3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Local and global changes in cell density induce reorganisation of 3D packing in a proliferating epithelium

Tissue morphogenesis is intimately linked to the changes in shape and organisation of individual cells. In curved epithelia, cells can intercalate along their own apicobasal axes, adopting a shape named 'scutoid' that allows energy minimization in the tissue. Although several geometric and biophysical factors have been associated with this 3D reorganisation, the dynamic changes underlying scutoid formation in 3D epithelial packing remain poorly understood. Here, we use live imaging of the sea star embryo coupled with deep learning-based segmentation to dissect the relative contributions of cell density, tissue compaction and cell proliferation on epithelial architecture. We find that tissue compaction, which naturally occurs in the embryo, is necessary for the appearance of scutoids. Physical compression experiments identify cell density as the factor promoting scutoid formation at a global level. Finally, the comparison of the developing embryo with computational models indicates that the increase in the proportion of scutoids is directly associated with cell divisions. Our results suggest that apico-basal intercalations appearing immediately after mitosis may help accommodate the new cells within the tissue. We propose that proliferation in a compact epithelium induces 3D cell rearrangements during development.

Local and global changes in cell density induce reorganisation of 3D packing in a proliferating epithelium

Tissue morphogenesis is intimately linked to the changes in shape and organisation of individual cells. In curved epithelia, cells can intercalate along their own apicobasal axes adopting a shape named "scutoid" that allows energy minimization in the tissue. Although several geometric and biophysical factors have been associated with this 3D reorganisation, the dynamic changes underlying scutoid formation in 3D epithelial packing remain poorly understood. Here we use live-imaging of the sea star embryo coupled with deep learning-based segmentation, to dissect the relative contributions of cell density, tissue compaction, and cell proliferation on epithelial architecture. We find that tissue compaction, which naturally occurs in the embryo, is necessary for the appearance of scutoids. Physical compression experiments identify cell density as the factor promoting scutoid formation at a global level. Finally, the comparison of the developing embryo with computational models indicates that the increase in the proportion of scutoids is directly associated with cell divisions. Our results suggest that apico-basal intercalations appearing just after mitosis may help accommodate the new cells within the tissue. We propose that proliferation in a compact epithelium induces 3D cell rearrangements during development.

Integrating cellular electron microscopy with multimodal data to explore biology across space and time

Biology spans a continuum of length and time scales. Individual experimental methods only glimpse discrete pieces of this spectrum but can be combined to construct a more holistic view. In this Review, we detail the latest advancements in volume electron microscopy (vEM) and cryo-electron tomography (cryo-ET), which together can visualize biological complexity across scales from the organization of cells in large tissues to the molecular details inside native cellular environments. In addition, we discuss emerging methodologies for integrating three-dimensional electron microscopy (3DEM) imaging with multimodal data, including fluorescence microscopy, mass spectrometry, single-particle analysis, and AI-based structure prediction. This multifaceted approach fills gaps in the biological continuum, providing functional context, spatial organization, molecular identity, and native interactions. We conclude with a perspective on incorporating diverse data into computational simulations that further bridge and extend length scales while integrating the dimension of time.

Cristae formation is a mechanical buckling event controlled by the inner mitochondrial membrane lipidome

Cristae are high-curvature structures in the inner mitochondrial membrane (IMM) that are crucial for ATP production. While cristae-shaping proteins have been defined, analogous lipid-based mechanisms have yet to be elucidated. Here, we combine experimental lipidome dissection with multi-scale modeling to investigate how lipid interactions dictate IMM morphology and ATP generation. When modulating phospholipid (PL) saturation in engineered yeast strains, we observed a surprisingly abrupt breakpoint in IMM topology driven by a continuous loss of ATP synthase organization at cristae ridges. We found that cardiolipin (CL) specifically buffers the inner mitochondrial membrane against curvature loss, an effect that is independent of ATP synthase dimerization. To explain this interaction, we developed a continuum model for cristae tubule formation that integrates both lipid and protein-mediated curvatures. This model highlighted a snapthrough instability, which drives IMM collapse upon small changes in membrane properties. We also showed that cardiolipin is essential in low-oxygen conditions that promote PL saturation. These results demonstrate that the mechanical function of cardiolipin is dependent on the surrounding lipid and protein components of the IMM.

Spine apparatus modulates Ca 2+ in spines through spatial localization of sources and sinks

Dendritic spines are small protrusions on dendrites in neurons and serve as sites of postsynaptic activity. Some of these spines contain smooth endoplasmic reticulum (SER), and sometimes an even further specialized SER known as the spine apparatus (SA). In this work, we developed a stochastic spatial model to investigate the role of the SER and the SA in modulating Ca 2+ dynamics. Using this model, we investigated how ryanodine receptor (RyR) localization, spine membrane geometry, and SER geometry can impact Ca 2+ transients in the spine and in the dendrite. Our simulations found that RyR opening is dependent on where it is localized in the SER and on the SER geometry. In order to maximize Ca 2+ in the dendrites (for activating clusters of spines and spine-spine communication), a laminar SA was favorable with RyRs localized in the neck region, closer to the dendrite. We also found that the presence of the SER without the laminar structure, coupled with RyR localization at the head, leads to higher Ca 2+ presence in the spine. These predictions serve as design principles for understanding how spines with an ER can regulate Ca 2+ dynamics differently from spines without ER through a combination of geometry and receptor localization.

Highlights

1RyR opening in dendritic spine ER is location dependent and spine geometry dependent. Ca 2+ buffers and SERCA can buffer against runaway potentiation of spines even when CICR is activated. RyRs located towards the ER neck allow for more Ca 2+ to reach the dendrites. RyRs located towards the spine head are favorable for increased Ca 2+ in spines.

Cristae formation is a mechanical buckling event controlled by the inner membrane lipidome

Cristae are high curvature structures in the inner mitochondrial membrane (IMM) that are crucial for ATP production. While cristae-shaping proteins have been defined, analogous mechanisms for lipids have yet to be elucidated. Here we combine experimental lipidome dissection with multi-scale modeling to investigate how lipid interactions dictate IMM morphology and ATP generation. When modulating phospholipid (PL) saturation in engineered yeast strains, we observed a surprisingly abrupt breakpoint in IMM topology driven by a continuous loss of ATP synthase organization at cristae ridges. We found that cardiolipin (CL) specifically buffers the IMM against curvature loss, an effect that is independent of ATP synthase dimerization. To explain this interaction, we developed a continuum model for cristae tubule formation that integrates both lipid and protein-mediated curvatures. The model highlighted a snapthrough instability, which drives IMM collapse upon small changes in membrane properties. We also showed that CL is essential in low oxygen conditions that promote PL saturation. These results demonstrate that the mechanical function of CL is dependent on the surrounding lipid and protein components of the IMM.

Spatiotemporal modelling reveals geometric dependence of AMPAR dynamics on dendritic spine morphology

The modification of neural circuits depends on the strengthening and weakening of synaptic connections. Synaptic strength is often correlated to the density of the ionotropic, glutamatergic receptors, AMPARs, (α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors) at the postsynaptic density (PSD). While AMPAR density is known to change based on complex biological signalling cascades, the effect of geometric factors such as dendritic spine shape, size and curvature remain poorly understood. In this work, we developed a deterministic, spatiotemporal model to study the dynamics of AMPARs during long-term potentiation (LTP). This model includes a minimal set of biochemical events that represent the upstream signalling events, trafficking of AMPARs to and from the PSD, lateral diffusion in the plane of the spine membrane, and the presence of an extrasynaptic AMPAR pool. Using idealized and realistic spine geometries, we show that the dynamics and increase of bound AMPARs at the PSD depends on a combination of endo- and exocytosis, membrane diffusion, the availability of free AMPARs and intracellular signalling interactions. We also found non-monotonic relationships between spine volume and the change in AMPARs at the PSD, suggesting that spines restrict changes in AMPARs to optimize resources and prevent runaway potentiation. KEY POINTS: Synaptic plasticity involves dynamic biochemical and physical remodelling of small protrusions called dendritic spines along the dendrites of neurons. Proper synaptic functionality within these spines requires changes in receptor number at the synapse, which has implications for downstream neural functions, such as learning and memory formation. In addition to being signalling subcompartments, spines also have unique morphological features that can play a role in regulating receptor dynamics on the synaptic surface. We have developed a spatiotemporal model that couples biochemical signalling and receptor trafficking modalities in idealized and realistic spine geometries to investigate the role of biochemical and biophysical factors in synaptic plasticity. Using this model, we highlight the importance of spine size and shape in regulating bound AMPA receptor dynamics that govern synaptic plasticity, and predict how spine shape might act to reset synaptic plasticity as a built-in resource optimization and regulation tool.

CellRemorph: A Toolkit for Transforming, Selecting, and Slicing 3D Cell Structures on the Road to Morphologically Detailed Astrocyte Simulations

Understanding functions of astrocytes can be greatly enhanced by building and simulating computational models that capture their morphological details. Novel computational tools enable utilization of existing morphological data of astrocytes and building models that have appropriate level of details for specific simulation purposes. In addition to analyzing existing computational tools for constructing, transforming, and assessing astrocyte morphologies, we present here the CellRemorph toolkit implemented as an add-on for Blender, a 3D modeling platform increasingly recognized for its utility for manipulating 3D biological data. To our knowledge, CellRemorph is the first toolkit for transforming astrocyte morphologies from polygonal surface meshes into adjustable surface point clouds and vice versa, precisely selecting nanoprocesses, and slicing morphologies into segments with equal surface areas or volumes. CellRemorph is an open-source toolkit under the GNU General Public License and easily accessible via an intuitive graphical user interface. CellRemorph will be a valuable addition to other Blender add-ons, providing novel functionality that facilitates the creation of realistic astrocyte morphologies for different types of morphologically detailed simulations elucidating the role of astrocytes both in health and disease.

High-resolution volumetric imaging constrains compartmental models to explore synaptic integration and temporal processing by cochlear nucleus globular bushy cells

Globular bushy cells (GBCs) of the cochlear nucleus play central roles in the temporal processing of sound. Despite investigation over many decades, fundamental questions remain about their dendrite structure, afferent innervation, and integration of synaptic inputs. Here, we use volume electron microscopy (EM) of the mouse cochlear nucleus to construct synaptic maps that precisely specify convergence ratios and synaptic weights for auditory nerve innervation and accurate surface areas of all postsynaptic compartments. Detailed biophysically based compartmental models can help develop hypotheses regarding how GBCs integrate inputs to yield their recorded responses to sound. We established a pipeline to export a precise reconstruction of auditory nerve axons and their endbulb terminals together with high-resolution dendrite, soma, and axon reconstructions into biophysically detailed compartmental models that could be activated by a standard cochlear transduction model. With these constraints, the models predict auditory nerve input profiles whereby all endbulbs onto a GBC are subthreshold (coincidence detection mode), or one or two inputs are suprathreshold (mixed mode). The models also predict the relative importance of dendrite geometry, soma size, and axon initial segment length in setting action potential threshold and generating heterogeneity in sound-evoked responses, and thereby propose mechanisms by which GBCs may homeostatically adjust their excitability. Volume EM also reveals new dendritic structures and dendrites that lack innervation. This framework defines a pathway from subcellular morphology to synaptic connectivity, and facilitates investigation into the roles of specific cellular features in sound encoding. We also clarify the need for new experimental measurements to provide missing cellular parameters, and predict responses to sound for further in vivo studies, thereby serving as a template for investigation of other neuron classes.

Close, but not too close: a mesoscopic description of (a)symmetry and membrane shaping mechanisms

Biomembranes are fundamental to our understanding of the cell, the basic building block of all life. An intriguing aspect of membranes is their ability to assume a variety of shapes, which is crucial for cell function. Here, we review various membrane shaping mechanisms with special focus on the current understanding of how local curvature and local rigidity induced by membrane proteins leads to emerging forces and consequently large-scale membrane deformations. We also argue that describing the interaction of rigid proteins with membranes purely in terms of local membrane curvature is incomplete and that changes in the membrane rigidity moduli must also be considered.

Crosstalk between biochemical signalling network architecture and trafficking governs AMPAR dynamics in synaptic plasticity

Synaptic plasticity involves modification of both biochemical and structural components of neurons. Many studies have revealed that the change in the number density of the glutamatergic receptor AMPAR at the synapse is proportional to synaptic weight update; an increase in AMPAR corresponds to strengthening of synapses while a decrease in AMPAR density weakens synaptic connections. The dynamics of AMPAR are thought to be regulated by upstream signalling, primarily the calcium-CaMKII pathway, trafficking to and from the synapse, and influx from extrasynaptic sources. Previous work in the field of deterministic modelling of CaMKII dynamics has assumed bistable kinetics, while experiments and rule-based modelling have revealed that CaMKII dynamics can be either monostable or ultrasensitive. This raises the following question: how does the choice of model assumptions involving CaMKII dynamics influence AMPAR dynamics at the synapse? To answer this question, we have developed a set of models using compartmental ordinary differential equations to systematically investigate contributions of different signalling and trafficking variations, along with their coupled effects, on AMPAR dynamics at the synaptic site. We find that the properties of the model including network architecture describing different stability features of CaMKII and parameters that capture the endocytosis and exocytosis of AMPAR significantly affect the integration of fast upstream species by slower downstream species. Furthermore, we predict that the model outcome, as determined by bound AMPAR at the synaptic site, depends on (1) the choice of signalling model (bistable CaMKII or monostable CaMKII dynamics), (2) trafficking versus influx contributions and (3) frequency of stimulus. KEY POINTS: The density of AMPA receptors (AMPARs) at the postsynaptic density of the synapse provides a readout of synaptic plasticity, which involves crosstalk between complex biochemical signalling networks including CaMKII dynamics and trafficking pathways including exocytosis and endocytosis. Here we build a model that integrates CaMKII dynamics and AMPAR trafficking to explore this crosstalk. We compare different models of CaMKII that result in monostable or bistable kinetics and their impact on AMPAR dynamics. Our results show that AMPAR density depends on the coupling between aspects of biochemical signalling and trafficking. Specifically, assumptions regarding CaMKII dynamics and its stability features can alter AMPAR density at the synapse. Our model also predicts that the kinetics of trafficking versus influx of AMPAR from the extrasynaptic space can further impact AMPAR density. Thus, the contributions of both signalling and trafficking should be considered in computational models.

Novel Ground-Up 3D Multicellular Simulators for Synthetic Biology CAD Integrating Stochastic Gillespie Simulations Benchmarked with Topologically Variable SBML Models

The elevation of Synthetic Biology from single cells to multicellular simulations would be a significant scale-up. The spatiotemporal behavior of cellular populations has the potential to be prototyped in silico for computer assisted design through ergonomic interfaces. Such a platform would have great practical potential across medicine, industry, research, education and accessible archiving in bioinformatics. Existing Synthetic Biology CAD systems are considered limited regarding population level behavior, and this work explored the in silico challenges posed from biological and computational perspectives. Retaining the connection to Synthetic Biology CAD, an extension of the Infobiotics Workbench Suite was considered, with potential for the integration of genetic regulatory models and/or chemical reaction networks through Next Generation Stochastic Simulator (NGSS) Gillespie algorithms. These were executed using SBML models generated by in-house SBML-Constructor over numerous topologies and benchmarked in association with multicellular simulation layers. Regarding multicellularity, two ground-up multicellular solutions were developed, including the use of Unreal Engine 4 contrasted with CPU multithreading and Blender visualization, resulting in a comparison of real-time versus batch-processed simulations. In conclusion, high-performance computing and client-server architectures could be considered for future works, along with the inclusion of numerous biologically and physically informed features, whilst still pursuing ergonomic solutions.

Ultraliser: a framework for creating multiscale, high-fidelity and geometrically realistic 3D models for in silico neuroscience

Ultraliser is a neuroscience-specific software framework capable of creating accurate and biologically realistic 3D models of complex neuroscientific structures at intracellular (e.g. mitochondria and endoplasmic reticula), cellular (e.g. neurons and glia) and even multicellular scales of resolution (e.g. cerebral vasculature and minicolumns). Resulting models are exported as triangulated surface meshes and annotated volumes for multiple applications in in silico neuroscience, allowing scalable supercomputer simulations that can unravel intricate cellular structure-function relationships. Ultraliser implements a high-performance and unconditionally robust voxelization engine adapted to create optimized watertight surface meshes and annotated voxel grids from arbitrary non-watertight triangular soups, digitized morphological skeletons or binary volumetric masks. The framework represents a major leap forward in simulation-based neuroscience, making it possible to employ high-resolution 3D structural models for quantification of surface areas and volumes, which are of the utmost importance for cellular and system simulations. The power of Ultraliser is demonstrated with several use cases in which hundreds of models are created for potential application in diverse types of simulations. Ultraliser is publicly released under the GNU GPL3 license on GitHub (BlueBrain/Ultraliser).

SIGNIFICANCE

There is crystal clear evidence on the impact of cell shape on its signaling mechanisms. Structural models can therefore be insightful to realize the function; the more realistic the structure can be, the further we get insights into the function. Creating realistic structural models from existing ones is challenging, particularly when needed for detailed subcellular simulations. We present Ultraliser, a neuroscience-dedicated framework capable of building these structural models with realistic and detailed cellular geometries that can be used for simulations.

Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry

Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared with approximation-based methods (e.g., finite element method [FEM]), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, Mem3DG, for modeling 3D mechanochemical dynamics of membranes based on discrete differential geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. To demonstrate, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid; and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions.

Dendritic spine morphology regulates calcium-dependent synaptic weight change

Dendritic spines act as biochemical computational units and must adapt their responses according to their activation history. Calcium influx acts as the first signaling step during postsynaptic activation and is a determinant of synaptic weight change. Dendritic spines also come in a variety of sizes and shapes. To probe the relationship between calcium dynamics and spine morphology, we used a stochastic reaction-diffusion model of calcium dynamics in idealized and realistic geometries. We show that despite the stochastic nature of the various calcium channels, receptors, and pumps, spine size and shape can modulate calcium dynamics and subsequently synaptic weight updates in a deterministic manner. Through a series of exhaustive simulations and analyses, we found that the calcium dynamics and synaptic weight change depend on the volume-to-surface area of the spine. The relationships between calcium dynamics and spine morphology identified in idealized geometries also hold in realistic geometries, suggesting that there are geometrically determined deterministic relationships that may modulate synaptic weight change.

Prolonged β-adrenergic stimulation disperses ryanodine receptor clusters in cardiomyocytes

Ryanodine receptors (RyRs) exhibit dynamic arrangements in cardiomyocytes, and we previously showed that ‘dispersion’ of RyR clusters disrupts Ca²⁺ homeostasis during heart failure (HF) (Kolstad et al., eLife, 2018). Here, we investigated whether prolonged β-adrenergic stimulation, a hallmark of HF, promotes RyR cluster dispersion and examined the underlying mechanisms. We observed that treatment of healthy rat cardiomyocytes with isoproterenol for 1 hr triggered progressive fragmentation of RyR clusters. Pharmacological inhibition of Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) reversed these effects, while cluster dispersion was reproduced by specific activation of CaMKII, and in mice with constitutively active Ser2814-RyR. A similar role of protein kinase A (PKA) in promoting RyR cluster fragmentation was established by employing PKA activation or inhibition. Progressive cluster dispersion was linked to declining Ca²⁺ spark fidelity and magnitude, and slowed release kinetics from Ca²⁺ propagation between more numerous RyR clusters. In healthy cells, this served to dampen the stimulatory actions of β-adrenergic stimulation over the longer term and protect against pro-arrhythmic Ca²⁺ waves. However, during HF, RyR dispersion was linked to impaired Ca²⁺ release. Thus, RyR localization and function are intimately linked via channel phosphorylation by both CaMKII and PKA, which, while finely tuned in healthy cardiomyocytes, underlies impaired cardiac function during pathology.

The many faces of membrane tension: Challenges across systems and scales

Our understanding of the role of membrane tension in the field of membrane biophysics is rapidly evolving from a passive construct to an active player in a variety of cellular phenomena. Membrane tension has been shown to be a key regulator of many cellular processes ranging including trafficking, ion channel activation, and the invasion of red blood cells by malaria parasites. Recent experimental advances in cells, including the development of a fluorescent tension reporter, have shown that membrane tension is heterogeneous. In this mini-review, I summarize the recent advances in membrane tension measurements and discuss the contributions from different cellular constituents such as the cortical cytoskeleton. Then, I will explore how these different complexities can be considered in biophysical models of different scales. Finally, I will elaborate on the need for iterations between models and experiments as technologies in both fields advance to enable us to obtain critical insights into the physiological role of membrane tension as a critical component of mechanotransduction.

Can biophysical models of dendritic spines be used to explore synaptic changes associated with addiction?

Effective treatments that prevent or reduce drug relapse vulnerability should be developed to relieve the high burden of drug addiction on society. This will only be possible by enhancing the understanding of the molecular mechanisms underlying the neurobiology of addiction. Recent experimental data have shown that dendritic spines, small protrusions from the dendrites that receive excitatory input, of spiny neurons in the nucleus accumbens exhibit morphological changes during drug exposure and withdrawal. Moreover, these changes relate to the characteristic drug-seeking behavior of addiction. However, due to the complexity of the dendritic spines, we do not yet fully understand the processes underlying their structural changes in response to different inputs. We propose that biophysical models can enhance the current understanding of these processes by incorporating different, and sometimes, discrepant experimental data to identify the shared underlying mechanisms and generate experimentally testable hypotheses. This review aims to give an up-to-date report on biophysical models of dendritic spines, focusing on those models that describe their shape changes, which are well-known to relate to learning and memory. Moreover, it examines how these models can enhance our understanding of the effect of the drugs and the synaptic changes during withdrawal, as well as during neurodegenerative disease progression such as Alzheimer's disease.

Single-Cell Transcriptomics Reveals a Conserved Metaplasia Program in Pancreatic Injury

BACKGROUND & AIMS

Acinar to ductal metaplasia (ADM) occurs in the pancreas in response to tissue injury and is a potential precursor for adenocarcinoma. The goal of these studies was to define the populations arising from ADM, the associated transcriptional changes, and markers of disease progression.

METHODS

Acinar cells were lineage-traced with enhanced yellow fluorescent protein (EYFP) to follow their fate post-injury. Transcripts of more than 13,000 EYFP+ cells were determined using single-cell RNA sequencing (scRNA-seq). Developmental trajectories were generated. Data were compared with gastric metaplasia, KrasG12D-induced neoplasia, and human pancreatitis. Results were confirmed by immunostaining and electron microscopy. KrasG12D was expressed in injury-induced ADM using several inducible Cre drivers. Surgical specimens of chronic pancreatitis from 15 patients were evaluated by immunostaining.

RESULTS

scRNA-seq of ADM revealed emergence of a mucin/ductal population resembling gastric pyloric metaplasia. Lineage trajectories suggest that some pyloric metaplasia cells can generate tuft and enteroendocrine cells (EECs). Comparison with KrasG12D-induced ADM identifies populations associated with disease progression. Activation of KrasG12D expression in HNF1B+ or POU2F3+ ADM populations leads to neoplastic transformation and formation of MUC5AC+ gastric-pit-like cells. Human pancreatitis samples also harbor pyloric metaplasia with a similar transcriptional phenotype.

CONCLUSIONS

Under conditions of chronic injury, acinar cells undergo a pyloric-type metaplasia to mucinous progenitor-like populations, which seed disparate tuft cell and EEC lineages. ADM-derived EEC subtypes are diverse. KrasG12D expression is sufficient to drive neoplasia when targeted to injury-induced ADM populations and offers an alternative origin for tumorigenesis. This program is conserved in human pancreatitis, providing insight into early events in pancreas diseases.

Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematicsand revealed by a three-dimensional computational framework

Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging and transport of nutrients, transmission of nerve impulses, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modelling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while robust and extensively deployed, suffer from their inability to model-symmetry breaking deformations and structural bifurcations. To address this limitation, a three-dimensional computational mechanics framework for high fidelity modelling of biomembrane deformation is presented. The proposed framework brings together Kirchhoff–Love thin-shell kinematics, Helfrich-energy-based mechanics, and state-of-the-art numerical techniques for modelling deformation of surface geometries. Lipid bilayers are represented as spline-based surface discretizations immersed in a three-dimensional space; this enables modelling of a wide spectrum of membrane geometries, boundary conditions, and deformations that are physically admissible in a three-dimensional space. The mathematical basis of the framework and its numerical machinery are presented, and their utility is demonstrated by modelling three classical, yet non-trivial, membrane deformation problems: formation of tubular shapes and their lateral constriction, Piezo1-induced membrane footprint generation and gating response, and the budding of membranes by protein coats during endocytosis. For each problem, the full three-dimensional membrane deformation is captured, potential symmetry-breaking deformation paths identified, and various case studies of boundary and load conditions are presented. Using the endocytic vesicle budding as a case study, we also present a ‘phase diagram’ for its symmetric and broken-symmetry states.

Morphological principles of neuronal mitochondria

In the highly dynamic metabolic landscape of a neuron, mitochondrial membrane architectures can provide critical insight into the unique energy balance of the cell. Current theoretical calculations of functional outputs like adenosine triphosphate and heat often represent mitochondria as idealized geometries, and therefore, can miscalculate the metabolic fluxes. To analyze mitochondrial morphology in neurons of mouse cerebellum neuropil, 3D tracings of complete synaptic and axonal mitochondria were constructed using a database of serial transmission electron microscopy (TEM) tomography images and converted to watertight meshes with minimal distortion of the original microscopy volumes with a granularity of 1.64 nanometer isotropic voxels. The resulting in-silico representations were subsequently quantified by differential geometry methods in terms of the mean and Gaussian curvatures, surface areas, volumes, and membrane motifs, all of which can alter the metabolic output of the organelle. Finally, we identify structural motifs present across this population of mitochondria, which may contribute to future modeling studies of mitochondrial physiology and metabolism in neurons.

Tetrahedral spectral feature-Based bayesian manifold learning for grey matter morphometry: Findings from the Alzheimer's disease neuroimaging initiative

Structural and anatomical analyses of magnetic resonance imaging (MRI) data often require a reconstruction of the three-dimensional anatomy to a statistical shape model. Our prior work demonstrated the usefulness of tetrahedral spectral features for grey matter morphometry. However, most of the current methods provide a large number of descriptive shape features, but lack an unsupervised scheme to automatically extract a concise set of features with clear biological interpretations and that also carries strong statistical power. Here we introduce a new tetrahedral spectral feature-based Bayesian manifold learning framework for effective statistical analysis of grey matter morphology. We start by solving the technical issue of generating tetrahedral meshes which preserve the details of the grey matter geometry. We then derive explicit weak-form tetrahedral discretizations of the Hamiltonian operator (HO) and the Laplace-Beltrami operator (LBO). Next, the Schrödinger's equation is solved for constructing the scale-invariant wave kernel signature (SIWKS) as the shape descriptor. By solving the heat equation and utilizing the SIWKS, we design a morphometric Gaussian process (M-GP) regression framework and an active learning strategy to select landmarks as concrete shape descriptors. We evaluate the proposed system on publicly available data from the Alzheimers Disease Neuroimaging Initiative (ADNI), using subjects structural MRI covering the range from cognitively unimpaired (CU) to full blown Alzheimer's disease (AD). Our analyses suggest that the SIWKS and M-GP compare favorably with seven other baseline algorithms to obtain grey matter morphometry-based diagnoses. Our work may inspire more tetrahedral spectral feature-based Bayesian learning research in medical image analysis.

Mechanical Principles Governing the Shapes of Dendritic Spines

Dendritic spines are small, bulbous protrusions along the dendrites of neurons and are sites of excitatory postsynaptic activity. The morphology of spines has been implicated in their function in synaptic plasticity and their shapes have been well-characterized, but the potential mechanics underlying their shape development and maintenance have not yet been fully understood. In this work, we explore the mechanical principles that could underlie specific shapes using a minimal biophysical model of membrane-actin interactions. Using this model, we first identify the possible force regimes that give rise to the classic spine shapes-stubby, filopodia, thin, and mushroom-shaped spines. We also use this model to investigate how the spine neck might be stabilized using periodic rings of actin or associated proteins. Finally, we use this model to predict that the cooperation between force generation and ring structures can regulate the energy landscape of spine shapes across a wide range of tensions. Thus, our study provides insights into how mechanical aspects of actin-mediated force generation and tension can play critical roles in spine shape maintenance.

Describing the movement of molecules in reduced-dimension models

When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is restricted to the reduced dimension, changing the nature of molecular movement. This change in molecular movement can lead to quantitatively and even qualitatively different results in the full and reduced systems. Within this manuscript we discuss the condition under which restricted molecular movement in reduced-dimension models accurately approximates molecular movement in the full system. For those systems which do not satisfy the condition, we present a general method for approximating unrestricted molecular movement in reduced-dimension models. We will derive a mathematically robust, finite difference method for solving the 2D diffusion equation within a 1D reduced-dimension model. The methods described here can be used to improve the accuracy of many reduced-dimension models while retaining benefits of system simplification.

Systems modeling predicts that mitochondria ER contact sites regulate the postsynaptic energy landscape

Spatiotemporal compartmentation of calcium dynamics is critical for neuronal function, particularly in postsynaptic spines. This exquisite level of Ca²⁺ compartmentalization is achieved through the storage and release of Ca²⁺ from various intracellular organelles particularly the endoplasmic reticulum (ER) and the mitochondria. Mitochondria and ER are established storage organelles controlling Ca²⁺ dynamics in neurons. Mitochondria also generate a majority of energy used within postsynaptic spines to support the downstream events associated with neuronal stimulus. Recently, high resolution microscopy has unveiled direct contact sites between the ER and the mitochondria (MERCs), which directly channel Ca²⁺ release from the ER into the mitochondrial membrane. In this study, we develop a computational 3D reaction-diffusion model to investigate the role of MERCs in regulating Ca²⁺ and ATP dynamics. This spatiotemporal model accounts for Ca²⁺ oscillations initiated by glutamate stimulus of metabotropic and ionotropic glutamate receptors and Ca²⁺ changes in four different compartments: cytosol, ER, mitochondria, and the MERC microdomain. Our simulations predict that the organization of these organelles and inter-organellar contact sites play a key role in modulating Ca²⁺ and ATP dynamics.

We further show that the crosstalk between geometry (mitochondria and MERC) and metabolic parameters (cytosolic ATP hydrolysis, ATP generation) influences the neuronal energy state. Our findings shed light on the importance of organelle interactions in predicting Ca²⁺ dynamics in synaptic signaling. Overall, our model predicts that a combination of MERC linkage and mitochondria size is necessary for optimal ATP production in the cytosol.

A spatial model of YAP/TAZ signaling reveals how stiffness, dimensionality, and shape contribute to emergent outcomes

YAP/TAZ is a master regulator of mechanotransduction whose functions rely on translocation from the cytoplasm to the nucleus in response to diverse physical cues. Substrate stiffness, substrate dimensionality, and cell shape are all input signals for YAP/TAZ, and through this pathway, regulate critical cellular functions and tissue homeostasis. Yet, the relative contributions of each biophysical signal and the mechanisms by which they synergistically regulate YAP/TAZ in realistic tissue microenvironments that provide multiplexed input signals remain unclear. For example, in simple two-dimensional culture, YAP/TAZ nuclear localization correlates strongly with substrate stiffness, while in three-dimensional (3D) environments, YAP/TAZ translocation can increase with stiffness, decrease with stiffness, or remain unchanged. Here, we develop a spatial model of YAP/TAZ translocation to enable quantitative analysis of the relationships between substrate stiffness, substrate dimensionality, and cell shape. Our model couples cytosolic stiffness to nuclear mechanics to replicate existing experimental trends, and extends beyond current data to predict that increasing substrate activation area through changes in culture dimensionality, while conserving cell volume, forces distinct shape changes that result in nonlinear effect on YAP/TAZ nuclear localization. Moreover, differences in substrate activation area versus total membrane area can account for counterintuitive trends in YAP/TAZ nuclear localization in 3D culture. Based on this multiscale investigation of the different system features of YAP/TAZ nuclear translocation, we predict that how a cell reads its environment is a complex information transfer function of multiple mechanical and biochemical factors. These predictions reveal a few design principles of cellular and tissue engineering for YAP/TAZ mechanotransduction.

Value of models for membrane budding

The budding of membranes and curvature generation is common to many forms of trafficking in cells. Clathrin-mediated endocytosis, as a prototypical example of trafficking, has been studied in great detail using a variety of experimental systems and methods. Recently, advances in experimental methods have led to great strides in insights on the molecular mechanisms and the spatiotemporal dynamics of the protein machinery associated with membrane curvature generation. These advances have been ably supported by computational models, which have given us insights into the underlying mechanical principles of clathrin-mediated endocytosis. On the other hand, targeted experimental perturbation of membranes has lagged behind that of proteins in cells. In this area, modeling is especially critical to interpret experimental measurements in a mechanistic context. Here, we discuss the contributions made by these models to our understanding of endocytosis and identify opportunities to strengthen the connections between models and experiments.

The complex three-dimensional organization of epithelial tissues

Understanding the cellular organization of tissues is key to developmental biology. In order to deal with this complex problem, researchers have taken advantage of reductionist approaches to reveal fundamental morphogenetic mechanisms and quantitative laws. For epithelia, their two-dimensional representation as polygonal tessellations has proved successful for understanding tissue organization. Yet, epithelial tissues bend and fold to shape organs in three dimensions. In this context, epithelial cells are too often simplified as prismatic blocks with a limited plasticity. However, there is increasing evidence that a realistic approach, even from a reductionist perspective, must include apico-basal intercalations (i.e. scutoidal cell shapes) for explaining epithelial organization convincingly. Here, we present an historical perspective about the tissue organization problem. Specifically, we analyze past and recent breakthroughs, and discuss how and why simplified, but realistic, in silico models require scutoidal features to address key morphogenetic events.

Cell shape regulates subcellular organelle location to control early Ca2+ signal dynamics in vascular smooth muscle cells

The shape of the cell is connected to its function; however, we do not fully understand underlying mechanisms by which global shape regulates a cell's functional capabilities. Using theory, experiments and simulation, we investigated how physiologically relevant cell shape changes affect subcellular organization, and consequently intracellular signaling, to control information flow needed for phenotypic function. Vascular smooth muscle cells going from a proliferative and motile circular shape to a contractile fusiform shape show changes in the location of the sarcoplasmic reticulum, inter-organelle distances, and differential distribution of receptors in the plasma membrane. These factors together lead to the modulation of signals transduced by the M3 muscarinic receptor/Gq/PLCβ pathway at the plasma membrane, amplifying Ca2+ dynamics in the cytoplasm, and the nucleus resulting in phenotypic changes, as determined by increased activity of myosin light chain kinase in the cytoplasm and enhanced nuclear localization of the transcription factor NFAT. Taken together, our observations show a systems level phenomenon whereby global cell shape affects subcellular organization to modulate signaling that enables phenotypic changes.