The endoplasmic reticulum as an active liquid network.

The peripheral endoplasmic reticulum (ER) forms a dense, interconnected, and constantly evolving network of membrane-bound tubules in eukaryotic cells. While individual structural elements and the morphogens that stabilize them have been described, a quantitative understanding of the dynamic large-scale network topology remains elusive. We develop a physical model of the ER as an active liquid network, governed by a balance of tension-driven shrinking and new tubule growth. This minimalist model gives rise to steady-state network structures with density and rearrangement timescales predicted from the junction mobility and tubule spawning rate. Several parameter-independent geometric features of the liquid network model are shown to be representative of ER architecture in live mammalian cells. The liquid network model connects the timescales of distinct dynamic features such as ring closure and new tubule growth in the ER. Furthermore, it demonstrates how the steady-state network morphology on a cellular scale arises from the balance of microscopic dynamic rearrangements.

Endoplasmic reticulum morphology regulation by RTN4 modulates neuronal regeneration by curbing luminal transport.

Cell functions rely on intracellular transport systems distributing bioactive molecules with high spatiotemporal accuracy. The endoplasmic reticulum (ER) tubular network constitutes a system for delivering luminal solutes, including Ca2+, across the cell periphery. How the ER structure enables this nanofluidic transport system is unclear. Here, we show that ER membrane-localized reticulon 4 (RTN4/Nogo) is sufficient to impose neurite outgrowth inhibition in human cortical neurons while acting as an ER morphoregulator. Improving ER transport visualization methodologies combined with optogenetic Ca2+ dynamics imaging and in silico modeling, we observed that ER luminal transport is modulated by ER tubule narrowing and dilation, proportional to the amount of RTN4. Excess RTN4 limited ER luminal transport and Ca2+ release, while RTN4 elimination reversed the effects. The described morphoregulatory effect of RTN4 defines the capacity of the ER for peripheral Ca2+ delivery for physiological releases and thus may constitute a mechanism for controlling the (re)generation of neurites.

Dendrite architecture determines mitochondrial distribution patterns in vivo.

Neuronal morphology influences synaptic connectivity and neuronal signal processing. However, it remains unclear how neuronal shape affects steady-state distributions of organelles like mitochondria. In this work, we investigated the link between mitochondrial transport and dendrite branching patterns by combining mathematical modeling with in vivo measurements of dendrite architecture, mitochondrial motility, and mitochondrial localization patterns in Drosophila HS (horizontal system) neurons. In our model, different forms of morphological and transport scaling rules-which set the relative thicknesses of parent and daughter branches at each junction in the dendritic arbor and link mitochondrial motility to branch thickness-predict dramatically different global mitochondrial localization patterns. We show that HS dendrites obey the specific subset of scaling rules that, in our model, lead to realistic mitochondrial distributions. Moreover, we demonstrate that neuronal activity does not affect mitochondrial transport or localization, indicating that steady-state mitochondrial distributions are hard-wired by the architecture of the neuron.

Luminal transport through intact endoplasmic reticulum limits the magnitude of localized Ca2+ signals.

The endoplasmic reticulum (ER) forms an interconnected network of tubules stretching throughout the cell. Understanding how ER functionality relies on its structural organization is crucial for elucidating cellular vulnerability to ER perturbations, which have been implicated in several neuronal pathologies. One of the key functions of the ER is enabling Ca[Formula: see text] signaling by storing large quantities of this ion and releasing it into the cytoplasm in a spatiotemporally controlled manner. Through a combination of physical modeling and live-cell imaging, we demonstrate that alterations in ER shape significantly impact its ability to support efficient local Ca[Formula: see text] releases, due to hindered transport of luminal content within the ER. Our model reveals that rapid Ca[Formula: see text] release necessitates mobile luminal buffer proteins with moderate binding strength, moving through a well-connected network of ER tubules. These findings provide insight into the functional advantages of normal ER architecture, emphasizing its importance as a kinetically efficient intracellular Ca[Formula: see text] delivery system.

Endoplasmic reticulum network heterogeneity guides diffusive transport and kinetics.

The endoplasmic reticulum (ER) is a dynamic network of interconnected sheets and tubules that orchestrates the distribution of lipids, ions, and proteins throughout the cell. The impact of its complex, dynamic morphology on its function as an intracellular transport hub remains poorly understood. To elucidate the functional consequences of ER network structure and dynamics, we quantify how the heterogeneity of the peripheral ER in COS7 cells affects diffusive protein transport. In vivo imaging of photoactivated ER membrane proteins demonstrates their nonuniform spreading to adjacent regions, in a manner consistent with simulations of diffusing particles on extracted network structures. Using a minimal network model to represent tubule rearrangements, we demonstrate that ER network dynamics are sufficiently slow to have little effect on diffusive protein transport. Furthermore, stochastic simulations reveal a novel consequence of ER network heterogeneity: the existence of "hot spots" where sparse diffusive reactants are more likely to find one another. ER exit sites, specialized domains regulating cargo export from the ER, are shown to be disproportionately located in highly accessible regions, further from the outer boundary of the cell. Combining in vivo experiments with analytic calculations, quantitative image analysis, and computational modeling, we demonstrate how structure guides diffusive protein transport and reactions in the ER.

Diffusive exit rates through pores in membrane-enclosed structures.

The function of many membrane-enclosed intracellular structures relies on release of diffusing particles that exit through narrow pores or channels in the membrane. The rate of release varies with pore size, density, and length of the channel. We propose a simple approximate model, validated with stochastic simulations, for estimating the effective release rate from cylinders, and other simple-shaped domains, as a function of channel parameters. The results demonstrate that, for very small pores, a low density of channels scattered over the boundary is sufficient to achieve substantial rates of particle release. Furthermore, we show that increasing the length of passive channels will both reduce release rates and lead to a less steep dependence on channel density. Our results are compared to previously-measured local calcium release rates from tubules of the endoplasmic reticulum, providing an estimate of the relevant channel density responsible for the observed calcium efflux.

Mitochondrial mRNA localization is governed by translation kinetics and spatial transport.

For many nuclear-encoded mitochondrial genes, mRNA localizes to the mitochondrial surface co-translationally, aided by the association of a mitochondrial targeting sequence (MTS) on the nascent peptide with the mitochondrial import complex. For a subset of these co-translationally localized mRNAs, their localization is dependent on the metabolic state of the cell, while others are constitutively localized. To explore the differences between these two mRNA types we developed a stochastic, quantitative model for MTS-mediated mRNA localization to mitochondria in yeast cells. This model includes translation, applying gene-specific kinetics derived from experimental data; and diffusion in the cytosol. Even though both mRNA types are co-translationally localized we found that the steady state number, or density, of ribosomes along an mRNA was insufficient to differentiate the two mRNA types. Instead, conditionally-localized mRNAs have faster translation kinetics which modulate localization in combination with changes to diffusive search kinetics across metabolic states. Our model also suggests that the MTS requires a maturation time to become competent to bind mitochondria. Our work indicates that yeast cells can regulate mRNA localization to mitochondria by controlling mitochondrial volume fraction (influencing diffusive search times) and gene translation kinetics (adjusting mRNA binding competence) without the need for mRNA-specific binding proteins. These results shed light on both global and gene-specific mechanisms that enable cells to alter mRNA localization in response to changing metabolic conditions.

Spatiotemporal analysis of axonal autophagosome-lysosome dynamics reveals limited fusion events and slow maturation.

Macroautophagy is a homeostatic process required to clear cellular waste. Neuronal autophagosomes form constitutively in the distal tip of the axon and are actively transported toward the soma, with cargo degradation initiated en route. Cargo turnover requires autophagosomes to fuse with lysosomes to acquire degradative enzymes; however, directly imaging these fusion events in the axon is impractical. Here we use a quantitative model, parameterized and validated using data from primary hippocampal neurons, to explore the autophagosome maturation process. We demonstrate that retrograde autophagosome motility is independent of fusion and that most autophagosomes fuse with only a few lysosomes during axonal transport. Our results indicate that breakdown of the inner autophagosomal membrane is much slower in neurons than in nonneuronal cell types, highlighting the importance of this late maturation step. Together, rigorous quantitative measurements and mathematical modeling elucidate the dynamics of autophagosome-lysosome interaction and autophagosomal maturation in the axon.

Morphology and Transport in Eukaryotic Cells.

Transport of intracellular components relies on a variety of active and passive mechanisms, ranging from the diffusive spreading of small molecules over short distances to motor-driven motion across long distances. The cell-scale behavior of these mechanisms is fundamentally dependent on the morphology of the underlying cellular structures. Diffusion-limited reaction times can be qualitatively altered by the presence of occluding barriers or by confinement in complex architectures, such as those of reticulated organelles. Motor-driven transport is modulated by the architecture of cytoskeletal filaments that serve as transport highways. In this review, we discuss the impact of geometry on intracellular transport processes that fulfill a broad range of functional objectives, including delivery, distribution, and sorting of cellular components. By unraveling the interplay between morphology and transport efficiency, we aim to elucidate key structure-function relationships that govern the architecture of transport systems at the cellular scale.

Optimizing microtubule arrangements for rapid cargo capture.

Cellular functions such as autophagy, cell signaling, and vesicular trafficking involve the retrograde transport of motor-driven cargo along microtubules. Typically, newly formed cargo engages in slow undirected movement from its point of origin before attaching to a microtubule. In some cell types, cargo destined for delivery to the perinuclear region relies on capture at dynein-enriched loading zones located near microtubule plus ends. Such systems include extended cell regions of neurites and fungal hyphae, where the efficiency of the initial diffusive loading process depends on the axial distribution of microtubule plus ends relative to the initial cargo position. We use analytic mean first-passage time calculations and numerical simulations to model diffusive capture processes in tubular cells, exploring how the spatial arrangement of microtubule plus ends affects the efficiency of retrograde cargo transport. Our model delineates the key features of optimal microtubule arrangements that minimize mean cargo capture times. Namely, we show that configurations with a single microtubule plus end abutting the distal tip and broadly distributed other plus ends allow for efficient capture in a variety of different scenarios for retrograde transport. Live-cell imaging of microtubule plus ends in Aspergillus nidulans hyphae indicates that their distributions exhibit these optimal qualitative features. Our results highlight important coupling effects between the distribution of microtubule tips and retrograde cargo transport, providing guiding principles for the spatial arrangement of microtubules within tubular cell regions.

Diffusive search and trajectories on tubular networks: a propagator approach.

Several organelles in eukaryotic cells, including mitochondria and the endoplasmic reticulum, form interconnected tubule networks extending throughout the cell. These tubular networks host many biochemical pathways that rely on proteins diffusively searching through the network to encounter binding partners or localized target regions. Predicting the behavior of such pathways requires a quantitative understanding of how confinement to a reticulated structure modulates reaction kinetics. In this work, we develop both exact analytical methods to compute mean first passage times and efficient kinetic Monte Carlo algorithms to simulate trajectories of particles diffusing in a tubular network. Our approach leverages exact propagator functions for the distribution of transition times between network nodes and allows large simulation time steps determined by the network structure. The methodology is applied to both synthetic planar networks and organelle network structures, demonstrating key general features such as the heterogeneity of search times in different network regions and the functional advantage of broadly distributing target sites throughout the network. The proposed algorithms pave the way for future exploration of the interrelationship between tubular network structure and biomolecular reaction kinetics.

Optimizing mitochondrial maintenance in extended neuronal projections.

Neurons rely on localized mitochondria to fulfill spatially heterogeneous metabolic demands. Mitochondrial aging occurs on timescales shorter than the neuronal lifespan, necessitating transport of fresh material from the soma. Maintaining an optimal distribution of healthy mitochondria requires an interplay between a stationary pool localized to sites of high metabolic demand and a motile pool capable of delivering new material. Interchange between these pools can occur via transient fusion / fission events or by halting and restarting entire mitochondria. Our quantitative model of neuronal mitostasis identifies key parameters that govern steady-state mitochondrial health at discrete locations. Very infrequent exchange between stationary and motile pools optimizes this system. Exchange via transient fusion allows for robust maintenance, which can be further improved by selective recycling through mitophagy. These results provide a framework for quantifying how perturbations in organelle transport and interactions affect mitochondrial homeostasis in neurons, a key aspect underlying many neurodegenerative disorders.

Design principles for the glycoprotein quality control pathway.

Newly-translated glycoproteins in the endoplasmic reticulum (ER) often undergo cycles of chaperone binding and release in order to assist in folding. Quality control is required to distinguish between proteins that have completed native folding, those that have yet to fold, and those that have misfolded. Using quantitative modeling, we explore how the design of the quality-control pathway modulates its efficiency. Our results show that an energy-consuming cyclic quality-control process, similar to the observed physiological system, outperforms alternative designs. The kinetic parameters that optimize the performance of this system drastically change with protein production levels, while remaining relatively insensitive to the protein folding rate. Adjusting only the degradation rate, while fixing other parameters, allows the pathway to adapt across a range of protein production levels, aligning with in vivo measurements that implicate the release of degradation-associated enzymes as a rapid-response system for perturbations in protein homeostasis. The quantitative models developed here elucidate design principles for effective glycoprotein quality control in the ER, improving our mechanistic understanding of a system crucial to maintaining cellular health.

Elastic wrinkling of keratocyte lamellipodia driven by myosin-induced contractile stress.

During actin-based cell migration, the actin cytoskeleton in the lamellipodium both generates and responds to force, which has functional consequences for the ability of the cell to extend protrusions. However, the material properties of the lamellipodial actin network and its response to stress on the timescale of motility are incompletely understood. Here, we describe a dynamic wrinkling phenotype in the lamellipodium of fish keratocytes, in which the actin sheet buckles upward away from the ventral membrane of the cell, forming a periodic pattern of wrinkles perpendicular to the cell's leading edge. Cells maintain an approximately constant wrinkle wavelength over time despite new wrinkle formation and the lateral movement of wrinkles in the cell frame of reference, suggesting that cells have a preferred or characteristic wrinkle wavelength. Generation of wrinkles is dependent upon myosin contractility, and their wavelength scales directly with the density of the actin network and inversely with cell adhesion. These results are consistent with a simple physical model for wrinkling in an elastic sheet under compression and suggest that the lamellipodial cytoskeleton behaves as an elastic material on the timescale of cell migration despite rapid actin turnover.

Getting around the cell: physical transport in the intracellular world.

Eukaryotic cells face the challenging task of transporting a variety of particles through the complex intracellular milieu in order to deliver, distribute, and mix the many components that support cell function. In this review, we explore the biological objectives and physical mechanisms of intracellular transport. Our focus is on cytoplasmic and intra-organelle transport at the whole-cell scale. We outline several key biological functions that depend on physically transporting components across the cell, including the delivery of secreted proteins, support of cell growth and repair, propagation of intracellular signals, establishment of organelle contacts, and spatial organization of metabolic gradients. We then review the three primary physical modes of transport in eukaryotic cells: diffusive motion, motor-driven transport, and advection by cytoplasmic flow. For each mechanism, we identify the main factors that determine speed and directionality. We also highlight the efficiency of each transport mode in fulfilling various key objectives of transport, such as particle mixing, directed delivery, and rapid target search. Taken together, the interplay of diffusion, molecular motors, and flows supports the intracellular transport needs that underlie a broad variety of biological phenomena.

Impact of global structure on diffusive exploration of organelle networks.

We investigate diffusive search on planar networks, motivated by tubular organelle networks in cell biology that contain molecules searching for reaction partners and binding sites. Exact calculation of the diffusive mean first-passage time on a spatial network is used to characterize the typical search time as a function of network connectivity. We find that global structural properties - the total edge length and number of loops - are sufficient to largely determine network exploration times for a variety of both synthetic planar networks and organelle morphologies extracted from living cells. For synthetic networks on a lattice, we predict the search time dependence on these global structural parameters by connecting with percolation theory, providing a bridge from irregular real-world networks to a simpler physical model. The dependence of search time on global network structural properties suggests that network architecture can be designed for efficient search without controlling the precise arrangement of connections. Specifically, increasing the number of loops substantially decreases search times, pointing to a potential physical mechanism for regulating reaction rates within organelle network structures.

Mitochondrial Fission and Fusion Dynamics Generate Efficient, Robust, and Evenly Distributed Network Topologies in Budding Yeast Cells.

The simplest configuration of mitochondria in a cell is as small separate organellar units. Instead, mitochondria often form a dynamic, intricately connected network. A basic understanding of the topological properties of mitochondrial networks, and their influence on cell function is lacking. We performed an extensive quantitative analysis of mitochondrial network topology, extracting mitochondrial networks in 3D from live-cell microscopic images of budding yeast cells. In the presence of fission and fusion, mitochondrial network structures exhibited certain topological properties similar to other real-world spatial networks. Fission and fusion dynamics were required to efficiently distribute mitochondria throughout the cell and generate highly interconnected networks that can facilitate efficient diffusive search processes. Thus, mitochondrial fission and fusion combine to regulate the underlying topology of mitochondrial networks, which may independently impact cell function.

Hitching a Ride: Mechanics of Transport Initiation through Linker-Mediated Hitchhiking.

In contrast to the canonical picture of transport by direct attachment to motor proteins, recent evidence shows that a number of intracellular "cargos" navigate the cytoplasm by hitchhiking on motor-driven "carrier" organelles. We describe a quantitative model of intracellular cargo transport via hitchhiking, examining the efficiency of hitchhiking initiation as a function of geometric and mechanical parameters. We focus specifically on the parameter regime relevant to the hitchhiking motion of peroxisome organelles in fungal hyphae. Our work predicts the dependence of transport initiation rates on the distribution of cytoskeletal tracks and carrier organelles, as well as the number, length, and flexibility of the linker proteins that mediate contact between the carrier and the hitchhiking cargo. Furthermore, we demonstrate that attaching organelles to microtubules can result in a substantial enhancement of the hitchhiking initiation rate in tubular geometries such as those found in fungal hyphae. This enhancement is expected to increase the overall transport rate of hitchhiking organelles and lead to greater efficiency in organelle dispersion. Our results leverage a quantitative physical model to highlight the importance of organelle encounter dynamics in noncanonical intracellular transport.

Thermal fracture kinetics of heterogeneous semiflexible polymers.

The fracture and severing of polymer chains plays a critical role in the failure of fibrous materials and the regulated turnover of intracellular filaments. Using continuum wormlike chain models, we investigate the fracture of semiflexible polymers via thermal bending fluctuations, focusing on the role of filament flexibility and dynamics. Our results highlight a previously unappreciated consequence of mechanical heterogeneity in the filament, which enhances the rate of thermal fragmentation particularly in cases where constraints hinder the movement of the chain ends. Although generally applicable to semiflexible chains with regions of different bending stiffness, the model is motivated by a specific biophysical system: the enhanced severing of actin filaments at the boundary between stiff bare regions and mechanically softened regions that are coated with cofilin regulatory proteins. The results presented here point to a potential mechanism for disassembly of polymeric materials in general and cytoskeletal actin networks in particular by the introduction of locally softened chain regions, as occurs with cofilin binding.

Drive, filter, and stick: A protein sorting conspiracy in photoreceptors.

The sorting of proteins into different functional compartments is a fundamental cellular task. In this issue, Maza et al. (2019. J. Cell Biol https://doi.org/10.1083/jcb.201906024) demonstrate that distinct protein populations are dynamically generated in specialized regions of photoreceptors via an interplay of protein-membrane affinity, impeded diffusion, and driven transport.