- 2. Computational method for analyzing the physical movements of atoms and molecules Molecular Dynamics Simulation Relating to molecules Study of Motion Imitation of a situation or process 2
- 3. Computational method for analyzing the physical movements of atoms and molecules Molecular Dynamics Simulation Relating to molecules Study of Motion Imitation of a situation or process Molecular System = Atom at initial stage = Atom after dT time 3
- 4. Computational method for analyzing the physical movements of atoms and molecules Molecular Dynamics Simulation Relating to molecules Study of Motion Imitation of a situation or process Molecular System = Atom at initial stage = Atom after dT time What do We Want to Know? 1. Acceleration (a) 2. Position (r) and of Atom “X” after time dT Acceleration is a vector. Thus, direction of a moving particle also can be known from acceleration. 4
- 5. Computational method for analyzing the physical movements of atoms and molecules Molecular Dynamics Simulation Relating to molecules Study of Motion Imitation of a situation or process Molecular System = Atom at initial stage = Atom after dT time What do We Want to Know? 1. Acceleration (a) 2. Position (r) and of Atom “X” after time dT How Newton’s Second Law: 5
- 6. Computational method for analyzing the physical movements of atoms and molecules Molecular Dynamics Simulation Relating to molecules Study of Motion Imitation of a situation or process Molecular System = Atom at initial stage = Atom after dT time What do We Want to Know? 1. Acceleration (a) 2. Position (r) and of Atom “X” after time dT How Newton’s Second Law: How to Find the Force (F)? The potential energy is negative the integral of the force: 6
- 7. Molecular System = Atom at initial stage = Atom after dT time What do We Want to Know? 1. Acceleration (a) 2. Position (r) and of Atom “X” after time dT How Newton’s Second Law: How to Find the Force (F)? The potential energy is negative the integral of the force: For More: https://scripts.mit.edu/~srayyan/PERwiki/index.php?title=Module_7_--_Force_and_Potential_Energy How to Use this Relationship between Force (F) and Potential Energy (dU)? 7
- 9. How to Use this Relationship between Force (F) and Potential Energy (dU)? By Using Interatomic Potentials. Interatomic potentials are mathematical functions for calculating the potential energy of a system of atoms with given positions in space. Interatomic potentials can be written as a series expansion of functional terms that depend on the position of one, two, three, etc. atoms at a time. Then the total potential of the system (Vtot) can be written as For More: https://en.wikipedia.org/wiki/Interatomic_potential Where are the Interatomic Potentials in Molecule? 9
- 10. Where are the Interatomic Potentials in Molecule? A single atom will be affected by the potential energy functions of every atom in the system: • Bonded Neighbors • Non-Bonded Atoms (either other atoms in the same molecule, or atoms from different molecules) 10
- 11. Where are the Interatomic Potentials in Molecule? A single atom will be affected by the potential energy functions of every atom in the system: • Bonded Neighbors • Non-Bonded Atoms (either other atoms in the same molecule, or atoms from different molecules) How to Calculate these HORRIBLE Interatomic Potentials? 11
- 12. How to Calculate these HORRIBLE Interatomic Potentials? Many research group already developed different Force Field to calculate all these interatomic potential equations Force field refers to the functional form and parameter sets used to calculate the potential energy of a system of atoms in molecular mechanics and molecular dynamics simulations. For More: https://en.wikipedia.org/wiki/Force_field_(chemistry) Example of Force Field: AMBER, CHARMM, OPLS, GROMOS Things to Explore: When to use which Force Field? Hint: People believe CHARMM forcefield is better for proteins while AMBER forcefield is better for DNA simulations. (Don’t Depend on People!) 12
- 13. Wait! At the Starting of the Simulation (When time, t=0), we know nothing about the atoms (acceleration, potentials) other than their positions. Then how to calculate the potentials of the molecule after dT time? Remember: Solution: Boltzmann Distribution is used to assign random potentials to all atoms that give total potentials of the system at a certain temperature. For More: https://en.wikipedia.org/wiki/Boltzmann_distribution 13
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- 15. DONE! We have learnt the basic theory about the Molecular Dynamics Simulation. ☺ 15
- 16. DONE! We have learnt the basic theory about the Molecular Dynamics Simulation. ☺ 16 Iterate the Process from Step2. to know the new position and acceleration after time dT+δ Now you have new position and acceleration for the atom “X” after time dt Step 2. Acceleration Calculation a. Interatomic Potential Calculation b. Force Calculation Step 1. Initial Stage a. Initial Position b. Boltzman Distribution Molecular Dynamics Simulation a. Acceleration b. Position Just A Recap
- 17. Why? •Imagine that an alien lands on Earth, hears about something called a ‘‘bicycle,’’ and wants to understand how it works, how to ride it, and how to fix it when it breaks. 17
- 18. Why? •A molecular biologist trying to understand how a protein or other biomolecule works faces a similar challenge. An atomic level structure is tremendously helpful The atoms in a biomolecule are in constant motion. Both molecular function and intermolecular interactions depend on the dynamics of the molecules involved Unfortunately, watching the motions of individual atoms and perturbing them in a desired fashion is difficult attractive alternative is to work with an atomic-level computer simulation of the relevant biomolecules 18
- 19. Image: Istvan Kolossvary & Annabel Todd, D. E. Shaw Research Protein Folding 19
- 20. Binding of Drugs to their Molecular Targets 20 Microsecond to millisecond time frame (This one shows the binding of imatinib, a tyrosine kinase inhibitor that’s now been approved by the FDA under the name Gleevec, to the BCR/ABL fusion protein.) Image: Nagar, et al., Cancer Res. 62, 4236 (2002)
- 22. Practical Considerations in Using MD Simulations 1. Cutoff Methods • Ideally, every atom should interact with every other atom. This creates a force calculation algorithm of quadratic order. We may be able to ignore atoms at large distances from each other without suffering too much loss of accuracy • Periodic boundary conditions (PBCs) are a set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a unit cell. • PBCs are often used in computer simulations and mathematical models. 3. Periodic Boundary Conditions (PBCs) 2. Molecules in Solution • In real situations, a molecule is rarely isolated. In biological systems, proteins, RNA, and DNA are immersed in a sea of water molecules • To accurately portray the effect of the solvent molecules on a system, the solvent molecules must be free flowing. • How do we establish computational boundaries while keeping a realistic solvent simulation? (Ans: PBCs) 22
- 23. Canonical ensemble or NVT ensemble: a statistical ensemble where the energy is not known exactly but the number of particles is fixed. In place of the energy, the temperature is specified. The canonical ensemble is appropriate for describing a closed system. A statistical ensemble is a collection of various microstates of an equilibrium macroscopic system as determined by the constraints operating on the system. The choice of ensemble is dictated by the nature of the physical system under consideration and properties to be computed. Statistical Ensemble Practical Considerations in Using MD Simulations 23
- 24. Happy Molecular Dynamics Simulating! ☺ 24