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 nonlinear 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. Author SummaryThe Golgi apparatus is a universal feature of eukaryotic cells, playing a critical role in post-translational modification of secreted proteins. Its importance is demonstrated by the variety of disorders caused by errors in its function. A major post-translational modification is glycosylation: the addition of sugar chains to protein cargo. The Golgi has a distinctive structure, being comprised of stacks of thin, hollow, flattened, cisternae. We develop a mathematical model of glycosylation, combining enzyme-mediated membrane-bound reactions with intra-cisternal diffusion, to quantify the effect of cisternal morphology on processing rate. The model identifies optimal and maximal cisternal thicknesses for glycosylation to proceed, in terms of biochemical parameters. The model offers a quantitative connection between the Golgis cisternal morphology and its function.