an exciton is a quasiparticle of an electron excitation in an atom/molecule) described by ψ(t) = c1 φ1 + c2 φ2 .

http://www.scribd.com/doc/116648289/Paper-Quantum-Phenomena-in-Biological-Materia-Juergen-Walther

Paper - Quantum Phenomena in Biological Materia - Juergen Walther

Quantum Phenomena in

Biological Materia
Juergen Walther
December 12, 2012
The question if quantum mechanics can play a functional role in biological processes is nearly as old as quantum mechanics itself. Recent experiments showed that biological processes indeed can be influenced by quantum mechanics. In this paper, I will outline the two most promising biological processes in which quantum mechanics can be involved: photosynthesis and magnetoreception.
1 Introduction
The influence of quantum mechanics in biological processes has a long history. Erwin Schr¨dinger o already suggested 1942 possible quantum mechanical effects in biology in his book ’What is Life?’ [12]. To clarify the term quantum mechanical effects, it is of course clear that the molecules and atoms are bound together by forces of ’quantum origin’. However, the meaning of quantum mechanical effects here is not atomic forces, but more complicated processes like quantum entanglement, quantum coherence or spin-spin coupling. Until recently and still today, quantum biology is a controversial topic. Quantum mechanics normally happens in a laboratory in vacuum with a low temperature environment on a micro-scale. Biological processes, though, take place at ambient temperatures, in a wet environment and on a macro-scale. This, of course, does not imply that quantum effects do not affect biological processes. But the thought was, that the environment at ambient temperatures disturbs and suppresses quantum processes so that these can not happen on time or energy scales relevant in biological functions. Nevertheless, recent experiments suggested quantum mechanical effects in important biological
processes [6]. In photosynthesis, quantum coherence between molecules makes the energy transport more efficient. There is another example, avian magnetoreception, where it is believed that singlet and triplet states of spatially-separated electron spins in radical pairs make the bird feel the earth’s magnetic field. These are right now the two most promising processes where quantum mechanical effects are involved. Other speculative examples of functional quantum biology (functional means that quantum mechanics achieves more efficiency than in classical mechanisms alone or makes a biological process even possible) are long-range quantum tunneling in proteins, biological photoreceptors, the flow of ions across a cell membrane and the sense of smell [6]. Since the purpose of this work is to get an overview of quantum phenomena in biological processes I want to focus on the two main candidates of ’quantum biology’: photosynthesis and magnetoreception. I will summarize the concept of the quantum effects in these processes, outline the main evidence and give a outlook.
2 Quantum effects in Photosynthesis
The most promising process for functional quantum biology is photosynthesis. Quantum effects in photosynthesis were found in the green sulfur bacteria. The photosynthetic process happens in the membrane of the bacteria. The primary appartus is the so called photosynthetic unit (PSU) [6]. This can be roughly divided in the light-harvesting complex (LHC) antenna and a reaction center (RC) (see figure 1). The LHC antenna is divided in the chlorosome antenna
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2.1 Models
The energy transfer process through the FMO protein can be modeled by a completely classical approach, the F¨rster model. At F¨rster resoo o nance energy transfer (FRET), an excited donor molecule can transfer its excitation energy to an acceptor molecule by dipole-dipole coupling without exchanging a photon. Due to this nonradiative process the excitation would find its way step-by-step down the molecular energy ladder from the start (molecule 1) to molecule 3, where the excitation enters the reaction center. However, the F¨rster model neglects quantum o coherences between different molecules [6]. Experiments have shown, that the excitation can move coherently among several BChl molecules leading to electronic quantum beating. Quantum beating describes coherent electronic oscillations in donor and acceptor molecules, like the ripples formed when stones are tossed into a pond. So quantum beating leads to a direct evidence of quantum coherence. Quantum beating is a completely quantum mechanical process derived from quantum electrodynamics [2], but one can imagine it like this (taken from [7]): Consider a system of two excitons (an exciton is a quasiparticle of an electron excitation in an atom/molecule) described by ψ(t) = c1 φ1 + c2 φ2 . The time evolution of the density matrix is then |ψ(t) ψ(t)| =|c1 |2 |φ1 φ1 | + |c2 |2 |φ2 φ2 | + c1 c∗ e−i(E1 −E2 )t/ |φ1 φ2 | 2 + c2 c∗ e−i(E2 −E1 )t/ |φ2 φ1 | 1
Figure 1: Schematic diagram of a photosynthetic unit (PSU) of green sulfur bacteria [10]
and the FMO protein complex (as shown in figure 1). The chlorosome antenna absorbs a photon and transfers the excitation energy over the FMO protein complex to the reaction center. It then irreversibly enters the RC where it ignites the charge separation process for the actual chemical reactions [6]. The important part of the described excitation energy transfer process is the transfer through the Fenna-Matthews-Olson (FMO) protein complex. On the right side of figure 1, there is a schematic drawing of one monomer of the FMO complex (three monomers form one FMO complex). It consists of eight bacteriochlorophyll-a (BChl-a) molecules. Surrounding beta sheets and alpha-helices (beige) form the protein environment in which the BChla molecules are embedded. Until recently the eighth BChl molecule was not discovered, that’s why most models only considered seven BChls [6]. The orientation in figure 1 reflects the real orientation of the FMO complex in the PSU. So, molecule number 1 is directly connected to the chlorosome antenna whereas molecule number 3 is linked with the reaction center. Thus the transfer of the excitation from the chlorosome antenna to the reaction center works as follows: the excitation received from the antenna at molecule 1 is passed from one BChl molecule to the next, until it reaches the molecule (here molecule number 3) closest to the reaction center. It is assumed that the monomers don’t influence each other. That’s why one only considers one monomer for the energy transfer process.
The latter two terms describe coherences. The phase factors in the coherence terms are responsible for quantum beating. In the FMO protein, these quantum beating oscillations meet and interfere constructively, forming wavelike motions of energy (superposition states) that can explore all potential energy pathways simultaneously, like quantum mechanical wave functions. When this wavelike motion of energy reaches molecule 3, the wave collapses and one gets directly the most efficient energy transport pathway through the FMO
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complex [1] in contrast to the classical FRET beat the rate at which excitations are lost due to model where kinetic traps can occur. fluorescence relaxation). So the quantum coherence lasts long enough to have an impact on the efficiency of the transport process. 2.2 Experimental evidence There are also theoretical models (based on an 2D electronic spectroscopy was used to detect effective Frenkel exciton model) which predict quantum beating. This spectroscopy method is that there is a higher efficiency of the transport suitable to follow the flow of light-induced exci- process due to quantum beating and interactions tation energy through molecular complexes with with the environment than it is possible with a femtosecond resolution. A complete theoretical F¨rster model alone [6]. o and experimental description is given in [4]. In short, the technique involves sequentially flashing 2.3 Outlook a sample with femtosecond laser pulses from three beams. A fourth beam is used as a local oscillator Even when the results are promising there is still to amplify and detect the resulting spectroscopic enough work to do. Classical models can be consignals as the excitation energy from the laser structed which produce both classical beating lights is transferred from one molecule to the next. and efficient energy transport without reference These oscillations were experimentally proved in to quantum coherence at all [6]. Such alternative figure 2 [7]. This experiment was done in-vitro, descriptions have to be eliminated before you can where the FMO protein complex was isolated. say that the FMO complex profits of quantum In figure 2, the amplitude of the beating signal mechanics. Also, a lot of experiments have to be done. Until now, only in-vitro experiments showed oscillations. In-vivo experiments have to be performed to confirm the beating [6]. Also the nature of the energy transport from the chlorosome antenna to the FMO complex is not understood. It is as well not clear if the three monomers of the FMO complex influence each other. According to Lambert et al. [6], perhaps the only way to really solve the whole energy transport process is to show that in more complex components of some light harvesting complex, there Figure 2: Quantum beating between molecule 1 exist significant energy traps which, without the assistance of quantum coherence, drastically imand 3 [7] pact/reduce the probability of an excitation sucis plotted against the waiting time T (the time cessfully navigating its way to a reaction center between second and third laser pulse). The graph before being lost to fluorescence relaxation. shows the signals for different temperatures. The Due to almost unity quantum yield, there may oscillation in the curves signals the quantum beat- be a possibility to design more efficient organic ing. At 77K, quantum beating lasts longer than solar cells based on quantum coherence. All in 1000 fs whereas at ambient temperatures around all, there remains still the questionable point, if 277K, the quantum coherence is destroyed after quantum coherence was used due to evolution or 300 fs. Normally, the effect of quantum beat- if it is just an accidental side effect of the way ing is neglected because fast electronic dephasing certain molecules are structured, which cannot generally destroys quantum coherence before it be answered yet [3]. can impact the transport process [7]. However, the overall transport process takes about 1000 fs 3 Magnetoreception in Birds whereas the transport through the FMO protein takes in the order of a few 100 fs [6] (the fast Another possible process which inhabits quantum transport through FMO complex is needed to mechanics is the magnetoreception of European
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robins. Magnetoreception is the ability to detect either the inclination or the polarity of the earth’s magnetic field as a navigation tool. The proposed model works as an inclination compass and takes place in the right eye of the bird [8].
3.1 Model
It is suggested that the magnetoreception in European robins works with a photo-activated radicalpair mechanism [6]. A sketch is drawn in figure 3. If this is true, magnetoreception would be the first biological process which could not function in a classical world [5]. There are three main steps in
mixing process can be seen in the middle of the lower part of figure 3. The left part of figure 3 symbolizes the coupling of the singlet and triplet electron spin states to the nucleus and the external magnetic field where B represents the earth’s magnetic field in the upper picture. In the last step, singlet and triplet radical pairs recombine into singlet and triplet products at a certain rate (in figure 3 symbolized with ΓRs and ΓRt ). It is proposed that the relative weight of the reaction products can be biologically detected. Thus, since the relative probabilities of having singlet or triplet pairs are influenced by the earth’s magnetic field, this affects the distribution of the singlet and triplet reaction products. So, a biologically detectable signal can be created to work as a compass. The whole proposed process requires a large degree of spin-spin entanglement and coherence [5]. According to Gauger et al. [5], for this model to function as desired, “superposition and entanglement are sustained in this living system for at least tens of microseconds, exceeding the durations achieved in the best comparable man-made molecular systems”.
3.2 Evidence
Many behavioral studies were made to test the radical-pair model. It was found that the compass was dependant on the frequency and the intensity of ambient light and on the intensity of the magnetic field [11]. The compass was also disrupted when repeated magnetic pulses were applied to migratory birds in a cage [6]. This all supports the assumed model. Another experiment was performed where the navigation system of the robins was tested when an external oscillating field in the MHz-range was applied at certain angles to the geomagnetic field [8]. In typical biomolecules, many hyperfine splittings occur in the MHz range (0.1 - 10 MHz). An oscillating magnetic field that is in resonance with the splitting between radical-pair spin states can perturb a radical-pair mechanism by directly driving singlet–triplet transitions. When the oscillating field was parallel to the geomagnetic field, the birds oriented in the migratory direction. In contrast, when the same oscillating field was presented at different angles relative to the geomagnetic field,
Figure 3: Illustration of the photo-induced radical-pair mechanism [6] this process [6]. The first step is the creation of a radical pair (a radical pair is a pair of molecules bound together, with one unpaired electron each). This happens by a light-induced electron transfer from one radical pair-forming molecule (cryptochrome) in the retina of the bird to an acceptor molecule which then creates the radical pair (top right of figure 3). The unpaired electrons naturally form singlet and triplet electron-spin states. In the second step, the singlet and triplet states inter-convert due to internal anisotropic interactions with the nucleus (hyperfinestructure) and external interactions with the earth’s static magnetic field (Zeeman-effect), the strength of mixing is dependant on the angle of the external geomagnetic field. In simple models, one assumes that only one spin interacts with its nucleus. The
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the birds were disoriented. Since the disorientation should among others result because of the alignment of the oscillating field with respect to the static field [8], this perfectly matches simple radical pair models.
involved in biological processes, but also these quantum processes turn out biologically advantageous. There is also a great possibility that further examples for functional quantum biology will be found [6].
3.3 Outlook
More evidence has to be found to confirm the radical pair model. This model requires that the many molecules which form the radical-pair based magnetic compass must be ordered in some pattern that the directional effects will not average out. This, however, requires that the radical pairs are ordered in a lattice or another given biological structure, which has not been identified yet [6]. Furthermore, the radical pair has to be found which sustains the whole mechanism, especially the long quantum coherence and entanglement, and which shows that it can act as a compass. All this has to be verified with further in-vitro experiments [6]. It is also completely unknown how the change in the concentration of the singlet and triplet reaction products leads to nerve impulses which then end in a signal of directionality [6]. More behavioral tests have to be done to give a stronger proof to the radical pair model. Some of the simple radical pair models predict that the oscillating field also induces a directionally sensitive change in the reaction yields if the amplitude of the oscillating field is similar to the strength of the geomagnetic static field (in an environment where the geomagnetic field is suppressed). Doing this experiment with animals would even be a stronger proof than the observed disruption effects [9].
References
[1] http://www.lbl.gov/ScienceArticles/Archive/PBD-quantumsecrets.html; [Online 12/12/12]. [2] Quantum optics. Marlan Orvil Scully and Muhammad Suhail Zubairy, 1997. [3] Michael Ball. The dawn of quantum biology. Nature, 2011. [4] Brixner et al. Phase-stabilized twodimensional electronic spectroscopy. J Chem Phys, 2004. [5] Gauger et al. Sustained quantum coherence and entanglement in the avian compass. Phys. Rev. Lett., 2011. [6] Lambert et al. Functional quantum biology in photosynthesis and magnetoreception. arXiv:1205.0883, 2012. [7] Panitchayangkoon et al. Long-lived quantum coherence in photosynthetic complexes at physiological temperature. PNAS, 2010. [8] Ritz et al. Resonance effects indicate a radical pair mechanism for avian magnetic compass. Nature, 2004. [9] Rodgers et al. Chemical magnetoreception in birds: the radical pair mechanism. Proc. Natl Acad. Sci, 2009.
4 Conclusion
Considering the atomic level, one can always say [10] Sarovar et al. Quantum entanglement in that we live in a quantum world. Though, it has photosynthetic light harvesting complexes. been mostly seen as a curiosity that quantum Nature Physics, 2010. processes like quantum coherence and entanglement can operate in a hot and wet environment [11] Wiltschko et al. Directional orientation of birds by the magnetic field under different on biological time and energy scales, so that the light conditions. Journal of The Royal Sociorganism can get an advantage out of it. Howety Interface, 2010. ever, there are promising candidates for functional quantum biology. The most auspicious processes are photosynthesis and magnetorecep- [12] E. Schrodinger. What is life? Cambridge University Press, 1992. tion. Thereby, not only quantum processes are