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Quantum Effects in Biology

Book Description

Quantum mechanics provides the most accurate microscopic description of the world around us, yet the interface between quantum mechanics and biology is only now being explored. This book uses a combination of experiment and theory to examine areas of biology believed to be strongly influenced by manifestly quantum phenomena. Covering subjects ranging from coherent energy transfer in photosynthetic light harvesting to spin coherence in the avian compass and the problem of molecular recognition in olfaction, the book is ideal for advanced undergraduate and graduate students in physics, biology and chemistry seeking to understand the applications of quantum mechanics to biology.

Table of Contents

  1. Cover
  2. Quantum Effects in Biology
  3. Title page
  4. Copyright page
  5. Content
  6. Foreword
  7. Contributors
  8. Preface
  9. Part I Introduction
    1. 1 Quantum biology: introduction
      1. 1.1 Introduction
      2. 1.2 Excited states in biology
        1. 1.2.1 Photosynthetic light-harvesting
        2. 1.2.2 Other excited state processes: from vision to circadian clocks
      3. 1.3 Light particles and tunnelling
        1. 1.3.1 Electron tunnelling
        2. 1.3.2 Proton tunnelling
        3. 1.3.3 Olfaction
      4. 1.4 Radical pairs
        1. 1.4.1 Magnetoreception
      5. 1.5 Questions for the present
        1. 1.5.1 Do quantum effects introduce new functions in biology?
        2. 1.5.2 Are our experimental methods adequate?
        3. 1.5.3 Are our theoretical methods adequate?
        4. 1.5.4 What opportunities do an understanding of quantum-biological phenomena bring?
      6. 1.6 Some wide-reaching questions
        1. 1.6.1 What is life and consciousness?
        2. 1.6.2 Did quantum mechanics play a role in the origin of life?
        3. 1.6.3 Is quantum-mechanical mechanism intrinsic or was it selected through evolution?
    2. 2 Open quantum system approaches to biological systems
      1. 2.1 Quantum mechanics concepts and notations
      2. 2.2 Open quantum systems: dynamical map approach
        1. 2.2.1 Non-completely positive quantum maps
      3. 2.3 Open quantum systems: master equation approach
      4. 2.4 Formally exact QME
      5. 2.5 QME in the weak system–bath coupling limit
      6. 2.6 QME for weak coupling to a Markovian bath
      7. 2.7 QMEs beyond weak and Markovian limits
        1. 2.7.1 Quantum modelling a pigment–protein complex
        2. 2.7.2 Electronic energy transfer in photosynthetic complexes: a case of failure for perturbative QMEs
      8. 2.8 Second-order cumulant time-non-local equation and its hierarchical representation
      9. 2.9 A post-perturbative time convolution QME
      10. 2.10 QME in the polaron picture
      11. 2.11 Path integral techniques
      12. 2.12 DMRG based approaches
    3. 3 Generalized Förster resonance energy transfer
      1. 3.1 Introduction
      2. 3.2 Förster’s rate expression: a complete derivation
        1. 3.2.1 Fermi’s golden rule
        2. 3.2.2 The relation between and
        3. 3.2.3 The relation between and
        4. 3.2.4 Transition dipole interaction
      3. 3.3 Transition density cube method
      4. 3.4 Generalized Förster theories
        1. 3.4.1 Non-equilibrium generalization
        2. 3.4.2 Inelastic generalization
        3. 3.4.3 Multichromophoric generalization
      5. 3.5 Important computational issues in an actual application
        1. 3.5.1 Identification of donors and acceptors
        2. 3.5.2 Evaluation of spectral overlap and averaging over inhomogeneous distribution
      6. 3.6 Applications of MC-FRET
        1. 3.6.1 Light-harvesting 2 (LH2) complex of purple bacteria
        2. 3.6.2 Antenna complexes in LHCII
      7. 3.7 Summary
    4. 4 Principles of multi-dimensional electronic spectroscopy
      1. 4.1 Photo-induced dynamics of molecular systems
        1. 4.1.1 Semi-classical description of light–matter interaction
        2. 4.1.2 Response functions
        3. 4.1.3 Meaning of response functions in time and frequency domains
        4. 4.1.4 Macroscopic polarization and the spectroscopic signal
      2. 4.2 Non-linear response of multi-state systems
        1. 4.2.1 Two- and three-band molecules
        2. 4.2.2 Liouville pathways
        3. 4.2.3 Third-order polarization in a rotating wave approximation
        4. 4.2.4 Third-order polarization in the impulsive limit
      3. 4.3 Cumulant expansion of a non-linear response
        1. 4.3.1 Energy gap correlation function
        2. 4.3.2 Energetic disorder
        3. 4.3.3 Response functions of a three-level system
      4. 4.4 Selected non-linear spectroscopic methods
        1. 4.4.1 Photon echo: learning about system–bath interactions
        2. 4.4.2 Two-dimensional spectroscopy: resonance coupling, population transfer and coherence dynamics
        3. 4.4.3 Electronic versus vibrational coherences
      5. 4.5 Conclusions
  10. Part II Quantum effects in bacterial photosynthetic energy transfer
    1. 5 Structure, function, and quantum dynamics of pigment–protein complexes
      1. 5.1 Introduction
      2. 5.2 Light-harvesting complexes from purple bacteria: structure, function and quantum dynamics
        1. 5.2.1 The photosynthetic reaction centre
        2. 5.2.2 The light-harvesting complex LH1
        3. 5.2.3 The light-harvesting complex LH2
      3. 5.3 Optical transitions in pigment–protein complexes
        1. 5.3.1 Linear absorption and lineshape function
        2. 5.3.2 Circular dichroism
      4. 5.4 Electron transfer in pigment–protein complexes
        1. 5.4.1 Electron transfer rate
    2. 6 Direct observation of quantum coherence
      1. 6.1 Detecting quantum coherence
        1. 6.1.1 What is ‘quantum coherence’?
        2. 6.1.2 How does quantum manifest in observations?
      2. 6.2 Observation of quantum coherence using 2D electronic spectroscopy
        1. 6.2.1 Biology of the Fenna–Matthews–Olson photosynthetic complex
        2. 6.2.2 Detecting quantum coherence among excited states
      3. 6.3 Identifying and characterizing quantum coherence signals
      4. 6.4 Quantum coherence in reaction centres using two colour electronic coherence photon echo spectroscopy
      5. 6.5 Observing quantum coherences at physiological temperatures
      6. 6.6 Outlook for future measurements of coherence
    3. 7 Environment-assisted quantum transport
      1. 7.1 Introduction
      2. 7.2 Master equations for quantum transport
      3. 7.3 Quantum transport in a two-chromophore system
      4. 7.4 The principles of noise-assisted quantum transport
      5. 7.5 Quantum transport in the Fenna–Matthews–Olson protein complex
      6. 7.6 Optimality and robustness of quantum transport
        1. 7.6.1 Efficient simulation of quantum transport beyond Markovian and perturbative limits
        2. 7.6.2 Optimality and robustness with respect to reorganization energy and cut-off frequency
        3. 7.6.3 Optimality and robustness with respect to reorganization energy and temperature
      7. 7.7 Conclusion
  11. Part III Quantum effects in higher organisms and applications
    1. 8 Excitation energy transfer and energy conversion in photosynthesis
      1. 8.1 Photosynthesis
      2. 8.2 Photosynthetic energy conversion: charge separation
        1. 8.2.1 In bacterial reaction centres charge separation is coupled to coherent nuclear motions
        2. 8.2.2 Alternative ultra fast pathways for charge separation in bacterial reaction centres
        3. 8.2.3 Electronic coherence in bacterial reaction centres
        4. 8.2.4 Charge separation in the photosystem II reaction centre
        5. 8.2.5 Quantum coherence and charge separation in the photosystem II reaction centre
      3. 8.3 Light-harvesting
        1. 8.3.1 Excitation energy transfer and excitons
        2. 8.3.2 Quantum coherence and photosynthetic light-harvesting
    2. 9 Electron transfer in proteins
      1. 9.1 Introduction
      2. 9.2 The rate for a single-step electron transfer reaction mediated by elastic through-bridge tunnelling
      3. 9.3 Dependence of tunnelling on protein structure: tunnelling pathways and their interferences
      4. 9.4 Tunnelling matrix element fluctuations in deep-tunnelling ET reactions
      5. 9.5 Vibrational quantum effects and inelastic tunnelling
      6. 9.6 Biological ET chains with tunnelling and hopping steps through the protein medium
      7. 9.7 Conclusions
      8. 9.8 Acknowledgements
    3. 10 A chemical compass for bird navigation
      1. 10.1 Introduction
      2. 10.2 Theoretical basis for a chemical compass
        1. 10.2.1 Theoretical model and origin of the low field effect
        2. 10.2.2 Requirements for a magnetic compass
        3. 10.2.3 Cryptochrome magnetoreception
      3. 10.3 In vitro magnetic field effects on radical pair reactions
        1. 10.3.1 Anisotropic magnetic field effects
        2. 10.3.2 Radiofrequency magnetic field effects
        3. 10.3.3 Magnetic field effects on a photoactive protein
      4. 10.4 Evidence for a radical pair mechanism in birds
        1. 10.4.1 Lack of evidence for alternative mechanisms
        2. 10.4.2 Neurobiology
        3. 10.4.3 Radiofrequency effects on magnetic orientation
      5. 10.5 Conclusion
    4. 11 Quantum biology of retinal
      1. 11.1 Introduction
      2. 11.2 Retinal in rhodopsin and bacteriorhodopsin
      3. 11.3 Quantum physics of excited state dynamics
      4. 11.4 Regulation of photochemical processes for biological function
      5. 11.5 Potential energy crossing and conical intersection
      6. 11.6 Electronic structure of protonated Schiff base retinal
      7. 11.7 Mechanism of spectral tuning in rhodopsins
      8. 11.8 Photoisomerization of retinal in rhodopsins
      9. 11.9 Summary and outlook
      10. 11.10 Acknowledgement
    5. 12 Quantum vibrational effects on sense of smell
      1. 12.1 Phonon assisted tunnelling in olfaction
      2. 12.2 Important processes and timescales
        1. 12.2.1 The electron-odourant force
      3. 12.3 Quantum rate equations
      4. 12.4 Putting in numbers
      5. 12.5 Can we make predictions?
      6. 12.6 Extensions of the theory for enantiomers
    6. 13 A perspective on possible manifestations of entanglement in biological systems
      1. 13.1 Introduction
      2. 13.2 Entanglement
        1. 13.2.1 Qualitative discussion
        2. 13.2.2 Entanglement: general definitions
        3. 13.2.3 Mixed-state entanglement
      3. 13.3 Non-local correlations
        1. 13.3.1 Entanglement: conclusions
      4. 13.4 Entanglement in biology
      5. 13.5 Open driven systems and entanglement
        1. 13.5.1 Simple models I: parametric down conversion
        2. 13.5.2 Simple models II: a gas of molecular spins
        3. 13.5.3 Simple models III: conformational changes and time-dependent Hamiltonians
        4. 13.5.4 Concrete examples of biological systems
      6. 13.6 Conclusions
    7. 14 Design and applications of bio-inspired quantum materials
      1. 14.1 Potential applications of bio-inspired quantum materials
        1. 14.1.1 Opportunities for novel energy and sensing applications with artificial light-harvesting systems
        2. 14.1.2 Magnetic sensing with radical pair materials
      2. 14.2 Progress in designing biomimetic quantum materials
        1. 14.2.1 Structured chromophoric assemblies for light-harvesting
        2. 14.2.2 Radical pair materials for magnetometry
    8. 15 Coherent excitons in carbon nanotubes
      1. 15.1 Structure
      2. 15.2 Electronic properties in 1D systems
      3. 15.3 Exciton–exciton interactions
      4. 15.4 Non-linear optical response of excitons
      5. 15.5 Simulations of intensity-dependent 3PEPS
      6. 15.6 Discussion and conclusions
      7. 15.7 Acknowledgement
  12. References
  13. Index