A simplified mass-transfer model for visual pigments in amphibian retinal-cone outer segments

When radiolabeled precursors and autoradiography are used to investigate turnover of protein components in photoreceptive cone outer segments (COSs), the labeled components—primarily visual pigment molecules (opsins)—are diffusely distributed along the COS. To further assess this COS labeling pattern, we derive a simplified mass-transfer model for quantifying the contributions of advective and diffusive mechanisms to the distribution of opsins within COSs of the frog retina. Two opsin-containing regions of the COS are evaluated: the core axial array of disks and the plasmalemma. Numerical solutions of the mass-transfer model indicate three distinct stages of system evolution. In the first stage, plasmalemma diffusion is dominant. In the second stage, the plasmalemma density reaches a metastable state and transfer between the plasmalemma and disk region occurs, which is followed by an increase in density that is qualitatively similar for both regions. The final stage consists of both regions slowly evolving to the steady-state solution. Our results indicate that autoradiographic and cognate approaches for tracking labeled opsins in the COS cannot be effective methodologies for assessing new disk formation at the base of the COS.Abbreviations used: A, area (μm²), COS, cone outer segment, D, mass diffusion coefficient (μm²/s), h_m, mass transfer coefficient (μm/s), L, cone outer segment length (μm), PDE, partial differential equation, r, radius (μm), t, time (s), T, plasmalemma thickness (μm), u, plasmalemma or disk region (axial) velocity (μm/s), V, volume (μm³), W, plasmalemma width (μm), x, axial direction, v, disk to plasmalemma velocity (μm/s), ρ₁, disk label density, ρ₂, plasmalemma label density, ϕ, nonvoid fraction