Review pubs.acs.org/CR
Mixed Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations of Biological Systems in Ground and Electronically Excited States Elizabeth Brunk†,‡ and Ursula Rothlisberger*,†,§ †
Laboratory of Computational Chemistry and Biochemistry, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland Joint BioEnergy Institute, Lawrence Berkeley National Laboratory, Emeryville, California 94618, United States § National Competence Center of Research (NCCR) MARVELMaterials’ Revolution: Computational Design and Discovery of Novel Materials, 1015 Lausanne, Switzerland ‡
3.10. Overcoming Limitations of QM/MM Simulations 3.10.1. Enhanced Sampling: Configuration and Systems Space 4. Applications of QM/MM MD 4.1. Electronic Ground State 4.1.1. Enzymes in Action 4.1.2. Transition Metal Ion Interactions with DNA, Proteins, and Nucleosome 4.2. Electronically Excited States 4.2.1. Photoactive Proteins: Rhodopsin 4.2.2. Photodamage in Proteins 4.2.3. Biological Applications of P-TDDFT 5. Analysis of High-Dimensional Data Sets 5.1. Correlation Analyses 5.2. Machine Learning Techniques 6. Combining Bioinformatics and QM/MM 6.1. Location and Refinement of Metal Binding Sites 7. Combining Systems Biology and QM/MM 7.1. Computational Systems Biology 7.2. Combining a Systems Scale Analysis with a Molecular Scale Analysis 7.3. Bridging the Gap between Systems and Molecular Scale Analyses 8. Outlook: QM/MM Quo Vadis? Author Information Corresponding Author Notes Biographies Acknowledgments References
CONTENTS 1. Introduction: Quantum Mechanical Phenomena in Biological Systems 2. Basic Theory 2.1. Starting from the Beginning: The Full Quantum Problem 2.1.1. Approximations to the Nuclear Dynamics 2.1.2. Approximate Solutions of the Electronic Problem 3. The QM/MM Approach 3.1. The General Idea 3.2. Some Historical Aspects 3.3. Subtractive and Additive QM/MM Schemes 3.4. Theoretical Formalism and Main Approximations 3.5. Pitfalls 3.5.1. Electron Spill-Out 3.5.2. QM/MM Boundaries through Covalent Bonds 3.5.3. Compatibility between QM and MM Electrostatics 3.6. Practical Issues 3.6.1. The QM Part 3.6.2. The MM Part 3.6.3. The QM/MM Boundary 3.7. QM/MM Static versus Dynamic Approaches 3.8. QM/MM Car−Parrinello MD 3.8.1. The QM/MM Extended Lagrangian 3.9. TDDFT/MM Implementations for Adiabatic and Nonadiabatic Excited-State Dynamics © XXXX American Chemical Society
A B B C E I I J J K M M
Q Q U U U Y Z Z AA AB AC AC AD AE AE AE AE AF AG AG AG AG AG AG AH AH
M
1. INTRODUCTION: QUANTUM MECHANICAL PHENOMENA IN BIOLOGICAL SYSTEMS The quantum nature of electrons and nuclei is manifested in countless countless biological events including the rearrangements of electrons in biochemical reactions, electron and proton tunneling, coupled proton−electron transfers, photo-
N N N N O O P P
Special Issue: Calculations on Large Systems Received: October 30, 2014
Q A
DOI: 10.1021/cr500628b Chem. Rev. XXXX, XXX, XXX−XXX
Chemical Reviews
Review
and the Hamilton operator is given by (for the sake of optimal clarity of the derivation, atomic units are only introduced later in the text):
excitations, and long-lived quantum coherences and quantum entanglement, observed in biological energy transfer.1 Quantum mechanical (QM) phenomena are thus at the base of fundamental biological processes, such as as light harvesting, photosynthesis, respiration, magnetoreception, and our sensory perceptions of vision, olfaction, and taste. However, describing such events with quantum mechanics seems essentially unreachable considering the large size of biological macromolecules (which are often comprised of 10,000−100,000 atoms) and the extended time scales (which range from ultrafast electronic processes on the order of atto- to femtoseconds to events that take place on time scales longer than seconds). Furthermore, both the large thermally accessible conformational space and the extremely small relevant energy scale of the order of kT (i.e.,
Mixed Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations of Biological Systems in Ground and Electronically Excited States Elizabeth Brunk†,‡ and Ursula Rothlisberger*,†,§ †
Laboratory of Computational Chemistry and Biochemistry, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland Joint BioEnergy Institute, Lawrence Berkeley National Laboratory, Emeryville, California 94618, United States § National Competence Center of Research (NCCR) MARVELMaterials’ Revolution: Computational Design and Discovery of Novel Materials, 1015 Lausanne, Switzerland ‡
3.10. Overcoming Limitations of QM/MM Simulations 3.10.1. Enhanced Sampling: Configuration and Systems Space 4. Applications of QM/MM MD 4.1. Electronic Ground State 4.1.1. Enzymes in Action 4.1.2. Transition Metal Ion Interactions with DNA, Proteins, and Nucleosome 4.2. Electronically Excited States 4.2.1. Photoactive Proteins: Rhodopsin 4.2.2. Photodamage in Proteins 4.2.3. Biological Applications of P-TDDFT 5. Analysis of High-Dimensional Data Sets 5.1. Correlation Analyses 5.2. Machine Learning Techniques 6. Combining Bioinformatics and QM/MM 6.1. Location and Refinement of Metal Binding Sites 7. Combining Systems Biology and QM/MM 7.1. Computational Systems Biology 7.2. Combining a Systems Scale Analysis with a Molecular Scale Analysis 7.3. Bridging the Gap between Systems and Molecular Scale Analyses 8. Outlook: QM/MM Quo Vadis? Author Information Corresponding Author Notes Biographies Acknowledgments References
CONTENTS 1. Introduction: Quantum Mechanical Phenomena in Biological Systems 2. Basic Theory 2.1. Starting from the Beginning: The Full Quantum Problem 2.1.1. Approximations to the Nuclear Dynamics 2.1.2. Approximate Solutions of the Electronic Problem 3. The QM/MM Approach 3.1. The General Idea 3.2. Some Historical Aspects 3.3. Subtractive and Additive QM/MM Schemes 3.4. Theoretical Formalism and Main Approximations 3.5. Pitfalls 3.5.1. Electron Spill-Out 3.5.2. QM/MM Boundaries through Covalent Bonds 3.5.3. Compatibility between QM and MM Electrostatics 3.6. Practical Issues 3.6.1. The QM Part 3.6.2. The MM Part 3.6.3. The QM/MM Boundary 3.7. QM/MM Static versus Dynamic Approaches 3.8. QM/MM Car−Parrinello MD 3.8.1. The QM/MM Extended Lagrangian 3.9. TDDFT/MM Implementations for Adiabatic and Nonadiabatic Excited-State Dynamics © XXXX American Chemical Society
A B B C E I I J J K M M
Q Q U U U Y Z Z AA AB AC AC AD AE AE AE AE AF AG AG AG AG AG AG AH AH
M
1. INTRODUCTION: QUANTUM MECHANICAL PHENOMENA IN BIOLOGICAL SYSTEMS The quantum nature of electrons and nuclei is manifested in countless countless biological events including the rearrangements of electrons in biochemical reactions, electron and proton tunneling, coupled proton−electron transfers, photo-
N N N N O O P P
Special Issue: Calculations on Large Systems Received: October 30, 2014
Q A
DOI: 10.1021/cr500628b Chem. Rev. XXXX, XXX, XXX−XXX
Chemical Reviews
Review
and the Hamilton operator is given by (for the sake of optimal clarity of the derivation, atomic units are only introduced later in the text):
excitations, and long-lived quantum coherences and quantum entanglement, observed in biological energy transfer.1 Quantum mechanical (QM) phenomena are thus at the base of fundamental biological processes, such as as light harvesting, photosynthesis, respiration, magnetoreception, and our sensory perceptions of vision, olfaction, and taste. However, describing such events with quantum mechanics seems essentially unreachable considering the large size of biological macromolecules (which are often comprised of 10,000−100,000 atoms) and the extended time scales (which range from ultrafast electronic processes on the order of atto- to femtoseconds to events that take place on time scales longer than seconds). Furthermore, both the large thermally accessible conformational space and the extremely small relevant energy scale of the order of kT (i.e.,
