C372_L2_mm - Molecular Modeling Molecular Mechanics C372...

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Unformatted text preview: Molecular Modeling: Molecular Mechanics C372 Introduction to Cheminformatics II Kelsey Forsythe Guidelines for Use What systems were used to parameterize How is energy calculated What assumptions are used in the force field How has it performed in the past Transferability AMBER (Assisted Model Building Energy Refinement) CHARMM (Chemistry at Harvard Specific to proteins and nucleic acids Macromolecular Mechanics) Specific to proteins and nucleic acids Widely used to model solvent effects Molecular dynamics integrator Transferability MM? (Allinger et. al.) Organic molecules MMFF (Merck Molecular Force Field) Organic molecules Molecular Dynamics Tripos/SYBYL Organic and bioorganic molecules Transferability UFF (Universal Force Field) Parameters for all elements Inorganic systems YETI Parameterized to model nonbonded interactions Docking (AmberYETI) How is Energy Calculated Valence Terms Cross Terms Nonbonding Terms Energy is ? Induced DipoleInduced Dipole Electrostatic/Ionic (Permanent Dipole) System not far from equilibrium geometry (harmonic) Strain Energy (E=0 at equilibrium bond length/angle) Field Energy (Energy due to Nonbonding terms) 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 Assumptions Hydrogens often not explicitly included (intrinsic hydrogen methods) "Methyl carbon" equated with 1 C and 3 Hs System not far from equilibrium geometry (harmonic) Solvent is vacuum or simple dielectric Modeling Potential energy dU U(r) = U(req ) dr 1 d 2U (r - req ) + 2 dr 2 r= req (r - req ) 2 r= req 1 d 3U - 3 dr r= req 1 d nU (r - req ) 3 ....+ n! dr n (r - req ) n r= req Modeling Potential energy U(r) 0 at minimum 2 1dU dU U(req ) - (r - req ) + 2 dr 2 dr r= req 0 (r - req ) 2 r= req U(r) o 1 d 2U 2 dr 2 (r - req ) r= req 2 1 kAB (r - req ) 2 2 Assumptions: Harmonic Approximation 8.35E28 8.35E28 8.35E28 8.35E28 8.35E28 1.4E-18 8.35E28 8.35E28 1.2E-18 8.35E28 8.35E28 1E-18 8.35E28 8.77567E+14 20568787140 2.03098E18 1.05374E18 8.77567E+14 20568787140 1.77569E18 Empirical Potential for Hydrogen Molecule9.66155E19 8.77567E+14 20568787140 1.54682E18 8.82365E19 8.77567E+14 20568787140 1.34201E18 8.02375E19 8.77567E+14 20568787140 1.15913E18 7.26185E19 8.77567E+14 20568787140 9.96207E19 6.53795E19 8.77567E+14 20568787140 8.51451E19 5.85205E19 8.77567E+14 20568787140 7.23209E19 5.20415E19 8.77567E+14 20568787140 6.09973E19 4.59425E19 8.77567E+14 20568787140 5.10362E19 4.02235E19 8.77567E+14 20568787140 4.2311E19 3.48845E19 8.77567E+14 20568787140 3.47061E19 2.99255E19 8.77567E+14 20568787140 2.81155E19 2.53465E19 8.77567E+14 20568787140 2.24426E19 2.11475E19 8.77567E+14 20568787140 1.75987E19 1.73285E19 8.77567E+14 20568787140 1.35031E19 1.38895E19 8.77567E+14 20568787140 1.0082E19 1.08305E19 8.77567E+14 20568787140 7.26787E20 8.15147E20 8.77567E+14 20568787140 4.99924E20 5.85247E20 8.77567E+14 20568787140 3.22001E20 3.93347E20 8.77567E+14 20568787140 1.87901E20 2.39447E20 8.77567E+14 1 20568787140 9.29638E21 1.23547E20 0.5 1.5 2 2.5 3 3.5 8.77567E+14 20568787140 3.29443E21 4.56475E21 8.35E28 8.35E28 8E-19 8.35E28 8.35E28 6E-19 8.35E28 8.35E28 4E-19 8.35E28 8.35E28 2E-19 8.35E28 8.35E28 8.35E28 0 8.35E28 0 8.35E28 4 Assumptions: Harmonic Approximation Determining k? 1 d 2U E(x 0 - Dx) @E(x 0 ) + ((x 0 - Dx) - x 0 ) 2 2 dx 2 x 0 1 d 2U E(x 0 + Dx) @E(x 0 ) + ((x 0 + Dx) - x 0 ) 2 2 dx 2 x 0 d 2U dx 2 x0 E(x 0 - Dx) + E(x 0 + Dx) - 2E(x 0 ) @ (Dx) 2 Assumptions: Harmonic Approximation 8.35E28 8.35E28 8.35E28 8.35E28 8.35E28 1.4E-18 8.35E28 8.35E28 1.2E-18 8.35E28 8.35E28 1E-18 8.35E28 8.77567E+14 20568787140 2.03098E18 1.05374E18 8.77567E+14 20568787140 1.77569E18 Empirical Potential for Hydrogen Molecule9.66155E19 8.77567E+14 20568787140 1.54682E18 8.82365E19 8.77567E+14 20568787140 1.34201E18 8.02375E19 8.77567E+14 20568787140 1.15913E18 7.26185E19 8.77567E+14 20568787140 9.96207E19 6.53795E19 8.77567E+14 20568787140 8.51451E19 5.85205E19 8.77567E+14 20568787140 7.23209E19 5.20415E19 8.77567E+14 20568787140 6.09973E19 4.59425E19 8.77567E+14 20568787140 5.10362E19 4.02235E19 8.77567E+14 20568787140 4.2311E19 3.48845E19 8.77567E+14 20568787140 3.47061E19 2.99255E19 8.77567E+14 20568787140 2.81155E19 2.53465E19 8.77567E+14 20568787140 2.24426E19 2.11475E19 8.77567E+14 20568787140 1.75987E19 1.73285E19 8.77567E+14 20568787140 1.35031E19 1.38895E19 E(.65)=3.22E-20J 8.77567E+14 20568787140 1.0082E19 1.08305E19 E(.83)=2.13E-20J 8.77567E+14 20568787140 7.26787E20 8.15147E20 x=.091 8.77567E+14 20568787140 4.99924E20 5.85247E20 8.77567E+14 20568787140 3.22001E20 3.93347E20 8.77567E+14 20568787140 1.87901E20 2.39447E20 8.77567E+14 1 20568787140 9.29638E21 1.23547E20 0.5 1.5 2 2.5 3 3.5 8.77567E+14 20568787140 3.29443E21 4.56475E21 8.35E28 8.35E28 8E-19 8.35E28 8.35E28 6E-19 8.35E28 8.35E28 4E-19 8.35E28 8.35E28 2E-19 8.35E28 8.35E28 8.35E28 0 8.35E28 0 8.35E28 4 Assumptions: Harmonic Approximation d 2U dx 2 d 2U dx 2 d 2U dx 2 E(x 0 - Dx) + E (x 0 + Dx) - 2E 0 @ Dx 2 (3.22 10- 20 J) + (2.126 10- 20 J) = 1m (.091A )2 1 1010 A kg = 6.45 10 2 2 k s x0 x0 x0 Assumptions: Harmonic Approximation d 2U dx 2 = 6.45 10 2 x0 kg s2 k HO - -- > k = mw 2 kg k s2 = 6.215 1014 Hz w= = m 1.67 10- 27 kg 6.45 10 2 w = 9.891 1013 Hz 2p 3.30 10 3 cm- 1 (Exp : 4.395 10 3 cm- 1 ) \ n= o Assumptions Hydrogens often not explicitly included (intrinsic hydrogen methods) "Methyl carbon" equated with 1 C and 3 Hs System not far from equilibrium geometry (harmonic) Solvent is vacuum or simple dielectric Assumptions: solvent effects Empirical Potentials for Hydrogen Molecule 10 9 8 7 6 5 4 3 2 1 0 0 0.5 1 1.5 2 2.5 2 DFT Christensen, O. B. et. al, Phys. Rev.in Pd 1993 H B. 40, (1989) Intermolecular/atomic models General form: LennardJones - well depth 12 6 s s V (rij ) = 4e - - distance at which = 0 2 3 r 1r 123 Van derWaals repulsion London Attraction MMFF Energy Electrostatics (ionic compounds) D Dielectric Constant electrostatic buffering constant qi q j Eelectrostatic = n D ( ij + d ) R MMFF Energy Analogous to LennardJones 612 potential London Dispersion Forces Van der Waals Repulsions EVDW = e ij 1.07 R * ij * ij 7 Rij + 0.07 R 1.07 R 7 *7 ij *7 Rij + 0.07 Rij - 2 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 Easily constructed Accuracy Not robust enough to describe subtle chemical effects Does not reproduce quantal nature Hydrophobicity Excited States Radicals Caveats Compare energy differences NOT energies Always compare results with higher order theory (ab initio) and/or experiments ...
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