Quantum modeling of radical pair magnetic sensor based on electric dipole moment

TL;DR

The paper addresses how a spin-correlated radical pair in cryptochrome can transduce Earth's magnetic field into an electric signal. It develops a quantum-mechanical model that combines hyperfine, Zeeman, and spin-orbit interactions in a 72-dimensional Hilbert space and treats the system as an open quantum system with Lindblad dynamics. The key finding is that the dipole moment component $P_x$ shows a clear, field-dependent response to both the inclination angle $\theta$ and field magnitude $B_0$, persisting under dissipation and enabling simultaneous directional and positional information. This work advances understanding of magnetoreception and informs bio-inspired magnetic sensing technologies, with potential implications for GPS-free navigation and biomarker detection.

Abstract

Photoreduction of cryptochrome protein in the retina is a well-known mechanism of navigation of birds through the geomagnetic field, yet the biosignal nature of the mechanism remains unclear. The absorption of blue light by the flavin adenine dinucleotide (FAD) chromophore can alter the distribution of electrons in cryptochrome and create radical pairs with separated charges. In this study, the spin dynamics of electrons in the radical pair and its coupling with spatial position were investigated by computational modeling from a quantum mechanical perspective. Several interactions were considered in the presence of an external magnetic field, and the resulting electric dipole moment in cryptochrome was computed as the quantity emerging from this coupling. The computations show the induced electric dipole moment clearly depend on the characteristics of the applied magnetic field even after considering dissipative effects. In fact, our findings indicate that the radical pair in cryptochrome protein is a magnetic biosensor, in the sense that in the presence of the geomagnetic field, variations in spin states can influence its electric dipole moment, which may be interpreted via the bird as an orientation signal. The results can be used in the advancement of bio-inspired technologies which replicate animal magnetic sensitivity. On the other hand, with increasing concern about the detrimental effects of electromagnetic fields on wildlife and human health, studying the phenomenon of magnetoreception can contribute to a deeper understanding of how biological structures interact with these fields.

Figures (9)

• Figure 1: Schematic representation of the protein cryptochrome and the energy levels (labeled ground and excited states) and spin entanglement of its radical pair.
• Figure 2: Schematic illustration of spherical coordinates of the geomagnetic field vector relative to the bird's location. .
• Figure 3: Time evolution of the x-component of the electric dipole moment $P_x$ for two inclination angles of the external magnetic field. Panel A Shows the variations of $P_x$ on a microsecond time scale, which depicts different behaviors for the two selected angles. For $\theta =\pi$, the dipole moment increases rapidly and reaches its maximum amplitude in the same simulated time scale, so that it looks like an exponential growth. In contrast, at a smaller angle ($\theta =\pi/4$), this increase is slower and the system enters a pronounced oscillatory state. The visible oscillations are related to the high-frequency component. Panel B Extends the time evolution for the same two angles on a millisecond scale. This longer time scale shows the full view of the oscillatory behavior of the dipole moment due to the lower frequency and confirms that the dynamics of the system are essentially stable and periodic.
• Figure 4: Time evolution of the electric dipole moment $P_x$ for different magnetic field inclination angles $\theta$, over a duration of one microsecond. As can be seen, the expected value of the electric dipole moment is different at different angles.
• Figure 5: Variations of the electric dipole moment $P_x$ with respect to the magnetic field inclination angle $\theta$ at two different time scales. (a) At t = $1\mu s$, the dipole moment shows a clear periodic dependence on $\theta$, with distinct peaks indicating the angular sensitivity of the system. (b) At t = $10\mu s$, the same periodic pattern persists but the dipole magnitude is significantly enhanced. Both plots correspond to a fixed oscillation frequency $\omega = 8.3\times 10^6$.