Endoplasmic reticulum structure as a fundamental physical constraint on ribosome density

Recent work has shown an increasing interest in understanding the structure of the endoplasmic reticulum (ER) and how ribosomes are displayed on it. While there has been much work on the biological factors that affect ER structure and ribosome density, we have not seen work exploring how the latter two are related. Here, we present a diffusion-limited model that shows how the geometry of the ER imposes fundamental constraints on the capture efficiency of ER-bound ribosomes, and in doing so explains the qualitative difference between ribosome densities on the rough and smooth ER. First, we find that flat sheets and a matrix of tubules have distinct regimes where the capture efficiency of one geometry is greater than the other. Then, we show how these different regimes strongly constrain the experimentally observed differences in ribosome densities on the structures of the ER. In particular, fewer ribosomes are needed on tubules, while for flat sheets, more ribosome coverage at biologically relevant separation distances is needed to match the same capture efficiency. The model further predicts that depending on the downstream life of the translated protein and overall demand for protein expression, the cell will utilize one structure of the ER over another. Predictions are compared with experimental data.