MD Simulation


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MD Simulation

  1. 1. MD SIMULATION Molecular Modeling and Drug Design Dr. Puneet Kacker
  2. 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. 3. Time Scales Vs. Biological Process
  4. 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. 5. Thermodynamics and Kinetics
  6. 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. 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. 8. Cont… Relation ?? Statistical Mechanics
  9. 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. 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. 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. 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. 13. Setting up and Running MD Simulations
  14. 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. 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. 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. 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. 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. 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. 20. Ebonded The Ebonded term is a sum of three terms: 1 2 3
  21. 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. 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. 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. 24. Enon-bonded Non-bonded interactions has two components Some other potential functions also include an additional term to account for hydrogen bonds
  25. 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. 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. 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. 28. MD Simulation Movies
  29. 29. MD Simulation Output MD Simulation Atomic Coordinates and Velocities
  30. 30. Analysis X-axis Y-axis Conformations PropertiesofInterest AllAtomRMSD PotentialEnergy RadiusofGyration
  31. 31. MD Simulation Packages AMBER GROMACS NAMD
  32. 32. MD Simulation Analysis Packages XMGrace (Plotting Tool) VMD (Trajectory Visualization and Plotting Tool)
  33. 33. Thanks!!