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