Introduction to: Mixed Quantum Mechanics/Classical Mechanics. Simulations
Applied to Biological Systems. EMBnet Workshop Basel. October 2005. M.
Meuwly.
Introduction to: Mixed Quantum Mechanics/Classical Mechanics Simulations Applied to Biological Systems
EMBnet Workshop Basel October 2005
M. Meuwly Department of Chemistry University of Basel
Overview I.
The Problem A. Force Fields B. Limitations
II.
Possible Roads towards Solutions and Perspectives A. The Electronic Schrodinger Equation B. Approximations C. Modern Developments
III. Examples A. Enzymatic Reactions B. Vibrational Spectroscopy
What is the Problem? A.
Chemical Reactions (Bond breaking/Bond forming)
B.
Electronically excited states (photosystem, vision)
C.
Infrared/Raman Spectroscopy (fluctuating charges)
D.
Deprotonation Energies
E.
Transition states in enzymatic catalysis
Difficulties of QM/MM? A.
Time consuming (factors of 104 to 109 slower than FF)
B.
Hartree-Fock iterations may not converge (technical)
C.
Accuracy of QM/MM is model dependent (correlation)
D.
Other technical issues (e.g. crossing electronic states) “No black box”
Practical Considerations
Force Field
Ab initio
System Size
Several 10´000 atoms
20 heavy atoms (correl.) 1000 atoms (HF, [DFT])
Application
Structures Conformational Search Non-covalent interactions
Structures Energetics Reactions
Limitations
Bond-breaking Fixed atomic charges [Quantitative Information]
Very time consuming Dynamics often impossible
Approximate Solutions of the Electronic Schroedinger Equation I.
Uncorrelated Methods A. Semiempirical Methods (approximate electron-repulsion integrals); introduce experimental data B. Hartree-Fock (self consistent field) C. Density Functional Tight Binding (DFTB)
II.
Correlated Methods A. Density Functional Theory (DFT) B. Perturbation Theory
Further Details:
A. Szabo, N. Ostlund Levine
Reaction pathway of TIM P. A. Bash et al., Biochemistry, 30 5826 (1991)
Assessing the role of including different amino acids in the QM part
Between states (b) and (a)
Between states (c) and (d)
Deprotonation energies for different QM methods
Electrostatic Interactions in Bacteriorhodopsin Proton Transfer A.-N. Bondar et al., JACS, 126 14668 (2004)
Isomeric states for the preproton transfer states Orientation towards cytoplasmic side (1A) or extracellular (B) QM/MM with frontier bonds QM at semiempirical DFT Accuracy (compared to B3LYP/ 6-31+G**) 2 to 4 kcal/mol. 86 atoms in QM (retinal, Asp85, Thr89, Asp212, w402)
Energy optimized structures of reactant and product state for cytoplasmic-oriented retinal.
Minimum energy profiles
Dependence of profiles from the quantum region used
Multiple-Steering QM/MM of Chorismate Mutase A. Crespo et al., JACS, 127 6940 (2005) QM region is chorismate (substrate) DZVP basis with PBE functional and plane wave basis
Human Carbonic Anhydrase D. S. Hartsough and K. M. Merz, JPC, 99 11266 (1995)
Link atoms for QM/MM connection His94/96/119, Zn, W/OH in QM (30 atoms) PM3 semiempirical method 100ps of MD simulations, 1fs time step
Fluctuations of partial charges along the MD simulation
Ligand Dynamics in Mb Experiments
F. Schotte et al., Science 300, 1944 (2003)
Ligand Dynamics in Mb
Protocol:
50 ps of MD simulations CO treated at B3LYP/6-31G** Stochastic boundary conditions
Simulations
D. R. Nutt and M. Meuwly, PNAS , 101, 5998 (2004)
Ligand Dynamics in Mb IR spectrum for dissociated CO in native Mb Experiment
M. Lim et al., J. Chem. Phys., 102 4355 (1995)
Simulations
Realizations
Single and Double Proton Transfer Double proton transfer in base pair analogues Motivation:
Experimental spectrum of 2PY-2HPY suggests double proton transfer
Borst et al. Chem. Phys. 283, 341 (2003)
Realizations
Single and Double Proton Transfer Double proton transfer in base pair analogues Approach:
Potential energy surfaces with B3LYP/MP2 Activated MD with semiempirical DFT (SCC-DFTB)
(local)
25 ps trajectory
H coordinates
Heavy atom coordinates
NH stretch
Realizations
Single and Double Proton Transfer Infrared Spectra from MD Simulations
Realizations
Single and Double Proton Transfer Double proton transfer in base pair analogues
A: Spectrum without PT phase (24.5 ps) B: Spectrum including PT phase (25 ps)
M. Meuwly, A. Müller, S. Leutwyler PCCP 5, 2663 (2003)
