Figure 3.

Relative orientation of coordinate frames used in the computations. The fixed (X, Y, Z) coordinate frame (a) is associated with the bird eye retina as shown in Fig. 2. The orientation of the cryptochrome molecules distributed over the retina are specified through the x, y, z-coordinate systems, which can be obtained from the initial (X, Y, Z) coordinate frame though a rotational transformation defined by the angles α, β, γ shown in panel b. Cryptochrome wiggling in the retina introduces rotational disorder of the ideally oriented proteins. (c) As a result, the ideal x, y, z-coordinate frame is to be replaced by a randomly oriented x′, y′, z′-coordinate frame, defined by the three Euler angles α′, β′, and γ′. (d) The external magnetic field vector $\overrightarrow{B}$ in the (X, Y, Z) coordinate frame is characterized by the polar angle Θ and azimuthal angle Φ. (e) However, in the x′, y′, z′-coordinate frame, it can be written in terms of angles θ′ and φ′.