A new type of radical-pair-based model for magnetoreception

Abstract

Certain migratory birds can sense the Earth's magnetic field. The nature of this process is not yet properly understood. Here we offer a simple explanation according to which birds literally see the local magnetic field through the impact of a physical rather than a chemical signature of the radical pair: a transient, long-lived electric dipole moment. Based on this premise, our picture can explain recent surprising experimental data indicating long lifetimes for the radical pair. Moreover, there is a clear evolutionary path toward this field-sensing mechanism: it is an enhancement of a weak effect that may be present in many species.

Figure 1

(a) (Left) Schematic diagram showing how the molecules might be aligned in the retina; a combination of light and a magnetic field could induce dipole moments for certain molecular orientations. (Right) These dipoles would create an electric field that would allow the bird literally to see the magnetic field direction. (b) Cycle of the compass molecule: after photoexcitation from |S₀〉 to |S₁〉, the branching ratio of direct relaxation into the ground state or via a long-lived triplet state |T₀〉 depends on the orientation of the molecule with the geomagnetic field. The purple color of |T₀〉 denotes a charge-separated state with an electric dipole moment, thus affecting the isomerization of retinal, which is a crucial step of the visual process.

Figure 2

Schematic diagram showing the key features of the compass mechanism: the system relaxes back into the singlet ground state |S₀〉 after most photoexcitation events. However, there is a small intersystem crossing rate, which depends on the orientation of an asymmetric g-tensor with the geomagnetic field. Population in |T₁〉 relaxes into a long-lived triplet state |T₀〉. (Red) Transitions between different charge states; (blue) change of the spin state. The decay from |T₀〉 to |S₀〉 involves both a charge and a spin transition.

Figure 3

Steady-state population of |T₀〉, 𝒯, is shown as a function of this state's lifetime 1/γ₀ and the angle θ between the axial g-tensor and the Earth's magnetic field for Δg = 0.2. For other parameters, see main text; note that 1/γ₀ is assumed to be long in contrast to the lifetimes of |S₁〉 and |T₁〉, which may be as short as 1 ns. (Upper right) Two-dimensional plot follows the cos²θ dependence of the squared relevant matrix element (see Eq. 3).

Figure 4

Possible explanation of the relaxation from |T₀〉 to the ground state |S₀〉: the charge relaxation follows a spin transition to the auxiliary singlet level |S′〉. Population in |t₀〉 is connected to |S′〉 via an ISC and thus decays quickly, whereas population in |t_±〉 is trapped for the duration of the spin coherence time. However, a resonant RF field mixes the spin states, leading to faster relaxation of the entire triplet population.

Figure 5

Surviving |T₀〉 population as a function of time and RF frequency ω. After an initial fast decay of the |t₀〉 population (see text), a slowly decaying plateau of triplet population is reached. However, on resonance with the either the electron or the hole spin, the oscillatory field drastically shortens the triplet lifetime. See text for parameters.