Determine the proper effective diffusivity in the drift-diffusion model

Determine the appropriate effective diffusivity to use in the drift–diffusion equation modeling the azimuthal density evolution of photophobic Chlamydomonas reinhardtii under ring illumination. Specifically, identify a principled value for the diffusion coefficient that reflects azimuthal dispersion during directed phototactic migration, for example by linking single-cell tracking measurements and/or the quantified growth rates of the most unstable azimuthal modes to an effective diffusion coefficient replacing the run‑and‑tumble diffusivity measured in the dark.

Background

In the theoretical analysis, the authors model the density instability with a one-dimensional drift–diffusion equation in which the diffusion coefficient D is taken as the run‑and‑tumble diffusivity measured in the dark. They note this choice is questionable because, during negative phototaxis, cell migration toward the center is highly directed, implying that azimuthal dispersion may be smaller than the dark diffusivity.

Although the model’s selected wavenumber depends on the ratio of parameters and the exact value of D can be partly absorbed into fitted parameters, a mechanistic determination of the proper effective diffusivity would improve the physical grounding of the model. The authors suggest this could be achieved by single-cell tracking and/or by quantifying the growth rates of the selected modes at onset.