Diffusive search and trajectories on tubular networks: a propagator approach

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.

FAST SOLVER FOR DIFFUSIVE TRANSPORT TIMES ON DYNAMIC INTRACELLULAR NETWORKS

The transport of particles in cells is influenced by the properties of intracellular networks they traverse while searching for localized target regions or reaction partners. Moreover, given the rapid turnover in many intracellular structures, it is crucial to understand how temporal changes in the network structure affect diffusive transport. In this work, we use network theory to characterize complex intracellular biological environments across scales. We develop an efficient computational method to compute the mean first passage times for simulating a particle diffusing along two-dimensional planar networks extracted from fluorescence microscopy imaging. We first benchmark this methodology in the context of synthetic networks, and subsequently apply it to live-cell data from endoplasmic reticulum tubular networks.

Tube geometry controls protein cluster conformation and stability on the endoplasmic reticulum surface

The endoplasmic reticulum (ER), a cellular organelle that forms a cell-spanning network of tubes and sheets, is an important location of protein synthesis and folding. When the ER experiences sustained unfolded protein stress, IRE1 proteins embedded in the ER membrane activate and assemble into clusters as part of the unfolded protein response (UPR). We use kinetic Monte Carlo simulations to explore IRE1 clustering dynamics on the surface of ER tubes. While initially growing clusters are approximately round, once a cluster is sufficiently large a shorter interface length can be achieved by 'wrapping' around the ER tube. A wrapped cluster can grow without further interface length increases. Relative to wide tubes, narrower tubes enable cluster wrapping at smaller cluster sizes. Our simulations show that wrapped clusters on narrower tubes grow more rapidly, evaporate more slowly, and require a lower protein concentration to grow compared to equal-area round clusters on wider tubes. These results suggest that cluster wrapping, facilitated by narrower tubes, could be an important factor in the growth and stability of IRE1 clusters and thus impact the persistence of the UPR, connecting geometry to signaling behavior. This work is consistent with recent experimental observations of IRE1 clusters wrapped around narrow tubes in the ER network.

High-resolution imaging of presynaptic ER networks in Atlastin mutants

The endoplasmic reticulum (ER) is a continuous organelle that extends to the periphery of neurons and regulates many neuronal functions including neurite outgrowth, neurotransmission, and synaptic plasticity. Mutations in proteins that control ER shape are linked to the neurodegenerative disorder Hereditary Spastic Paraplegia (HSP). However, the ultrastructure and dynamics of the neuronal ER have been under-investigated, particularly at presynaptic terminals. Here we developed new super-resolution and live imaging methods in D. melanogaster larval motor neurons to investigate ER structure at presynaptic terminals from wild-type animals, and in null mutants of the HSP gene Atlastin. Previous studies indicated diffuse localization of an ER lumen marker at Atlastin mutant presynaptic terminals, which was attributed to ER fragmentation. By contrast, we found using an ER membrane marker that the ER in Atlastin mutants formed robust networks. Further, our high-resolution imaging results suggest that overexpression of luminal ER proteins in Atlastin mutants causes their progressive displacement to the cytosol at synapses, perhaps due to proteostatic stress and/or changes in ER membrane integrity. Remarkably, these luminal ER proteins remain correctly localized in cell bodies, axons, and other cell types such as body wall muscles, suggesting that ER tubules at synapses have unique structural and functional characteristics. This displacement phenotype has not been reported in numerous studies of Atlastin in non-neuronal cells, emphasizing the importance of conducting experiments in neurons when investigating the mechanisms leading to upper motor neuron dysfunction in HSP.

Quantitative modeling of EGF receptor ligand discrimination via internalization proofreading

The epidermal growth factor receptor (EGFR) is a central regulator of cell physiology that is stimulated by multiple distinct ligands. Although ligands bind to EGFR while the receptor is exposed on the plasma membrane, EGFR incorporation into endosomes following receptor internalization is an important aspect of EGFR signaling, with EGFR internalization behavior dependent upon the type of ligand bound. We develop quantitative modeling for EGFR recruitment to and internalization from clathrin domains, focusing on how internalization competes with ligand unbinding from EGFR. We develop two model versions: a kinetic model with EGFR behavior described as transitions between discrete states and a spatial model with EGFR diffusion to circular clathrin domains. We find that a combination of spatial and kinetic proofreading leads to enhanced EGFR internalization ratios in comparison to unbinding differences between ligand types. Various stages of the EGFR internalization process, including recruitment to and internalization from clathrin domains, modulate the internalization differences between receptors bound to different ligands. Our results indicate that following ligand binding, EGFR may encounter multiple clathrin domains before successful recruitment and internalization. The quantitative modeling we have developed describes competition between EGFR internalization and ligand unbinding and the resulting proofreading.

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.

Mitochondrial networks through the lens of mathematics

Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like, mitochondria often form interconnected networks within cells that exhibit dynamic restructuring through a variety of physical changes. Further, though relationships between form and function in biology are well established, the extant toolkit for understanding mitochondrial morphology is limited. Here, we emphasize new and established methods for quantitatively describing mitochondrial networks, ranging from unweighted graph-theoretic representations to multi-scale approaches from applied topology, in particular persistent homology. We also show fundamental relationships between mitochondrial networks, mathematics, and physics, using ideas of graph planarity and statistical mechanics to better understand the full possible morphological space of mitochondrial network structures. Lastly, we provide suggestions for how examination of mitochondrial network form through the language of mathematics can inform biological understanding, and vice versa.

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.

Dispersive transport dynamics in porous media emerge from local correlations

Understanding and controlling transport through complex media is central for a plethora of processes ranging from technical to biological applications. Yet, the effect of micro-scale manipulations on macroscopic transport dynamics still poses conceptual conundrums. Here, we demonstrate the predictive power of a conceptual shift in describing complex media by local micro-scale correlations instead of an assembly of uncorrelated minimal units. Specifically, we show that the non-linear dependency between microscopic morphological properties and macroscopic transport characteristics in porous media is captured by transport statistics on the level of pore junctions instead of single pores. Probing experimentally and numerically transport through two-dimensional porous media while gradually increasing flow heterogeneity, we find a non-monotonic change in transport efficiency. Using analytic arguments, we built physical intuition on how this non-monotonic dependency emerges from junction statistics. The shift in paradigm presented here broadly affects our understanding of transport within the diversity of complex media.

Dispersive transport through complex media, relevant for semiconductors, liquid crystals, and biological soft matter, is influenced by their microscopic, porous structure. The authors consider the statistics of pore-junction units, in contrast to individual pores, to link morphology and macroscopic transport characteristics.

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. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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.