Elstner_QMMM_Calculations - QM/MM Calculations and...

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Unformatted text preview: QM/MM Calculations and Applications to QM/MM Calculations and Applications to Biophysics Biophysics Marcus Elstner Physical and Theoretical Chemistry, Technical University of Braunschweig Proteins, DNA, lipids Proteins, DNA, lipids N Computational challenge Computational challenge ~ 1.000-10.000 atoms in protein ~ ns molecular dynamics simulation (MD, umbrella sampling) QM - chemical reactions: proton transfer - treatment of excited states Computational problem I: number of atoms Computational problem I: number of atoms chemical reaction which needs QM treatment immediate environment: electrostatic and steric interactions solution, membrane: polarization and structural effects on protein and reaction! 10.000... - several 100.000 atoms Computational problem II: sampling with MD Computational problem II: sampling with MD flexibility: not one global minimum conformational entropy solvent relaxation ps – ns timescale (timestep ~ 1fs) (folding anyway out of reach!) Optimal setup Optimal setup Water: = 80 = 20 Membrane: = 10 Protein active = 20 Water: = 80 Membrane: = 10 Combined QM/MM Combined QM/MM ε=80 Quantum mechanical (QM) • • Bond breaking/formation Computationally demanding – DFT, AI: ~ 50 atoms – Semi-Empirical: ~102-3 atoms Molecular mechanical (MM) • • Computationally efficient – ~103-5 atoms Generally for structural properties Combined QM/MM • Chemical Rx in macromolecules ˆ QM + H QM / MM Ψ + E QM / MM + E MM • DFT (AI) /MM: Reaction path ˆ E= Ψ H van el • •No polarization of MM region! •No charge transfer between QM and MM Semi-Empirical/MM: Potential of mean force, rate constants Combined QM/MM Combined QM/MM 1976 Warshel and Levitt 1986 Singh and Kollman 1990 Field, Bash and Karplus QM • Semi-empirical • quantum chemistry packages: DFT, HF, MP2, LMP2 • DFT plane wave codes: CPMD MM • CHARMM, AMBER, GROMOS, SIGMA,TINKER, ... Hierarchy of methods Hierarchy of methods Continuum electrostatics Continuum electrostatics ns Molecular Mechanics Molecular Mechanics ps SE-QM SE-QM approx-DFT approx-DFT time fs HF, DFT HF, DFT CI, MP CI, MP CASPT2 CASPT2 nm Length scale Empirical Force Fields: Molecular Mechanics Empirical Force Fields: Molecular Mechanics MM MM V = ∑ k ( b − b ) + ∑ k (θ − θ 2 bonds b 0 angles θ )+ 2 0 σ + ∑ 4ε r i,j ∑ ∑ kφ [1 + cos( ( nφ − δ ) ] + ∑ kω ( ω − ω N (n) dihedrals n =1 impropers σ qq − + ∑ r Dr 12 i,j i,j i,j 6 i,j i j i,j i, j ij models protein + DNA structures quite well Problem: - polarization - charge transfer - not reactiv in general kb k k 0 ) 2 QM/MM Methods QM/MM Methods Mechanical embedding: only steric effects Electrostatic embedding: polarization of QM due to MM Electrostatic embedding + polarizable MM Larger environment: - box + Ewald summ. - continuum electrostatics ? ? QM - coarse graining MM Ho to study reactions and (rare) dynamical events Ho to study reactions and (rare) dynamical events direct MD accelerated MD - hyperdynamics (Voter) - chemical flooding (Grubmüller) - metadynamics (Parinello) reaction path methods - NEB (nudged elastic band, Jonsson) - CPR (conjugate peak refinement, Fischer, Karplus) - dimer method (Jonsson) free energy sampling techniques - umbrella sampling - free energy perturbation - transition path sampling Ho to study reactions and (rare) dynamical events Ho to study reactions and (rare) dynamical events accelerated MD - metadynamics reaction path methods - CPR free energy sampling techniques - umbrella sampling QM/MM Methods QM/MM Methods Subtractive vs. additive models Subtractive vs. additive models - subtractive: several layers: QM-MM doublecounting on the regions is subtracted - additive: different methods in different regions + interaction between the regions QM MM Additive QM/MM Additive QM/MM total energy = + QM MM + interaction QM MM Subtractive QM/MM:: ONIOM Subtractive QM/MM ONIOM Morokuma and co.: GAUSSIAN Morokuma and co.: GAUSSIAN total energy = MM + QM - MM The ONIOM Method (an ONION-like method) Bond-format ion/breaking t akes place. Use the "High level" (H) method. Sm a ll Mod e l Sys t e m ( SM) I nt e r m e d i a t e Mod e l Sys t e m( IM) R e a l Sys t e m( R ) First Layer Second Layer Elect ronic effect on t he first layer. Use the "Medium level" (M) method. T hird Layer Environment al effect s on t he first layer. Use the "Low level" (L) method. Example: The binding energy of φ3C-C φ3 ( HPE) ONIOM: 16.4 kcal/mol C C Hexaphenylethane (HPE) 2 C Triphenylmethyl radical (T PMR) from S. Irle Link Atoms Real system H H H LAYER 1 Model system H C C RL RLAH Link atom Link atom host C LAYER 2 H H H F F RL = g x RLAH F g: constant from S. Irle ONIOM Energy: The additivity assumption Level Effect and Size Effect assumed uncoupled E(HIGH ,REAL) ≅ E(ONIOM) = = E(LOW,MODEL + ) SIZE (S-value) + LEVEL = E(LOW,MODEL) + [E(LOW ,REAL)-E(LOW,MODEL) ] + [E(HIGH,MODEL)-E(LOW,MODEL)] H H H H C C + F HIGH F F LEVEL HIGH H H H C H H LOW H C H Approximation - MODEL E(ONIOM ) = E(LOW,REAL ) + E(HIGH ,MODEL) - E(LOW,MODEL ) + SIZE H H H C C F LOW F F REAL from S. Irle S(ubstituent)-Value test: Does the low level work? Choice of combination of levels is critical Combinations can be investigated using the S-Value test S(LEVEL) = E(LEVEL,REAL) - E( LEVEL, MODEL) Several E(HIGH,REAL) calculations necessary HIGH If S(HIGH) = S(LOW) E(ONIOM) = E(HIGH, REAL) LEV EL S(HIGH) Low level describes subst it uent effect as good as high level does! S(HIGH) - S(LOW) L OW S(LOW) MODEL REAL SIZE Must be as close t o zero as possible from S. Irle ONIOM Potential Energy Surface and Properties ONIOM energy E(ONIOM, Real) = E(Low,Real) + E(High,Model) - E(Low,Model) Potential energy surface well defined, and also derivatives are available. ONIOM gradient G(ONIOM, Real) = G(Low,Real) + G(High,Model) x J - E(Low,Model) x J J = ∂ (Real coord.)/ ∂ (Model coord.) is the Jacobian that converts the model system coordinate to the real system coordinate ONIOM Hessian H(ONIOM,Real) = H(Low,Real) + JT x H(High,Model) x J - JT x H(Low,Model) x J Scale each Hessian by s(Low)**2 or s(High)**2 to get scaled H(ONIOM) ONIOM density ρ(ONIOM, Real) = ρ(Low,Real) + ρ(High,Model) - ρ(Low,Model) ONIOM properties < o (ONIOM, Real)> = < o (Low,Real) > + < o (High,Model) > - < o (Low,Model) > from S. Irle Three-layer ONIOM (ONIOM3) E(ONIOM)= E(LOW,REAL) HIGH + - E (LOW,INT ERMEDIAT E ) Target + E (MEDIUM,INT ERMEDIATE ) LE V E L - E (MEDIUM,MODEL) + E (HIGH,MODEL) MEDIUM - LOW MODEL + INT ERMEDIAT E + REAL MO:MO:MO MO:MO:MM SIZE from S. Irle Additive QM/MM: linking Additive QM/MM: linking Additive QM/MM Additive QM/MM total energy = + QM MM + interaction QM MM Additive QM/MM: Additive QM/MM: ˆ ˆ ˆ ˆ H = H QM + H MM + H QM / MM A Zq B q ˆ H QM / MM = −∑ M + ∑ α M + ∑ αM − αM 12 6 RαM i , M riM α , M RαM α , M RαM Elecrostatic ˆ int .coor + H QM / MM mechanical embedding Combined QM/MM Combined QM/MM Bonds: Amaro , Field , Chem Acc. 2003 a) take force field terms b) - link atom - pseudo atoms - frontier bonds Nonbonding: - VdW - electrostatics A Zq B q ˆ H QM / MM = −∑ M + ∑ α M + ∑ αM − αM 12 6 riM α , M RαM α , M RαM RαM i,M ˆ int .coor + H QM / MM Combined QM/MM Combined QM/MM Bonds: a) from force field Reuter et al, JPCA 2000 Combined QM/MM: link atom Combined QM/MM: link atom a) constrain or not? (artificial forces) relevant for MD b) Electrostatics - LA included – excluded (include!) - QM-MM: exclude MM-host exclude MM-hostgroup - Amaro & Field , T. Chem Acc. 2003 DFT, HF: gaussian broadening of MM point charges, pseudopotentails (e spill out) Combined QM/MM: ffrozen orbitals Combined QM/MM: rozen orbitals Reuter et al, JPCA 2000 Warshel, Levitt 1976 Rivail + co. 1996-2002 Gao et al 1998 A Zq B q ˆ H QM / MM = −∑ M + ∑ α M + ∑ αM − αM 12 6 riM α , M RαM α , M RαM RαM i,M ˆ int .coor + H QM / MM Combined QM/MM: Pseudoatoms Combined QM/MM: Pseudoatoms Amaro & Field ,T Chem Acc. 2003 Pseudobond- connection atom Zhang, Lee, Yang, JCP 110, 46 Antes&Thiel, JPCA 103 9290 X No link atom: parametrize Cβ H2 as pseudoatom A Zq B q ˆ H QM / MM = −∑ M + ∑ α M + ∑ αM − αM 12 6 riM α , M RαM α , M RαM RαM i,M ˆ int .coor + H QM / MM Combined QM/MM Combined QM/MM Nonbonding terms: Amaro & Field ,T Chem Acc. 2003 VdW - take from force field - reoptimize for QM level Coulomb: which charges? A Zq B q ˆ H QM / MM = −∑ M + ∑ α M + ∑ αM − αM 12 6 RαM i , M riM α , M RαM α , M RαM ˆ int .coor + H QM / MM Combined QM/MM Combined QM/MM Tests: - C-C bond lengths, vib. frequencies - C-C torsional barrier - H-bonding complexes - proton affinities, deprotonation energies Subtractive vs. additive QM/MM Subtractive vs. additive QM/MM - parametrization of methods for all regions required e.g. MM for Ligands SE for metals + QM/QM/MM conceptionally simple and applicable Local Orbital vs. plane wave approaches: Local Orbital vs. plane wave approaches: PW implementations (most implementations in LCAO) - periodic boundary conditions and large box! lots of empty space in unit cell - hybride functionals have better accuracy: B3LYP, PBE0 etc. + no BSSE + parallelization (e.g. DNA with ~1000 Atoms) Problems Problems • QM and MM accuracy • QM/MM coupling • model setup: solvent, restraints • PES vs. FES: importance of sampling All these factors CAN introduce errors in similar magnitude Modelling Stratgies Modelling Stratgies How much can we treat ? = How much can we treat ? = How much can we afford How much can we afford Water: = 80 = 20 Membrane: = 4 Protein active = 20 Water: = 80 Membrane: = 4 How to model the environment How to model the environment 1) Only QM (implicit solvent) 2) QM/MM w/wo MM polarization 3) Truncated systems and charge scaling System in water with periodic boundary conditions: pbc and Ewald summation Truncated system and implicit solvent models How much can we treat ? = How much can we treat ? = How much can we afford How much can we afford Don‘t have or don‘t trust QM/MM or too complicated Only active site models active = ?? How much can we treat ? = How much can we treat ? = How much can we afford How much can we afford Small protein Simple QM/MM: - fix most of the protein - neglect polarization of environment Protein active First approximations: First approximations: • solvation charge scaling • freezing vs. stochastic boundary • size of movable MM? • size of QM? How much can we treat ? = How much can we treat ? = How much can we afford How much can we afford Small protein Simple QM/MM: - fix most of the protein - include polarization from environment Protein: polarizable active Absolute excitation energies S1 excitation energy (eV) exp vacuum 2.1 8 Hayashi[2000] bR (QM:RET) Vreven[2003] 2 1 TDB3LYP1 TDDFTB OM2/ CIS CASSCF2 OM2/ MRCI SORCI 2.42 2.14 2.34 2.86 2.13 1.86 2.53 2.21 2.54 3.94 2.53 2.34 0.2 1.0 0.1 • TDDFT nearly zero • CIS shifts still too small ~50% • SORCI, CASPT2 • OM2/MRCI compares very well 0.5 Polarizable force field for environment • MM charges • MM polarization RESP charges for residues in gas phase atomic polarizabilities: µ = α E Polarization red shift of about 0.1 eV: How much can we treat ? = How much can we treat ? = How much can we afford How much can we afford pbc Protein active Explicit Watermolecules How much can we treat ? = How much can we treat ? = How much can we afford How much can we afford Water: = 80 = 20 Membrane: = 4 Protein active = 20 Water: = 80 Membrane: = 4 Ion channels Ion channels Water: = 80 Explicit water Membrane: = 4 Membrane: = 4 Explicit water Water: = 80 Implicit solvent: Generalized Solvent Boundary Implicit solvent: Generalized Solvent Boundary Potential (GSBP, B. Roux) Potential (GSBP, B. Roux) •Drawback of conventional implicit solvation: e.g. specific water molecules important •Compromise: 2 layers, one explicit solvent layer before implicit solvation model. • inner region: MD, geomopt • outer region: fixed QM/MM explicit MM implicit GSBP GSBP φrf = φs − φv Solvation free energy of point charges GSBP GSBP Depends on inner coordinates! Basis set expansion of inner density calculate reaction field for basis set QM/MM DFTB implementation by Cui group (Madison) Water structure in Aquaporin Water structure in Aquaporin Water structure only in agreement with full solvent simulations when GSBP is used! Problems with the PES: CPR, NEB etc. Problems with the PES: CPR, NEB etc. -differences in protein conformations Zhang et al JPCB 107 (2003) 44459 Problems with the PES: complex energy Problems with the PES: complex energy llandscape andscape - differences in protein conformations (starting the reaction path calculation) - problems along the reaction pathway * flipping of water molecules * size of movable MM region different H-bonding pattern average over these effects: potential of mean force/free energy Ion channels Ion channels ...
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