Wednesday, 18 April 2012

A quantum compass for birds

During migration, birds like the European robin use the earth's natural magnetic field to know which direction to go. Like with a compass, such migratory birds can sense if the earth's magnetic field changes direction as they fly. But beyond that, they can also detect subtle differences in the strength of magnetic field. This ability to perceive magnetic fields and use them for navigation is called magnetoreception. It is an ability shared by other organisms such as sea turtles, fruit flies, honey bees, and even certain bacteria. Because different organisms detect magnetic fields in different ways, we focus on the case of birds, where a simple hypothesis is known.

The most widely accepted explanation for magnetoreception in birds is called the radical pair (RP) mechanism. If it's proven correct, it demonstrates one of the ways in which a living system exploits quantum effects to perform certain biological tasks.

So what's the basic idea behind the RP mechanism? The RP refers to two molecules that are bound together, one is called a donor (D) while the other is an acceptor (A). The mechanism says that there is a pair of electrons-- one electron with the donor molecule, the other one being the electron shared with the acceptor molecule--where the combined quantum state of the electron spins will either be a singlet or a triplet.  

(Singlet and triplet states are distinguished by the total spin angular momentum they carry: a singlet state has total spin zero while the three triplet states have total spin one. )

If there are many of these pairs of molecules, then a certain fraction of them has the electron pair in a singlet state while the rest are in a triplet state. The idea then is that birds can tell the fraction of singlet states and this tells them how strong the magnetic field is at each location. 

The quantum part has to do with the fact that the singlet state is an entangled quantum state, that is, the state describes both electrons together but not each electron individually. This means that in order for the birds' internal compasses to work, the quantum entanglement between the electrons must persist for a time that's extraordinarily long for a noisy biochemical environment.

Now for some specifics. Here we consider only the situation where we have a pair of electrons and the nucleus of one of the molecules, say the donor molecule. We also suppose that the nucleus (N1) of the donor molecule interacts only with one electron (e1). This simplified picture captures all the essential features of the bird's quantum compass.

The magnetic field is sensed through the bird's eye, that is, the orientation and strength of the magnetic field is received as light particles or photons in the bird's eye. The photon hits the radical pair found in a so-far-unknown protein (believed to be a chryptochrome sensitive to blue light) in the bird's retina, the tissue in the back wall of the eye where light triggers nerve impulses needed for vision.

When the donor molecule is hit by a photon, it gets excited (D*) and gives away one of its electrons to the acceptor molecule, in such a way that there is a pair of electrons shared by the donor and acceptor whose spins forms either a singlet or triplet state. Which state it chooses depends on the interaction of the electron spins (e1 and e2) with the surrounding magnetic field (B) in what's called the Zeeman effect. To make things easy, we may assume that the electron spins always start in a singlet state.

Recall that we also have the interaction between the nucleus and an electron, which is called the hyperfine interaction. This hyperfine interaction causes the singlet state to change to any of the triplet states and back again. But the average effect of the interaction is to orient the nucleus so that it aligns with the direction of the magnetic field. So while the magnetic field strength is obtained from the fraction of singlet states, its direction is obtained from the orientation of the nuclear spin. 

(More precisely, birds only know the inclination of the magnetic field, that is, the orientation of the line where the north and south poles are. However, it does not perceive which pole is north or south. In practice, a bird has to check if it's upright or upside-down relative to the ground to know where the magnetic north pole is.)

How do we know the RP model makes sense? It helps to look at the numerical results shown above. (The picture included in the graph shows a European robin.) 

The number k in just refers to a decay rate that's related to the effect of having other sources of magnetic fields. The blue line is the one that uses the known value (B0 = 0.5 Gauss) for the strength of earth's magnetic field. The red lines introduce an extra oscillatory magnetic field on top of the earth's field. The graph illustrates that for high enough decay rate, even if there are other sources of magnetic field, the fraction of singlet states (singlet yield) can be used to know the relative field strength. 

It should be mentioned that the explanation derived from this model agrees well to the fair amount of experimental observations made on these birds.


E. Gauger, E. Rieper, J. J. L. Morton, S. C. Benjamin, V. Vedral, "Sustained Quantum Coherence and Entanglement in the Avian Compass",  Physical Review Letters 106, (2011) 040503.

K. Schulten, "Quantum Biology of Animal Navigation", Lecture at University of British Columbia  (April 2011).

C. T. Rodgers and P. J. Hore,  "Chemical magnetoreception in birds: the radical pair mechanism",  PNAS 106, 2 (2009) 353-360.

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