Molecular Modeling: Molecular Mechanics C372 Introduction to Cheminformatics II Kelsey Forsythe

Guidelines for Use What systems were used to parameterize What systems were used to parameterize How is energy calculated How is energy calculated What assumptions are used in the force field What assumptions are used in the force field How has it performed in the past How has it performed in the past

Transferability AMBER (Assisted Model Building Energy Refinement) AMBER (Assisted Model Building Energy Refinement) Specific to proteins and nucleic acids Specific to proteins and nucleic acids CHARMM (Chemistry at Harvard Macromolecular Mechanics) CHARMM (Chemistry at Harvard Macromolecular Mechanics) Specific to proteins and nucleic acids Specific to proteins and nucleic acids Widely used to model solvent effects Widely used to model solvent effects Molecular dynamics integrator Molecular dynamics integrator

Transferability MM? – (Allinger et. al.) MM? – (Allinger et. al.) Organic molecules Organic molecules MMFF (Merck Molecular Force Field) MMFF (Merck Molecular Force Field) Organic molecules Organic molecules Molecular Dynamics Molecular Dynamics Tripos/SYBYL Tripos/SYBYL Organic and bio-organic molecules Organic and bio-organic molecules

Transferability UFF (Universal Force Field) UFF (Universal Force Field) Parameters for all elements Parameters for all elements Inorganic systems Inorganic systems YETI YETI Parameterized to model non-bonded interactions Parameterized to model non-bonded interactions Docking (Amber  YETI) Docking (Amber  YETI)

How is Energy Calculated Valence Terms Valence Terms Cross Terms Cross Terms Non-bonding Terms Non-bonding Terms Induced Dipole-Induced Dipole Induced Dipole-Induced Dipole Electrostatic/Ionic (Permanent Dipole) System not far from equilibrium geometry (harmonic) Electrostatic/Ionic (Permanent Dipole) System not far from equilibrium geometry (harmonic) Energy is ? Energy is ? Strain Energy (E=0 at equilibrium bond length/angle) Strain Energy (E=0 at equilibrium bond length/angle) Field Energy (Energy due to Non-bonding terms) Field Energy (Energy due to Non-bonding terms) Atomistic Heats of Formation (Parameterized so as to yield chemically meaningful values for thermodynamics) Atomistic Heats of Formation (Parameterized so as to yield chemically meaningful values for thermodynamics) K. Gilbert: This is only in the MM?-type force fields K. Gilbert: This is only in the MM?-type force fields

Assumptions Hydrogens often not explicitly included (intrinsic hydrogen methods) Hydrogens often not explicitly included (intrinsic hydrogen methods) “Methyl carbon” equated with 1 C and 3 Hs “Methyl carbon” equated with 1 C and 3 Hs System not far from equilibrium geometry (harmonic) System not far from equilibrium geometry (harmonic) Solvent is vacuum or simple dielectric Solvent is vacuum or simple dielectric

Modeling Potential energy

0 at minimum 0

Assumptions: Harmonic Approximation

Determining k?

Assumptions: Harmonic Approximation E(.65)=3.22E-20J E(.83)=2.13E-20J  x=.091

Assumptions: Harmonic Approximation

Assumptions Hydrogens often not explicitly included (intrinsic hydrogen methods) Hydrogens often not explicitly included (intrinsic hydrogen methods) “Methyl carbon” equated with 1 C and 3 Hs “Methyl carbon” equated with 1 C and 3 Hs System not far from equilibrium geometry (harmonic) System not far from equilibrium geometry (harmonic) Solvent is vacuum or simple dielectric Solvent is vacuum or simple dielectric

Assumptions: solvent effects Christensen, O. B. et. al, Phys. Rev. B. 40, 1993 (1989 ) H 2 in Pd DFT

Intermolecular/atomic models General form: General form: Lennard-Jones Lennard-Jones Van derWaals repulsion London Attraction

MMFF Energy Electrostatics (ionic compounds) Electrostatics (ionic compounds) Electrostatics (ionic compounds) Electrostatics (ionic compounds) D – Dielectric Constant D – Dielectric Constant  - electrostatic buffering constant  - electrostatic buffering constant

MMFF Energy Analogous to Lennard-Jones 6-12 potential Analogous to Lennard-Jones 6-12 potential Analogous to Lennard-Jones 6-12 potential Analogous to Lennard-Jones 6-12 potential London Dispersion Forces London Dispersion Forces Van der Waals Repulsions Van der Waals Repulsions The form for the repulsive part has no physical basis and is for computational convenience when working with large macromolecules. K. Gilbert: Force fields like MM2 which is used for smaller organic systems will use a Buckingham potential (or expontential) which accurately reflects the chemistry/physics.

Pros and Cons N >> 1000 atoms N >> 1000 atoms Easily constructed Easily constructed Accuracy Not robust enough to describe subtle chemical effects Hydrophobicity Excited States Radicals Does not reproduce quantal nature

Caveats Compare energy differences NOT energies Compare energy differences NOT energies Always compare results with higher order theory (ab initio) and/or experiments Always compare results with higher order theory (ab initio) and/or experiments