Molecular Dynamics Simulations

Molecular Dynamics Simulations

Yaoquan Tu

Division of Theoretical Chemistry and Biology, Royal Institute of Technology (KTH)

2011-06

Outline

I. Introduction

II. Molecular Mechanics Force Field

III. Molecular Dynamics Simulations

IV. Applications

I. Introduction

Evolution of molecular simulations

Pre-computer era Computer simulation

Molecular dynamics simulation

Molecular systems

Molecular dynamics simulations

Properties of the molecular

systems

Carried out on computers

Molecular Dynamics simulation

• Virtual experiment at atomistic scale

• Direct observation and manipulation of atoms and molecules

Molecular Modeling

Computer Simulation Statistical

Mechanics MD

& others

Molecular dynamics simulation

Inter-atomic interactions

MD

simulation program

output

How to describe them?

How does an MD program work?

Carried out on computer(s)

What can be obtained ?

II. Molecular Mechanical

Force Fields

Molecular dynamics simulation

Inter-atomic interactions

MD

simulation program

output

How to describe them?

Basic ideas

• If we want to study a protein, a piece of DNA, biological membranes, crystal lattice, nanomaterials, diffusion in liquids,… the number of electrons become impossible to handle even with present-day computers.

• Instead, we replace the nuclei and electrons, and their interactions, by

”classical” atoms and new potential functions.

• No cumbersome integrals to solve - Enables us to study very large

systems (100.000 atoms).

Molecular mechanics force fields

• Force fields use simplified functions (potential functions) to describe the interactions between atoms.

• Force fields are constructed by parameterising the potential functions using either experimental data (X- ray and electron diffraction, NMR and IR spectroscopy) or ab initio and semi-empirical quantum mechanical calculations.

• Despite classical nature, force fields can mimic the behaviour of atomistic systems with an accuracy which approaches the high level of quantum mechanical calculations in a fraction of the time.

Force Field Function Form

bond angle torsion improper vdW elec

VFF V V V V V V

V_bonded V_non-bonded

angle bending i k

j bond stretching

i j

r

 Bonded terms

van der Waals

electrostatic q⁺ q⁺q^- proper

torsional angle

i j k

l

ϕ improper

torsional angle

d i

j

k l

 Non-Bonded terms

 Bonded terms

Widely Used Force Fields

 OPLS/AA Force Field

 Empirically fitted charges

 Electrically neutral subunits

 AMBER Force Field

 AMBER94, AMBER99, AMBER03

 Charges from RESP (restrained electrostatic potential) fitting

 CHARMM Force Field

 Charges based on the solute-water complexes

 Urey-Bradley term accounting for 1-3 interaction

• TIP3P

• SPC/E

 TIP4P

Water Models

+0.417e

+0.417e

−0.834e

104.52 0.9572 Å

+0.52e

+0.52e

−1.04e 104.52 0.9572 Å

+0.4238e

+0.4238e

−0.8476e

109.47 1.0 Å

III. Molecular Dynamics

Simulations

Molecular dynamics simulation

Inter-atomic interactions

MD

simulation program

output

How does an MD program work?

Carried out on computer(s)

Molecular dynamics simulation

How does an MD program work?

Inter-atomic interactions

Force acting on each atom

Acceleration on each atom

Changes of velocity and

position New velocity

and position

Next time step

Molecular dynamics simulations simulate the collisions between atoms !

Equation of Motion and Integrator

 Newton’s Equation of Motion

i i

i m a

F

Calculated from inter-atomic

interactions

Making the

changes of velocity, position of atom i

 Leap-frog Algorithm

 Velocity-Verlet algorithm

Periodic Boundary Condition

Periodic boundary condition is used to simulate an infinite system

 Minimum image convention

 Recovery of the electrostatic interactions beyond cut-off:

Ewald summation & Particle mesh Ewald

 Cut-off radius

Treatment of non-

bonded Interaction

Molecular dynamics simulation

Inter-atomic interactions

MD

simulation program

output

What can be obtained ?

What can be obtained from Molecular Dynamics simulation ?

MD

simulations

• Cooperative phenomena;

• Collective properties;

The effects from:

• temperature, pressure, …

• solvents, intermolecular interactions, … Structures:

• bulk materials, solutions, aggregates, …

• DNAs, proteins,clusters, molecules, … Dynamics properties:

• diffusion coefficients; relaxation times, …

IV. Applications

1. Protein adsorption onto TiO

 Background

 Titanium is a promising biocompatible material

 TiO₂ film exists on the titanium surface

 Water molecules are known to dissociate on TiO₂ surface

 Question

 What is the effect of water dissociation on the biocompatibility of TiO₂?

Dental implant

Protein adsorption onto TiO

 Snapshots on hydroxylated and non-hydroxylated surface

(kJ/mol)

Protein adsorption onto TiO

 Vertical number densities of interfacial water and protein

Protein adsorption onto TiO

 What do we obtain?

 Protein adsorption onto TiO₂ surface is strongly mediated by the interfacial

water molecules.

 Protein affinity of the surface is enhanced by dissociated water molecules.

 Biocompatibility can be manipulated

through appropriate surface modification.

2. O

-induced

F NMR Shift

 Background

 O₂-induced ¹⁹F NMR shift can be used to determine the immersion depth of

transmembrane protein

 O₂ is inhomogeneously distributed in membrane

 ¹⁹F NMR shift is sensitive to O₂ concentration

 ¹⁹F labels can be conveniently introduced into cysteine residue of protein

 Question

 How does O₂ molecule reside around ¹⁹F label and affect the ¹⁹F NMR shift?

Hydrophilic

Hydrophobic

Hydrophilic

[O₂]

O

-induced

F NMR Shift

 Force fields

 Fluorinated cysteine

 General AMBER force field

 RESP partial atomic charges

 Water model

 TIP4P

 O₂ model

 Designed to reproduce the experimental quadrupole moment

 Zasetsky, A. Y., et al. (2001) Chem.

Phys. Lett., Vol. 334, pp. 107−111.

− + − oxygen virtual oxygen

site

O

-induced

F NMR Shift

 Shortest O-F distance: cutoff at 4.0 Å

 Computational method

 Pennanen, T. O., et al. (2008) Phys. Rev. Lett., Vol. 100, p. 133002.

7.6%

O

-induced

F NMR Shift

 Results

O

-induced

F NMR Shift

 What do we obtain?

 The paramagnetic shift depends on both the shortest O-F distance and the corresponding F-O-O angle.

 Positive spin density → downfield ¹⁹F shifts; negative spin density

→ upfield ¹⁹F shifts.

 Downfield shift of 3.38 ± 0.60 ppm is comparable with the experimental data.

Thank you!