Discrete, continuous, and stochastic models of protein sorting in the Golgi apparatus

The Golgi apparatus plays a central role in processing and sorting proteins and lipids in eukaryotic cells. Golgi compartments constantly exchange material with each other and with other cellular components, allowing them to maintain and reform distinct identities despite dramatic changes in structure and size during cell division, development, and osmotic stress. We have developed three minimal models of membrane and protein exchange in the Golgi—a discrete, stochastic model, a continuous ordinary differential equation model, and a continuous stochastic differential equation model—each based on two fundamental mechanisms: vesicle-coat-mediated selective concentration of cargoes and soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins during vesicle formation and SNARE-mediated selective fusion of vesicles. By exploring where the models differ, we hope to discover whether the discrete, stochastic nature of vesicle-mediated transport is likely to have appreciable functional consequences for the Golgi. All three models show similar ability to restore and maintain distinct identities over broad parameter ranges. They diverge, however, in conditions corresponding to collapse and reassembly of the Golgi. The results suggest that a continuum model provides a good description of Golgi maintenance but that considering the discrete nature of vesicle-based traffic is important to understanding assembly and disassembly of the Golgi. Experimental analysis validates a prediction of the models that altering guanine nucleotide exchange factor expression levels will modulate Golgi size.

Figure 1

(Color online) Vesicular transport pathway. Transport between compartments is mediated by vesicular carriers. Three types of vesicles mediate intracellular transport. Coat protein complex II (COPII) vesicles mediate transport from the ER. Coat protein complex I (COPI) vesicles act in intra-Golgi transport and retrograde transport from the Golgi to the ER. Clathrin vesicles mediate transport between the Golgi and the plasma membrane.

Figure 2

High-level pseudocode for the discrete event simulation.

Figure 3

(Color online) Compartment surface area vs time for the baseline simulation with the (a) DS, (b) ODE, (c) and SDE simulations.

Figure 4

(Color online) GEF concentration vs time for the baseline simulation with the (a)–(c) DS simulator, (d)–(f) ODE simulator, and (g)–(i) SDE simulator. The first column (a, d, g) shows concentrations in the ER, the second column (b), (e), and (h) concentrations in the cis Golgi, and the third column (c), (f), and (i) concentrations in the trans Golgi.

Figure 5

(Color online) Compartment sizes vs time during Golgi disassembly for (a) DS, (b) ODE, and (c) SDE simulations.

Figure 6

(Color online) Compartment GEF marker concentrations vs time in the ER during Golgi disassembly in (a) DS, (b) ODE, and (c) SDE simulations.

Figure 7

(Color online) Golgi disassembly time vs GEF2 concentration in cis Golgi for (a) DS, (b) ODE, and (c) SDE simulations.

Figure 8

(Color online) Steady-state protein contamination in the ER as a function of sorting affinity for (a) DS, (b) ODE, and (c) SDE simulations. The affinity constant is dimensionless and therefore lacks a unit label.

Figure 9

(Color online) Compartment size changes vs changes in sorting affinity in (a) DS, (b) ODE, and (c) SDE simulations. The affinity constant is dimensionless and therefore lacks a unit label.

Figure 10

(Color online) Time to steady state vs changes in affinity constant for (a) DS, (b) ODE, and (c) SDE simulations. The affinity constant is dimensionless and therefore lacks a unit label.

Figure 11

(Color online) Assembly time vs changes in budding constant for (a) DS, (b) ODE, and (c) SDE simulations.

Figure 12

(Color online) Sensitivity of compartment sizes to changes in starting ER GEF1 protein concentration in (a) DS, (b) ODE, and (c) SDE simulations.

Figure 13

(Color online) Golgi size is increased by expression of the ER-localized GEF. HeLa cells transiently transfected with HA-tagged ER-localized GEF (mSec12) were analyzed to reveal (a) and (b) HA staining as well as (c) and (d) GPP130 shown after 3D rendering. (e) Golgi size normalized to cell volume was quantified in control cells and the cells expressing HA-mSec12. (f) The Golgi size and expression level were also compared on a cell-by-cell basis, with the correlation plot showing a slope of 0.0009. As might be expected, concomitant with the Golgi size increase was an up to 20% decrease in the mean intensity per pixel of GPP130 staining in the defined Golgi region, consistent with dilution of GPP130 in a larger compartment (not shown). Sizes are expressed in voxels, each of which has dimension $0.05\times 0.05\times 0.3\mu {\text{m}}^3$. Bar, $10\mu \text{m}$.