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FORCE
FIELD PARAMETERS FOR CHARGED
GROUPS IN PROTEINS
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- Structures and free energies of biomolecules
are mainly determined by electrostatic
interactions.
- These are strongest between charged groups.
- Relative free energies (of hydration) between
typical charged molecules can have errors > 10
kcal/mol when modeld with standard force fields.
- No force field consistently describes e.g. the
relative free energies of charged side chains.
- Thus, we are optimizing new force field
parameters for charged amino acids and ions.
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EACH WATER MODEL REQUIRES A UNIQUE
CHARGED-MOLECULE FORCE FIELD.
The free energy of hydration of a charged group can
differ by more than 10 kcal/mol when computed in
TIP4P or TIP3P water. We work mainly with TIP4P but
have parameterized protein parameters for TIP3P /
SPC as well.
The free energy of a salt bridge is given by the
free energy of the paired amino acids minus the
hydrated amino acids (see Figure 1).
FIGURE 1.
A salt
bridge illustrates the problem of obtaining proper
force field parameters for charged residues, due to
long-range electrostatic effects and the critical
importance of the free energy of hydration. |
Protein folding is e.g. crucially determined by the total dehydration free
energy of charged residues forming salt bridges and other interactions within
the native protein.
When any charged amino acid in a protein changes environment, e.g.
upon ligand binding or protein-protein interactions, it will change its free
energy relative to other charged groups.
It is thus
exceedingly important to put all charged amino acids on the same free energy
scale.
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New OPLS-AA Parameters for TIP4P
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Molecule |
OPLS Atom type |
New Parameters |
|
Q |
s |
e |
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Acetate & Propionate |
O272
C271 |
-0.59
0.28 |
2.96
3.75 |
0.21
0.105 |
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n-propyl-guanidinium |
N300
H301 |
-1.06
0.59 |
3.25
0.00 |
0.17
0.00 |
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n-butyl-ammonium |
N287
H290 |
-0.72
0.47 |
3.25
0.00 |
0.17
0.00 |
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4-methyl-imidazolium |
512N
513H
59C |
-0.72
0.64
-0.065 |
3.25
0.00
3.50 |
0.17
0.00
0.066 |
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Performance of OPLS-AA, OPLS-AA + CM1
Charges, and an Electrostatic Free
Energy-Calibrated Force Field
|
|
Exp. |
OPLS-AA Standard |
OPLS-AA CM1P |
OPLS-AA New |
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Acetate |
-80.7 |
-91.7 |
-84.7 |
-81.2 |
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Propionate |
-79.1 |
-88.0 |
-82.3 |
-80.1 |
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n-propyl-guanidinium |
-66.1 |
-58.9 |
-61.8 |
-65.9 |
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n-butyl-ammonium |
-69.2 |
-66.5 |
-66.4 |
-69.6 |
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4-methyl-imidazolium |
-64.1 |
-57.9 |
-57.1 |
-65.0 |
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MAE |
|
7.2 |
4.3 |
0.6 |
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The treatment of long-range electrostatics is the
crucial aspect of this problem.
To put anions and cations on the same free-energy
scale, full account of the electrostatic
interactions is necessary.
For any ion in water, the water-water interactions
are unfavorable as they align water molecules
towards the ion. The ion-water interactions
compensate this interaction and are always
favorable.
A spherical model with constraints worked well for
including all interactions within a given radius,
and was shown to be size-consistent beyond a radius
of 10 Å, incl. Born correction, Figure 2, left.
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References
K. P. Jensen, J. Phys.
Chem. B 2008, 112, 1820-1827.
"Improved Interaction
Potentials for Charged Residues in Proteins"
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copyright 2008 k.p. kepp |
