).
• Self-organization cellular structures and
  multicomponent protein complexes.
• Important to understand, both quantitatively and
  qualitatively.

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• Solvent (water, ionic strength)
• pH
• Conformational flexibility
• Interactions
• Entropic effects

P L ? PL
Major Histocompatibility Complex
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Continuum approach
Solvation free energy
Thermodynamical cycle
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A standard calculation method (2)
Difference in solvation free energy between
complex and individual molecules.
Affinity in vacuum
Affinity In solvent
Indirect calculation of affinity
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Contributions to the solvation free energy of a
protein

• Hydrogen bond formation with polar groups of the
  macromolecule.
• Entropy change of water molecules due to binding
  with polar groups or their release into bulk
  water (hydrophobic effect).
• Cavity formation due to solute excluded volume.
• Non-valent interaction of non-hydrogen bonded
  water molecules with protein atoms at the
  surface.
• The polarization of bulk water and of the protein
  volume inside the macromolecule and the changes
  of salt density.

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Protein-ligand affinity calculations A test case

• Empirical calculation of the relative free
  energies of peptide binding to the molecular
  chaperone DnaK.
• Kasper et al., Proteins, 40185-192 (2000).
• Computation and measurement of the affinities of
  11 different peptides for DnaK.

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DnaK-peptide complexation
NRL peptide Asn-Arg-Leu-Leu-Leu-Thr-Gly
1dkx.pdb
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DnaK protein

• Molecular chaperone
• It prevents misfolding and aggregation.
• Structure consists two domains
• Peptide binding domain (?-subdomain).
• ATPase (enzyme) domain (?-helical subdomain)
• No direct contact with ?-subdomain, but electric
  field of the helical subdomain significantly
  influences peptide binding.
• Both domains must move apart to allow peptide in
  or out
• ?-helical subdomain acts as a lid.
• Binding and release of peptide is regulated by
  ATP binding/release to/from helical subdomain.

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NRL peptide
Peptide structure from 1dkx.pdb
Asn-Arg-Leu-Leu-Leu-Thr-Gly

• Peptide has a hydrophobic core (Leu-Leu-Leu)
• Charged and polar residues flank hydrophobic
  core
• Affinity for these residues is affected by
  electrostatic field of the DnaK protein.
• Peptide must have a significant effect on
  stability of protein, since the structure of the
  free protein could not be resolved.

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Experimental determination of affinities

• Mutation of a His in the ?-helical subdomain into
  Cys.
• Measurement of flueresence signal emitted by Cys
  labelled with a fluorophor (MIANS)
• Binding of peptides results in a decrease of the
  signal.
• Affinities have been determined for a mutant
  instead of the original protein
• How representative are the experimental values
  for wild type DnaK?
• Computation were carried out for original protein.

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Set of peptides
Calculations were performed for green residues,
experiment for full peptide.
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Computational procedure
Refined peptide
NRL peptide
Peptide
EM/MD
Mutation
e.g. NRA
MD 290 ps
Protein- Peptide complex
DnaK- NRL

• Analysis of last 50 ps
• Surface calculation
• Electrostatics

Delphi Naccess
Mutation
Complex
Refined complex
EM/MD
MD 290 ps
Affinity
Free protein?
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Calculation of ?Gb (1)
Non-polar contribution
Side-chain entropy
Empirical scale
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Calculation of ?Gb (2)
Change of solvation free energy
Thermodynamic process for calculating the change
in the total electrostatic energy upon
intermolecular binding.
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Results after fitting
Many contributions were ignored, such
as Rotational, translation and backbone
entropies, van der Waals interactions,
strain. Many contributions were assumed to
cancel, since relative binding free energies were
computed.
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Continuum approach for large set of
protein-ligand complexes
S. Donnini and A.H. Juffer, Calculation of
affinities of peptides for proteins, J. Comput.
Chem. 25, 393-411, 2004
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Problems

• Different protein families require different
  values of parameters
• Assumption contributions to free energy are
  independent
• Physical basis not always clear
• Predictive power seems weak