Minimal Models for Quantum Decoherence in Coupled Biomolecules

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Minimal Models forQuantum Decoherence in
Coupled Biomolecules

• Joel Gilmore
• Ross H. McKenzie
• University of Queensland, Brisbane, Australia

Gilmore and McKenzie, J. Phys.Cond. Matt. 17,
1735 (2005) and quant-ph/0412170, to appear in
Chem. Phys. Lett
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Why should physicists be interested in biology?
Why should biologists be interested in quantum?

• Quantum mechanics plays a critical role in much
  of biology!

Theyre all highly efficient, highly refined,
self assembling quantum nanoscale devices.

• Retinal, responsible for vision
• Ultrafast vision receptor

• Light harvesting complexes in photosynthesis
• Ultraefficient collection conversion of light
• Green Fluorescent Protein
• Highly efficient marker

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Biology is hot and wet!
Protein environment
Retinal
Models must include system bath
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The spin-boson model

• Popular model for describing decoherence
• Extensively studies by Leggett, Weiss, Saleur,
  Costi, et al.
• Applications to SQUIDS, decoherence of qubits
• Describes the coupling of a two level system to a
  bath of harmonic oscillators
• Works for many, very different, environments
• All coupling to enviornment is in the spectral
  density

We can apply this to systems of coupled
biomolecules!
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Experimental realisation of spin-boson model
What is the two level system?

• Two molecules
• Each with two energy levels

If only one excitation is available, effectively
a two level system
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Experimental realisation of spin-boson model
What is ???the coupling?

• Excitations may be transferred by dipole-dipole
  interactions
• Shine in blue, get out yellow!
• Basis of Fluorescent Resonant Energy Transfer
  (FRET) spectroscopy
• Used in photosynthesis to move excitations around

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Experimental realisation of spin-boson model
What is J(????the bath coupling?

• Use a minimal model to find an analytic
  expression
• Protein and solvent treated as dielectric mediums

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Obtaining spectral density, J(?)

• Central dipole polarises solvent
• Causes electric reaction field which acts on
  dipole
• Two sources of dynamics
• Solvent dipoles fluctuate (captured by
  )
• Chromophore dipole different in ground and
  excited states

• To obtain spectral density
• Quantise reaction field
• Apply fluctuation-dissipation theorem

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Spectral density for the minimal model
?? chromophore dipole diff. b protein
radius ?s(?) solvent dielectric constant ?p
protein dielectric constant

• Ohmic spectral density
• Cut-off determined by solvent dielectric
  relaxation time, 8ps

• Microscopic derivation of spin-boson model and
  spectral density

• Slope is critical parameter
• For chromophore in water, ???
• Protein can shield chromophore, so ??????
• c.f., ???????????for Joesephson Junction qubits
• Strong decoherence - quantum consciousness
  unlikely!

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Dynamics of the spin-boson model

• Usually interested in ?z, which describes
  location of excitation
• How does the excitation move between molecules?
• Three possible scenarios for expectation value of
  ?z

Location of excitation with time

• System is eventually in a mixed state
• One molecule or the other is definitely excited
• Here, its most likely the yellow one

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Dynamics of the spin-boson model

• Behaviour depends on ? and relative size of
  parameters
• ?????c
• ?????
• kBT????c
• Rich, non-trivial dynamics
• Cross-over from coherent-incoherent in many ways

All known in terms of experimental parameters
For identical (???) molecules and ????c
For ????c, coherent oscillations remain even for
high T, ? Bias ??can help or hinder coherent
oscillations
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Experimental detection of coherent oscillations

• Under most normal conditions, incoherent
  transfer
• Good for experimentalists using classical theory!

• Identical molecules
• Very close
• Dipoles unparallel

Seeing coherent oscillations

• Selectively excite one with polarised laser pulse
• Measure fluorescence anisotropy as excitation
  moves
• Each molecule fluoresces different polarisation -
  directly monitor ?z
• Highly tunable system (T,???????c?
• Change separation, temperature, solvent, genetic
  engineering

Property Values
? 0-800 meV
? 0-100 meV
h?c 1-10 meV
kBT 1-30 meV
??between 0.01 - 10
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Key Results Conclusions

• Demonstrated an experimental realisation of the
  spin-boson model in terms of coupled biomolecules
• Microscopic derivation of the spectral density
  through minimal models of the surrounding protein
  and solvent
• Dynamics can be observed directly through
  experiment
• Model applicable to other scenarios
• Retinal in vision
• Photosynthesis
• More complex protein models
• Molecular biophysics may be a useful testing
  ground for models of quantum decoherence
• Complex but tuneable systems - self assembling
  too!
• It doesnt always have to be physics helping
  advance biology!Sometimes, biology can help
  physics too!

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Acknowledgements

• Ross McKenzie (UQ)
• Paul Meredith (UQ)
• Ben Powell (UQ)
• Andrew Briggs all at QIPIRC (Oxford)

Gilmore and McKenzie, J. Phys.Cond. Matt. 17,
1735 (2005) and quant-ph/0412170, to appear in
Chem. Phys. Lett
15
Quantum mechanics in biology

• Classical biology!
• Ball and stick models
• DNA
• No quantum courses for biologists

• Quantum biology!
• Highly efficient photosynthesis
• Ultrafast vision receptors
• Tunneling in enzymes
• Quantum consciousness?!
• (Okay, probably not)

Quantum or classical -What decides?
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A Quantum Vision
Rhodopsin undergoes an ultra-fast,
ultra-efficient shape change when it absorbs a
photon. How?
Quantum models, involving conical intersections,
are necessary.
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Modelling

• Need to model many atoms
• At very least, choromophore is QM
• A number of approaches
• Direct QM methods (e.g., DFT)
• QM/MM models (some molecules quantum, some not)
• Were trying minimal models
• As simple as possible, but no simpler
• Capture essential physics, but quick to solve
• Very valuable in condensed matter (e.g., Kondo
  effect)

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Model for chromophore and its environment

• Chromophore properties
• Two state system
• Point dipole

• Protein properties
• Spherical, radius b
• Continuous medium
• Dielectric constant ?p

• Solvent properties
• Dielectric constant ?s(?)

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Model for chromophore and its environment

• Important physics
• Water is strongly polar
• Dipole causes polarised solvent cage
• Reaction field affects dipole
• Dynamics
• Solvent is fluctuating
• Dielectric relaxation, 8ps
• Chromophore dipole is different in excited state

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