Multispecies model with interconversion, chipping, and injection

Theoretical approaches for understanding the self-organized formation of the Golgi apparatus

Eukaryotic cells fold their membranes into highly organized structures called membrane-bound organelles. Organelles display characteristic structures and perform specialized functions related to their structures. Focusing on the Golgi apparatus, we provide an overview of recent theoretical studies to explain the mechanism of the architecture of the Golgi apparatus. These studies are classified into two categories: those that use equilibrium models to describe the robust Golgi morphology and those that use non-equilibrium models to explain the stationarity of the Golgi structures and the constant streaming of membrane traffic. A combinational model of both categories was used for computational reconstruction of the de novo Golgi formation process, which might provide an insight into the integrated understanding of the Golgi structure.

Nonequilibrium description of de novo biogenesis and transport through Golgi-like cisternae

A central issue in cell biology is the physico-chemical basis of organelle biogenesis in intracellular trafficking pathways, its most impressive manifestation being the biogenesis of Golgi cisternae. At a basic level, such morphologically and chemically distinct compartments should arise from an interplay between the molecular transport and chemical maturation. Here, we formulate analytically tractable, minimalist models, that incorporate this interplay between transport and chemical progression in physical space, and explore the conditions for de novo biogenesis of distinct cisternae. We propose new quantitative measures that can discriminate between the various models of transport in a qualitative manner–this includes measures of the dynamics in steady state and the dynamical response to perturbations of the kind amenable to live-cell imaging.

Condensation and intermittency in an open-boundary aggregation-fragmentation model

We study real space condensation in aggregation-fragmentation models where the total mass is not conserved, as in phenomena such as cloud formation and intracellular trafficking. We study the scaling properties of the system with influx and outflux of mass at the boundaries using numerical simulations, supplemented by analytical results in the absence of fragmentation. The system is found to undergo a phase transition to an unusual condensate phase, characterized by strong intermittency and giant fluctuations of the total mass. A related phase transition also occurs for biased movement of large masses, but with some crucial differences which we highlight.

(Re)modeling the Golgi

In this chapter, we summarize recent theoretical efforts to address a variety of issues in Golgi morphogenesis: de novo biogenesis of compartments with precise chemical identity, the transport of proteins through the Golgi, the maintenance of chemical identity, and the morphology of Golgi compartments, from the perspective of nonequilibrium physics.