Stochastic Model of Maturation and Vesicular Exchange in Cellular Organelles

Emergent Spatiotemporal Organization in Stochastic Intracellular Transport Dynamics

The interior of a living cell is an active, fluctuating, and crowded environment, yet it maintains a high level of coherent organization. This dichotomy is readily apparent in the intracellular transport system of the cell. Membrane-bound compartments called endosomes play a key role in carrying cargo, in conjunction with myriad components including cargo adaptor proteins, membrane sculptors, motor proteins, and the cytoskeleton. These components coordinate to effectively navigate the crowded cell interior and transport cargo to specific intracellular locations, even though the underlying protein interactions and enzymatic reactions exhibit stochastic behavior. A major challenge is to measure, analyze, and understand how, despite the inherent stochasticity of the constituent processes, the collective outcomes show an emergent spatiotemporal order that is precise and robust. This review focuses on this intriguing dichotomy, providing insights into the known mechanisms of noise suppression and noise utilization in intracellular transport processes, and also identifies opportunities for future inquiry.

Deterministic early endosomal maturations emerge from a stochastic trigger-and-convert mechanism

Endosomal maturation is critical for robust and timely cargo transport to specific cellular compartments. The most prominent model of early endosomal maturation involves a phosphoinositide-driven gain or loss of specific proteins on individual endosomes, emphasising an autonomous and stochastic description. However, limitations in fast, volumetric imaging long hindered direct whole cell-level measurements of absolute numbers of maturation events. Here, we use lattice light-sheet imaging and bespoke automated analysis to track individual very early (APPL1-positive) and early (EEA1-positive) endosomes over the entire population, demonstrating that direct inter-endosomal contact drives maturation between these populations. Using fluorescence lifetime, we show that this endosomal interaction is underpinned by asymmetric binding of EEA1 to very early and early endosomes through its N- and C-termini, respectively. In combination with agent-based simulation which supports a 'trigger-and-convert' model, our findings indicate that APPL1- to EEA1-positive maturation is driven not by autonomous events but by heterotypic EEA1-mediated interactions, providing a mechanism for temporal and population-level control of maturation.

Robustness and Universality in Organelle Size Control

One of the grand challenges in cellular biophysics is understanding the precision with which cells assemble and maintain subcellular structures. Organelle sizes, for example, must be flexible enough to allow cells to grow or shrink them as environments demand yet be maintained within homeostatic limits. Despite identification of molecular factors that regulate organelle sizes we lack insight into the quantitative principles underlying organelle size control. Here we show experimentally that cells can robustly control average fluctuations in organelle size. By demonstrating that organelle sizes obey a universal scaling relationship we predict theoretically, our framework suggests that organelles grow in random bursts from a limiting pool of building blocks. Burstlike growth provides a general biophysical mechanism by which cells can maintain on average reliable yet plastic organelle sizes.

From cartoons to quantitative models in Golgi transport

BACKGROUND

Cell biology is evolving to become a more formal and quantitative science. In particular, several mathematical models have been proposed to address Golgi self-organisation and protein and lipid transport. However, most scientific articles about the Golgi apparatus are still using static cartoons that miss the dynamism of this organelle.

RESULTS

In this report, we show that schematic drawings of Golgi trafficking can be easily translated into an agent-based model using the Repast platform. The simulations generate an active interplay among cisternae and vesicles rendering quantitative predictions about Golgi stability and transport of soluble and membrane-associated cargoes. The models can incorporate complex networks of molecular interactions and chemical reactions by association with COPASI, a software that handles ordinary differential equations.

CONCLUSIONS

The strategy described provides a simple, flexible and multiscale support to analyse Golgi transport. The simulations can be used to address issues directly linked to the mechanism of transport or as a way to incorporate the complexity of trafficking to other cellular processes that occur in dynamic organelles.

SIGNIFICANCE

We show that the rules implicitly present in most schematic representations of intracellular trafficking can be used to build dynamic models with quantitative outputs that can be compared with experimental results.

Stochastic reaction networks in dynamic compartment populations

Many biochemical processes in living systems take place in compartmentalized environments, where individual compartments can interact with each other and undergo dynamic remodeling. Studying such processes through mathematical models poses formidable challenges because the underlying dynamics involve a large number of states, which evolve stochastically with time. Here we propose a mathematical framework to study stochastic biochemical networks in compartmentalized environments. We develop a generic population model, which tracks individual compartments and their molecular composition. We then show how the time evolution of this system can be studied effectively through a small number of differential equations, which track the statistics of the population. Our approach is versatile and renders an important class of biological systems computationally accessible.

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress toward addressing this problem in the context of specific biological systems, but a general and sufficiently effective approach remains lacking. In this work, we propose a mathematical framework based on counting processes that allows us to study dynamic compartment populations with arbitrary interactions and internal biochemistry. We derive an efficient description of the dynamics in terms of differential equations which capture the statistics of the population. We demonstrate the relevance of our approach by analyzing models inspired by different biological processes, including subcellular compartmentalization and tissue homeostasis.

A minimal self-organisation model of the Golgi apparatus

The design principles dictating the spatio-temporal organisation of eukaryotic cells, and in particular the mechanisms controlling the self-organisation and dynamics of membrane-bound organelles such as the Golgi apparatus, remain elusive. Although this organelle was discovered 120 years ago, such basic questions as whether vesicular transport through the Golgi occurs in an anterograde (from entry to exit) or retrograde fashion are still strongly debated. Here, we address these issues by studying a quantitative model of organelle dynamics that includes: de-novo compartment generation, inter-compartment vesicular exchange, and biochemical conversion of membrane components. We show that anterograde or retrograde vesicular transports are asymptotic behaviors of a much richer dynamical system. Indeed, the structure and composition of cellular compartments and the directionality of vesicular exchange are intimately linked. They are emergent properties that can be tuned by varying the relative rates of vesicle budding, fusion and biochemical conversion.

A novel combinatorial approach of quantitative microscopy and in silico modeling deciphers Arf1-dependent Golgi size regulation

Regulation of organelle size and shape is a poorly understood but fascinating subject. Several theoretical studies were reported on Golgi size regulation, but a combination of experimental and theoretical approaches is rare. In combination with the quantitative microscopy and a coarse-grained simulation model, we have developed a technique to gain insights into the functions of potential regulators of Golgi size in budding yeast Saccharomyces cerevisiae. To validate our method, we tested wild-type and arf1[Formula: see text] strain harboring early and late Golgi cisternae labeled with green and red fluorescent fusions. Our concentration-dependent maturation model prediction concurs with most of the experimental results for both wild-type and arf1[Formula: see text] strains. Decisive match of simulation and experimental data provide insight into such specific factor's function in regulating the Golgi size. Details of the complex multifactorial network of Golgi size regulation can be deciphered in the future using a similar combination of quantitative microscopy and in silico model.

Postsynaptic Stability and Variability Described by a Stochastic Model of Endosomal Trafficking

Neurons undergo dynamic processes of constitutive AMPA-type glutamate receptor (AMPAR) trafficking, such as the insertion and internalization of AMPARs by exocytosis and endocytosis, while stably maintaining synaptic efficacy. Studies using advanced imaging techniques have suggested that the frequency of these constitutive trafficking processes, as well as the number of AMPARs that are involved in a particular event highly fluctuate. In addition, mechanisms that trigger some forms of synaptic plasticity have been shown to include not only these processes but also additional fluctuating processes, such as the sorting of AMPARs to late endosomes (LEs). Thus, the regulation of postsynaptic AMPARs by the endosomal trafficking system appears to have superficially conflicting properties between the stability or organized control of plasticity and highly fluctuating or stochastic processes. However, it is not clear how the endosomal trafficking system reconciles and utilizes such conflicting properties. Although deterministic models have been effective to describe the stable maintenance of synaptic AMPAR numbers by constitutive recycling, as well as the involvement of endosomal trafficking in synaptic plasticity, they do not take stochasticity into account. In this study, we introduced the stochasticity into the model of each crucial machinery of the endosomal trafficking system. The specific questions we solved by our improved model are whether stability is accomplished even with a combination of fluctuating processes, and how overall variability occurs while controlling long-term synaptic depression (LTD). Our new stochastic model indeed demonstrated the stable regulation of postsynaptic AMPAR numbers at the basal state and during LTD maintenance, despite fast fluctuations in AMPAR numbers as well as high variability in the time course and amounts of LTD. In addition, our analysis suggested that the high variability arising from this stochasticity is beneficial for reproducing the relatively constant timing of LE sorting for LTD. We therefore propose that the coexistence of stability and stochasticity in the endosomal trafficking system is suitable for stable synaptic transmission and the reliable induction of synaptic plasticity, with variable properties that have been observed experimentally.