Molecular Dynamics Simulations Yaoquan Tu Division of Theoretical Chemistry and Biology, Royal Institute of Technology (KTH) 2011-06 1
Outline I. Introduction II. Molecular Mechanics Force Field III. Molecular Dynamics Simulations IV. Applications 2
I. Introduction 3
Evolution of molecular simulations Pre-computer era Computer simulation 4
Molecular dynamics simulation Molecular systems Molecular dynamics simulations Properties of the molecular systems Carried out on computers 5
Molecular Dynamics simulation Virtual experiment at atomistic scale Direct observation and manipulation of atoms and molecules Statistical Mechanics MD & others Molecular Modeling Computer Simulation 6
Molecular dynamics simulation Carried out on computer(s) Inter-atomic interactions MD simulation program output How to describe them? How does an MD program work? What can be obtained? 7
II. Molecular Mechanical Force Fields 8
Molecular dynamics simulation Inter-atomic interactions MD simulation program output How to describe them? 9
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). 10
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 (Xray 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. 11
Force Field Function Form V V V V V V V FF bond angle torsion improper vdw elec V bonded V non-bonded Bonded terms bond stretching i j r angle bending i k j 12
Bonded terms proper torsional angle i j k l ϕ improper torsional angle i k j d l Non-Bonded terms van der Waals electrostatic q + q + q - 13
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 14
Water Models TIP3P 0.834e 0.9572 Å +0.417e +0.417e 104.52 TIP4P 0.9572 Å +0.52e +0.52e 1.04e 104.52 SPC/E 0.8476e 1.0 Å +0.4238e 109.47 +0.4238e 15
III. Molecular Dynamics Simulations 16
Molecular dynamics simulation Carried out on computer(s) Inter-atomic interactions MD simulation program output How does an MD program work? 17
Molecular dynamics simulation How does an MD program work? Inter-atomic interactions Force acting on each atom Acceleration on each atom Next time step New velocity and position Changes of velocity and position Molecular dynamics simulations simulate the collisions between atoms! 18
Equation of Motion and Integrator Newton s Equation of Motion F i m i a i Calculated from inter-atomic interactions Making the changes of velocity, position of atom i 19
Leap-frog Algorithm Velocity-Verlet algorithm 20
Periodic Boundary Condition Periodic boundary condition is used to simulate an infinite system Treatment of nonbonded Interaction Cut-off radius Minimum image convention Recovery of the electrostatic interactions beyond cut-off: Ewald summation & Particle mesh Ewald 21
Molecular dynamics simulation Inter-atomic interactions MD simulation program output What can be obtained? 22
What can be obtained from Molecular Dynamics simulation? Cooperative phenomena; Collective properties; MD simulations The effects from: temperature, pressure, solvents, intermolecular interactions, Structures: bulk materials, solutions, aggregates, DNAs, proteins,clusters, molecules, Dynamics properties: diffusion coefficients; relaxation times, 23
IV. Applications 24
1. Protein adsorption onto TiO 2 Background Titanium is a promising biocompatible material TiO 2 film exists on the titanium surface Water molecules are known to dissociate on TiO 2 surface Dental implant Question What is the effect of water dissociation on the biocompatibility of TiO 2? 25
Protein adsorption onto TiO 2 Snapshots on hydroxylated and non-hydroxylated surface (kj/mol) 26
Protein adsorption onto TiO 2 Vertical number densities of interfacial water and protein 27
Protein adsorption onto TiO 2 What do we obtain? Protein adsorption onto TiO 2 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. 28
2. O 2 -induced 19 F NMR Shift Background O 2 -induced 19 F NMR shift can be used to determine the immersion depth of transmembrane protein O 2 is inhomogeneously distributed in membrane 19 F NMR shift is sensitive to O 2 concentration 19 F labels can be conveniently introduced into cysteine residue of protein Question How does O 2 molecule reside around 19 F label and affect the 19 F NMR shift? Hydrophilic Hydrophobic Hydrophilic [O 2 ] 29
O 2 -induced 19 F NMR Shift Force fields Fluorinated cysteine General AMBER force field RESP partial atomic charges Water model TIP4P O 2 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 30
O 2 -induced 19 F NMR Shift Shortest O-F distance: cutoff at 4.0 Å 7.6% Computational method Pennanen, T. O., et al. (2008) Phys. Rev. Lett., Vol. 100, p. 133002. 31
O 2 -induced 19 F NMR Shift Results 32
O 2 -induced 19 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 19 F shifts; negative spin density upfield 19 F shifts. Downfield shift of 3.38 ± 0.60 ppm is comparable with the experimental data. 33
Thank you! 34