Morphological determinants of glycosylation efficiency in Golgi cisternae

The Golgi apparatus has an intricate spatial structure characterized by flattened membrane-bound compartments, known as cisternae. Cisternae house integral membrane enzymes that catalyse glycosylation, the addition of polymeric sugars to protein cargo, which is important for the trafficking and function of the products. The unusual and specific shape of Golgi cisternae is highly conserved across eukaryotic cells, suggesting significant influence in the correct functioning of the Golgi. Motivated by experimental evidence that disruption to Golgi morphology can lead to observable changes in secreted cargo mass distribution, we develop and analyse a mathematical model of polymerisation in a cisterna that combines chemical kinetics, spatial diffusion and adsorption and desorption between lumen and membrane. Exploiting the slender geometry, we derive a non-local non-linear advection-diffusion equation that predicts secreted cargo mass distribution as a function of cisternal shape. The model predicts a maximum cisternal thickness for which successful glycosylation is possible, demonstrates the existence of an optimal thickness for most efficient glycosylation, and suggests how kinetic and geometric factors may combine to promote or disrupt polymer production.