Modeling the homeostatic length of the rod outer segment in zerbrafish

Retinal photoreceptor cells, rods and cones, in the eye convert light energy into electrical signals that stimulate sight. In humans, peripherally located rods are important for night vision, while centrally located cones are responsible for daytime/color vision. Rods consist of a rod outer segment (ROS), inner segment, cell body and synaptic terminal. The ROS, consisting of stacked, discrete membraneous discs, undergoes a process of continuous renewal in which newly constructed discs are added at the base (growth) and oldest discs are shed from the tip. The ROS maintains a homeostatic length by balancing growth and shedding. How this balance is controlled is unknown. If ROS homeostatic length control is lost, for example by ROS shortening, the rods can degenerate leading to blindness. We develop a model of ROS homeostatic length control, supported by experiments using data from zebrafish where ROS renewal is controlled experimentally. An ODE describes the length of ROS over time according to constant growth and ROS length-dependent shortening. Here, equilibrium analysis helps us understand the balance between growth and shortening mechanisms in maintaining homeostatic length. Also, an advection-reaction PDE describes disk addition (through a boundary condition), translocation (via advection), and shedding (reaction) in populations of ROS.