Optimal composition of chloride cells for osmoregulation in a randomly fluctuating environment

Fish live in water with a different osmotic pressure from that in the body. Their gills have chloride cells that transport ions to maintain an appropriate level of osmotic pressure in the body. The direction of ion transport is different between seawater and freshwater. There are two types of chloride cells that specialize in unidirectional transport and generalist cells that can switch their function quickly in response to environmental salinity. In species that experience salinity changes throughout life (euryhaline species), individuals may replace some chloride cells with cells of different types upon a sudden change in environmental salinity. In this paper, we develop a dynamic optimization model for the chloride cell composition of an individual living in an environment with randomly fluctuating salinity. The optimal solution is to minimize the sum of the workload of chloride cells in coping with the difference in osmotic pressure, the maintenance cost, and the temporal cost due to environmental change. The optimal fraction of generalist chloride cells increases with the frequency of salinity changes and the time needed for new cells to be fully functional but decreases with excess maintenance cost.