Ion Solvation Thermodynamics from Simulation with a Polarizable

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					  Ion Solvation Thermodynamics from
Simulation with a Polarizable Force Field

 Alan Grossfeild       Pengyu Ren     Jay W. Ponder

                    Gaurav Chopra
                   07 February 2005
                       CS 379 A
Ion Solvation : Why do we care?
 Ion Solvation: Relative stability of ions as a
 function of solvent and force field
 Surface & environmental chemistry
 Study of molecules such as surfactants, colloids
 and polyelectrolyte
 Biologically: Structure and function of nucleic
 acids, proteins and lipid membranes
 Thermodynamics: Development of continuum
 solvation models – Interested in Free Energy of
 Solvation for individual ionic species
           Why Simulate?
Motivation: Solvation free energy of salts known
experimentally but cannot separate into
individual contributions of ions
Molecular dynamics used to resolve this using
Polarizable Force Field (AMOEBA)
Simulations with CHARMM27 and OPLS-AA
done for comparison
Ions: K+, Na+ and Cl-
Solvent: Water (TIP3P model for non-polarizable
force field) and Formamide
   Molecular Model and Force Field
  N-body Problem

                         Non-bonded two

Inclusion of Polarization: e.g. binding of a charged ligand polarizes receptor part
-by inducing point dipoles
-by changing the magnitude of atomic charges
-by changing the position of atomic charges

                         3N x 3N Matrix
      Summary of the paper
Experiments and standard molecular mechanics
force fields (non-polarizable) cannot give correct
values for ion solvation free energy for an ion
AMOEBA parameters reproduce in vacuo
quantum mechanical results, experimental ion-
cluster solvation enthalpies, and experimental
solvation energies for whole salt
Result: Best estimation of ion-solvation free
energy for ions using AMOEBA
                                                                                      Ion Solvation

                                                    Extra-                                                          Simulation: Using
                                                thermodynamic                                                          TINKER 3.9

                                      Estimation of
                                    proton solvation:                                                                                   Atomic Multipole
                                     entropies of H+      Born equation:                                                                   Optimized
             Cation and Anion                                                                          High-level
                                    and OH- are equal      Effective ionic        Cluster Pair                                           Energetics for
            Identical Solvation                                                                         quantum     QM/MM Methods
                                    in water and then      radii = crystal       Approximation                                            Biomolecular
             Thermodynamics                                                                            mechanics
                                         use self-        radii + constant                                                                Applications
                                        consistent                                                                                         (AMOEBA)

                                                                                                      AMOEBA VdW parameters:
                                                                      avoids the use of
                                                                                                      • High-level QM (Na+, K+)
                           Differential near
                          IR: Anions better
                                                                        reference salt
                                                                                                      • Experimental Cluster Hydration
Tetraphenyl Borate
                            solvated than
                                                                      Data deviate from
                                                                       Born equations
                                                                                                      enthalpies combined with solvent
                                                                       and constants
                                                                                                      parameters using neat-liquid and
                                                                                                      gas-phase cluster simulation (Cl-)
           Force Field Parameters

AMOEBA Force Field
• Each atom has a permanent partial charge, dipole and quadrupole moment
• Represents electronic many-body effects
• Self-consistent dipole polarization procedure
• Repulsion-dispersion interaction between pairs of non-bonded atoms uses
buffered 14-7 potential

AMOEBA dipole Polarizabilities of Potassium, sodium and chloride ions is set to
0.78, 0.12 and 4.00 cubic Ang.
            Cluster Calculations
Stochastic Molecular dynamics of clusters
of 1-6 water molecules with a single
chloride ion
Velocity Verlet implementation of Langevin
dynamics used to integrate equations of

Hydration enthalpy of water molecules
n = number of water molecules
<E(n,Cl)> = average potential energy over simulations with n waters and a
chloride ion
       Molecular Dynamics and Free
            Energy Simulation
                                    For each value of l energy minimization is
                                    performed until RMS gradient per atom is
                                    less than 1 kcal/(mol A)

• AMOEBA took more than 7 days, OPLS-AA and CHARMM27 took less than a day
• Final structure for l = 1 particle growth simulation used as starting structure for
each trajectory in the charging portion

                                                E = potential energy of system
Statistical Uncertainity

                                                            N = number of points in
                                                            time series
                                                            s = statistical efficiency
         Ion Solvent Dimers Results

• Gas-phase behavior gives ion-solvent
interaction without statistical sampling
• High level QM only possible for gas phase
unless implicit solvent model used
•Table 2: Overestimated values
• Ion-oxygen separation > 2.3 Ang.: less
electrostatic attraction than TIP3P water
• Molecular orbital calculations problematic
for chloride
Cation-Amide Dimers Results
Chloride-Water Clusters Results

Van der Waals parameters for chloride ion compared with enthalpy of formation
of chloride-water dimer as molecular orbital calculations is problematic
Ion Solvation Results
Solvent Structure around ions

             g(r) = radial distribution function
To quote Albert Einstein:

The properties of water [and aqueous solutions] are not only strange but
perhaps stranger than what we can conceive


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