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Motivation Access to unprecedented amounts of quantitative biological data allows us to build and test biochemically accurate reaction–diffusion models of intracellular processes. However, any increase in model complexity increases the number of unknown parameters and, thus, the computational cost of model analysis. To efficiently characterize the behavior and robustness of models with many unknown parameters remains, therefore, a key challenge in systems biology. Results We propose a novel computational framework for efficient high-dimensional parameter space characterization of reaction–diffusion models in systems biology. The method leverages the Lp-Adaptation algorithm, an adaptive-proposal statistical method for approximate design centering and robustness estimation. Our approach is based on an oracle function, which predicts for any given point in parameter space whether the model fulfills given specifications. We propose specific oracles to efficiently predict four characteristics of Turing-type reaction–diffusion models: bistability, instability, capability of spontaneous pattern formation and capability of pattern maintenance. We benchmark the method and demonstrate that it enables global exploration of a model’s ability to undergo pattern-forming instabilities and to quantify robustness for model selection in polynomial time with dimensionality. We present an application of the framework to pattern formation on the endosomal membrane by the small GTPase Rab5 and its effectors, and we propose molecular mechanisms underlying this system. Availability and implementation Our code is implemented in MATLAB and is available as open source under https://git.mpi-cbg.de/mosaic/software/black-box-optimization/rd-parameter-space-screening. Supplementary information Supplementary data are available at Bioinformatics online.

ATPases are a group of enzymes that can cyclically convert the free energy of ATP hydrolysis into mechanical work. GTPases are another class of enzymes that are predominantly associated with signal transduction processes, but their role in mechanotransduction is less established. It was previously shown that the binding of the GTPase Rab5 to the tethering protein EEA1 induces a large conformational change in EEA1 from a rigid, extended to a flexible, collapsed state. This entropic collapse of EEA1 gives rise to an effective force that can pull tethered membranes closer. It currently remains unclear if EEA1 can return from the collapsed to the extended conformation without the aid of chaperone proteins. Here we show that EEA1 in a bulk solution can undergo multiple flexibility transition cycles driven by the energetics of Rab5 binding and unbinding as well as GTP hydrolysis. Each cycle can perform up to 20kBT of mechanical work. Hence, Rab5 and EEA1 constitute a two-component molecular motor driven by the chemical energy derived from the Rab5 GTPase cycle. We conclude that tethering proteins and their small GTPase partners can have active mechanical roles in membrane trafficking.

Hepatocytes grow their apical surfaces anisotropically to generate a 3D network of bile canaliculi (BC). BC elongation is ensured by apical bulkheads, membrane extensions that traverse the lumen and connect juxtaposed hepatocytes. We hypothesize that apical bulkheads are mechanical elements that shape the BC lumen in liver development but also counteract elevated biliary pressure. Here, by resolving their structure using STED microscopy, we found that they are sealed by tight junction loops, connected by adherens junctions, and contain contractile actomyosin, characteristics of mechanical function. Apical bulkheads persist at high pressure upon microinjection of fluid into the BC lumen, and laser ablation demonstrated that they are under tension. A mechanical model based on ablation results revealed that apical bulkheads double the pressure BC can hold. Apical bulkhead frequency anticorrelates with BC connectivity during mouse liver development, consistent with predicted changes in biliary pressure. Our findings demonstrate that apical bulkheads are load-bearing mechanical elements that could protect the BC network against elevated pressure.

Three dimensional (3D) geometrical models are not only a powerful tool for quantitatively characterizing complex tissues but also useful for probing structure-function relationships in a tissue. However, these models are generally incomplete due to experimental limitations in acquiring multiple (>4) fluorescent channels simultaneously. Indeed, predictive geometrical and functional models of the liver have been restricted to few tissue and cellular components, excluding important cellular populations such as hepatic stellate cells (HSCs) and Kupffer cells (KCs). Here, we performed deep-tissue immunostaining, multiphoton microscopy, deeplearning techniques, and 3D image processing to computationally expand the number of simultaneously reconstructed tissue structures. We then generated a spatio-temporal singlecell atlas of hepatic architecture (Hep3D), including all main tissue and cellular components at different stages of post-natal development in mice. We used Hep3D to quantitatively study 1) hepatic morphodynamics from early post-natal development to adulthood, and 2) the structural role of KCs in the murine liver homeostasis. In addition to a complete description of bile canaliculi and sinusoidal network remodeling, our analysis uncovered unexpected spatiotemporal patterns of non-parenchymal cells and hepatocytes differing in size, number of nuclei, and DNA content. Surprisingly, we found that the specific depletion of KCs alters the number and morphology of the HSCs. These findings reveal novel characteristics of liver heterogeneity and have important implications for both the structural organization of liver tissue and its function. Our next-gen 3D single-cell atlas is a powerful tool to understand liver tissue architecture, under both physiological and pathological conditions.

The recognition of vesicles by their correct target compartment depends on the pairing of small GTPases with effector proteins (1–3). Whereas ATPases can cyclically convert the free energy of ATP hydrolysis into mechanical work, the function of small GTPases is predominantly associated with signal transduction processes, and their role in mechano-transduction is less established (4–6). However, binding of the GTPase Rab5 to the long coiled-coil tethering protein EEA1 on an early endosome induces a rigidity transition resulting in a large conformational change in EEA1 from a rigid and extended to a flexible and collapsed state. This entropic collapse of EEA1 gives rise to an effective force that can pull tethered membranes closer (7). It currently remains unclear if EEA1 can return from the collapsed to the extended conformation without the aid of chaperones. Here, we use fluorescence correlation spectroscopy to reveal that EEA1 in bulk solution can undergo multiple flexibility transition cycles that are associated with the binding and release of Rab5(GTP) and Rab5(GDP). Using semi-flexible polymer theory we provide evidence that the cyclic transitioning of Rab5-EEA1 between extended and collapsed conformations is driven by the energetics of Rab5 binding/unbinding and GTP hydrolysis. Cyclic flexibility transitions represent a complete mechanical work cycle that is able to perform up to 20 kBT of mechanical work per cycle, against an opposing force. Hence, Rab5 and EEA1 constitute a two-component molecular motor driven by the chemical energy derived from GTP hydrolysis by Rab5. We conclude that coiled-coil tethering proteins and their small GTPase partners can have active mechanical roles in membrane trafficking.

Paramasivam et al. compared the endosomal trafficking of six LNP-mRNA formulations. LNP-mRNA accumulates in large endosomes impaired in acidification and unproductive for delivery. Super-resolution microscopy allowed visualization of single LNP-mRNA within endosomes and escape of mRNA from endosomal recycling tubules., Delivery of exogenous mRNA using lipid nanoparticles (LNPs) is a promising strategy for therapeutics. However, a bottleneck remains in the poor understanding of the parameters that correlate with endosomal escape versus cytotoxicity. To address this problem, we compared the endosomal distribution of six LNP-mRNA formulations of diverse chemical composition and efficacy, similar to those used in mRNA-based vaccines, in primary human adipocytes, fibroblasts, and HeLa cells. Surprisingly, we found that total uptake is not a sufficient predictor of delivery, and different LNPs vary considerably in endosomal distributions. Prolonged uptake impaired endosomal acidification, a sign of cytotoxicity, and caused mRNA to accumulate in compartments defective in cargo transport and unproductive for delivery. In contrast, early endocytic/recycling compartments have the highest probability for mRNA escape. By using super-resolution microscopy, we could resolve a single LNP-mRNA within subendosomal compartments and capture events of mRNA escape from endosomal recycling tubules. Our results change the view of the mechanisms of endosomal escape and define quantitative parameters to guide the development of mRNA formulations toward higher efficacy and lower cytotoxicity.

Detection of nucleic acids within subcellular compartments is key to understanding their function. Determining the intracellular distribution of nucleic acids requires quantitative retention and estimation of their association with different organelles by immunofluorescence microscopy. This is particularly important for the delivery of nucleic acid therapeutics, which depends on endocytic uptake and endosomal escape. However, the current protocols fail to preserve the majority of exogenously delivered nucleic acids in the cytoplasm. To solve this problem, by monitoring Cy5-labeled mRNA delivered to primary human adipocytes via lipid nanoparticles (LNP), we optimized cell fixation, permeabilization, and immunostaining of a number of organelle markers, achieving quantitative retention of mRNA and allowing visualization of levels that escape detection using conventional procedures. The optimized protocol proved effective on exogenously delivered siRNA, miRNA, as well as endogenous miRNA. Our protocol is compatible with RNA probes of single molecule fluorescence in situ hybridization (smFISH) and molecular beacon, thus demonstrating that it is broadly applicable to study a variety of nucleic acids in cultured cells.

© 2022 The Authors. This is an open access article under the CC BY-NC-ND license http://creativecommons.org/licenses/by-nc-nd/4.0/)., Intracellular pathogens manipulate host cells to survive and thrive. Cellular sensing and signaling pathways are among the key host machineries deregulated to favor infection. In this study, we show that liver-stage Plasmodium parasites compete with the host to sequester a host endosomal-adaptor protein (APPL1) known to regulate signaling in response to endocytosis. The enrichment of APPL1 at the parasitophorous vacuole membrane (PVM) involves an atypical Plasmodium Rab5 isoform (Rab5b). Depletion of host APPL1 alters neither the infection nor parasite development; however, upon overexpression of a GTPase-deficient host Rab5 mutant (hRab5_Q79L), the parasites are smaller and their PVM is stripped of APPL1. Infection with the GTPase-deficient Plasmodium berghei Rab5b mutant (PbRab5b_Q91L) in this case rescues the PVM APPL1 signal and parasite size. In summary, we observe a robust correlation between the level of APPL1 retention at the PVM and parasite size during exoerythrocytic development., This work was supported by grants from the la Caixa Banking Foundation and Fundação para a Ciência e a Tecnologia (HR17-00264 and PTDC/SAU-PAR/30751/2017 respectively, both to M.M.M.). A.L and S.S.B were sponsored by Fundação para a Ciência e a Tecnologia fellowships (PD/BD/114036/2015, SFRH/BD/114464/2016, respectively). V.S acknowledges funding from the Science and Engineering Research Board (SERB) (EMR/2016/006810), Department of Science and Technology (DST), Government of India. V.P. and C.S. were supported by GRK2581 (P6) SPHINGOINF of the Growing Spine Foundation (DFG).

Hydrogen deuterium exchange mass spectrometry (HDX-MS) gives insight into the structure of proteins. By monitoring the rate of exchange of the amide hydrogens on the protein backbone with deuterium atoms in the solvent, one can determine if a given region is highly structured or dynamic, map binding sites of interacting molecules or determine if a binding event is associated with allosteric structural alterations in a protein. Herein, we illustrate the use of this technique to monitor the nucleotide exchange process in Rab5, using the guanine nucleotide exchange factor (GEF)-effector complex, Rabex5:Rabaptin5. By simultaneously monitoring the HDX in Rab5, Rabex5 and Rabaptin5, we can directly visualize nucleotide exchange in Rab5, gain mechanistic insights into the exchange reaction and, by witnessing the transfer of Rab5 from Rabex5 to Rabaptin5, provide direct evidence for the positive feedback loop generated by a GEF-effector complex. HDX-MS can be used to monitor a variety of Rab protein-effector and -regulator interactions and be widely applied to other enzymatic processes as well.

[This corrects the article DOI: 10.1371/journal.pcbi.1008412.].

Early disease diagnosis is key to the effective treatment of diseases. Histopathological analysis of human biopsies is the gold standard to diagnose tissue alterations. However, this approach has low resolution and overlooks 3D (three-dimensional) structural changes resulting from functional alterations. Here, we applied multiphoton imaging, 3D digital reconstructions and computational simulations to generate spatially resolved geometrical and functional models of human liver tissue at different stages of non-alcoholic fatty liver disease (NAFLD). We identified a set of morphometric cellular and tissue parameters correlated with disease progression, and discover profound topological defects in the 3D bile canalicular (BC) network. Personalized biliary fluid dynamic simulations predicted an increased pericentral biliary pressure and micro-cholestasis, consistent with elevated cholestatic biomarkers in patients’ sera. Our spatially resolved models of human liver tissue can contribute to high-definition medicine by identifying quantitative multiparametric cellular and tissue signatures to define disease progression and provide new insights into NAFLD pathophysiology. A combination of high-resolution imaging and modeling approaches facilitates the study of the mechanisms and clinical progression of non-alcoholic fatty liver disease in humans.

International audience; Many cellular organelles, including endosomes, show compartmentalization into distinct functional domains, which, however, cannot be resolved by diffraction-limited light microscopy. Single molecule localization microscopy (SMLM) offers nanoscale resolution but data interpretation is often inconclusive when the ultrastructural context is missing. Correlative light electron microscopy (CLEM) combining SMLM with electron microscopy (EM) enables correlation of functional subdomains of organelles in relation to their underlying ultrastructure at nanometer resolution. However, the specific demands for EM sample preparation and the requirements for fluorescent single-molecule photo-switching are opposed. Here, we developed a novel superCLEM workflow that combines triple-color SMLM (dSTORM & PALM) and electron tomography using semi-thin Tokuyasu thawed cryosections. We applied the superCLEM approach to directly visualize nanoscale compartmentalization of endosomes in HeLa cells. Internalized, fluorescently labeled Transferrin and EGF were resolved into morphologically distinct domains within the same endosome. We found that the small GTPase Rab5 is organized in nanodomains on the globular part of early endosomes. The simultaneous visualization of several proteins in functionally distinct endosomal sub-compartments demonstrates the potential of superCLEM to link the ultrastructure of organelles with their molecular organization at nanoscale resolution.

Long-distance axonal trafficking plays a critical role in neuronal function, and transport defects have been linked to neurodegenerative disorders. Various lines of evidence suggest that the small GTPase Rab5 plays a role in neuronal signaling via early endosomal transport. Here, we characterized the motility of Rab5 endosomes in primary cultures of mouse hippocampal pyramidal cells by live-cell imaging and showed that they exhibit bi-directional long-range motility in axons, with a strong bias toward retrograde transport. Characterization of key Rab5 effectors revealed that endogenous Rabankyrin-5, Rabenosyn-5 and APPL1 are all present in axons. Further analysis of APPL1-positive endosomes showed that, similar to Rab5-endosomes, they display more frequent long-range retrograde than anterograde movement, with the endosomal levels of APPL1 correlated with faster retrograde movement. Interestingly, APPL1-endosomes transport the neurotrophin receptor TrkB and mediate retrograde axonal transport of the kinase Akt1. FRET analysis revealed that APPL1 and Akt1 interact in an endocytosis-dependent manner. We conclude that Rab5-APPL1 endosomes exhibit the hallmarks of axonal signaling endosomes to transport Akt1 in hippocampal pyramidal cells.

Belicova et al. report previously unrecognized apical membrane extensions, forming a pattern reminiscent of the bulkheads of boats, that determine the anisotropic expansion of hepatocyte lumina. Loss of the bulkheads caused by Rab35 silencing leads to re-engineering of epithelial polarity and liver tissue architecture., Lumen morphogenesis results from the interplay between molecular pathways and mechanical forces. In several organs, epithelial cells share their apical surfaces to form a tubular lumen. In the liver, however, hepatocytes share the apical surface only between adjacent cells and form narrow lumina that grow anisotropically, generating a 3D network of bile canaliculi (BC). Here, by studying lumenogenesis in differentiating mouse hepatoblasts in vitro, we discovered that adjacent hepatocytes assemble a pattern of specific extensions of the apical membrane traversing the lumen and ensuring its anisotropic expansion. These previously unrecognized structures form a pattern, reminiscent of the bulkheads of boats, also present in the developing and adult liver. Silencing of Rab35 resulted in loss of apical bulkheads and lumen anisotropy, leading to cyst formation. Strikingly, we could reengineer hepatocyte polarity in embryonic liver tissue, converting BC into epithelial tubes. Our results suggest that apical bulkheads are cell-intrinsic anisotropic mechanical elements that determine the elongation of BC during liver tissue morphogenesis., Graphical Abstract

Detection of nucleic acids within sub-cellular compartments is key to understanding their function. Determining the intracellular distribution of nucleic acids requires quantitative retention and estimation of their association with different organelles by immunofluorescence microscopy. This is important also for the delivery of nucleic acid therapeutics which depends on endocytic uptake and endosomal escape. However, the current methods fail to preserve the majority of exogenously delivered nucleic acids in the cytoplasm. To solve this problem, by monitoring Cy5-labeled mRNA delivered to primary human adipocytes via lipid nanoparticles (LNP), we optimized cell fixation, permeabilization and immuno-staining of a number of organelle markers, achieving quantitative retention of mRNA and allowing visualization of levels which escape detection using conventional procedures. Additionally, we demonstrated the protocol to be effective on exogenously delivered siRNA, miRNA, as well as endogenous miRNA. Our protocol is compatible with RNA probes of single molecule fluorescence in-situ hybridization (smFISH) and molecular beacon, thus demonstrating that it is broadly applicable to study a variety of nucleic acids.

Long-range mRNA transport is crucial for the spatio-temporal regulation of gene expression, and its malfunction leads to neurological disorders. The pentameric FERRY Rab5 effector complex is the molecular link between mRNA and early endosomes in mRNA intracellular distribution. Here, we determine the cryo-EM structure of the human FERRY complex, composed of Fy-1 to Fy-5. The structure reveals a clamp-like architecture, where two arm-like appendages of Fy-2 and a Fy-5 dimer, protrude from the central Fy-4 dimer. The coiled-coil domains of Fy-2 are flexible and project into opposite directions from the core. While the Fy-2 C-terminal coiled-coil acts as binding region for Fy-1/3 and Rab5, both coiled-coils and Fy-5 concur to bind mRNA. Mutations causing truncations of Fy-2 in patients with neurological disorders impair Rab5 binding or FERRY complex assembly. Thus, Fy-2 serves as a binding hub connecting all five complex subunits and mediating the binding to mRNA and early endosomes via Rab5. The FERRY structure provides novel mechanistic insights into long-distance mRNA transport.

We present a novel method for model-based segmentation of extended, blob-like objects on curved surfaces. Our method addresses several challenges arising when imaging curved biological membrane, such as out-of-membrane signal and geometry-induced background variations. We use a particle-based reconstruction of the membrane geometry, moment-conserving intensity interpolation from pixels to surface particles, and model-based in-surface segmentation. Our method denoises and deconvolves images, corrects for background variations, and quantifies the number, size, and intensity of segmented objects. We benchmark the accuracy of the method and present two applications to (1) neuroepithelial focal adhesion sites during optic cup morphogenesis in zebrafish and (2) reconstituted membrane domains bearing the small GTPase Rab5 on spherical beads.

Hydrogen deuterium exchange mass spectrometry (HDX-MS) gives insight into the structure of proteins. By monitoring the rate of exchange of the amide hydrogens on the protein backbone with deuterium atoms in the solvent, one can determine if a given region is highly structured or dynamic, map binding sites of interacting molecules or determine if a binding event is associated with allosteric structural alterations in a protein. Herein, we illustrate the use of this technique to monitor the nucleotide exchange process in Rab5, using the guanine nucleotide exchange factor (GEF)-effector complex, Rabex5:Rabaptin5. By simultaneously monitoring the HDX in Rab5, Rabex5 and Rabaptin5, we can directly visualize nucleotide exchange in Rab5, gain mechanistic insights into the exchange reaction and, by witnessing the transfer of Rab5 from Rabex5 to Rabaptin5, provide direct evidence for the positive feedback loop generated by a GEF-effector complex. HDX-MS can be used to monitor a variety of Rab protein-effector and -regulator interactions and be widely applied to other enzymatic processes as well.

Delivery of exogenous mRNA using lipid nanoparticles (LNP) is a promising strategy for therapeutics. However, a bottleneck remains the poor understanding of the parameters that correlate with endosomal escape vs. cytotoxicity. To address this problem, we compared the endosomal distribution of six LNP-mRNA formulations of diverse chemical composition and efficacy, similar to those employed in mRNA-based vaccines, in primary human adipocytes, fibroblasts and HeLa cells. Surprisingly, we found that total uptake is not a sufficient predictor of delivery and different LNP vary considerably in endosomal distributions. Prolonged uptake impaired endosomal acidification, a sign of cytotoxicity, and caused mRNA to accumulate in compartments defective in cargo transport and unproductive for delivery. In contrast, early endocytic/recycling compartments have the highest probability for mRNA escape. By super-resolution microscopy we could resolve single LNP-mRNA within sub-endosomal compartments and capture events of mRNA escape from endosomal recycling tubules. Our results change the view of the mechanisms of endosomal escape and define quantitative parameters to guide the development of mRNA formulations towards higher efficacy and lower cytotoxicity.

How epithelial cells coordinate their polarity to form functional tissues is an open question in cell biology. Here, we characterize a unique type of polarity found in liver tissue, nematic cell polarity, which is different from vectorial cell polarity in simple, sheet-like epithelia. We propose a conceptual and algorithmic framework to characterize complex patterns of polarity proteins on the surface of a cell in terms of a multipole expansion. To rigorously quantify previously observed tissue-level patterns of nematic cell polarity (Morales-Navarrete et al., eLife 2019), we introduce the concept of co-orientational order parameters, which generalize the known biaxial order parameters of the theory of liquid crystals. Applying these concepts to three-dimensional reconstructions of single cells from high-resolution imaging data of mouse liver tissue, we show that the axes of nematic cell polarity of hepatocytes exhibit local coordination and are aligned with the biaxially anisotropic sinusoidal network for blood transport. Our study characterizes liver tissue as a biological example of a biaxial liquid crystal. The general methodology developed here could be applied to other tissues and in-vitro organoids., Author summary Cell polarity enables cells to carry out specific functions. Cell polarity is characterized by the formation of different plasma membrane domains, each with specific composition of proteins, phospholipids and cytoskeletal components. In simple epithelial sheets, or tube-like tissues such as kidney, epithelial cells are known to display a single apical domain, facing a lumenal cavity, and a single basal domain on the opposite side of the cell, facing a basal layer of extracellular matrix. This apico-basal polarity defines a vector of cell polarity, which provides a direction of fluid transport, e.g., from the basal side of the sheet to the lumen-facing side. In more complex, three-dimensional epithelial tissues, such as liver tissue with its complex network of blood-transporting sinusoids, the membrane domains of hepatocyte cells display more intricate patterns, including rings and antipodal pairs of apical membrane. Here, we develop a mathematical framework to precisely characterize and quantify complex polarity patterns. Thereby, we reveal ordered patterns of cell polarity that span across a liver lobule. Our new method builds on physical concepts originally developed for ordered phases of liquid crystals. It provides a versatile tool to characterize the spatial organization of a complex three-dimensional tissue.

Imaging biological systems at subcellular resolution and across scales is essential to under-standing how cells form tissues, organs, and organisms. However, existing large-scale optical techniques often require harsh tissue-clearing methods that cause significant morphological changes, compromise the integrity of cell membranes, and reduce the signal of fluorescent proteins. Here, we demonstrate multifocal two-photon microscopy that enables imaging mesoscopic scattering samples in their native tissue environment at high resolution and high speed.

Can three-dimensional, microvasculature networks still ensure blood supply if individual links fail? We address this question in the sinusoidal network, a plexus-like microvasculature network, which transports nutrient-rich blood to every hepatocyte in liver tissue, by building on recent advances in high-resolution imaging and digital reconstruction of adult mice liver tissue. We find that the topology of the three-dimensional sinusoidal network reflects its two design requirements of a space-filling network that connects all hepatocytes, while using shortest transport routes: sinusoidal networks are sub-graphs of the Delaunay graph of their set of branching points, and also contain the corresponding minimum spanning tree, both to good approximation. To overcome the spatial limitations of experimental samples and generate arbitrarily-sized networks, we developed a network generation algorithm that reproduces the statistical features of 0.3-mm-sized samples of sinusoidal networks, using multi-objective optimization for node degree and edge length distribution. Nematic order in these simulated networks implies anisotropic transport properties, characterized by an empirical linear relation between a nematic order parameter and the anisotropy of the permeability tensor. Under the assumption that all sinusoid tubes have a constant and equal flow resistance, we predict that the distribution of currents in the network is very inhomogeneous, with a small number of edges carrying a substantial part of the flow—a feature known for hierarchical networks, but unexpected for plexus-like networks. We quantify network resilience in terms of a permeability-at-risk, i.e., permeability as function of the fraction of removed edges. We find that sinusoidal networks are resilient to random removal of edges, but vulnerable to the removal of high-current edges. Our findings suggest the existence of a mechanism counteracting flow inhomogeneity to balance metabolic load on the liver., Author summary The liver is the largest metabolic organ of the human body and pivotal for blood detoxification and the uptake of many medically relevant drugs. Inside liver tissue, a dense meshwork of blood micro-vessels, the sinusoidal network, contacts every hepatocyte cell. The architecture of these networks, and especially how their function responds to local damage is not well understood. Previous theoretical work addressed network resilience in simple two-dimensional networks such as vein networks of leaves but not in three-dimensional networks, partly due to the considerable difficulties of imaging three-dimensional tissues. Here, we build on unprecedented advances in imaging mouse liver tissue. By simulating arbitrarily-sized networks that faithfully reproduce the statistical features of spatially restricted experimental samples, we computationally characterize the relation between a weak alignment of the network along the flow direction and enhanced transport along this direction. A simple transport model predicts an inhomogeneous distribution of flow in the sinusoidal network. Concomitantly, these networks are resilient against the random removal of edges, but vulnerable against removal of ‘highway’ edges that carried a high flow in the unperturbed state. We speculate that yet unknown adaptive mechanisms balance the distribution of flows and thereby increase the resilience of this physiologically important network.

Background & Aims Most cholesterol gallstones have a core consisting of inorganic and/or organic calcium salts, although the mechanisms of core formation are poorly understood. We examined whether the paracellular permeability of ions at hepatic tight junctions is involved in the core formation of cholesterol gallstones, with particular interest in the role of phosphate ion, a common food additive and preservative. Methods We focused on claudin-3 (Cldn3), a paracellular barrier-forming tight junction protein whose expression in mouse liver decreases with age. Since Cldn3-knockout mice exhibited gallstone diseases, we used them to assess the causal relationship between paracellular phosphate ion permeability and the core formation of cholesterol gallstones. Results In the liver of Cldn3-knockout mice, the paracellular phosphate ion permeability through hepatic tight junctions was significantly increased, resulting in calcium phosphate core formation. Cholesterol overdose caused cholesterol gallstone disease in these mice. Conclusion We revealed that in the hepatobiliary system, Cldn3 functions as a paracellular barrier for phosphate ions, to help maintain biliary ion homeostasis. We provide in vivo evidence that elevated phosphate ion concentrations play a major role in the lifestyle- and age-related risks of developing cholesterol gallstone disease under cholesterol overdose. Lay summary Herein, we reveal a new mechanism for cholesterol gallstone formation, in which increased paracellular phosphate ion permeability across hepatobiliary epithelia causes calcium phosphate core formation and cholesterol gallstones. Thus, altered phosphate ion metabolism under cholesterol overdose plays a major role in the lifestyle- and age-related risks of developing cholesterol gallstone disease.