Theoretical constraints on the uptake of silicic acid species by marine diatoms

Diatoms, one of the most productive phytoplankton groups in the ocean, have an essential requirement for silicic acid for the construction of their opaline shells. In seawater, silicic acid is present in three chemical species (H4SiO4, H3SiO4−, and H2SiO42−). The silicic acid molecule actually taken up by diatoms is still under discussion. Algal cells are surrounded by a diffusive boundary layer (DBL) which has an effective thickness of the order of the cell radius. The nutrient transport through this layer is by diffusion only and thus may limit the supply of silicic acid to the cell. Due to uptake of one of the species of silicic acid by the cell, the chemical system in the DBL is out of equilibrium. We have developed a diffusion–reaction model for the components H4SiO4, H3SiO4−, H2SiO42−, OH−, and H+ in the DBL which allows us to calculate maximum silicic acid supply rates as a function of the total concentration of dissolved silicon, pH, algal radius, and silicic acid species taken up by the cell. In addition, analytical solutions for the simplified diffusion–reaction system are presented. Model calculations of the silicic acid maximum uptake rates are compared with uptake data for Thalassiosira weissflogii from recent laboratory experiments. Results indicate that the supply of H4SiO4 to T. weissflogii by diffusion–reaction processes is sufficient to sustain the observed growth rates. Thus, the H4SiO4 uptake of T. weissflogii is not diffusion-limited. This does not hold true for H3SiO4−.