The quantum Zeno effect immunizes the avian compass against the deleterious effects of exchange and dipolar interactions

Magnetic-sensitive radical-ion-pair reactions are understood to underlie the biochemical magnetic compass used by avian species for navigation. Recent experiments have provided growing evidence for the radical-ion-pair magnetoreception mechanism, while recent theoretical advances have unravelled the quantum nature of radical-ion-pair reactions, which were shown to manifest a host of quantum-information-science concepts and effects, like quantum measurement, quantum jumps and the quantum Zeno effect. We here show that the quantum Zeno effect provides for the robustness of the avian compass mechanism, and immunizes its magnetic and angular sensitivity against the deleterious and molecule-specific exchange and dipolar interactions.     

New model for the avian magnetic compass

It is proposed that the avian magnetic compass depends on the angle between the horizontal component B(h) of the geomagnetic field (GMF) and E(r), the radial electric field distribution generated by gamma-oscillations within the optic tectum (TeO). We hypothesize that the orientation of the brain relative to B(h) is perceived as a set of electric field ion cyclotron resonance (ICR) frequencies that are distributed in spatially recognizeable regions within the TeO. For typical GMF intensities, the expected ICR frequencies fall within the 20-50 Hz range of gamma-oscillation frequencies observed during visual stimulation. The model builds on the fact that the superficial lamina of the TeO receive signals from the retina that spatially map the visual field. The ICR frequencies are recruited from the local wide-band gamma-oscillations and are superposed on the tectum for interpretation along with other sensory data. As a first approximation, our analysis is restricted to the medial horizontal plane of the TeO. For the bird to fly in a preferred, previously mapped direction relative to B(h), it hunts for that orientation that positions the frequency maxima at appropriate locations on the TeO. This condition can be maintained even as B(h) varies with geomagnetic latitude during the course of long-distance flights. The magnetovisual coordinate system (straight phi, omega) overlaying the two halves of the tectal surface in a nonsymmetric way may imply an additional orienting function for the TeO over and above that of a simple compass (e.g., homing navigation as distinct from migrational navigation).     

The role of lone pair and dipolar interactions in the non-planarity of 1,3-dioxolane and 1,3-dioxole

1,3-Dioxole has been shown to be non-planar by infrared and Raman spectroscopy. An MM3 study of this molecule enabled the investigators to suggest that this non-planarity was due to the anomeric effect. Subsequently, an ab initio theoretical study of this molecule was performed, which also concluded that the non-planarity of 1,3-dioxole was due to the anomeric effect and not to dipole-dipole interactions. Neither study used rigorous methods for assessing the role of dipolar interactions in the geometry of 1,3-dioxole. A new study of 1,3-dioxole, 1,3-dioxolane, tetrahydrofuran, cyclopentane, and some related molecules using the new QVBMM (molecular mechanics) force field shows conclusively that the non-planarity of 1,3-dioxole and 1,3-dioxolane is due primarily to torsional and dipolar effects, and not secondary molecular orbital overlap interactions.     

Neural basis of the magnetic compass: interactions of visual,magnetic and vestibular inputs in the pigeon's brain

Summary Single unit electrical activity was recorded extracellularly in the lateral and superior vestibular nuclei, the vestibulo-cerebellum and the nucleus of the basal optic root (nBOR) under earth-strength magnetic stimulation. Units in the vestibular system responded with either inhibition or excitation to the magnetic stimuli only if the animal was moved out of the horizontal plane. No responses to the artificial magnetic field were observed when enucleation was performed contralateral to the recording site or when magnetic stimuli were applied in total darkness.Most of the units in the nBOR responded to slow direction changes in the magnetic field with a gradual augmentation of activity. The responses were generally weak but nevertheless statistically significant and seemed to be direction selective, i.e. different cells responded to a different distinct direction change of the magnetic field.The results indicate, that information provided by magnetic cues in the earth's strength range may be conveyed from the visual to the vestibular system via a projection from the nBOR and then related to active movements of the animal.Abbreviation nBOR nucleus of the basal optic root     

Effects of very weak magnetic fields on radical pair reformation

We can expect that biological responses to very weak ELF electromagnetic fields will be masked by thermal noise. However, the spin of electrons bound to biologically important molecules is not strongly coupled to the thermal bath, and the effects of the precession of those spins by external magnetic fields is not bounded by thermal noise. Hence, the known role of spin orientation in the recombination of radical pairs (RP) may constitute a mechanism for the biological effects of very weak fields. That recombination will generally take place only if the valence electrons in the two radicals are in a singlet state and the effect of the magnetic field is manifest through differential spin precessions that affect the occupation of that state. Because the spin relaxation times are of the order of microseconds, any effects must be largely independent of frequency up to values of a few megahertz. Using exact calculations on an appropriately general model system, we show that one can expect small, but significant, modifications of the recombination rate by a 50 microT field only under a narrow range of circumstances: the cage time during which the two elements are together must be exceptionally long--of the order of 50 ns or longer; the hyperfine field of either radical must not be so great as to generate a precession period greater than the cage containment time; and the characteristic recombination time of the radical pair in the singlet state must be about equal to the containment time. Thus, even under such singularly favorable conditions, fields as small as 5 microT (50 milligauss) cannot change the recombination rate by as much as 1%. Hence, we conclude that environmental magnetic fields much weaker than the earth's field cannot be expected to affect biology significantly by modifying radical pair recombination probabilities.     

Electroretinographic study of the magnetic compass in European robins

Migratory birds are known to be sensitive to external magnetic field (MF). Much indirect evidence suggests that the avian magnetic compass is localized in the retina. Previously, we showed that changes in the MF direction could modulate retinal responses in pigeons. In the present study, we performed similar experiments using the traditional model animal to study the magnetic compass, European robins. The photoresponses of isolated retina were recorded using ex vivo electroretinography (ERG). Blue- and red-light stimuli were applied under an MF with the natural intensity and two MF directions, when the angle between the plane of the retina and the field lines was 0° and 90°, respectively. The results were separately analysed for four quadrants of the retina. A comparison of the amplitudes of the a- and b-waves of the ERG responses to blue stimuli under the two MF directions revealed a small but significant difference in a- but not b-waves, and in only one (nasal) quadrant of the retina. The amplitudes of both the a- and b-waves of the ERG responses to red stimuli did not show significant effects of the MF direction. Thus, changes in the external MF modulate the European robin retinal responses to blue flashes, but not to red flashes. This result is in a good agreement with behavioural data showing the successful orientation of birds in an MF under blue, but not under red illumination.     

Model for magnetic field effects on radical pair recombination in enzyme kinetics.

A prototypical model for describing magnetic field effects on the reaction kinetics of enzymes that exhibit radical pair recombination steps in their reaction cycle is presented. The model is an extended Michaelis-Menten reaction scheme including an intermediate enzyme-substrate complex where a spin-correlated radical pair state exists. The simple structure of the scheme makes it possible to calculate the enzyme reaction rate explicitly by combining chemical kinetics with magnetic field-dependent spin kinetics (radical pair mechanism). Recombination probability is determined by using the exponential model. Simulations show that the size of the magnetic field effect depends on relations between different rate constants, such as 1) the ratio between radical pair-lifetime and the magnetic field-sensitive intersystem crossing induced by the hyperfine interaction and the delta g mechanisms and 2) the chemical rate constants of the enzyme reaction cycle. An amplification factor that is derived from the specific relations between the rate constants is defined. It accounts for the fact that although the magnetic field-induced change in radical pair recombination probability is very small, the effect on the enzyme reaction rate is considerably larger, for example, by a factor of 1 to 100. Model simulations enable a qualitative comparison with recent experimental studies reporting magnetic field effects on coenzyme B12-dependent ethanolamine ammonia lyase in vitro activity that revealed a reduction in Vmax/KM at low flux densities and a return to the zero-field rate or an increase at high flux densities.     

An in vitro model for studies on bacterial interactions in the avian caecum

An in vitro intermittent-flow model was developed for studying bacterial interactions in the avian caecum. The model provides a closer simulation of caecal conditions than others described previously but does not require elaborate instrumentation. In preliminary trials, growth of caecal bacteria from an adult chicken was shown to be inhibitory to both Salmonella infantis and entero-haemorrhagic Escherichia coli.     

The puzzle of magnetic resonance effect on the magnetic compass of migratory birds

Experiments on the effect of radio‐frequency (RF) magnetic fields on the magnetic compass orientation of migratory birds are analyzed using the theory of magnetic resonance. The results of these experiments were earlier interpreted within the radical‐pair model of magnetoreception. However, the consistent analysis shows that the amplitudes of the RF fields used are far too small to noticeably influence electron spins in organic radicals. Other possible agents that could mediate the birds' response to the RF fields are discussed, but apparently no known physical system can be responsible for this effect. Bioelectromagnetics 30:402–410, 2009. © 2009 Wiley‐Liss, Inc.     

Development of lateralization of the magnetic compass in a migratory bird

The magnetic compass of a migratory bird, the European robin (Erithacus rubecula), was shown to be lateralized in favour of the right eye/left brain hemisphere. However, this seems to be a property of the avian magnetic compass that is not present from the beginning, but develops only as the birds grow older. During first migration in autumn, juvenile robins can orient by their magnetic compass with their right as well as with their left eye. In the following spring, however, the magnetic compass is already lateralized, but this lateralization is still flexible: it could be removed by covering the right eye for 6 h. During the following autumn migration, the lateralization becomes more strongly fixed, with a 6 h occlusion of the right eye no longer having an effect. This change from a bilateral to a lateralized magnetic compass appears to be a maturation process, the first such case known so far in birds. Because both eyes mediate identical information about the geomagnetic field, brain asymmetry for the magnetic compass could increase efficiency by setting the other hemisphere free for other processes.     

Improvements in technical assessment and protocol for EPR evaluation of magnetic fields effects on a radical pair reaction

The effects of either static or pulsed magnetic fields on the reaction rate of Fremy's salt-ascorbic acid were studied directly by EPR spectroscopy. Radical pair mechanism (RPM) accounts for the magnetic field effects, but the expected amounts are so small that they need to be observed with particular care with EPR technique. The method is based on the resolution of a pair of EPR signals by the addition of a stationary field gradient, where the signals are coming from the exposed and control capillary sample. To this purpose, a suitable device for the gradient generation was used. Others improvements were the strictly keeping of the same boundary temperature condition in the capillary pairs, obtained by a refrigerating system controlled by a thermocouple, and the use of a pair of Helmholtz coils to generate an external high homogeneous magnetic field. By this experimental set up, we found that the magnetic field induce the decrease of the studied radical reaction rate. This EPR approach is a significant alternative to the spectrophotometric one. Moreover, it offers the advantage to detect both the radicals and/or intermediates involved in the reaction.     

Exploring the possibilities for radical pair effects in cryptochrome

The ability of some animals to sense magnetic fields has long captured the human imagination. In our recent paper, we explored how radical pair effects in the protein cryptochrome may underlie the magnetic orientation sense of migratory birds. Here we explain our model and discuss its relationship to experimental results on plant cryptochromes, as well as discuss the next steps in refining our model, and explore alternate but related possibilities for modeling and understanding cryptochrome as a magnetic sensor.Key words: cryptochrome, radical pair machanism, avian orientation, magnetic field effect, Arabidopsis thaliana, avian magnetoreception, magnetic sensorThe ability of some animals to sense magnetic fields is a long-standing open problem in biology. Over the past 50 years, scientific studies have shown that a wide variety of living organisms have the ability to perceive magnetic fields and can use information from the earth''s magnetic field in orientation behavior. The best-studied example of animal magnetoreception is the case of migratory birds, who use the earth''s magnetic field, as well as a variety of other environmental cues, to find their way during migration.The two prevailing hypotheses for the mechanism of avian magnetoreception are an iron-mineral-based explanation, wherein birds use small deposits of magnetic iron minerals^1,2,12 in the base of their beaks for magnetic orientation, and a radical-pair-based explanation, in which a magnetically sensitive chemical reaction in the eye of the bird enables perception of the magnetic field via its effects on reaction products. The latter hypothesis is based on the idea that a radical pair reaction may take place in the protein cryptochrome in the retina of the bird.^3,4 Cryptochrome contains a blue-light-absorbing chromophore, flavin adenine dinucleotide (FAD); this FAD cofactor is reduced via a series of light-induced electron transfers from a chain of three tryptophans that bridge the space between FAD and the protein surface (see Fig. 1). The hypothesis explored in our paper⁴ is that a radical pair reaction takes place between FAD and the tryptophans in the photoreduction pathway which modulates the signaling activity of cryptochrome. The specifics of this idea are outlined in Figure 1.Open in a separate windowFigure 1Right: Cryptochrome internally binds the FAD cofactor and contains a three-tryptophan photoreduction pathway conserved from photolyase, consisting of Trp400, Trp377, and Trp324, with Trp400 nearest the FAD and Trp324 closest to the protein surface. After the FAD cofactor absorbs a photon, bringing it into an excited state, it is protonated from a nearby acidic residue, and then electron transfer proceeds from Trp400. At this stage, the semireduced FADH and Trp400⁺ comprise a radical pair—that is, each partner has an unpaired electron, and the spins of those electrons are in a correlated state. Cryptochrome is thought to be in its active, signaling state when the FAD cofactor is in this semireduced FADH form. An electron is then transferred from Trp377 to Trp400 and from Trp324 to Trp377, forming radical pairs FADH + Trp377⁺ and FADH + Trp324⁺ in the process. The Trp324 radical is then deprotonated. Before this final deprotonation, it is possible for the electron to back transfer from the tryptophan to FADH. If this occurs, FADH reverts to the oxidized FAD form, and cryptochrome is no longer in its active state. Left: This schematic of the electron transfer pathway in cryptochrome shows the estimated lifetimes of each of the radical pair states. The system spends most of its time in the FADH + Trp324 radical pair state. Also shown are the electron and nuclear spins on the FADH and Trp324 radicals. Each nuclear spin adds a small contribution to the local magnetic field. The unpaired electron spins are shown here in the singlet (antiparallel) state. They precess around the local magnetic field, which consists of contributions from the external field and from each of the nuclear spins, causing interconversion to the triplet (parallel) state and back again. This singlet-triplet interconversion is the basis of the radical pair effect in the following sense. Electron back-transfer from Trp324 to FADH proceeds only when the unpaired electrons on each radical are in the singlet state. Cryptochrome remains in its active state so long as this back-transfer is impeded. Therefore, singlet-triplet interconversion influences the time cryptochrome can spend in its active state, and so this magnetic-field-driven effect can alter the protein''s signaling behavior.That magnetic field effects do occur in cryptochrome is supported indirectly by experiments done by Margaret Ahmad and co-workers, as reported in their recent paper⁵ on the effects of magnetic fields on cryptochrome-dependent responses in Arabidopsis thaliana seedlings. In our paper, Magnetic Field Effects in Arabidopsis thaliana Cryptochrome-1 (4), we sought to evaluate this possibility computationally, to see whether a magnetic field effect in the FADH - tryptophan radical pair is reasonable. We found that it is possible to see a change in cryptochrome activation yield (the amount of time cryptochrome stays in its active state) of about 10%.Unfortunately, the magnetic field dependence of cryptochrome activation seen in our calculations cannot be taken as exact because of several limitations. Chief among these are that the models of the radical pair did not include all nuclei, and the hyperfine coupling constants were taken from DNA photolyase, which is a protein highly similar to cryptochrome in structure, but which does not necessarily have precisely the same hyperfine coupling for the FAD cofactor and the tryptophans in the photoreduction pathway as does cryptochrome. However, the suggested theory is general and with the knowledge of correct hyperfine coupling constants for the radical pair partners it can be used to calculate the activation yield precisely. Although it would be ideal to obtain hyperfine parameters from experiment, it is also possible to calculate the hyperfine coupling constants with advanced ab initio techniques using the Gaussian package.⁶ Our preliminary calculations of the hyperfine couplings in tryptophan radicals compare well with the values used in our paper.⁴ This sort of calculation creates the opportunity not only to refine our current picture of the radical pair mechanism in cryptochrome, but also to explore other possible radical pairs in the system.In light of work being done by Margaret Ahmad and co-workers (not yet published), it has been suggested recently that the radical pair reaction in cryptochrome may not occur between the FAD cofactor and tryptophan, but in some other radical pair within the protein. It is possible that rather than occurring in the FAD photoreduction process, the radical pair reaction actually takes place in the reoxidation reaction wherein the semireduced FADH is brought back to the oxidized FAD form. One possible radical pair in the back reaction is between FAD and an oxygen molecule which is thought to be involved in the reoxidization process. This radical pair is of particular interest because an oxygen radical would be devoid of hyperfine interactions. Such a radical pair, where one radical has no hyperfine coupling, would be consistent with studies on the effects of weak radio-frequency oscillating magnetic fields on migratory bird orientation. Thorsten Ritz and co-workers found that appropriate orientation behavior depended not only on the strength and angle of the oscillating field, but also that the minimum field strength necessary to disrupt orientation depended on the frequency of the oscillating field in a resonance-like behavior that would be predicted by just such a radical pair^7–9 (personal communication with T. Ritz).The scientific community is still a long way from a complete understanding of avian magnetoreception. The best that may be said of our understanding of it is that birds do demonstrably perceive and use magnetic field information, and that their responses to magnetic fields under different conditions—light intensity and color, magnetic field strength and presence and frequency of oscillating fields—belies a complex phenomenon which is probably the result of multiple receptors which interact in unknown ways.^10,11 However, disorientation responses to low-intensity oscillating magnetic fields are strongly suggestive of the involvement of a radical-pair mechanism, making the exploration of radical pair effects in cryptochrome a useful endeavor. Much remains to be done. Even if cryptochrome is confirmed as magnetoreceptor, it remains for biologists to determine how its signaling modulation enters into a bird''s sensory perception and ultimately its orientation behavior. Nevertheless, radical pair effects in cryptochrome seem promising as a possible source of magnetoreception in birds, and continued investigation may yet shed light on this complex behavior.     

Involvement of the sun and the magnetic compass of domestic fowl in its spatial orientation

Domestic chicks are able to find a food goal at different times of day, with the sun as the only consistent visual cue. This suggests that domestic chickens may use the sun as a time-compensated compass, rather than as a beacon. An alternative explanation is that the birds might use the earth's magnetic field. In this study, we investigated the role of the sun compass in a spatial orientation task using a clock-shift procedure. Furthermore, we investigated whether domestic chickens use magnetic compass information when tested under sunny conditions.Ten ISA Brown chicks were housed in outdoor pens. A separate test arena comprised an open-topped, opaque-sided, wooden octagonal maze. Eight goal boxes with food pots were attached one to each of the arena sides. A barrier inside each goal box prevented the birds from seeing the food pot before entering. After habituation, we tested in five daily 5-min trials whether chicks were able to find food in an systematically allocated goal direction. We controlled for the use of olfactory cues and intra-maze cues. No external landmarks were visible. All tests were done under sunny conditions. Circular statistics showed that nine chicks significantly oriented goalwards using the sun as the only consistent visual cue during directional testing. Next, these nine chicks were subjected to a clock-shift procedure to test for the role of sun-compass information. The chicks were housed indoors for 6 days on a light-schedule that was 6 h ahead of the natural light–dark schedule. After clock-shifting, the birds were tested again and all birds except one were disrupted in their goalward orientation. For the second experiment, six birds were re-trained and fitted with a tiny, powerful magnet on the head to disrupt their magnetic sense. The magnets did not affect the chicks’ goalward orientation.In conclusion, although the strongest prediction of the sun-compass hypothesis (significant re-orientation after clock-shifting) was neither confirmed nor refuted, our results suggest that domestic chicks use the sun as a compass rather than as a beacon. These findings suggest that hens housed indoors in large non-cage systems may experience difficulties in orientation if adequate alternative cues are unavailable. Further research should elucidate how hens kept in non-cage systems orient in space in relation to available resources.     

A three-state model for energy trapping and chlorophyll fluorescence in photosystem II incorporating radical pair recombination

The multiphasic fluorescence induction kinetics upon a high intensity light pulse have been measured and analyzed at a time resolution of 10 micros in intact leaves of Peperomia metallica and Chenopodium album and in chloroplasts isolated from the latter. Current theories and models on the relation between chlorophyll fluorescence yield and primary photochemistry in photosystem II (PSII) are inadequate to describe changes in the initial phase of fluorescence induction and in the dark fluorescence level F(0) caused by pre-energization of the system with single turnover excitation(s). A novel model is presented, which gives a quantitative relation between the efficiencies of primary photochemistry, energy trapping, and radical pair recombination in PSII. The model takes into account that at least two turnovers are required for stationary closure of a reaction center. An open reaction center is transferred with high efficiency into its semiclosed (-open) state. This state is characterized by Q(A) and P680 in the fully reduced state and a lifetime equal to the inverse of the rate constant of Q(A)(-) oxidation (approx. 250 micros). The fluorescence yield of the system with 100% of the centers in the semiclosed state is 50% of the maximal yield with all centers in the closed state at fluorescence level F(m). A situation with approximately 100% of the centers in the semiclosed state is reached after a single turnover excitation in the presence of 3-(3',4'-dichlorophenyl)-1,1-dimethylurea (DCMU). The lifetime of this state under these conditions is approximately 10 s. Closure of a semiclosed (-open) center occurs with low efficiency in a second turnover. The low(er) efficiency is caused by the rate of P(+) reduction by the secondary donor Y(Z) being competitive with the rate of radical pair recombination in second and following turnovers. The single-turnover-induced alterations in the initial kinetics of the fluorescence concomitantly with a 15-25% increase in F(o) can be simulated with the present so called three-state model of energy trapping. The experimental data suggest evidence for an electrostatic effect of local charges in the vicinity of the reaction center affecting the rate of radical pair recombination in the reaction center.     

An evaluation of the potential triggers of photoinactivation of photosystem II in the context of a Stern-Volmer model for downregulation and the reversible radical pair equilibrium model

Photoinactivation of photosystem II (PS II) is a light-dependent process that frequently leads to break-down and replacement of the D1 polypeptide. Photoinhibition occurs when the rate of photoinactivation is greater than the rate at which D1 is replaced and results in a decrease in the maximum efficiency of PS II photochemistry. Downregulation, which increases non-radiative decay within PS II, also decreases the maximum efficiency of PS II photochemistry and plays an important role in protecting against photoinhibition by reducing the yield of photoinactivation. The yield of photoinactivation has been shown to be relatively insensitive to photosynthetically active photon flux density (PPFD). Formation of the P680 radical (P680+), through charge separation at PS II, generation of triplet-state P680 (3P680*), through intersystem crossing and charge recombination, and double reduction of the primary stable electron acceptor of PS II (the plastoquinone, Q(A)) are all potentially critical steps in the triggering of photoinactivation. In this paper, these processes are assessed using fluorescence data from attached leaves of higher plant species, in the context of a Stern-Volmer model for downregulation and the reversible radical pair equilibrium model. It is shown that the yield of P680+ is very sensitive to PPFD and that downregulation has very little effect on its production. Consequently, it is unlikely to be the trigger for photoinactivation. The yields of 3P680* generated through charge recombination or intersystem crossing are both less sensitive to PPFD than the yield of P680+ and are both decreased by down regulation. The yield of doubly reduced Q(A) increases with incident photon flux density at low levels, but is relatively insensitive at moderate to high levels, and is greatly decreased by downregulation. Consequently, 3P680* and doubly reduced Q(A) are both viable as triggers of photoinactivation.