1. Lecture 3 – 4. October 2010 Molecular force field 1

2. 2 What is a force field? Based on QM and experimental data Additive and non-additive (polarizable forcefields) Components of intra- and inter molecular forces Polarizable force fields Optimization parameters An iterative approach to obtain self-consistent inter- and intramolecular parameters Analogy and experimentally optimized parameters

3. Specialized force fields 3 Most force fields are specialized e.g.: CHARMM – biomolecules OPLS – mostly proteins and organic liquids AMBER – proteins and DNA GROMOS – biomolecular systems

4. Molecular force field 4 A molecular force field is a potential function Geometric representation of a system Born-Oppenheimer approximation makes it possible to use nuclei as coordinates Formulas based on QM and experimental data Calculates the total energy of a system and minimizes it with respect to the atomic coordinates.

5. Additive force fields 5 Total energy is a sum of: Intramolecular: Bond lengths Angle bending Bond rotation (torsion) Intermolecular Non-bonded interactions

6. Additive force fields 6 Bond stretching energy:

7. Additive force fields 7 Intramolecular standard terms:

8. Additive force fields 8 Intermolecular terms

9. Additive force fields 9 Different force fields uses different additional terms CHARMm uses an improper torsion term: AMBER uses an explicit terms for hydrogen bonds

10. Polarizable force fields 10 Additive force fields use only point charges The electron distribution changes however as a function of the surrounding electrostatic field Compensation by enhancing atomic charges Works well in most cases Most critical in active sites

11. Polarizable force fields 11 Polarizable force fields are still under development Methods to include electronic polarization in force fields Self-consistent field calculation and Matrix diagonalization mostly gives a too high computational demand Fluctuating charge Induced dipoles

12. Polarizable force fields 12 Fluctuating charge model Based on the movement of charge between bonded atoms in response to the surrounding electrostatic field Electronegativities Hardness of bonded atom

13. Polarizable force fields 13 Induced Dipole Model A point dipole is induced at each contributing center in response to the total electric field: E i 0 is the field due to the permanent atomic charges E i induced is the field due to the (other) induced dipoles α i is the polarizability of atom

14. Optimization parameters 14 The parameters of a force field are the constants of the used formulas that must be optimized whenever a new molecule is introduced. The intermolecular and intramolecular parameters are coupled An iterative approach is required to obtain self-consistent parameters Optimization of intramolecular parameters ->Optimization of intermolecular parameters ->Intramolecular parameters rechecked Typically, this only requires one or two iterations, but it may be more with highly flexible molecules.

15. Optimization parameters 15

16. Optimization parameters 16 Using analogy or experimental values to optimize parameters Structure analogy Identify internal parameters to be optimized Optimize only new parameters!

17. Optimization parameters 17 Optimization of intermolecular parameters using experimental or QM values: Local/Small Molecule Interaction enthalpies (MassSpec) Interaction geometries (microwave, crystal) Dipole moments QM Global/condensed phase Pure solvents (heats of vaporization, density, heat capacity, isocompressibility) Aqueous solution (heats/free energies of solution, partial molar volumes) Crystals (heats of sublimation, lattice parameters, interaction geometries)

18. Optimization parameters 18 Optimization of intramolecular parameters: For most drug molecules the amount of experimental data is minimal, requiring the use of QM data Geometries (equilibrium values) Microwave, electron diffraction, ab initio, small molecule x-ray crystallography (CSD), crystal surveys of geometries Vibrational spectra (force constants) Infrared, raman, ab initio Conformational energies (force constants) Microwave, ab initio