To investigate how cellular variations arise across spatiotemporal scales in a population of identical healthy cells, we performed a data-driven analysis of nuclear growth variations in hiPS cell colonies as a model system. We generated a 3D timelapse dataset of thousands of nuclei over multiple days and developed open-source tools for image and data analysis and feature-based timelapse data exploration. Together, these data, tools, and workflows comprise a framework for systematic quantitative analysis of dynamics at individual and population levels, and the analysis further highlights important aspects to consider when interpreting timelapse data. We found that individual nuclear volume growth trajectories arise from short-timescale variations attributable to their spatiotemporal context within the colony. We identified a time-invariant volume compensation relationship between nuclear growth duration and starting volume across the population. Notably, we discovered that inheritance plays a crucial role in determining these two key nuclear growth features while other growth features are determined by their spatiotemporal context and are not inherited.

A key challenge in understanding subcellular organization is quantifying interpretable measurements of intracellular structures with complex multi-piece morphologies in an objective, robust and generalizable manner. Here we introduce a morphology-appropriate representation learning framework that uses three-dimensional rotation-invariant autoencoders and point clouds. This framework is used to learn representations of complex shapes that are independent of orientation, compact and interpretable. We apply our framework to intracellular structures with punctate morphologies (for example, DNA replication foci) and polymorphic morphologies (for example, nucleoli). We explore the trade-offs in the performance of this framework compared to image-based autoencoders by performing multi-metric benchmarking across efficiency, generative capability and representation expressivity metrics. We find that the proposed framework, which embraces the underlying morphology of multi-piece structures, can facilitate the unsupervised discovery of subclusters for each structure. We show how this approach can also be applied to phenotypic profiling using a dataset of nucleolar images following drug perturbations.

The Allen Institute for Cell Science aims to understand the principles by which human induced pluripotent stem cells (hiPSCs) establish and maintain robust dynamic localization of cellular structures, and how they transition between states during differentiation and disease. To do this, we take advantage of 3D microscopy images of the Allen Cell Collection (www.allencell.org), a collection of endogenous fluorescently tagged hiPSC lines, each representing a particular cellular organelle or structure. As an initial step towards this goal, we developed a computational framework using a combination of spherical harmonics expansion and principal component analysis (PCA) to achieve interpretable representations for cell and nuclear shapes. However, spherical harmonics are not suitable to describe complex morphologies such as tubular networks, spatial distributions and multi-piece structures. To extend our framework to these cases, we developed an approach using point clouds and signed distance functions as inputs to a rotation equivariant Variational Autoencoder. We showed that point clouds are appropriate representations for spatial protein patterns like DNA replication foci (via PCNA) and signed distance functions are appropriate for intricate, multi-piece shapes like nucleoli (via nucleophosmin). We found that a combination of pretraining on appropriate datasets and using loss functions based on optimal transport provide high-fidelity reconstructions and compact representations. In addition, we showed that the learned latent representations recapitulate known sources of variation of these structures, such as changes in number of nucleoli pieces, and characteristic spatial pattern across the cell cycle for PCNA. We further evaluated the strength of coupling of each structure to nuclear shape and rotation across the cell cycle using a conditional probability approach that we validated with a synthetic dataset. Future work will extend these analyses to intracellular structures with other characteristic geometries and interactions.

Understanding how a subset of expressed genes dictates cellular phenotype is a considerable challenge owing to the large numbers of molecules involved, their combinatorics and the plethora of cellular behaviours that they determine 1,2 . Here we reduced this complexity by focusing on cellular organization—a key readout and driver of cell behaviour 3,4 —at the level of major cellular structures that represent distinct organelles and functional machines, and generated the WTC-11 hiPSC Single-Cell Image Dataset v1, which contains more than 200,000 live cells in 3D, spanning 25 key cellular structures. The scale and quality of this dataset permitted the creation of a generalizable analysis framework to convert raw image data of cells and their structures into dimensionally reduced, quantitative measurements that can be interpreted by humans, and to facilitate data exploration. This framework embraces the vast cell-to-cell variability that is observed within a normal population, facilitates the integration of cell-by-cell structural data and allows quantitative analyses of distinct, separable aspects of organization within and across different cell populations. We found that the integrated intracellular organization of interphase cells was robust to the wide range of variation in cell shape in the population; that the average locations of some structures became polarized in cells at the edges of colonies while maintaining the ‘wiring’ of their interactions with other structures; and that, by contrast, changes in the location of structures during early mitotic reorganization were accompanied by changes in their wiring.

Actin assembly provides force for a multitude of cellular processes. Compared to actin-assembly-based force production during cell migration, relatively little is understood about how actin assembly generates pulling forces for vesicle formation. Here, cryo-electron tomography identified actin filament number, organization, and orientation during clathrin-mediated endocytosis in human SK-MEL-2 cells, showing that force generation is robust despite variance in network organization. Actin dynamics simulations incorporating a measured branch angle indicate that sufficient force to drive membrane internalization is generated through polymerization and that assembly is triggered from ∼4 founding “mother” filaments, consistent with tomography data. Hip1R actin filament anchoring points are present along the entire endocytic invagination, where simulations show that it is key to pulling force generation, and along the neck, where it targets filament growth and makes internalization more robust. Actin organization described here allowed direct translation of structure to mechanism with broad implications for other actin-driven processes.

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.

SummaryActin assembly provides force for a multitude of cellular processes. Compared to actin assembly- based force production during cell migration, relatively little is understood about how actin assembly generates pulling forces for vesicle formation. Here, cryo-electron tomography revealed actin filament number, organization, and orientation during clathrin-mediated endocytosis in human cells, showing that force generation is robust despite variance in network organization. Actin dynamics simulations incorporating a measured branch angle indicate that sufficient force to drive membrane internalization is generated through polymerization, and that assembly is triggered from ∼4 founding “mother” filaments, consistent with tomography data. Hip1R actin filament anchoring points are present along the entire endocytic invagination, where simulations show that it is key to pulling force generation, and along the neck, where it targets filament growth and makes internalization more robust. Actin cytoskeleton organization described here allowed direct translation of structure to mechanism with broad implications for other actin-driven processes.Highlights-Filament anchorage points are key to pulling force generation and efficiency.-Native state description of CME-associated actin force-producing networks.-Branched actin filament assembly is triggered from multiple mother filaments.-Actin force production is robust despite considerable network variability.

Many cellular processes, including clathrin-mediated endocytosis (CME), depend on actin filament networks. During CME, the plasma membrane is deformed, forming clathrin-coated vesicles (CCVs) containing cargo. With an experimentally constrained mathematical model, we previously demonstrated that a self-organizing actin network can produce sufficient force to internalize the coated pit (Akamatsu et al., eLife 2020). The study revealed gaps in knowledge of actin's structural organization necessary to understand its precise function in CME. Here we used cryo-electron tomography (cryo-ET) of intact mammalian cells to directly visualize actin organization during CME, and used mathematical modeling to identify the mechanistic implications of this architecture. Surprisingly, actin networks at CME sites consisted of both branched and unbranched filaments. The branched filaments arranged in multiple discrete clusters, in agreement with model simulations, implying that actin networks arise from several distinct “founding” mother filaments. Long filaments stretching from the coat toward the plasma membrane are oriented to allow for plasma membrane deformation and CCV transport. Filaments also oriented toward the neck of CME sites, indicating an additional function in CCV scission. Consistently, we found densities resembling the actin/CME linker Hip1R, both in the coat and around the neck. Mathematical modeling showed that this Hip1R neck localization not only directs filament growth toward the neck of CME sites, it also results in increased internalization efficiency. Taken together, our results reveal the complex actin filament organization at CME sites in unprecedented structural and mechanistic detail. By combining biophysical modeling and in situ cryo-ET, deeper insights into actin mechanism during CME were achieved than either approach alone. This approach generally will permit a mechanistic understanding of force-producing protein complexes in cellular processes.

Author(s): Vasan, Ritvik | Advisor(s): Rangamani, Padmini | Abstract: Cell and tissue movement are essential to embryonic development, cancer metastasis, wound healing, cargo delivery etc. These movements span multiple length scales — collective cell behavior occurs at ~ 10^-2m, membrane trafficking occurs at ~ 10^-8m, and the growth of the actin cytoskeleton occurs at ~ 10^-10m. The forces needed to drive movement begins with actin polymerization and other molecular motors, enabling local deformations that can translate into movement across length scales. Experimental methods for quantification of such forces are often difficult to implement in a high-throughput context and can be disruptive. In this work, we present mathematical and computational models to understand the relationship between cell movements and forces at two different length scales. At the sub-cellular length scale, we use Helfrich-energy theory in an axisymmetric and continuum framework to probe traction stress distributions generated along membrane tubules and buds. After discussing the applicability of this model to predict traction stresses from 2D electron micrograph (EM) images of membrane bud shapes, we then use a 3D Finite Element Model (FEM) to analyze a spontaneous symmetry breaking instability of the membrane neck during the pinching step of membrane trafficking. We draw similarities with classical buckling in many thin elastic structures, and proceed to analyze the effect of helical loading to compare against polymers like Dynamin. We then pair a continuum membrane mechanics model with an agent based model of filament dynamics to show that actin filaments self-organize to promote axial force production towards the base of the endocytic pit. At the tissue length scale, we use a vertex model of colony morphogenesis to validate a data-driven force-inference toolkit applicable to time-series 2D images of cell monolayers. We show that including a regularization term in the opitimization formulation boosts model prediction across time. We also discuss the potential for high-throughput imaging to model pipelines through machine learning algorithms for segmentation, generation, and meshing of cellular structures. Our models identify mechanisms of cell movement at two different length scales, enabling future work to establish the contribution of endocytic pathways in directing cell topologies and tissue morphogenesis.

Membrane neck formation is essential for scission, which, as recent experiments on tubules have demonstrated, can be location dependent. The diversity of biological machinery that can constrict a neck such as dynamin, actin, ESCRTs and BAR proteins, and the range of forces and deflection over which they operate, suggest that the constriction process is functionally mechanical and robust to changes in biological environment. In this study, we used a mechanical model of the lipid bilayer to systematically investigate the influence of location, symmetry constraints, and helical forces on membrane neck constriction. Simulations from our model demonstrated that the energy barriers associated with constriction of a membrane neck are location-dependent. Importantly, if symmetry restrictions are relaxed, then the energy barrier for constriction is dramatically lowered and the membrane buckles at lower values of forcing parameters. Our simulations also show that constriction due to helical proteins further reduces the energy barrier for neck formation compared to cylindrical proteins. These studies establish that despite different molecular mechanisms of neck formation in cells, the mechanics of constriction naturally leads to a loss of symmetry that can lower the energy barrier to constriction. Significance statement Membrane tubule constriction is a critical step of cellular membrane trafficking processes and is thought to be mechanically regulated. Mechanical modeling techniques employing the Helfrich Hamiltonian and axisymmetric continuum frameworks have previously described energy barriers to constriction as a function of location along a 26 membrane tubule. Recent advances in numerical modeling using spline basis functions (Isogeometric Analysis) enable us to conduct our analyses of membrane mechanics in a generalized 3D framework. Here, we implement a novel 3D Isogeometric Analysis framework and juxtapose it against an axisymmetric model to study the influence of location, symmetry constraints and helical collars on the constriction pathway. We show that an unsymmetric, “crushed soda can” neck consistently displays a lower energy barrier than a symmetric neck.

In this perspective, we examine three key aspects of an end-to-end pipeline for realistic cellular simulations: reconstruction and segmentation of cellular structures; generation of cellular structures; and mesh generation, simulation, and data analysis. We highlight some of the relevant prior work in these distinct but overlapping areas, with a particular emphasis on current use of machine learning technologies, as well as on future opportunities.

Summary Despite the intimate link between cell organization and function, the principles underlying intracellular organization and the relation between organization, gene expression and phenotype are not well understood. We address this by creating a benchmark for mean cell organization and the natural range of cell-to-cell variation. This benchmark can be used for comparison to other normal or abnormal cell states. To do this, we developed a reproducible microscope imaging pipeline to generate a high-quality dataset of 3D, high-resolution images of over 200,000 live cells from 25 isogenic human induced pluripotent stem cell (hiPSC) lines from the Allen Cell Collection. Each line contains one fluorescently tagged protein, created via endogenous CRISPR/Cas9 gene editing, representing a key cellular structure or organelle. We used these images to develop a new multi-part and generalizable analysis approach of the locations, amounts, and variation of these 25 cellular structures. Taking an integrated approach, we found that both the extent to which a structure’s individual location varied (“stereotypy”) and the extent to which the structure localized relative to all the other cellular structures (“concordance”) were robust to a wide range of cell shape variation, from flatter to taller, smaller to larger, or less to more polarized cells. We also found that these cellular structures varied greatly in how their volumes scaled with cell and nuclear size. These analyses create a data-driven set of quantitative rules for the locations, amounts, and variation of 25 cellular structures within the hiPSC as a normal baseline for cell organization.

Force generation by actin assembly shapes cellular membranes. An experimentally constrained multiscale model shows that a minimal branched actin network is sufficient to internalize endocytic pits against membrane tension. Around 200 activated Arp2/3 complexes are required for robust internalization. A newly developed molecule-counting method determined that ~200 Arp2/3 complexes assemble at sites of clathrin-mediated endocytosis in human cells. Simulations predict that actin self-organizes into a radial branched array with growing ends oriented toward the base of the pit. Long actin filaments bend between attachment sites in the coat and the base of the pit. Elastic energy stored in bent filaments, whose presence was confirmed by cryo-electron tomography, contributes to endocytic internalization. Elevated membrane tension directs more growing filaments toward the base of the pit, increasing actin nucleation and bending for increased force production. Thus, spatially constrained actin filament assembly utilizes an adaptive mechanism enabling endocytosis under varying physical constraints.

Cell shapes and connectivities evolve over time as the colony changes shape or embryos develop. Shapes of intercellular interfaces are closely coupled with the forces resulting from actomyosin interactions, membrane tension, or cell-cell adhesions. Although it is possible to computationally infer cell-cell forces from a mechanical model of collective cell behavior, doing so for temporally evolving forces in a manner robust to digitization difficulties is challenging. Here, we introduce a method for dynamic local intercellular tension estimation (DLITE) that infers such evolution in temporal force with less sensitivity to digitization ambiguities or errors. This method builds upon previous work on single time points (cellular force-inference toolkit). We validate our method using synthetic geometries. DLITE's inferred cell colony tension evolutions correlate better with ground truth for these synthetic geometries as compared to tension values inferred from methods that consider each time point in isolation. We introduce cell connectivity errors, angle estimate errors, connection mislocalization, and connection topological changes to synthetic data and show that DLITE has reduced sensitivity to these conditions. Finally, we apply DLITE to time series of human-induced pluripotent stem cell colonies with endogenously expressed GFP-tagged zonulae occludentes-1. We show that DLITE offers improved stability in the inference of cell-cell tensions and supports a correlation between the dynamics of cell-cell forces and colony rearrangement.

The shape of cell-cell interfaces and the forces resulting from actomyosin interactions, mem-brane tension, or cell-cell adhesion are closely coupled. For example, the tight junction protein, ZO-1, forms a link between the force-bearing actin cortex and the rest of the tight junction protein (TJP) complex, regulating epithelial cell differentiation and the flux of solutes across epithelia. Here we introduce a method for Dynamic Local Intercellular Tension Estimation (DLITE) to computationally infer the evolution of cell-cell forces from a mechanical model of collective cell behaviour. This builds upon prior work in the field (CellFIT, Brodland et al., PloS one 9.6 (2014): e99116). We validate our estimated forces against those predicted by Surface Evolver simulations. Inferred tensions of a cell colony rearranging over time correlate better with the ground truth for our method (DLITE) than for prior methods intended for single time-points. DLITE is robust to both skeletonization errors and topological changes. Finally, we used DLITE in WTC-11 human induced pluripotent stem (hIPS) cells endogenously expressing ZO-1 GFP to find that major topo-logical changes in cell connectivity, e.g. mitosis, can result in an increase in tension. This suggests a correlation between the dynamics of cell-cell forces and colony rearrangement.

Cell mechanics is thought to play a key role in the dynamical rearrangement of cells in a colony. Several studies have thus proposed methods to infer the distribution of force from shape. However, a tool for inferring the dynamical evolution of cell force from change in colony shape remains open to interpretation. In this study, we build upon previous work to devise a tool that can predict colony tensions and pressures across time given the evolution of cell shape. We validate this method by comparison to both prior work in the field and to finite element simulations of force development in synthetic colonies. We show that by conditioning the solution with information from a previous time step, we can obtain solutions that are smoother across time and are less sensitive to noise. Using this method, we predict tensions and pressures in a skeletonized time-series of mEGFP tagged tight junction protein ZO-1 in human induced pluripotent stem cells (hiPS) observed under a spinning confocal-disk microscope. Our results suggest that major topological changes, such as a mitotic event, lead to large stochasticity (i.e sudden large change) in tension and that tension changes play a key role during differentiation.

Curvature of biological membranes can be generated by a variety of molecular mechanisms including protein scaffolding, compositional heterogeneity, and cytoskeletal forces. These mechanisms have the net effect of generating tractions (force per unit length) on the bilayer that are translated into distinct shapes of the membrane. Here, we demonstrate how the local shape of the membrane can be used to infer the traction acting locally on the membrane. We show that buds and tubes, two common membrane deformations studied in trafficking processes, have different traction distributions along the membrane and that these tractions are specific to the molecular mechanism used to generate these shapes. Furthermore, we show that the magnitude of an axial force applied to the membrane as well as that of an effective line tension can be calculated from these tractions. Finally, we consider the sensitivity of these quantities with respect to uncertainties in material properties and follow with a discussion on sources of uncertainty in membrane shape.