1. Molecular Mechanics Studies involving covalent interactions (enzyme reaction): quantum mechanics; extremely slow Studies involving noncovalent interactions (conformational references, molecular recognition): classical mechanics; acceptable for a few structures Studies involving sequences only: statistical formalisms; extremely fast

2. Molecular Mechanics Study how protein/protein, protein/ligand, protein/NA interactions. Why they are specific? how to mimic them? Use them in structure-based drug design, docking. Study how proteins/NAs change conformations. How a specific function/mechanism is realized?

3. Theoretical Ground: Classical Mechanics Building on the work of Galileo and others, Newton unveiled his laws of motion in 1686. According to Newton: I. A body remains at rest or in uniform motion (constant velocity - both speed and direction) unless acted on by a net external force. II. In response to a net external force, F, a body of mass m accelerates with acceleration a = F/m. III. If body i pushes on body j with a force F ij, then body j pushes on body i with a force F ji.

4. Theoretical Ground: Classical Mechanics How to obtain forces? Easy if an energy model is given.

5. Where to use Molecular Mechanics Energy Model? Molecules containing thousands of atoms Organics, oligonucleotides, and peptides Vacuum, implicit, or explicit solvent environments Ground state only Thermodynamic and kinetic via simulations.

6. Building Principles of Molecular Mechanics (Energy Model) Nuclei and electrons are lumped into atom-like particles Atom-like particles are spherical (radii obtained from measurements or theory) and have a net charge (obtained from theory) Interactions are based on springs and classical potentials Interactions must be preassigned to specific sets of atoms Interactions determine the spatial distribution of atom-like particles and their energies

7. Simplistic Molecular Mechanics Force Field Van der WaalsCharge - Charge Bond Angle Improper Dihedral  

8. Bond Stretching Energy

10. Angle Bending Energy

12. Significance of Energy Parameters

13. Torsion Energy

14. The torsion energy is modeled by a simple periodic function:

15. Significance of Energy Parameters

16. The Roles of Torsion Energy The torsion energy in molecular mechanics is primarily used to correct the remaining energy terms rather than to represent a physical process. The torsional energy represents the amount of energy that must be added to or subtracted from the Stretching + Bending + Non-Bonded interaction terms to make the total energy agree with experiment or rigorous quantum mechanical calculation for a model dihedral angle (ethane, for example might be used a model for any H-C- C-H bond).

17. Cross Terms Possible cross terms: stretch-stretch, stretch-bend, strech- torsion; bend-bend, bend-torsion; torsion-torsion. (Fig. 4.13, Leach) Needed in studies of high-frequency motions, i.e. vibrational spectra.

18. Non-Bonded Energy

19. Van der Waals Energy

20. Significance of Energy Parameters

21. Electrostatic Energy The electrostatic contribution is modeled using a Coulombic potential. The electrostatic energy is a function of: o (a) charges on the non-bonded atoms; o (b) inter-atomic distance; o (c) molecular dielectric expression that accounts for the attenuation of electrostatic interaction by the molecule itself.

22. Electrostatic Energy: Dielectrics The molecular dielectric is set to a constant value between 1.0 and 4.0. However, it has to be consistent with how a force field is designed. (not a free parameter) A linearly varying distance-dependent dielectric (i.e. 1/r) is sometimes used to account for the increase in the solvent (aka, water) dielectrics as the separation distance between interacting atoms increases. (This is being abandoned) When it is needed, the Poisson’s equation, or its approximation, has to be used. (This is gaining popularity)

23. Other Nonbonded Interactions: Hydrogen Bonding Hydrogen bonding term is usually wrapped into the electrostatic term in force fields widely used today. However it does not imply that hydrogen bonding is purely electrostatic in nature. Hydrogen bonding, if explicitly represented, uses a 10-12 Lennard-Jones potentials. This replaces the 6-12 Lennard-Jones term for atoms involved in hydrogen-bonding.

24. Other Nonbonded Interactions: Polarization Polarization is important when large environmental changes occur, i.e. from protein interior to water, or from membrane to water. Usually modeled as inducible dipole: μ =  E Note it is not free to induce a dipole: the work done is 1/2  E 2. Finally, electrostatic energy includes charge-charge, charge-dipole, and dipole-dipole; or electrostatic field is from charge and dipole. No stable force fields with polarization available right now!

25. Scaling of Nonbonded Terms Scaling of electrostatic energy: charge- charge 1/r; charge-dipole 1/r 2, dipole- dipole 1/r 3. Scaling of van der Waals energy: 1/r 6. The example of two point charges on z- axis.