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Force Field Development for Proteins and Ions


- 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.

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 

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 OPLS-AA, OPLS-AA + CM1 Charges, and an 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

 



CAPRAD

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.

 


Copyright 2014. Kasper P. Kepp.