Fig. 4: Modelling the magnetoreceptive potential of giant magnetofossils.

a Schematic model of the torque-transducer mechanism (modified after²⁹). The magnetic particle with remanent and/or induced moment M is attached to a torsional elastic pivot (vertical grey bar) with stiffness K. The rest position of the particle (grey position) corresponds to no elastic deformation of the pivot. A magnetic field B applied at an angle \(\theta\) to the rest position creates a magnetic torque, causing the particle to rotate (blue position). As the particle rotates, the elastic pivot is deformed, creating a restoring elastic torque that balances the magnetic torque at an equilibrium deflection angle \(\psi\). Thermal energy causes fluctuations of amplitude \(\Delta \psi\) about the equilibrium deflection angle (red shaded region). A filament (yellow) attached to the base of the particle pulls on a force-gated transmembrane ion channel, causing it to open or close. b Plot of \(\Delta \psi\) as a function of MB/K for the case of magnetic fields applied antiparallel to the rest position (\(\theta\) = 180°)²⁹ (Supplemental Information). Lines are shown for two different values of the torsional stiffness: K = 6 k_BT (dashed line) and K = 121 k_BT (solid line). The shaded region highlights the critical point around MB/K = 1 where \(\Delta \psi\) varies most rapidly as a function of field intensity for a given value of K. The inset shows the derivative of \(\Delta \psi\) with respect to MB/K. Around the critical point, the sensitivity of \(\Delta \psi\) to small variations in B for a fixed value of K is ~2.5 times higher for a ‘giant-like’ particle with MB = 121 k_BT attached to an elastic pivot with K = 121 k_BT (solid line) compared to a minimum baseline ‘trout-like’ cluster⁵² with MB/K = 6 k_BT attached to an elastic pivot with K = 6 k_BT. c Plot of d(\(\Delta \psi\))/d(MB/K) at MB/K = 1 for a range of K (left axis, black line), the minimum detectable angle of deviation from antiparallel alignment with the magnetic field⁵⁶, \(\eta \,\)(right inner axis, blue line), and a histogram of calculated magnetic energies for a range of giant magnetofossil morphologies (far right axis, red shaded bars). Symbols show magnetic energy clusters for giant bullets and needles, spearheads, kinked giant bullets, and spindles.