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arXiv:2512.05974

The rationality of radical pair mechanism in real biological systems

Xiaoyu Chen, Haibin Liu, Jianming Cai

physics.bio-phquant-phSubmitted Nov 25, 2025• Announced Nov 26, 2025
arXivHTMLPDF

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.

Comments
7 pages, 5 figures

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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.
Quantum biology is now taken rather seriously. Photosynthesis and avian navigation are two key applications of quantum biology. The basic problem in both cases is posed by the fact that the magnetic interaction energy in Earth's magnetic field is roughly million times smaller than thermal energy. The so called radical-pair mechanism (RPM) was proposed already in the 60's as a possible solution to the problem posed by anomalously large effect in EPR and NMR experiments. According to RPM, a radical pair is accompanied by electron pair, which is in a superposition of spin triplet and singlet states and behaves as quantum coherent system for a time sufficiently long to induce chemical effects. The hyperfine interaction of the members of the electron pair with the nuclei of radicals would amplify the effect. The neutralization of radical pair puts an end to the coherence interaction period. The proposal is that RPM gives rise to chemical compass making possible avian navigation. There is however a problem. RPM has been observed in laboratory only for magnetic fields in the range 1 mT-10 T. Earth's magnetic field is only 2 per cent of the lower bound so that it is quite possible that RPM is not at work. This opens up the door for new quantum physics proposed by TGD based model of quantum biology. In this approach magnetic body acts as as intentional agent using biological body as a sensory receptor and motor instrument. Macroscopic quantum coherence is made possible by dark matter realized as a hierarchy of heff = n x h phases. In this article RMP is summarized and compared with the TGD based vision. Also the possible connection between avian navigation and circadian clock suggested by the fact that both involve photoreceptor known as cryptocrome and a possible connection with gravitaxis are considered in TGD framework.
Magnetic measurement can be performed by various sensors, such as SQUID and Giant Magnetoresistance. This device can achieve high accuracy while losing efficiency and convenience. The model of biological magnetic sensing in avian proposes a radical pair response to the external field on the FLY results in regulating animal behaviour. Inspired by the radical pair system found in biological system, the effect of intra-radical coupling and the initial condition is studied in this simplified radical pair model as the quantum advantage results from entanglement and superposition are investigated in metrology. To identify the sensing benefit from the cooperation between the radical pairs, the inter-radical coupling is considered. We find the intra-radical coupling determines the sensing regime while the coupled radical pair system enables a new sensing scheme that provides a more general and flexible way for magnetic sensing in a broader range through a easier manipulation to the system.
The spin-chemical radical pair mechanism (RPM) has emerged as a leading theory for explaining the biological effects of low-intensity magnetic fields. These intriguing effects occur when the quantum system of radicals is well isolated from the disturbing influence of the environment. In other words, these effects are closely related to the spin coherence relaxation time τ, but an explicit relationship has not yet been established. In our study, we found an analytical solution to the Liouville-Neumann equation for an open system made up of two electrons and one nucleus, considering minimal interactions while concentrating on spin relaxation and chemical kinetics. This solution, supported by numerical integration, highlights the crucial role of quantum coherence. A straightforward expression is proposed that describes the RPM effect as a function of τ, within the ranges of magnetic field strength H and rate κ of chemical kinetics relevant to magnetobiology. Our findings reveal that RPM effects become significant only when fundamental relation γHτ>1+κτ holds: it controls the magnitude of the effects, and it is consistent with the principles of spin chemistry. Additionally, by comparing our results with existing experimental data, we estimate that the plausible spin decoherence times in magnetosensitive radical pairs within cryptochromelike proteins range from units to tens of nanoseconds. The effects of radio-frequency magnetic fields at the nT level were also examined, taking into account decoherence. These effects turned out to be negligible and incapable of disrupting the RPM patterns. The role of the quantum Zeno effect in magnetobiology is inspected from the perspective of the τ dependence of the RPM effect.
The radical pair mechanism (RPM) is a quantum-chemical mechanism that relates magnetic fields to the spin states of a pair of electrons, thereby affecting their availability for chemical reactions. The mathematics of electron spin and magnetic fields can be discouragingly complex. However, if biological systems can be assumed to respond to at most a subset of an electron’s spin state prior to that spin state being randomized, the relevant mathematics simplifies. A construction of the RPM under that assumption is developed step by step. A single electron is examined first, where a common representation of an electron’s spin state using the surface of a sphere is reduced to a line. A uniform magnetic field is then added. Next, an electron pair is examined, with the spin of each electron represented using a unit circle and the spin of the pair by a torus. Entanglement is represented by a probability distribution over the surface of the torus. Iwo magnetic fields are added, completing the construction of the RPM; the effect of magnetic fields on energy levels are also discussed. The resulting construction illuminates various aspects of the singlet (S0) and triplet (T+, T0, T-) states, though also has certain limitations, which are discussed.
Abstract Quantum sensing enables the ultimate precision attainable in parameter estimation. Circumstantial evidence suggests that certain organisms, most notably migratory songbirds, also harness quantum-enhanced magnetic field sensing via a radical-pair-based chemical compass for the precise detection of the weak geomagnetic field. However, what underpins the acuity of such a compass operating in a noisy biological setting, at physiological temperatures, remains an open question. Here, we address the fundamental limits of inferring geomagnetic field directions from radical-pair spin dynamics. Specifically, we compare the compass precision, as derived from the directional dependence of the radical-pair recombination yield, to the ultimate precision potentially realisable by a quantum measurement on the spin system under steady-state conditions. To this end, we probe the quantum Fisher information and associated Cramér–Rao bound in spin models of realistic complexity, accounting for complex inter-radical interactions, a multitude of hyperfine couplings, and asymmetric recombination kinetics, as characteristic for the magnetosensory protein cryptochrome. We compare several models implicated in cryptochrome magnetoreception and unveil their optimality through the precision of measurements ostensibly accessible to nature. Overall, the comparison provides insight into processes honed by nature to realise optimality whilst constrained to operating with mere reaction yields. Generally, the inference of compass orientation from recombination yields approaches optimality in the limits of complexity, yet levels off short of the theoretical optimal precision bounds by up to one or two orders of magnitude, thus underscoring the potential for improving on design principles inherent to natural systems.
The radical pair (RP) mechanism, which describes the quantum dynamics of a spatially separated electron pair, is considered as one of the principal models of avian magnetoreception. Different from the conventional phenomenological approach where the sensitivity of avian magnetoreception is characterized by the singlet yield ΦSΦ_{S}ΦS​, we introduce the quantum Fisher information (QFI), which represents the maximum information about the magnetic field's direction extracted from the RP state, to give a precise measure of sensitivity of avian compass essentially. The consistency between our results and experimental observations suggests that QFI plays a decisive role in avian magnetoreception. Besides, within the framework of quantum metrology, we can judge the feasibility of any possible measurement scheme for avian magnetoreception, and shed light on an intrinsic relevance between the singlet yield and a concrete measurement scheme of our approach. The present work allows us to understand many things about avian magnetoreception from a fully new perspective of quantum metrology, and provide a new route to establish a direct connection between quantum information and many other biological functions.