Paper - Quantum Phenomena in Biological Materia - Juergen Walther

7/30/2019 Paper - Quantum Phenomena in Biological Materia - Juergen Walther

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Figure 1: Schematic diagram of a photosyntheticunit (PSU) of green sulfur bacteria [10]

and the FMO protein complex (as shown in

figure 1). The chlorosome antenna absorbs aphoton and transfers the excitation energy overthe FMO protein complex to the reaction center.It then irreversibly enters the RC where it ignitesthe charge separation process for the actualchemical reactions [6]. The important part of thedescribed excitation energy transfer process isthe transfer through the Fenna-Matthews-Olson(FMO) protein complex. On the right sideof figure 1, there is a schematic drawing ofone monomer of the FMO complex (three

monomers form one FMO complex). It consistsof eight bacteriochlorophyll-a (BChl-a) molecules.Surrounding beta sheets and alpha-helices (beige)form the protein environment in which theBChla molecules are embedded. Until recentlythe eighth BChl molecule was not discovered,thats why most models only considered sevenBChls [6]. The orientation in figure 1 reflectsthe real orientation of the FMO complex inthe PSU. So, molecule number 1 is directlyconnected to the chlorosome antenna whereas

molecule number 3 is linked with the reactioncenter. Thus the transfer of the excitation fromthe chlorosome antenna to the reaction centerworks as follows: the excitation received fromthe antenna at molecule 1 is passed from oneBChl molecule to the next, until it reaches themolecule (here molecule number 3) closest to thereaction center. It is assumed that the monomersdont influence each other. Thats why one onlyconsiders one monomer for the energy transferprocess.

2.1 Models

The energy transfer process through the FMOprotein can be modeled by a completely classicalapproach, the Forster model. At Forster reso-nance energy transfer (FRET), an excited donormolecule can transfer its excitation energy toan acceptor molecule by dipole-dipole couplingwithout exchanging a photon. Due to this non-radiative process the excitation would find itsway step-by-step down the molecular energy lad-der from the start (molecule 1) to molecule 3,where the excitation enters the reaction center.However, the Forster model neglects quantumcoherences between different molecules [6].Experiments have shown, that the excitation canmove coherently among several BChl moleculesleading to electronic quantum beating. Quantum

beating describes coherent electronic oscillationsin donor and acceptor molecules, like the rip-ples formed when stones are tossed into a pond.So quantum beating leads to a direct evidenceof quantum coherence. Quantum beating is acompletely quantum mechanical process derivedfrom quantum electrodynamics [2], but one canimagine it like this (taken from [7]): Consider asystem of two excitons (an exciton is a quasiparti-cle of an electron excitation in an atom/molecule)described by (t) = c11 + c22. The time evo-lution of the density matrix is then

|(t) (t)| =|c1|2 |1 1| + |c2|

2 |2 2|

+ c1c

2ei(E1E2)t/ |1 2|

+ c2c

1ei(E2E1)t/ |2 1|

The latter two terms describe coherences. Thephase factors in the coherence terms are respon-sible for quantum beating. In the FMO protein,these quantum beating oscillations meet and in-terfere constructively, forming wavelike motionsof energy (superposition states) that can exploreall potential energy pathways simultaneously, like

quantum mechanical wave functions. When thiswavelike motion of energy reaches molecule 3, thewave collapses and one gets directly the most effi-cient energy transport pathway through the FMO

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robins. Magnetoreception is the ability to detecteither the inclination or the polarity of the earthsmagnetic field as a navigation tool. The proposedmodel works as an inclination compass and takesplace in the right eye of the bird [8].

3.1 Model

It is suggested that the magnetoreception in Euro-pean robins works with a photo-activated radical-pair mechanism [6]. A sketch is drawn in figure 3.If this is true, magnetoreception would be the firstbiological process which could not function in aclassical world [5]. There are three main steps in

Figure 3: Illustration of the photo-inducedradical-pair mechanism [6]

this process [6]. The first step is the creation of aradical pair (a radical pair is a pair of moleculesbound together, with one unpaired electron each).This happens by a light-induced electron transferfrom one radical pair-forming molecule (cryp-tochrome) in the retina of the bird to an accep-

tor molecule which then creates the radical pair(top right of figure 3). The unpaired electronsnaturally form singlet and triplet electron-spinstates. In the second step, the singlet and tripletstates inter-convert due to internal anisotropicinteractions with the nucleus (hyperfinestructure)and external interactions with the earths staticmagnetic field (Zeeman-effect), the strength ofmixing is dependant on the angle of the externalgeomagnetic field. In simple models, one assumesthat only one spin interacts with its nucleus. The

mixing process can be seen in the middle of thelower part of figure 3. The left part of figure 3symbolizes the coupling of the singlet and tripletelectron spin states to the nucleus and the exter-nal magnetic field where B represents the earthsmagnetic field in the upper picture. In the last

step, singlet and triplet radical pairs recombineinto singlet and triplet products at a certain rate(in figure 3 symbolized with Rs and Rt). Itis proposed that the relative weight of the reac-tion products can be biologically detected. Thus,since the relative probabilities of having singletor triplet pairs are influenced by the earths mag-netic field, this affects the distribution of thesinglet and triplet reaction products. So, a bio-logically detectable signal can be created to workas a compass.

The whole proposed process requires a large de-gree of spin-spin entanglement and coherence [5].According to Gauger et al. [5], for this model tofunction as desired, superposition and entangle-ment are sustained in this living system for atleast tens of microseconds, exceeding the dura-tions achieved in the best comparable man-mademolecular systems.

3.2 Evidence

Many behavioral studies were made to test theradical-pair model. It was found that the com-pass was dependant on the frequency and theintensity of ambient light and on the intensity ofthe magnetic field [11]. The compass was alsodisrupted when repeated magnetic pulses wereapplied to migratory birds in a cage [6]. Thisall supports the assumed model. Another experi-ment was performed where the navigation systemof the robins was tested when an external oscillat-ing field in the MHz-range was applied at certain

angles to the geomagnetic field [8]. In typicalbiomolecules, many hyperfine splittings occur inthe MHz range (0.1 - 10 MHz). An oscillatingmagnetic field that is in resonance with the split-ting between radical-pair spin states can perturba radical-pair mechanism by directly driving sin-glettriplet transitions. When the oscillating fieldwas parallel to the geomagnetic field, the birdsoriented in the migratory direction. In contrast,when the same oscillating field was presented at

different angles relative to the geomagnetic field,

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the birds were disoriented. Since the disorienta-tion should among others result because of thealignment of the oscillating field with respect to

the static field [8], this perfectly matches simpleradical pair models.

3.3 Outlook

More evidence has to be found to confirm theradical pair model. This model requires thatthe many molecules which form the radical-pairbased magnetic compass must be ordered in somepattern that the directional effects will not aver-age out. This, however, requires that the radicalpairs are ordered in a lattice or another givenbiological structure, which has not been identi-fied yet [6]. Furthermore, the radical pair has to

be found which sustains the whole mechanism,especially the long quantum coherence and en-tanglement, and which shows that it can act as acompass. All this has to be verified with furtherin-vitro experiments [6]. It is also completelyunknown how the change in the concentrationof the singlet and triplet reaction products leadsto nerve impulses which then end in a signal ofdirectionality [6]. More behavioral tests have tobe done to give a stronger proof to the radicalpair model. Some of the simple radical pair mod-

els predict that the oscillating field also inducesa directionally sensitive change in the reactionyields if the amplitude of the oscillating field issimilar to the strength of the geomagnetic staticfield (in an environment where the geomagneticfield is suppressed). Doing this experiment withanimals would even be a stronger proof than theobserved disruption effects [9].

4 Conclusion

Considering the atomic level, one can always saythat we live in a quantum world. Though, it hasbeen mostly seen as a curiosity that quantumprocesses like quantum coherence and entangle-ment can operate in a hot and wet environmenton biological time and energy scales, so that theorganism can get an advantage out of it. How-ever, there are promising candidates for func-tional quantum biology. The most auspiciousprocesses are photosynthesis and magnetorecep-tion. Thereby, not only quantum processes are

involved in biological processes, but also thesequantum processes turn out biologically advan-tageous. There is also a great possibility thatfurther examples for functional quantum biologywill be found [6].

References

[1] http://www.lbl.gov/Science-Articles/Archive/PBD-quantum-secrets.html; [Online 12/12/12].

[2] Quantum optics. Marlan Orvil Scully andMuhammad Suhail Zubairy, 1997.

[3] Michael Ball. The dawn of quantum biology.Nature, 2011.

[4] Brixner et al. Phase-stabilized two-dimensional electronic spectroscopy. J ChemPhys, 2004.

[5] Gauger et al. Sustained quantum coher-ence and entanglement in the avian compass.Phys. Rev. Lett., 2011.

[6] Lambert et al. Functional quantum biol-ogy in photosynthesis and magnetoreception.arXiv:1205.0883, 2012.

[7] Panitchayangkoon et al. Long-lived quantumcoherence in photosynthetic complexes atphysiological temperature. PNAS, 2010.

[8] Ritz et al. Resonance effects indicate a radi-cal pair mechanism for avian magnetic com-pass. Nature, 2004.

[9] Rodgers et al. Chemical magnetoreceptionin birds: the radical pair mechanism. Proc.Natl Acad. Sci, 2009.

[10] Sarovar et al. Quantum entanglement inphotosynthetic light harvesting complexes.Nature Physics, 2010.

[11] Wiltschko et al. Directional orientation ofbirds by the magnetic field under differentlight conditions. Journal of The Royal Soci-ety Interface, 2010.

[12] E. Schrodinger. What is life? CambridgeUniversity Press, 1992.

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Paper - Quantum Phenomena in Biological Materia - Juergen Walther

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