The rationality of radical pair mechanism in real biological systems

TL;DR

The paper addresses whether the radical pair mechanism (RPM) is a rational basis for biological magnetoreception under realistic constraints, by contrasting it with Ramsey-like interferometry in both highly controllable and natural settings. The authors build two-level models for both approaches, derive angular sensitivities via $F$ and $\Phi$, and extend RPM to a multi-spin, hyperfine-coupled system governed by a Lindblad master equation to incorporate recombination and pure dephasing. They find that Ramsey-like sensing can surpass RPM under ideal timing and prior knowledge, but RPM remains more practical and robust when such information is unavailable, with RPM’s sensitivity saturating over longer times while Ramsey-like sensitivity is limited to short windows by noise. This work provides a mechanistic justification for the evolutionary plausibility of RPM in birds, and yields guidance for designing bio-inspired quantum sensors that operate under realistic, noisy conditions with minimal control over experimental parameters.

Abstract

The radical pair mechanism (RPM) in the chemical magnetic compass model is considered to be one of the most promising candidates for the avian magnetic navigation, and quantum needle phenomenon further boosts the navigation precision to a new high level. It is well known that there are also a variety of methods in the field of magnetic field sensing in laboratory, e.g. Ramsey protocol of NV centers in diamond. Here, we compare the RPM model and Ramsey-like model under laboratory conditions and under in vivo conditions respectively. The results are both surprising and reasonable. Under laboratory conditions, if we have precise control over time and a reasonably accurate prior knowledge of the magnetic field direction, the Ramsey-like model will outperform the RPM model. However, when such information is unavailable, as under in vivo conditions, the RPM model stands out. The RPM model achieves greater practicality at the cost of reduced accuracy.

Figures (5)

• Figure 1: The maximum absolute value of the slope of product yield $\Phi$ for angle $\theta \in [0,\pi]$.
• Figure 2: The maximum absolute value of the slope of product yield $\Phi_i$ for recombination rates ${k_i}\in [10^5,10^6]~\rm{Hz}$ and pure dephasing rate $\gamma \in [0.02,1.0]~{\rm MHz}(i=1,2)$. (a)Another recombination rate ${k_2}$ is set to be $10^5~\rm{Hz}$. (b)The red solid line with squares(longest coherence time) and the blue solid line with circles(equal recombination rate obtained at the highest accuracy) correspond to equal $k_i$ values of $10^5~\rm Hz$ and $5\times10^5~\rm Hz$ respectively. And the green solid line and the black dashed line(unequal recombination rates obtained at the highest accuracy) correspond to the changes of $\abs{\frac{\partial \Phi_2}{\partial \theta}}_{\rm{max}}$ and $\abs{\frac{\partial \Phi_1}{\partial \theta}}_{\rm{max}}$ with evolution time when $k_1=10\times10^5~\rm Hz$ and $k_2=2.6\times10^5~\rm Hz$, respectively. In addition, in (b) and (c), $\gamma$ is taken as $0.5~\rm{MHZ}$.
• Figure 3: The variation of fidelity $F$(Ramsey-like, left) and singlet yield $\Phi_s$(RPM, right) with angle $\theta \in [0,\pi]$. (b)The data $\textbf{A}_1=$diag[$0.0500$, $0.0006$, $0.0005$] $\rm{mT}$, $\textbf{B}_1=$diag[$-0.0002$,$-0.0866$, $-0.0002$] $\rm{mT}$, $M=R_{z}(-1.1465)R_{y}(-2.2840)R_{x}(1.2461)$, and $\textbf{A}_2=M\textbf{B}_1 M^T$ is taken from Ref. chen2024identifying.
• Figure 4: Noise dependence of the absolute maximum slope in (a) Ramsey-like and (b) RPM models. Evolution time spans $1-50~\rm{\mu s}$, with dephasing rates $\gamma$ ranging from $0.1$ to $0.4~\rm{MHz}$. And the radical pair lifetime is chosen as $k^{-1}=10$${\mu \rm{s}}$.
• Figure 5: The maximum absolute value of the slope of product yield $\Phi_{s,t}$ for recombination rates ${k_{s,t}}\in [10^5,10^6]~\rm{Hz}$ and pure dephasing rate $\gamma \in [0.1,0.4]~{\rm MHz}$. (a)Another recombination rate ${k_t}$ is set to be $10^5~\rm{Hz}$. In (b)-(f), $\gamma$ is taken as $0.1, 0.2 ,0.3,0.4~\rm{MHZ}$. (f)The time evolution of the precision of singlet and triplet products for three sets of recombination rates(equal and minimum recombination rate, highest precision achieved with equal recombination rates, and highest precision achieved with unequal recombination rates) for given $\gamma=0.2~\rm{MHZ}$.