Theory of Cell Body Lensing and Phototaxis Sign Reversal in "Eyeless" Mutants of Chlamydomonas

Phototaxis of many species of green algae relies upon directional sensitivity of their membrane-bound photoreceptors, which arises from the presence of a pigmented "eyespot" behind them that blocks light passing through the cell body from reaching the photoreceptor. A decade ago it was discovered that the spherical cell body of the alga Chlamydomonas reinhardtii acts as a lens to concentrate incoming light, and that in "eyeless" mutants of Chlamydomonas the consequence of that focused light reaching the photoreceptor from behind is a reversal in the sign of phototaxis relative to the wild type behavior. We present a quantitative theory of this sign reversal by completing a recent simplified analysis of lensing [Yang, et al., Phys. Rev. E 113, 022401 (2026)] and incorporating it into an adaptive model for Chlamydomonas phototaxis. This model shows that phototactic dynamics in the presence of lensing is subtle because of the existence of internal light caustics when the cellular index of refraction exceeds that of water. During each period of cellular rotation about its body-fixed axis, the photoreceptor receives two competing signals: a relatively long, slowly-varying signal from the direct illumination, and a stronger, shorter, rapidly-varying lensed signal. The reversal of the sign of phototaxis is then a consequence of the dominance of the flagellar photoresponse to the signal with the higher time derivative. These features lead to a quantitative understanding of phototaxis sign reversal, including bistability in the direction choice, a prediction that can be tested in single-cell tracking studies of mutant phototaxis.