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

TL;DR

A quantitative understanding of phototaxis sign reversal is presented, including bistability in the direction choice, a prediction that can be tested in single-cell tracking studies of mutant phototaxis.

Abstract

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.

Figures (6)

• Figure 1: Phototaxis of Chlamydomonas. Photoreceptor is shown in blue, eyespot in red. Adapted from Ueki2016 and AlgalOptics.
• Figure 2: Cross section of a spherical cell illuminated from the left. Cell swims with its body-fixed axis $\hat{\bf e}_3$ along the positive $y$-axis and rotates counterclockwise when viewed from behind, as in the drawing. Visible body-fixed axes are $\hat{\bf e}_1$ and $\hat{\bf e}_2$. The top ray of light (blue) enters the cell at $Q$ and intercepts the photoreceptor (red arc) at $P$.
• Figure 3: Geometrical optics for spherical cells. (a) Relationship \ref{['implicit']} between the incident angle $\gamma$ and the angle $\zeta$ of the photoreceptor shown in Fig. \ref{['fig2']}. (b) Ray-tracings rayoptics illustrating caustic formation for relative index of refraction $n=1.1$. (c) The angle $\zeta_m$ of the caustic and angle $\zeta^*$ bounding the double-valued region of light, as function of the relative index $n$.
• Figure 4: Angular dependence of lensing. Intensity versus rotation angle $\zeta$ for various values of $n$. Direct contributions are shown as heavy black curves. Dashed blue line is local approximation near $\zeta=0$ for representative value $n=1.1$.
• Figure 5: Coordinate system of Chlamydomonas, adapted from Raikwar2025. Eyespot is shown as red disc, with outward normal $\hat{\bf o}$. Cell rotates continuously around $\hat{\bf e}_3$ and transiently around $\hat{\bf e}_1$ due to the photoresponse of its cis and trans flagella.