Abstract
A proposed mechanism for magnetic compasses in animals is that systems of radical pairs transduce magnetic field information to the nervous system. One can show that perfectly ordered arrays of radical pairs are sensitive to the direction of the external magnetic field and can thus operate, in principle, as a magnetic compass. Here, we investigate how disorder, inherent in biological cells, affects the ability of radical pair systems to provide directional information. We consider biologically inspired geometrical arrangements of ensembles of radical pairs with increasing amounts of disorder and calculate the effect of changing the direction of the external magnetic field on the rate of chemical signal production by radical pair systems. Using a previously established signal transduction model, we estimate the minimum number of receptors necessary to allow for detection of the change in chemical signal owing to changes in magnetic field direction. We quantify the required increase in the number of receptors to compensate for the signal attenuation through increased disorder. We find radical-pair-based compass systems to be relatively robust against disorder, suggesting several scenarios as to how a compass structure can be realized in a biological cell.