In-vivo biomagnetic characterisation of the American cockroach

We present a quantitative method, utilising a highly sensitive quantum sensor, that extends applicability of magnetorelaxometry to biological samples at physiological temperature. The observed magnetic fields allow for non-invasive determination of physical properties of magnetic materials and their surrounding environment inside the specimen. The method is applied to American cockroaches and reveals magnetic deposits with strikingly different behaviour in alive and dead insects. We discuss consequences of this finding to cockroach magneto-reception. To our knowledge, this work represents the first characterisation of the magnetisation dynamics in live insects and helps to connect results from behavioural experiments on insects in magnetic fields with characterisation of magnetic materials in their corpses.


I. MEASURED DATA
Tables below list experimental data used in statistical analysis of the main text.

II. FASTED COCKROACH
We verified that the food pallets given to cockroaches can be magnetised and therefore conducted the experiment with fasted cockroach in order to exclude the hypothesis that the observed decay is due to ingested magnetism of the food. The mean food transit time was determined to be 20.6 hours, with a part of each meal retained in the crop for up to 4 days [1]. We therefore fasted the cockroach for 7 days, giving it only water, and found that this had no effect on the decaying magnetic field. This is not a conclusive proof of biogenic magnetism because environmental ferromagnetic contaminants could still be present in the tissues [2].

III. MAGNETIC FIELD REVIVAL
The theory outlined in the main text explains exponential magnetic field decay which was observed for most cockroaches. For this one insect, however, we have seen a revival of the magnetic field as shown in the figure.

ΜG
IV. ALIGNMENT TIME Consider a spherical particle endowed with magnetic moment µ and surrounded by an environment with viscosity η at room temperature T . If the particle is subject to an external magnetic field B, its rotational motion is described by the Newton law: Here θ denotes the angle between B and µ (counted from B), I stands for the moment of inertia of the sphere, I = 2 5 ρV R 2 , and f is the rotational friction coefficient, f = 8πηR 3 . The next term gives magnetic torque and the last term is the thermal torque whose influence we will ignore here because the strong aligning field gives rise to µB kT even for very small magnetic moments. Despite its simplicity, for particles embedded in a highly viscous environment subjected to a constant field, similar models have successfully explained experimental results [3].
Our aim is to calculate the time it takes the particle to align with the field, t ⊗ . Note that t ⊗ is longer than the alignment time t ↓ obtained when the magnetic torque is replaced by a stronger torque. Similarly, t ⊗ is shorter than the alignment time t ↑ obtained if the magnetic torque is replaced by a weaker torque. We show a simple upper and lower bound on the strength of the magnetic torque leading to alignment times that differ only by a constant factor of order one. Hence the obtained formula also holds for t ⊗ .
Consider first the stronger torque µB sin θ ≤ µBθ. The original nonlinear problem now reduces to the damped harmonic oscillator. Due to the assumed high viscosity f 2 − 4IµB 0, the oscillation is overdamped with the particular solution where The initial conditions are: θ(0) = θ 0 for the angle andθ(0) = 0 for the angular velocity. Since (f /I) 2 4µB/I we simplify: Furthermore, both r ± are negative with r − r + and therefore exp(r − t) quickly decays to zero. The long time dynamics is governed by the decay exp(r + t), which admits alignment time: