- Structures and free
energies of biomolecules are mainly determined by electrostatic interactions.
-
These are in particular
between charged groups.
-
Relative free energies (of hydration) can have
errors > 10
kcal/mol per charged group.
- No force field
consistently describes e.g. the relative free
energies of charged side chains.
- This is the major reason for the failure of many
current protein simulations.
-
Thus, we are optimizing new force field
parameters for charged amino acids and ions.
|
BECAUSE OF
THEIR DIFFERENT PROPERTIES, EACH WATER MODEL REQUIRES SEPARATE FORCE FIELD PARAMETERS TO
MODEL FREE ENERGIES OF HYDRATION CORRECTLY.
As an example, 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.
|
|
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. |
To illustrate the problem, 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, on the right).
Protein folding is for example mainly described 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.
|
 |
New OPLS-AA
Parameters for TIP4P
|
Molecule |
OPLS Atom type |
New Parameters |
|
Q |
s |
e |
|
Acetate & Propionate |
O272
C271
|
-0.59
0.28 |
2.96
3.75 |
0.21
0.105 |
|
n-propyl-guanidinium |
N300
H301
|
-1.06
0.59 |
3.25
0.00 |
0.17
0.00 |
|
n-butyl-ammonium |
N287
H290
|
-0.72
0.47 |
3.25
0.00 |
0.17
0.00 |
|
4-methyl-imidazolium |
512N
513H
59C
|
-0.72
0.64
-0.065 |
3.25
0.00
3.50 |
0.17
0.00
0.066 |
|
Performance of Standard OPLS-AA, OPLS-AA
with Semi-Empirical CM1 Charges, and the
Electrostatic Free Energy-Calibrated Force
Field
|
|
Exp. |
OPLS-AA Standard |
OPLS-AA CM1P |
OPLS-AA New |
|
Acetate |
-80.7 |
-91.7 |
-84.7 |
-81.2 |
|
Propionate |
-79.1 |
-88.0 |
-82.3 |
-80.1 |
|
n-propyl-guanidinium
|
-66.1 |
-58.9 |
-61.8 |
-65.9 |
|
n-butyl-ammonium
|
-69.2 |
-66.5 |
-66.4 |
-69.6 |
|
4-methyl-imidazolium |
-64.1 |
-57.9 |
-57.1 |
-65.0 |
|
MAE |
|
7.2 |
4.3 |
0.6 |
|
 |
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. This model thus gives
converged free energies of charged species
and was used.
|
References
-
K.
P. Jensen, W. L. Jorgensen,
"Halide, Ammonium, and Alkali Metal Ion
Parameters for Modeling Aqueous Solutions",
-
J. Chem. Theory. Comput. 2006, 2, 1499-1509.
-
-
K. P. Jensen,
"Improved Interaction Potentials for Charged
Residues in Proteins",
-
J. Phys. Chem. B 2008, 112, 1820-1827.
|
