MD Simulation

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  • 1. MD SIMULATION Molecular Modeling and Drug Design Dr. Puneet Kacker www.puneetsclassroom.in
  • 2. MD Simulation: Introduction One of the principal tools in the theoretical study of biological molecules Calculates the time dependent behavior of a molecular system Provides detailed information on the fluctuations and conformational changes of proteins and nucleic acids Used to investigate the structure, dynamics and thermodynamics of biological molecules and their complexes Reading Material: CHARMM Theory of MD Simulation
  • 3. Time Scales Vs. Biological Process
  • 4. Applications Protein stability Conformational changes Protein folding Molecular recognition: proteins, DNA, membranes, complexes Ion transport in biological systems Drug Design & Structure determination (X-ray and NMR)
  • 5. Thermodynamics and Kinetics
  • 6. Historical Background First introduced by Alder and Wainwright by study of hard sphere interactions (1957) Rahman carried out the first simulation using a realistic potential for liquid argon (1964) First protein simulations by McCammon appeared in 1977 with the simulation of the bovine pancreatic trypsin inhibitor (BPTI)
  • 7. Statistical Mechanics The conversion of microscopic information (e.g. atomic positions and velocities) to macroscopic observables (e.g. pressure, energy, heat capacities) requires statistical mechanics Statistical mechanics provides the rigorous mathematical expressions that relate macroscopic properties to the distribution and motion of the atoms and molecules
  • 8. Cont… Relation ?? Statistical Mechanics
  • 9. Some Definitions Thermodynamic state: of a system is usually defined by a small set of parameters, e.g. the temperature– T, the pressure– P, and the number of particles– N Mechanical or microscopic state: of a system is defined by the atomic positions– q, and momenta– p; these can also be considered as coordinates in a multidimensional space called phase space Ensemble: is a collection of points in phase space satisfying the conditions of a particular thermodynamic state
  • 10. An Ensemble An ensemble is a collection of all possible systems which have different microscopic states but have an identical macroscopic or thermodynamic state. There exist different ensembles with different characteristics
  • 11. Classical Mechanics MD simulation method is based on Newton’s second law of motion Fi is the force exerted on particle i, mi is the mass of particle i and ai is the acceleration of particle i
  • 12. Integration Algorithms There is no analytical solution to the equations of motion; they must be solved numerically Numerous numerical algorithms have been developed for integrating the equations of motion – Verlet algorithm – Leap-frog algorithm – Velocity Verlet – Beeman’s algorithm
  • 13. Setting up and Running MD Simulations
  • 14. Potential Energy Function Potential Energy is the energy of the object or a system due to the position of the body or arrangements of particles of the system Some Function Input Atomic Positions Output Energy
  • 15. Force Fields Biological systems involve many atoms Quantum Mechanics not a feasible method PEF* are less computationally demanding Numerous approximations are introduced which lead to certain limitations Provides a reasonably good compromise between accuracy and computational efficiency *Potential Energy Functions
  • 16. Cont… Often calibrated to experimental results and quantum mechanical calculations of small model compounds Their ability to reproduce physical properties measurable by experiment is tested The development of parameter sets is a very laborious task, requiring extensive optimization
  • 17. Most commonly used potential energy functions AMBER (Assisted Model Building with Energy Refinement) CHARMM (Chemistry at HARvard Macromolecular Mechanics) GROMOS (Groningen Molecular Simulation) OPLS (Optimized Potentials for Liquid Simulations)/AMBER force fields
  • 18. Force Field Limitation No drastic changes in electronic structure are allowed, i.e., no events like bond making or breaking can be modeled Solution Mixed quantum mechanical - molecular mechanical (QM/MM) method Molecular Mechanics (MM) Quantum Mechanics (QM)
  • 19. The CHARMM Potential Energy Function The energy, E, is a function of the atomic positions, R, of all the atoms in the system Atomic Positions are usually expressed in terms of Cartesian coordinates Describes the bonds, angles and bond rotations in a molecule Describes the interactions between nonbonded atoms or atoms separated by 3 or more covalent bonds
  • 20. Ebonded The Ebonded term is a sum of three terms: 1 2 3
  • 21. Ebond-stretch A harmonic potential representing the interaction between atomic pairs where atoms are separated by one covalent bond Force constants Kb are specific for each pair of bound atoms, i.e. depend on chemical type of atoms- constituents Ideal bond length Force constants Values of force constant: from infrared stretching frequencies or from QM calculations. Values of bond length: from high resolution crystal structures or microwave spectroscopy data.
  • 22. Ebond-bend Associated with alteration of bond angles θ from ideal values θo Kθ depends on chemical type of atoms constituting the angle Ideal angle
  • 23. Erotate-along-bond Models the presence of steric barriers between atoms separated by 3 covalent bonds (1,4 pairs) The motion associated with this term is a rotation, described by a dihedral angle and coefficient of symmetry n=1,2,3), around the middle bond Function is assumed to be periodic and is often expressed as a cosine function Coefficient of symmetry n=1,2,3)
  • 24. Enon-bonded Non-bonded interactions has two components Some other potential functions also include an additional term to account for hydrogen bonds
  • 25. Eelectrostatic The electrostatic interaction between a pair of atoms is represented by Coulomb Potential Effective dielectric function for the medium Distance between two atoms having charges qi and qk
  • 26. Evan-der-Waals One of the most important interactions for the stability of the biological macromolecules Modelled using the Lennard-Jones 6-12 potential Expresses the interaction energy using the atom-type dependent constants A and C
  • 27. Force Field Limitations  Fixed set of atom types for parameterization  Aliphatic carbon atom in an sp3 bonding situation has different properties than a carbon atom found in the His ring  An approximation introduced to decrease the computational demand is the pair-wise additive approximation  The simultaneous interaction between three or more atoms is not calculated, so certain polarization effects are not explicitly included in the force field  Potential energy function does not include entropic effects  E calculated as a sum of potential functions does not necessarily correspond to the equilibrium, or the most probable state
  • 28. MD Simulation Movies
  • 29. MD Simulation Output MD Simulation Atomic Coordinates and Velocities
  • 30. Analysis X-axis Y-axis Conformations PropertiesofInterest AllAtomRMSD PotentialEnergy RadiusofGyration
  • 31. MD Simulation Packages AMBER http://ambermd.org/ GROMACS http://www.gromacs.org/ NAMD http://www.ks.uiuc.edu/Research/namd/
  • 32. MD Simulation Analysis Packages XMGrace (Plotting Tool) http://plasma-gate.weizmann.ac.il/Grace/ VMD (Trajectory Visualization and Plotting Tool) http://www.ks.uiuc.edu/Research/vmd/
  • 33. Thanks!! www.puneetsclassroom.in