Abstract

The Golgi apparatus is comprised of stacked cisternal membranes forming subcompartments specialized for post-translational processing of newly synthesized secretory cargo. It 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. Different mathematical models have been developed and implemented in this thesis to simulate the de novo self-assembly, growth, and maintenance of the Golgi apparatus based on two fundamental mechanisms—vesicle budding and targeted fusion—which are well established and essential for Golgi function.

The thesis first describes a minimal model of vesicle trafficking involving selective concentration of protein components into vesicles and selective fusion of these vesicles to target compartments. It presents a series of simulation experiments designed to test whether this model is sufficient to explain self-assembly, growth and maintenance of the Golgi apparatus, and it also gives some testable predictions regarding some parameters that determine trafficking kinetics and compartment size, which have been used to develop in vivo validation experiments for the model.

While vesicle-based sorting and trafficking are stochastic and discrete processes, the discrete nature of molecules is ignored in commonly used continuous models. Accurately capturing both the discretization and stochasticity effects may be important to our understanding of the assembly and disassembly of Golgi apparatus. To examine this issue, this thesis further investigates three analogous models: a discrete, stochastic model; a continuous, deterministic ordinary differential equation (ODE) model; and a continuous, stochastic differential equation (SDE) model. All three simulate the same set of fundamental budding and fusion reactions at different levels of abstraction. By exploring where outputs of the models differ, we hope to better identify those features essential to minimal models of various Golgi behaviors, and determine the significance of discretization and stochasticity effects in the Golgi function.

Our studies were primarily based on a stable compartment model, which assumes that different Golgi cisterna contain different resident proteins and maintain their identities. A final direction of this thesis concerns development of a cisternal maturation model, which proposes that Golgi cisternae constantly mature into later compartments by disposing of their enzymes while accepting new sets of enzymes from "older" cisternae. This thesis describes a simple maturation model based on ordinary differential equation simulations to test whether the minimal model with two fundamental vesicle budding and fusion mechanisms is adequate to reproduce the cisternal maturation process.