Minimal Models for Quantum Decoherence in Coupled Biomolecules
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Transcript of Minimal Models for Quantum Decoherence in Coupled Biomolecules
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
Quantum mechanics plays a critical role in much of biology!
• Light harvesting complexes in photosynthesis– Ultraefficient collection & conversion of light
• Green Fluorescent Protein– Highly efficient marker
Why should physicists be interested in biology?
Why should biologists be interested in quantum?
• Retinal, responsible for vision– Ultrafast vision receptor
They’re all highly efficient, highly refined, self assembling quantum nanoscale devices.
Biology is hot and wet!
Retinal
Protein environment
Models must include system + bath
• 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:
The spin-boson model
We can apply this to systems of coupled biomolecules!
Experimental realisation of spin-boson model
• Two molecules
• Each with two energy levels
If only one excitation is available, effectively a two level system
What is the two level system?
Experimental realisation of spin-boson model
• 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
What is the coupling?
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
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
Spectral density for the minimal model = chromophore dipole diff.b = protein radiuss() = solvent dielectric constantp = protein dielectric constant
• Slope is critical parameter- For chromophore in water, - Protein can shield chromophore, so
- c.f., for Joesephson Junction
qubits- Strong decoherence - quantum
consciousness unlikely!
• Microscopic derivation of spin-boson model and spectral density
• Ohmic spectral density- Cut-off determined by solvent dielectric relaxation time, 8ps
Localised
t
Coherent
t
Incoherent
t
Location of excitation with time
• Usually interested in z, which describes location of excitation
– How does the excitation move between molecules?
• Three possible scenarios for expectation value of z:
Dynamics of the spin-boson model
• System is eventually in a mixed state– One molecule or the other is definitely excited– Here, it’s most likely the yellow one
• Behaviour depends on and relative size of parameters: c
- kBTc
• Rich, non-trivial dynamics• Cross-over from coherent-incoherent in many ways
For identical () molecules and c
For c, coherent oscillations
remain even for high T,
Bias can help or hinder coherent oscillations
Dynamics of the spin-boson model
All known in terms of experimental parameters
Experimental detection of 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
• Under most “normal” conditions, incoherent transfer– Good for experimentalists using classical theory!
• Identical molecules• Very close• Dipoles unparallel
Property Values
0-800 meV
0-100 meV
hc 1-10 meV
kBT 1-30 meV
between 0.01 - 10+
Seeing coherent oscillations:
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 doesn’t always have to be physics helping advance biology!
Sometimes, biology can help physics too!
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
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?
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()
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
Model for chromophore and its environment