Molecular Dynamics Simulation A Short Introduction Michel Cuendet 1 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Plan • Introduction • The classical force field • Setting up a simulation • Connection to statistical mechanics • Usage of MD simulation 2 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Why we do simulation In some cases, experiment is : 1. impossible Inside of stars Weather forecast 2. too dangerous Flight simulation Explosion simulation 3. expensive High pressure simulation Windchannel simulation 4. blind Some properties cannot be observed on very short time-scales and very small space-scales Simulation is a useful complement, because it can : replace experiment provoke experiment explain experiment aid in establishing intellectual property 3 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Molecular modeling What is Molecular Modeling? Molecular Modeling is concerned with the description of the atomic and molecular interactions that govern microscopic and macroscopic behaviors of physical systems What is it good for? The essence of molecular modeling resides in the connection between the macroscopic world and the microscopic world provided by the theory of statistical mechanics Macroscopic Average of observable observable over selected microscopic (Solvation energy, states affinity between two proteins, H-H distance, conformation, ... ) 4 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Computational tools • Quantum Mechanics (QM) Electronic structure (Schrödinger) 10-100 atoms 10-100 ps – ACCURATE – EXPENSIVE small system • Classical Molecular Mechanics (MM) Empirical forces (Newton) 10 4 -10 5 atoms – LESS ACCURATE 10-100 ns – FAST • Mixed Quantum/Classical (QM/MM) MM 10 4 -10 5 atoms 10-100 ps QM 5 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Types of phenomena Goal : simulate/predict processes such as 1. polypeptide folding thermodynamic equilibria 2. biomolecular association governed by weak 3. partitioning between solvents (non-bonded) forces 4. membrane/micelle formation 5. chemical reactions, enzyme catalysis chemical transformations 6. enzyme catalysis governed by strong forces 7. photochemical ractions, electron transfer characteristics (1-4) : - degrees of freedom: atomic (solute + solvent) classical MD - equations of motion: classical dynamics - governing theory: statistical mechanics characteristics (5-7) : quantum MD - degrees of freedom: electronic, nuclear - equations of motion: quantum dynamics - governing theory: quantum statistical mechanics 6 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Processes: Thermodynamic Equilibria Folding Micelle Formation folded/native denatured micelle mixture Complexation Partitioning in membrane bound unbound in water in mixtures 7 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Plan • Introduction • The classical force field • Setting up a simulation • Connection to statistical mechanics • Usage of MD simulation 8 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Definition of a model for molecular simulation Every molecule consists of atoms that are very strongly bound to each other Degrees of freedom: atoms as elementary particles + topology Forces or interactions Boundary conditions between atoms MOLECULAR MODEL system Force field = temperature physico-chemical pressure Methods to generate knowledge walls configurations of external forces atoms: Newton 9 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Classical force fields Goals of classical (semi-empirical) force fields - Definition of empirical potential energy functions V( r ) to model the molecular interactions - These functions need to be differentiable in order to compute the forces acting on each atom: F =- ∇ V( r ) Implementation of calssical potential energy functions 1. Theoretical functional forms are derived for the potential energy V( r ) . 2. Definition of atom types that differ by their atomic number and chemical environment, e.g. the carbons in C=O or C-C are of different types. 3. Parameters are determined so as to reproduce the interactions between the various atom types by fitting procedures - experimental enthalpies (CHARMM) - experimental free energies (GROMOS, AMBER) Parametrization available for proteins, lipids, sugars, ADN, ... 10 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Covalent bonds and angles Bonds Type: CT1-CT1 r r 0 E bond = K b (r � r 0 ) 2 Type: CT1-CT1-CT3 Angles θ 0 E angle = K � ( � � � 0 ) 2 11 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Dihedrals and Improper torsions Type: X-CT1-CT1-X Dihedral angles [ ] ( ) E dihedral = K � 1 + cos n � � � Type: OC-OC-CT1-CC Improper angles O O C C ψ 0 H 2 N R 2 ( ) E improper = K � � � � 0 12 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Van der Waals interactions Lennard -Jones potential : σ : collision parameter � � � � 12 6 12 6 � � � � � � � � � � r � 2 r � � � m m E VdW = 4 � ε : well depth � = � � � � � � � � � � � r � � r � � r � � r � m = 2 1 6 � � � � � r m : distance at min r r m = r m , i + r Combination rule for two different atoms i, j : � = � i � j m , j Type: CT3-CT3 Repulsive : Pauli exclusion principle � 1 r 12 σ Attractive: ε induced dipole / induced dipole E VdW �� 1 r 6 r m 13 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Electrostatic interactions where ε is the dielectric constant : q i q j E elec = 1 for vacuum, Coulomb law 4 �� 0 � r 4-20 for protein core, ij 80 for water The Coulomb energy decreases only as 1/r Despite dielectric shielding effects, it is a long range interaction Special techniques to deal with this : - PME : for stystems with periodic boundary conditions - Reaction Field : suppose homogeneous dielectric outside cutoff 14 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Derived Interactions Some interactions are often referred to as particular interactions, but they result from the two interactions previously described, i.e. the electrostatic and the van der Waals interactions. −δ A φ 1) Hydrogen bonds (Hb) - Interaction of the type D-H ··· A −δ + δ D H - The origin of this interaction is a dipole-dipole attraction - Typical ranges for distance and angle: d 2.4 < d < 4.5Å and 180º < φ < 90º 2) Hydrophobic effect Water - Collective effect resulting from the energetically unfavorable surface of contact between the water and an apolar medium (loss of water-water Hb) - The apolar medium reorganizes to minimize the water exposed surface (compaction, association... ) Oil Oil Oil Oil Oil Oil Oil Oil Oil 15 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
The total potential energy function 2 2 2 � � � [ ] � ( ) ( ) ( ) ( ) E = K b r � r K � � � � 0 K � 1 + cos n � � � K � � � � 0 + + + 0 bonds angles dihedrals impropers � 12 6 � q i q j � � � � � r � 2 r � � � � m m + � � + � � � � r r 4 �� 0 � r 4 � � � � � � i > j i > j i > j i > j For a system with 1500 atoms ~ 10 6 pairs of interacting atoms Introduction of cutoff 16 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Cutoff for non-bonded interactions For an atom A, only non-bonded interactions with atoms within δ Å are calculated A Non-bonded neighbour lists Generally, δ = 8 to 14 Å δ Three cutoff schemes: strict, shift, switch Three cutoff schemes: strict, shift, switch Shift and switch: cutofnb E '( r ) = E ( r ) � S ( r ) S(r) differentiable cutnb cutonnb 17 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
Effect of cutoff No cutoff 8 Å cutoff Elec Elec VdW VdW Total Total 18 Molecular Dynamics Simulation - Michel Cuendet - EMBL 2008
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