Quantum biology

Abstract

Recent evidence suggests that a variety of organisms may harness some of the unique features of quantum mechanics to gain a biological advantage. These features go beyond trivial quantum effects and may include harnessing quantum coherence on physiologically important timescales. In this brief review we summarize the latest results for non-trivial quantum effects in photosynthetic light harvesting, avian magnetoreception and several other candidates for functional quantum biology. We present both the evidence for and arguments against there being a functional role for quantum coherence in these systems.

Full text

REVIEW ARTICLE
PUBLISHED ONLINE: 9 DECEMBER 2012 | DOI: 10.1038/NPHYS2474
Quantum biology
Neill Lambert
1
*
, Yueh-Nan Chen
2
, Yuan-Chung Cheng
3
, Che-Ming Li
4
, Guang-Yin Chen
2
and Franco Nori
1,5
*
Recent evidence suggests that a variety of organisms may harness some of the unique features of quantum mechanics to gain
a biological advantage. These features go beyond trivial quantum effects and may include harnessing quantum coherence on
physiologically important timescales. In this brief review we summarize the latest results for non-trivial quantum effects in
photosynthetic light harvesting, avian magnetoreception and several other candidates for functional quantum biology. We
present both the evidence for and arguments against there being a functional role for quantum coherence in these systems.
B
efore the twentieth century, biology and physics rarely crossed
paths. Biological systems were often seen as too complex to be
penetrable with mathematical methods. After all, how could
a set of differential equations or physical principles shed light on
something as complex as a living being? In the early twentieth
century, with the advent of more powerful microscopes and
techniques, researchers began to delve more deeply into possible
physical and mathematical descriptions of microscopic biological
systems
1
. Some famous examples
1–3
(among many) include Turing
patterns and morphogenesis, and Schrödinger’s lecture series and
book ‘What is Life?’, in which he predicted several of the functional
features of DNA. The pace of progress in this field is now rapid, and
many branches of physics and mathematics have found applications
in biology; from the statistical methods used in bioinformatics,
to the mechanical and factory-like properties observed at the
microscale within cells.
This progress leads naturally to the question: can quantum
mechanics play a role in biology? In many ways it is clear that it
already does. Every chemical process relies on quantum mechanics
3
.
However, in many ways quantum mechanics is still a concept
alien to biology, especially on a scale that can have a physiological
impact
4
. Recent technological progress in physics in harnessing
quantum mechanics for information processing and encryption
puts the question in a different light: are there any biological systems
that use quantum mechanics to perform a task that either cannot be
done classically, or can do that task more efficiently than even the
best classical equivalent? In other words, do some organisms take
advantage of quantum mechanics to gain an advantage over their
competitors? Many attempts to find examples of such phenomenon
have been met with fierce criticism by both physicists and biologists
(see, for example, refs 5,6). However, over the past decade a range
of experiments have suggested that there may be some cases in
which quantum mechanics is harnessed for a biological advantage.
In what form do these quantum effects usually appear? In quantum
information, arguably the most important quantum effect is that
quantum bits can exist in superpositions whereas classical bits
cannot. In quantum biology, the role of quantum effects can be
subtle and will be described for each system we discuss in this
review. However, we may consider a biological system that exploits
coherent superpositions of states for some practical purpose to be
1
Advanced Science Institute, RIKEN, Saitama 351-0198, Japan,
2
Department of Physics and National Center for Theoretical Sciences, National Cheng Kung
University, Tainan 701, Taiwan,
3
Department of Chemistry and Center for Quantum Science and Engineering, National Taiwan University, Taipei 106,
Taiwan,
4
Department of Engineering Science and Supercomputing Research Center, National Cheng Kung University, Tainan 701, Taiwan,
5
Department of
Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA. *e-mail: nwlambert@riken.jp; fnori@riken.jp.
the clearest example of functional quantum biology. Some of the
systems we discuss are thought to fit into this category, but not all.
Here we present a very brief overview of some of these cases in
which quantum effects may assist or enhance a biological function.
Our goal is to give a clear basic introduction to each system and to
outline in what way quantum coherence or other quantum effects
might be harnessed by this system. We also attempt to present
the latest evidence both for and against these quantum effects
actually being functional. We begin by discussing the observation
of quantum coherence (superpositions) at room temperature in
the transport of excitation energy through photosynthetic systems.
We briefly summarize the latest research about the role this
coherence might play in the efficiency of photosynthesis in bacteria
and plants. We then move onto an entirely different system: the
radical-pair model used to describe the magnetic sense of some
avian species. The evidence supporting the radical-pair model
is primarily based on behavioural experiments, although very
recent in vitro experiments
7
on candidate radical pairs are in its
favour. The possibility that a macroscopic cognitive species could
respond to fundamentally quantum effects is fascinating, but a
cautious approach of course needs to be taken to fully verify
and understand this phenomenon. Finally, we will briefly discuss
several other biological functions in which quantum mechanics may
play a vital but less direct role, including long-range tunnelling
of electrons through proteins and the rapid photoisomerization in
photoreceptors. Some of these last examples could be considered as
a class of quantum phenomena in biological systems that depends
only on trivial quantization and discrete energy levels, not on
quantum coherence. A brief list of selected works that demonstrate
quantum effects in the examples we discuss here is shown in Table 1.
Quantum coherent energy transport in photosynthesis
Photosynthesis provides energy for almost all life on Earth. This
energy, in the form of photons, is absorbed by light-harvesting
antennas as an electronic excitation
8,9
. This excitation is then
transported from each antenna to a reaction centre where charge
separation creates more stable forms of chemical energy. The
precise biological structures and pigment constituents used, from
the antenna to the reaction centre and onwards, vary between
organisms
9,10
. For example, purple bacteria use highly symmetric
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NATURE PHYSICS DOI: 10.1038/NPHYS2474
REVIEW ARTICLE
Table 1 | Summary of a selection of the main experimental and theoretical works on functional quantum biology.
Biological system Reference
Photosynthesis Cryogenic-temperature quantum coherence
12,14
Ambient/room-temperature quantum coherence (FMO)
16
Ambient/room-temperature quantum coherence (algae)
15
Environment-assisted transport
19,26,27,29
Entanglement, tests of quantumness
48,49,103
Alternative views
46,47,51
Radical-pair magnetoreception Early proposals and evidence
60,66
Mathematical models
66,67
Indirect evidence (light dependence, magnetic field)
58,61,64,65,78,104
Experiments on radical pairs
7,71–73,105
Other examples Olfaction
92,93
Vision
97,99
Long-range electron transfer
81,82
Enzyme catalysis
84,85
ring-like structures for light harvesting
11
, whereas green plants
and cyanobacteria have photosystems with chlorophylls (light-
absorbing pigment molecules) that seem to be randomly arranged.
Moreover, most photosynthetic organisms use arrangements
of such chlorophyll molecules complexed with proteins, but
cyanobacteria and red algae use a unique chromophore called a
phycobillin. This diversity in light-harvesting apparatus reflects the
necessity for photosynthetic organisms to adapt in response to
different physiological conditions and natural habitats
10
. One of
the simplest and most well-studied examples is the light-harvesting
apparatus of green-sulphur bacteria (Fig. 1). These have a very
large chlorosome antenna that allows them to thrive in low-light
conditions. The energy collected by these chlorosomes is transferred
to the reaction centre through a specialized structure called the
Fenna–Matthews–Olson (FMO) complex. Owing to its relatively
small size and solubility in water, the FMO complex has attracted
much research attention and as a result has been well characterized.
What is remarkable is the observed efficiency of this and other
photosynthetic units. Almost every photon (nearly 100%) that is
absorbed is successfully transferred to the reaction centre, even
though the intermediate electronic excitations are very short-lived
(∼1 ns). In 2007, Fleming and co-workers demonstrated evidence
for quantum coherent energy transfer in the FMO complex
12
, and
since then the FMO protein has been one of the main subjects of
research in quantum biology.
The FMO complex itself normally exists in a trimer of
three complexes, of which each complex consists of eight
bacteriochlorophyll a (BChl-a) molecules. These molecules are
bound to a protein scaffold, which is the primary source of
decoherence and noise, but which also may assist in protecting the
coherent excitations in the complex and play a role in promoting
high transport efficiency
13
. The complex is connected to the
chlorosome antenna through what is called a baseplate. Excitations
enter the complex from this baseplate, exciting one of the BChl
molecules into its first singlet excited state. The molecules are in
close proximity to one another (roughly 1.5 nm), enabling the
excitation energy to transfer from one BChl molecule to another,
until it reaches the reaction centre.
Quantum properties. As mentioned, direct evidence for the pres-
ence of quantum coherence over appreciable length scales and
timescales in the FMO complex was observed by Engel et al.
12
in
2007. They presented the spectroscopic observation, at low tem-
perature (77 K), of quantum coherent dynamics (that is, coherent
superpositions evolving in time) of an electronic excitation across
multiple pigments within the FMO complex. Since that time a huge
body of literature has arisen, and further experiments
14–17
suggest
that the coherence is non-negligible even at room temperature,
for up to 300 fs. If quantum coherent dynamics are present at
room temperature in the FMO complex (and other parts of a
light-harvesting apparatus), what purpose does it serve? As we
will discuss in the next section, a higher transport efficiency
18
is
the typical answer, and a large variety of theoretical models have
been employed to explain if, how and why nature uses quantum
coherence to move this electronic excitation through the FMO
complex
19
more efficiently than classically possible. The closest
equivalent classical model against which one can compare such
quantum effects is the Förster model that treats the transfer of
the excitation between sites as an incoherent rate, and neglects
all coherences or superpositions between sites. One should also
note that the excitonic nature of the system, manifested in the co-
herent delocalization of photoexcitation among several molecular
sites, is also important and strongly influences the spectroscopic
properties and energy relaxation of the complex, which should be
discussed independently
20–22
.
At first the notion of observing quantum coherence at room
temperature in a biological system may be quite surprising.
However, even a naive comparison
23,24
of the relevant energy scales
suggests that in fact quantum effects could be important in this case.
These energy scales are the environment’s temperature (∼300 K),
the coupling strength between the excitation in the FMO complex
and the protein environment (∼100 cm
−1
) and the electronic
coupling strength that transfers the excitation between BChl
molecules (∼100 cm
−1
). Precisely calculating or measuring the
energies and coupling strengths in a photosynthetic complex such as
FMO requires a combination of spectroscopy and ab initio quantum
chemistry methods based on atomistic models
23,24
. Fortunately
FMO is one of the most well-studied models, and generally speaking
both measurements and calculations of the coupling strengths and
energies agree quantitatively
25
.
Environment-assisted transport. One can argue that the goal of
the FMO complex is to maximize the efficiency of transporting a
single excitation from the BChl-a molecule nearest the antenna to
the BChl-a nearest the reaction centre (see Fig. 1). To this end,
apart from the energy and couplings mentioned earlier, there are
two other important timescales to be considered. One is the rate
at which the excitation leaves the target molecule and enters the
reaction centre (∼1 ps). The other is the rate at which the excitation
in any of the BChl is lost owing to fluorescence relaxation (∼1 ns).
It is this latter rate that the excitation must beat, in its race to
reach the reaction centre. Remarkably, the excitation is almost
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REVIEW ARTICLE
NATURE PHYSICS DOI: 10.1038/NPHYS2474
FMO
O
M
M
M
M
M
M
M
M
F
M
F
F
F
F
F
F
M
O
O
O
O
O
O
Chl-a
BChl-a
reaction
centre
Putative transporter
ab
Periplasm
Cytoplasm
Antenna
BChl-c
2
1
3
4
5
6
7
Initial excitation site 1
Light
Site 3 is
coupled to
reaction centre
CsmD
CsmD
CsmD
Csm
C
CsmF
Csm
C
Csm
X
CsmJ
CsmA protein baseplate
CsmE
Csml
CsmB
FMO
Pre
Csm
A
FMOFMO
Figure 1 | A quantum machine for efficient light-energy harvesting. The well-studied FMO complex in the light-harvesting apparatus of green-sulphur
bacteria exhibits some signatures of quantum coherent energy transfer. Experimental and theoretical works have scrutinized the precise mechanisms and
quantumness of the energy transduction through this protein. Research in this field might reveal new quantum mechanical principles for improving the
efficiency of energy harvesting in biology. a, Diagram of the photosynthetic apparatus of green sulphur bacteria, including its antenna, energy-conducting
baseplate and FMO complexes, and reaction centre. The chlorosome antenna (green discs) is composed of roughly 200,000 BChl-c molecules, and is an
exceptionally large structure that is designed to capture as many photons as possible in the low-light conditions the bacteria thrive in. Sunlight creates an
excitation in this antenna that is transferred (red arrows) to the reaction centre through one of several FMO complexes. b, The BChl-a arrangements of one
of the FMO pigment-protein complexes through X-ray diffraction. The FMO complex comprises eight (although only seven are shown here)
bacteriochlorophyll-a (BChl-a) molecules that are encased in a protein scaffolding (not shown). The excitation arrives from the chlorosome at one of the
sites, typically thought to be the site denoted as 1. This excitation is then transported from one BChl molecule to the next. Once it arrives at site 3 it can
irreversibly enter the reaction centre and start a charge-separation process.
always transferred to the reaction centre faster than it can be lost
to fluorescence relaxation.
How then might quantum coherence in the transport process
help the excitation get to where it needs to go? Several physically
plausible explanations have been proposed. Some theoretical
approaches focused on treating the protein environment as a
Markovian and uncorrelated thermal bath. This meant that each site
in the FMO complex feels its own individual random environmental
noise. Such treatments
26,27
suggest that the combination of the
coherence of the excitation transport and the thermal environment
creates a level-broadening effect. Simple models
19,26–28
predict that
this allows the excitation to easily escape any local minima in
the uneven excitation energy landscape of the FMO complex.
Other authors
29
have demonstrated that the coherent dynamics
of the excitation can also conspire with the rapid (incoherent)
rate of transfer from the site closest to the reaction centre to
the reaction centre itself. They showed that this collaboration
between quantum coherent evolution and incoherent tunnelling
creates a high-efficiency energy trap, drawing the excitation
into the reaction centre.
Recent progress. Much of the latest theoretical work on the FMO
complex has been on the nature of the protein environment.
As mentioned earlier, the simplest treatment is to consider each
molecule to be in contact with an uncorrelated Markovian thermal
bath. However, because of the strong coupling (100 cm
−1
) between
the electronic excitations and nuclear motion in the protein
environments around the FMO (refs 30,31) complex, the consensus
is that this treatment is insufficient. There are three approximations
that may break down in this limit: the perturbative-coupling
approximation (sometimes termed the Born approximation in
system–bath models), the memory-less (or Markovian) approxi-
mation and the independent-bath approximation. A great deal of
work has been done on understanding what happens when these
three approximations are relaxed
13,19,31–38
.
Evidence, both theoretical and experimental, does hint that the
non-perturbative and non-Markovian environment can enhance
both the coherence time
19
and the efficiency of the excitation
transport
39
. Similarly, a recent analysis argued that coherent vi-
bronic excitations may play an important role in the coherent oscil-
lations seen in experiments
40–42
. However, the role of correlations
between the baths of different BChl molecules is still not fully un-
derstood. Recent work
39
showed that the correlations can in princi-
ple improve the efficiency in some cases, but can also decrease it, and
that there is an optimal overall noise level. In comparison, molec-
ular dynamics simulations
43,44
indicated that the uncorrelated-bath
approximations may hold, and thus independent-bath models may
be sufficient to explain any enhancement in efficiency. Ultimately,
the real role of correlated-bath effects and vibronic excitations in
photosynthetic units, FMO and otherwise, is still not clear, and
requires further experimental studies.
Despite the positive results and predictions we discussed in the
last section, recent analysis has shown that the efficiency benefits
provided by quantum models in comparison to the classical Förster
model (which can be seen as a perturbative expansion of the
quantum one, with no quantum coherence) may be only a few
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NATURE PHYSICS DOI: 10.1038/NPHYS2474
REVIEW ARTICLE
per cent
45
. However, even a few per cent improvement in efficiency
may be vital for a plant or bacteria attempting to survive in
low-light conditions. Is the Förster model the only classical model
against which we should compare efficiencies? For example, recent
work
46,47
proposed an alternative model of the type of transport
that occurs in the FMO complex that predicts oscillations and
quantum-like behaviour, but is entirely classical. Several studies
48,49
have proposed ways to unambiguously verify that quantum effects
are the correct way to describe the observed experiments, although
they are as yet beyond experimental implementation.
One should also note that most of these results omit the recently
discovered eighth BChl-a molecule
50
. Ritschel et al.
36
recently
studied the full FMO trimer, including the eighth BChl molecule
in each complex in the trimer. They found that if one considers this
new molecule as the site that accepts the excitation from the antenna
(which may be the case because it is located close to the baseplate)
almost no coherent exciton dynamics occur because of its weak
coupling and large energy detuning to the other sites. In this case
they observed only exponential decay in the population dynamics.
On the other hand, molecular dynamics simulations indicate that
the quantum coherent effects in a single FMO were larger than
expected because of an increase in the coupling strength attributable
to the influence of the other monomers of the trimer
51
. Despite this,
they
51
hypothesized that fast site-energy fluctuations (for example,
due to thermal effects) are the main source of efficient transport, not
the coherent quantum effects predicted by other studies.
Open problems. The observation at room temperature of quantum
effects in a biological system
14–17
is itself remarkable. A great deal of
evidence does suggest that in principle such coherence can enhance
the efficiency of photosynthetic units, such as the FMO complex,
even if just by a few per cent. Still, more work remains to be
done to completely understand and validate this role. For example,
no in vivo observations of coherence have yet been performed. In
experiments, the excitations are created with laser pulses. In vivo, the
excitations are generated by incoherent sunlight or through energy
transfer from another antenna complex. Does quantum coherence
still play a significant role in this situation? In addition, it is not
yet clear whether the small enhancement in efficiency predicted by
the quantum models provides a biological advantage
4,45
. Certain
species, such as green sulphur bacteria or algae, live in very low-light
conditions
15
. In such cases, any small enhancement in efficiency
may be biologically important.
In higher plants the photosynthetic apparatus tends to be more
complex and seems in some ways less ordered. This suggests that the
energy landscape of these complexes is very rugged
15
. Thus, it may
be that the quantum coherence seen in FMO plays an even more
important role in maintaining high transport efficiency in such
complex systems. Observation and validation of this hypothesis
is one of the largest open problems in this field. For example,
recent work
52
applied a renormalization analysis and found results
that suggest the coherence in larger networks is limited by static
disorder and not thermal effects. Similarly, an investigation
53
of the excitation transfer dynamics in the large chlorosome
antenna of green sulphur bacteria found that the disordered
energy landscape washed out all excitonic coherences. Inevitably,
a broader understanding of the role of coherence in a larger
range of photosynthetic complexes and organisms (for example,
LH-1, LH-2 and LHCII) is needed. Typically, robustness
54,55
and
photoprotection
56,57
are thought to be more of a natural necessity,
rather than high efficiencies.
Avian magnetoreception
Magnetoreception is the ability of some migrating species to
navigate using the Earth’s magnetic field. The precise mechanism
used, and its features, seem to vary greatly from animal to animal. A
mechanism based on magnetite, deposits of magnetic iron minerals,
has been used to describe this ability in some organisms
58
(although
recent reports suggest that, at least in pigeons, these deposits are
in fact macrophages and play no role in the magnetic sense
59
).
However, behavioural experiments on other organisms seem to rule
out the magnetite-based mechanism. For example, European robins
have a magnetic sense that acts as an inclination compass insensitive
to polarity
60
, whereas most (although not all) magnetite-based
compass models operate as a polarity-sensitive sense
58
.
A series of behavioural experiments have revealed several more
intriguing properties of this non-polar magnetic sense. Again, in
European robins (and some other species) the navigation sense
was shown to be photoreceptor based, that is, dependent on
the presence of certain frequencies of ambient light
58,61
. It was
also shown to be sensitive to changes in the intensity of the
external magnetic field
58,62
, but that it readjusted over time to
these changes
62,63
. Finally, it has been shown that the navigation
sense was disrupted by magnetic pulses
64
, and very weak external
oscillating magnetic fields
65
.
In response to the early experiments showing the light-
dependent properties of magnetoreception, Schulten et al.
66
proposed the radical-pair mechanism as a plausible biological
chemical-compass. It was already well known that radical pairs
can mediate magnetic-field-sensitive and light-activated chemical
reactions, but up to that point only with external fields much
stronger than the Earth’s. The standard radical-pair model can
be summarized as follows, although the exact details and steps
involved can be quite complex: a radical pair is (typically) a pair of
bound molecules that each has an unpaired electron. These pairs are
created, by a photochemical process, in spin-correlated states; that
is, singlets or triplets. The state of these spins then evolves under
the combined effect of the Earth’s weak magnetic field and internal
nuclear hyperfine interactions with the host nuclei. Finally, the
rate of charge recombination depends on the spin of the separated
charges, directly influencing the reaction products of these radical
pairs. These differing reaction products are in principle biologically
detectable. Thus, if the relative weights of the singlet and triplet
states are sensitive to the angle of the external (geo-magnetic) field,
the reaction products will be also, leading to a magnetic compass.
The precise nature of the radical pair that might be involved
in this mechanism is as yet unknown. The prime suspect is a
series of radical-pair reactions that are known to occur within
cryptochromes
67,68
, which, because they are resident in the eye,
could induce a visual signal by which the host species navigates.
Simple models
69
of these kinds of radical pair, using highly
anisotropic nuclear spin configurations, are sufficient to show
that in principle the radical-pair reaction products are sensitive
to the inclination of the external field, and can reproduce the
disruptive effect of time-dependent external magnetic fields at
radio frequencies.
Quantum properties. How then might this mechanism be de-
scribed as an example of quantum biology? Although spin singlet
(S
0
) and triplet (T
0
) states are certainly ubiquitous in atomic and
molecular physics, they are also some of the most quantum of
states. The T
0
and S
0
states are equivalent to Bell states, maximally
entangled states that are highly desired in quantum information
schemes. How much of a role does the quantum nature of these
states play in this mechanism? A recent analysis of the lifetime and
decoherence of these states in the radical-pair mechanism
70
suggests
that the answer is quite complex. Essentially, some dephasing
models leave the sensitivity of the radical-pair reactions to the
external fields mostly intact. However, any kind of strong dephasing
prevents the radical-pair model from being able to explain the
disruptive effects of very weak oscillating fields. In addition, because
these disrupting fields were so weak, of the order of 50–100 nT, they
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Singlet
Triplets
Singlet
products
Triplet
products
Electron spin
Nuclear spin
Retina
European Robin
Electron
spins
Nuclear
spin
T
+
T
¬
B
T
0
Angle
Reference
With noise
π/8 π/4 3π/8 π/2
κ = 10
6
s
¬1
κ = 10
5
s
¬1
κ = 10
4
s
¬1
Reference, κ = 10
6
s
¬1
Oscillatory field on
1/ = 1 ms
1/ = 100 μs
1/ = 10 μs
Singlet yield Singlet yield
0.25
0
π/8 π/4 3π/8 π/2
0
0.30
0.35
0.40
0.25
0.30
0.35
0.40
κ
κ
e
f
a
bc d
¬¬
+
+
θ
Angle
θ
Γ
Γ
Γ
Figure 2 | The avian quantum compass. The radical-pair mechanism for avian magnetoreception explains many of the behavioural studies performed on
some species of migrating birds. Key properties of the proposed radical-pair model for avian magnetoreception are dependent on quantum mechanics;
therefore, this may represent a functional piece of biological quantum hardware. a, A schematic of the radical-pair mechanism for magnetoreception that
could potentially be employed by European robins and other species. It is thought to occur within cryptochromes, proteins residing in the retina. There are
three main steps in this mechanism. First, light-induced electron transfer from one radical-pair-forming molecule (for example, in a cryptochrome in the
retina of a bird) to an acceptor molecule creates a radical pair. b,c, Second, the singlet (S) and triplet (T) electron-spin states inter-convert owing to the
external (Zeeman) and internal (hyperfine) magnetic couplings. d, Third, singlet and triplet radical pairs recombine into singlet and triplet products,
respectively, which are biologically detectable. e, Singlet yield (a measure of the probability of the radical pair to decay into a singlet state) as a function of
the external-field angle θ in the presence of an oscillatory field (taken from Gauger et al.
70
). The blue top curve shows the yield for a static geomagnetic
field (B
0
= 47 µT), and the red curves show the singlet yield in the case where a 150 nT field oscillating at 1.316 MHz is superimposed perpendicular to the
direction of the static field. The sensitivity of the compass can be understood as the difference in the yield between θ = 0 and θ = π/2. An appreciable
effect on this sensitivity occurs once κ (the decay rate of the radical) is of order 10
4
s
−1
. f, Singlet yield as a function of the magnetic field angle θ for
differing noise magnitudes (from Gauger et al.
70
). The blue curve shows the optimal case with no noise (but with decay rate κ = 10
4
s
−1
). The red curves
indicate that a general noise rate of 0 > 0.1κ has a detrimental effect on the sensitivity. Both of these results indicate that the electron spin state must have
a remarkably long coherence time.
demand that the radical-pair model maintain quantum coherence
of its spins for tens of microseconds (see Fig. 2). It seems then that
this disruption due to external fields is a purely quantum effect,
and that both the quantum coherence and entanglement properties
must be sustained for timescales ‘exceeding the best man-made
molecular systems’
70
. Ironically, although these experiments with
disruptive time-dependent fields are some of the best evidence so
far for the radical-pair model, they also set challenging criteria for
spin coherence and radical-pair lifetimes to match.
Recent progress. There is a long history of experimental studies
of magnetic-field sensitivity on radical-pair reactions in solution
71
.
However, in those early experiments sensitivity was observed only
for field strengths between 10 mT and several tesla, much larger than
Earth’s (∼50 µT). Within the past decade, the observed sensitivity
of such reactions has gradually increased. Woodward et al.
72
studied
the photoactivated reaction of pyrene and N ,N -dimethylaniline in
solution, and applied external oscillating fields of order ∼500 µT.
This resulted in a change of concentration of reaction products of
25%. Maeda et al.
73
reported the most sensitive radical-pair reaction
so far: a triad composed of linked carotenoid (C), porphyrin (P)
and fullerene (F). They found magnetic field sensitivities down
to 50 µT, of the same order as the geomagnetic field. However,
there was an angular dependence (between the molecule and
the externally applied field) only for stronger field strengths, of
the order of milli-tesla.
As mentioned earlier, cryptochrome, a ubiquitous photoactive
protein that resides in the eye and is also present in plants and
bacteria, is a prime candidate as the host of the radical-pair
mechanism. Ritz et al.
67
originally proposed that it may play a role
as the host of the magnetically sensitive radical-pair reaction. Very
recent results
7
(again in vitro) have successfully shown magnetically
sensitive radical-pair reactions in a cryptochrome extracted from
the plant Arabidopsis thaliana. They saw a change in yields of order
25% at 30 mT and 1% at 1 mT. Although this is still much larger
than the geomagnetic field, the authors speculate that the response
in vivo may be much stronger.
The question of how the sensitivity might be maximized by
different configurations and parameters within the radical-pair
model has also been addressed in recent theoretical work. Cai et al.
74
argued that in fact a highly anisotropic but weak nuclear hyperfine
interaction is preferable, and produces the overall maximum for
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NATURE PHYSICS DOI: 10.1038/NPHYS2474
REVIEW ARTICLE
reasonable choice in radical-pair lifetimes. Most other studies
have used a stronger choice of nuclear hyperfine coupling. In
addition, recent works
70,74
discuss the effect of environmental noise
on the sensitivity and, as mentioned earlier, illustrate that the
behaviour can be counter-intuitive. One proposal
75
argued that the
behavioural experiments strongly suggest that quantum coherence
is present within the radical-pair compass, but to a degree that is
not actually required for normal functioning of the compass. To
explain why high levels of quantum coherence might be useful,
they suggested a modified, and rather speculative, version of the
radical-pair model. In their new scheme, a biologically detectable
signal is not given by reaction products but by a long-lived dipole
moment. In their proposal, the quantum coherence improves the
sensitivity to external fields in a very direct way.
Recent results show that pigeons have an identifiable neural
substrate for processing magnetic sense information
76
. This sub-
strate was shown to respond to several different kinds of magnetic
sense information: direction, intensity and polarity. In addition,
previously it was thought
77
that the magnetic sense of pigeons was
mediated by magnetite deposits in their beaks. However, further
work
59
has recently shown that these deposits are in fact a kind of
macrophage, and play no role in the magnetic sense. These results
do not directly affect the implications of the radical-pair model, as
it was already well known that pigeons have a polarity-based sense.
However, it does indicate that similar experiments on the neural
properties of organisms in which the radical-pair model is hoped to
exist are vital, and may shed further light on whether radical pairs
do or do not play a role in magnetoreception.
Open problems. The main obstacle to verification of the radical-
pair model is to show that cryptochromes (a host for radical pairs
in the eye
67,68
), or some other candidate radical pair, have the
right properties to respond to the extremely weak geomagnetic
field
7,63,68
. To do so they must have a sufficiently long lifetime
(≥1 µs), and a sufficiently anisotropic nuclear spin coupling (or
some other anisotropic mechanism to couple the singlet and triplet
states). An obvious next step is to show that a radical pair, such as
cryptochrome, can exhibit sufficient sensitivity to external fields in
conditions that mimic those that might occur in vivo
7
.
Another demanding aspect is the even longer lifetime and low
environmental noise, or spin dephasing, that seem to be needed
to explain the disruptive effects due to weak radiofrequency fields
observed in behavioural experiments (see Fig. 2). As mentioned,
this disruptive effect has been seen in robins
65,78
for fields as weak
as 50 nT. Typically, the effect of such a weak field can be observed
only on a timescale of 100 µs, demanding that the radical pairs must
have an equally long coherence time. A recent theoretical work
79
hypothesized that a lifetime of 5 µs is sufficient to explain these
experiments. Their argument was based on the observation that,
in a theoretical model, the weak oscillating field can cause a small
change in the overall singlet yield. A similar change occurs when
an additional static field is applied. By comparing this observation
to some behavioural experiments that observed magnetic sense
disruption when static fields
62,63
were applied, they argue that there
is a small window of operation (in terms of magnitude of singlet
yield) outside of which the sense becomes disrupted.
Apart from these microscopic studies, one may imagine several
more complex behavioural experiments to bolster the evidence
for the radical-pair model
63,68
. One intriguing possibility is that of
applying quantum control to mimic the effect of the static field.
An appropriate choice of time-dependent external fields should,
in principle, have the same effect on the radical-pair model as the
static fields
74,80
. If it could be shown that the birds are able to
respond to the encoded directional information in these oscillating
fields, this would strongly imply that the radical-pair model does
play a role. Such effects would be almost impossible to describe
using any other magnetic field transduction mechanism. Thus, an
experimental example of quantum control of birds would represent
strong evidence in favour of the radical-pair scheme.
Finally, almost nothing is known about the biological circuitry
connecting the radical-pair yield to a neurological signal. Some
proposals
67,69
argue for an optical/visual signal, particularly because
of the role cryptochromes may play. However, a deeper under-
standing of the chain of events connecting the singlet/triplet yield
to a neurological signal is vital to understand why the magnetic
sense (if it is transduced by radical pairs) is so sensitive to small
changes in this yield.
Other quantum biological systems
Apart from photosynthesis and magnetoreception there are already
several other biological processes in which quantum effects are
thought to play a vital but more indirect role. In this section, we
examine briefly a few of these examples.
Tunnelling in biological systems. Tunnelling of light-mass parti-
cles is a quintessential quantum effect well studied even at the dawn
of quantum physics. In biology, it is evident that long-range electron
tunnelling
81–83
and hydrogen tunnelling
84,85
play important roles
in biological redox reactions and enzyme catalysis, respectively.
Experimental data
81,86
have clearly demonstrated that long-range
electron transfer between redox centres in proteins separated by dis-
tances of the order of 15–30 Å plays important roles in respiration
and photosynthesis. These processes could depend critically on the
specific electron transfer pathways encoded in the protein structures
and specific intermediate relays in the amino-acid sequences
81,86,87
.
Observations of long-range electron transfer through proteins
often show exponential distance dependence as well as weak
temperature dependence
81,83
, providing a strong indication that
a single-step tunnelling mechanism is responsible for these
biological processes. It is remarkable that such long-distance
electron transfer in biology occurs through quantum mechanical
tunnelling, because electron tunnelling over such long distances
would be impossible in vacuum. Still, whether or not the electron-
conducting proteins have evolved specifically for coherent electron
tunnelling remains a major open question
81,86,87
. Quantum theory
predicts that electron transfer pathways could interfere with one
another, and there is evidence that electron transfer through
the azurin protein depends critically on quantum interferences
between multiple distinct pathways
88,89
. Several recent works
90,91
proposed a molecular which-way interferometer experiment in
which localized normal modes coupled to bridge atoms can be
vibrationally excited to control interferences between transfer
pathways. Such experimental probes of pathway coherence in
electron-transfer proteins in a single-protein level would provide
decisive proof for the quantumness of the electron tunnelling
process. In addition, another biological function that might
depend on electron tunnelling concerns our sense of smell.
Recent experimental data suggest that the traditional models of
a docking-type mechanism, based solely on the size and shape
of odorant molecules, is inadequate to explain our sensitivity
of olfaction. Turin
92
proposed a mechanism in which phonon-
assisted inelastic tunnelling of an electron from a donor to
an acceptor mediated by the odorant molecule gives a further
level of selectivity to the process. A recent model proposed by
Brookes
93
expanded on this idea, and presented evidence that
such a mechanism fits the observed features of smell. However,
it should be noted that their model is semi-classical, and does
not depend directly on quantum coherence or superposition.
Thus, so far it sits on the border of what might be classified
as quantum biology.
Hydrogen tunnelling also plays an important role in a wide
range of biological enzymatic catalytic reactions
84,85
. Observations
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REVIEW ARTICLE
NATURE PHYSICS DOI: 10.1038/NPHYS2474
of strong intrinsic kinetic isotope effects in enzymatic reactions
have clearly demonstrated nuclear quantum effects in enzymes
84,85
.
However, in enzyme catalysis, a large portion of the quantum
improvement over the classical catalytic rates could be attributed
to the zero-point energy that gives a quantum correction to the
barrier height and the hydrogen tunnelling rates
85
. Such nuclear
quantum effects actually represent a class of quantum phenomena
in biological systems that depends only on trivial quantization and
discrete energy levels, not quantum coherence.
Photoreceptors. For the survival of many organisms, the ability
to sense and respond to various light conditions through light-
sensing proteins plays a crucial role. Such biological photoreceptors
contain chromophores that absorb photons and then undergo
rapid chemical transformation on their excited states, eventually
leading to light-induced signal transduction
94,95
. Owing to the
quantum nature of electronically excited states and nuclear
quantum coherences that often accompany excited-state molecular
dynamics, quantum mechanics is required to describe these
photoactivated dynamics in biological photoreceptors
96
.
The prototypical example here is the trans-membrane pro-
tein called rhodopsin that is responsible for the primary event
in vision. Rhodopsin contains a retinal molecule that undergoes
photoisomerization following light absorption. This photoisomer-
ization reaction
97
proceeds with remarkable rate (<200 fs, one
of the fastest chemical reactions known) and high specificity
(quantum yield of ∼0.65). It then triggers a protein conforma-
tional change that is subsequently amplified by signal-transduction
proteins, leading to the visual signal. The remarkably rapid and
efficient photoactivated one-way reaction dynamics in rhodopsin
is a result of the ultrafast coherent wave-packet dynamics that
depends critically on the quantum mechanical positioning of
the excited-state potential energy surfaces and the symmetries
of the electronic states
94,95,98–100
. In these systems, nature most
likely uses trivial quantum effects to shape the ground-state and
excited-state potentials of the photoreceptors to achieve high
specificity and yield.
Evidence of quantum-coherent effects (for example, the inter-
ference between wave packets) in photoisomerization of natural
photoreceptors is still lacking. Intriguingly, coherent optical control
of retinal isomerization in bacteriorhodopsin, a protein related to
vertebrate rhodopsins, has been demonstrated experimentally
101,102
.
Although this is directly relevant only to experiments with lasers,
it is interesting to determine whether coherent light can be used
to take advantage of the quantum nature of the photoreceptors to
direct chemical dynamics through coherent interferences of nuclear
wave packets to achieve even higher reaction yields.
Conclusions
Here, we return to the question we posed in the introduction to this
short review, has nature already beaten us in leveraging quantum
effects to achieve something an equivalent classical system cannot?
Certainly nature can harvest energy extremely efficiently, sense
weak magnetic fields and create human minds complex enough
to even be asking these questions. Now preliminary evidence
suggests that nature may also leverage quantum effects to enhance
the efficiency, or functionality, of some of these amazing feats.
There is some evidence of room-temperature quantum effects
(superposition and coherence) on physically important timescales
in the electronic excitation transfer process in photosynthesis.
Theoretical models suggest that this may enhance the overall
efficiency of this transport, although larger or more complex
systems need to be studied in more detail to ascertain both how vital
and universal this enhancement is.
In the case of the avian magnetoreception, if the interpretation
of behavioural experiments on certain avian species is correct, then
it could be that the ability of these species to navigate by the Earth’s
magnetic field is transduced by a magnetically sensitive chemical
reaction that relies on certain subtle quantum effects. Strong
evidence in favour of this model could come from further in vitro
experiments on candidate radical pairs that show anisotropic
sensitivity to very weak magnetic fields, or more sophisticated
behavioural experiments. Finally, there are already a range of other
functional biological systems that may rely on processes that can
be thought of as fundamentally quantum (although as yet in a less
direct way than magnetoreception and photosynthesis).
The fact that there is even the possibility of a functional role
for quantum mechanics in all of these systems suggests that the
field of quantum biology is entering a new stage. There may be
many more examples of functional quantum behaviour waiting
to be discovered. In addition, there are several obvious broader
questions that arise: can we learn from nature’s example and
develop bio-mimetic quantum technologies for efficient energy
harvesting, long-coherence-time chemical reactions and so on?
Alternatively, if it turns out that non-trivial quantum coherent
effects do not play a strong functional role in biology, then this
begs the question ‘why not?’ Are all quantum effects destroyed
or limited by the hot and wet biological environment, or do
these quantum effects simply not provide a biologically significant
advantage over classical equivalents?
Received 1 July 2012; accepted 4 October 2012; published online
9 December 2012
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Acknowledgements
We thank A. Pisliakov, L. Valkunas, E. Gauger, P. Nation, S. Darroch,
I. Mahboob, A. Y. Smirnov, A. Ishizaki, K. Jacobs and S. De Liberato
for helpful discussions and feedback. Y-C.C. thanks the National Science Council,
Taiwan (Grant No. NSC 100-2113-M-002-004-MY2), the National Taiwan University
(Grant No. 10R80912-5) and the Center for Quantum Science and Engineering
(Subproject: 10R80914-1) for financial support. Y-N.C. thanks the National Science
Council, Taiwan (Grant No. NSC 101-2628-M-006-003-MY3) for financial support.
F.N. acknowledges partial support from the ARO, JSPS-RFBR contract No. 12-02-92100,
MEXT Kakenhi on Quantum Cybernetics and the JSPS-FIRST Program. C-M.L
thanks the National Science Council, Taiwan (No. NSC 101-2112-M-006-016-MY3, No.
NSC 101-2738-M-006-005 and No. NSC 103-2911-I-006 -301) for financial support.
Additional information
Reprints and permissions information is available online at www.nature.com/reprints.
Correspondence and requests for materials should be addressed to N.L. or F.N.
Competing financial interests
The authors declare no competing financial interests.
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