Scaling of Subcellular Structures.

As cells grow, the size and number of their internal organelles increase in order to keep up with increased metabolic requirements. Abnormal size of organelles is a hallmark of cancer and an important aspect of diagnosis in cytopathology. Most organelles vary in either size or number, or both, as a function of cell size, but the mechanisms that create this variation remain unclear. In some cases, organelle size appears to scale with cell size through processes of relative growth, but in others the size may be set by either active measurement systems or genetic programs that instruct organelle biosynthetic activities to create organelles of a size appropriate to a given cell type.

Differential geometry meets the cell.

A new study by Terasaki et al. highlights the role of physical forces in biological form by showing that connections between stacked endoplasmic reticulum cisternae have a shape well known in classical differential geometry, the helicoid, and that this shape is a predictable consequence of membrane physics.

Extraordinary model systems for regeneration.

Regeneration is the remarkable phenomenon through which an organism can regrow lost or damaged parts with fully functional replacements, including complex anatomical structures, such as limbs. In 2019, Development launched its 'Model systems for regeneration' collection, a series of articles introducing some of the most popular model organisms for studying regeneration in vivo. To expand this topic further, this Perspective conveys the voices of five expert biologists from the field of regenerative biology, each of whom showcases some less well-known, but equally extraordinary, species for studying regeneration.

Modeling homologous chromosome recognition via nonspecific interactions.

In many organisms, most notably Drosophila, homologous chromosomes associate in somatic cells, a phenomenon known as somatic pairing, which takes place without double strand breaks or strand invasion, thus requiring some other mechanism for homologs to recognize each other. Several studies have suggested a "specific button" model, in which a series of distinct regions in the genome, known as buttons, can associate with each other, mediated by different proteins that bind to these different regions. Here, we use computational modeling to evaluate an alternative "button barcode" model, in which there is only one type of recognition site or adhesion button, present in many copies in the genome, each of which can associate with any of the others with equal affinity. In this model, buttons are nonuniformly distributed, such that alignment of a chromosome with its correct homolog, compared with a nonhomolog, is energetically favored; since to achieve nonhomologous alignment, chromosomes would be required to mechanically deform in order to bring their buttons into mutual register. By simulating randomly generated nonuniform button distributions, many highly effective button barcodes can be easily found, some of which achieve virtually perfect pairing fidelity. This model is consistent with existing literature on the effect of translocations of different sizes on homolog pairing. We conclude that a button barcode model can attain highly specific homolog recognition, comparable to that seen in actual cells undergoing somatic homolog pairing, without the need for specific interactions. This model may have implications for how meiotic pairing is achieved.

Aging induces aberrant state transition kinetics in murine muscle stem cells.

Murine muscle stem cells (MuSCs) experience a transition from quiescence to activation that is required for regeneration, but it remains unknown if the trajectory and dynamics of activation change with age. Here, we use time-lapse imaging and single cell RNA-seq to measure activation trajectories and rates in young and aged MuSCs. We find that the activation trajectory is conserved in aged cells, and we develop effective machine-learning classifiers for cell age. Using cell-behavior analysis and RNA velocity, we find that activation kinetics are delayed in aged MuSCs, suggesting that changes in stem cell dynamics may contribute to impaired stem cell function with age. Intriguingly, we also find that stem cell activation appears to be a random walk-like process, with frequent reversals, rather than a continuous linear progression. These results support a view of the aged stem cell phenotype as a combination of differences in the location of stable cell states and differences in transition rates between them.

The flagellar length control system: exploring the physical biology of organelle size.

How cells build and maintain dynamic structures of defined size is currently an important unsolved problem in quantitative cell biology. The flagella of the unicellular green algaChlamydomonasprovide a highly tractable model system to investigate this general question, but while the powerful genetics of this organism have revealed numerous genes required for proper flagellar length, in most cases we do not understand their mechanistic role in length control. Flagellar length can be viewed as the steady state solution of a dynamical system involving assembly and disassembly of axonemal microtubules, with assembly depending on an active transport process known as intraflagellar transport (IFT). The inherent length dependence of IFT gives rise to a family of simple models for length regulation that can account for many previously described phenomena such as the ability of flagella to maintain equal lengths. But these models requires that the cell has a way to measure flagellar length in order to adjust IFT rates accordingly. Several models for length sensing have been modeled theoretically and evaluated experimentally, allowing them to be ruled out. Current data support a model in which the diffusive return of the kinesin motor driving IFT provides a length dependence that ultimately is the basis for length regulation. By combining models of length sensing with a more detailed representation of cargo transport and availability, it is now becoming possible to formulate concrete hypotheses to explain length altering mutants.

Mitochondrial networks through the lens of mathematics.

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

Modeling cell biological features of meiotic chromosome pairing to study interlock resolution.

During meiosis, homologous chromosomes become associated side by side in a process known as homologous chromosome pairing. Pairing requires long range chromosome motion through a nucleus that is full of other chromosomes. It remains unclear how the cell manages to align each pair of chromosomes quickly while mitigating and resolving interlocks. Here, we use a coarse-grained molecular dynamics model to investigate how specific features of meiosis, including motor-driven telomere motion, nuclear envelope interactions, and increased nuclear size, affect the rate of pairing and the mitigation/resolution of interlocks. By creating in silico versions of three yeast strains and comparing the results of our model to experimental data, we find that a more distributed placement of pairing sites along the chromosome is necessary to replicate experimental findings. Active motion of the telomeric ends speeds up pairing only if binding sites are spread along the chromosome length. Adding a meiotic bouquet significantly speeds up pairing but does not significantly change the number of interlocks. An increase in nuclear size slows down pairing while greatly reducing the number of interlocks. Interestingly, active forces increase the number of interlocks, which raises the question: How do these interlocks resolve? Our model gives us detailed movies of interlock resolution events which we then analyze to build a step-by-step recipe for interlock resolution. In our model, interlocks must first translocate to the ends, where they are held in a quasi-stable state by a large number of paired sites on one side. To completely resolve an interlock, the telomeres of the involved chromosomes must come in close proximity so that the cooperativity of pairing coupled with random motion causes the telomeres to unwind. Together our results indicate that computational modeling of homolog pairing provides insight into the specific cell biological changes that occur during meiosis.

Ciliogenesis: building the cell's antenna.

The cilium is a complex organelle, the assembly of which requires the coordination of motor-driven intraflagellar transport (IFT), membrane trafficking and selective import of cilium-specific proteins through a barrier at the ciliary transition zone. Recent findings provide insights into how cilia assemble and disassemble in synchrony with the cell cycle and how the balance of ciliary assembly and disassembly determines the steady-state ciliary length, with the inherent length-dependence of IFT rendering the ciliary assembly rate a decreasing function of length. As cilia are important in sensing and processing developmental signals and directing the flow of fluids such as mucus, defects in ciliogenesis and length control are likely to underlie a range of cilium-related human diseases.

A simple method to generate human airway epithelial organoids with externally orientated apical membranes.

Organoids, which are self-organizing three-dimensional cultures, provide models that replicate specific cellular components of native tissues or facets of organ complexity. We describe a simple method to generate organoid cultures using isolated human tracheobronchial epithelial cells grown in mixed matrix components and supplemented at day 14 with the Wnt pathway agonist R-spondin 2 (RSPO2) and the bone morphogenic protein antagonist Noggin. In contrast to previous reports, our method produces differentiated tracheobronchospheres with externally orientated apical membranes without pretreatments, providing an epithelial model to study cilia formation and function, disease pathogenesis, and interaction of pathogens with the respiratory mucosa. Starting from 3 × 105 cells, organoid yield at day 28 was 1,720 ± 302. Immunocytochemistry confirmed the cellular localization of airway epithelial markers, including CFTR, Na+/K+ ATPase, acetylated-α-tubulin, E-cadherin, and ZO-1. Compared to native tissues, expression of genes related to bronchial differentiation and ion transport were similar in organoid and air-liquid interface (ALI) cultures. In matched primary cultures, mean organoid cilia length was 6.1 ± 0.2 µm, similar to that of 5.7 ± 0.1 µm in ALI cultures, and ciliary beating was vigorous and coordinated with frequencies of 7.7 ± 0.3 Hz in organoid cultures and 5.3 ± 0.8 Hz in ALI cultures. Functional measurement of osmotically induced volume changes in organoids showed low water permeability. The generation of numerous single testable units from minimal starting material complements prior techniques. This culture system may be useful for studying airway biology and pathophysiology, aiding diagnosis of ciliopathies, and potentially for high-throughput drug screening.

Dynamics of living cells in a cytomorphological state space.

Cells are nonequilibrium systems that exchange matter and energy with the environment to sustain their metabolic needs. The nonequilibrium nature of this system presents considerable challenges to developing a general theory describing its behavior; however, when studied at appropriate spatiotemporal scales, the behavior of ensembles of nonequilibrium systems can resemble that of a system at equilibrium. Here we apply this principle to a population of cells within a cytomorphological state space and demonstrate that cellular transition dynamics within this space can be described using equilibrium formalisms. We use this framework to map the effective energy landscape underlying the cytomorphological state space of a population of mouse embryonic fibroblasts (MEFs) and identify topographical nonuniformity in this space, indicating nonuniform occupation of cytomorphological states within an isogenic population. The introduction of exogenous apoptotic agents fundamentally altered this energy landscape, inducing formation of additional energy minima that correlated directly with changes in sensitivity to apoptosis induction. An equilibrium framework allows us to describe the behavior of an ensemble of single cells, suggesting that although cells are complex nonequilibrium systems, the application of formalisms derived from equilibrium thermodynamics can provide insight into the basis of nongenetic heterogeneities within cell populations, as well as the relationship between cytomorphological and functional heterogeneity.

Microfluidic guillotine reveals multiple timescales and mechanical modes of wound response in Stentor coeruleus.

BACKGROUND: Wound healing is one of the defining features of life and is seen not only in tissues but also within individual cells. Understanding wound response at the single-cell level is critical for determining fundamental cellular functions needed for cell repair and survival. This understanding could also enable the engineering of single-cell wound repair strategies in emerging synthetic cell research. One approach is to examine and adapt self-repair mechanisms from a living system that already demonstrates robust capacity to heal from large wounds. Towards this end, Stentor coeruleus, a single-celled free-living ciliate protozoan, is a unique model because of its robust wound healing capacity. This capacity allows one to perturb the wounding conditions and measure their effect on the repair process without immediately causing cell death, thereby providing a robust platform for probing the self-repair mechanism. RESULTS: Here we used a microfluidic guillotine and a fluorescence-based assay to probe the timescales of wound repair and of mechanical modes of wound response in Stentor. We found that Stentor requires ~ 100-1000 s to close bisection wounds, depending on the severity of the wound. This corresponds to a healing rate of ~ 8-80 µm2/s, faster than most other single cells reported in the literature. Further, we characterized three distinct mechanical modes of wound response in Stentor: contraction, cytoplasm retrieval, and twisting/pulling. Using chemical perturbations, active cilia were found to be important for only the twisting/pulling mode. Contraction of myonemes, a major contractile fiber in Stentor, was surprisingly not important for the contraction mode and was of low importance for the others. CONCLUSIONS: While events local to the wound site have been the focus of many single-cell wound repair studies, our results suggest that large-scale mechanical behaviors may be of greater importance to single-cell wound repair than previously thought. The work here advances our understanding of the wound response in Stentor and will lay the foundation for further investigations into the underlying components and molecular mechanisms involved.

Speed and Diffusion of Kinesin-2 Are Competing Limiting Factors in Flagellar Length-Control Model.

Flagellar length control in Chlamydomonas is a tractable model system for studying the general question of organelle size regulation. We have previously proposed that the diffusive return of the kinesin motor that powers intraflagellar transport can play a key role in length regulation. Here, we explore how the motor speed and diffusion coefficient for the return of kinesin-2 affect flagellar growth kinetics. We find that the system can exist in two distinct regimes, one dominated by motor speed and one by diffusion coefficient. Depending on length, a flagellum can switch between these regimes. Our results indicate that mutations can affect the length in distinct ways. We discuss our theory's implication for flagellar growth influenced by beating and provide possible explanations for the experimental observation that a beating flagellum is usually longer than its immotile mutant. These results demonstrate how our simple model can suggest explanations for mutant phenotypes.

Towards computer-aided design of cellular structure.

Cells are complex machines with tremendous potential for applications in medicine and biotechnology. Although much effort has been devoted to engineering the metabolic, genetic, and signaling pathways of cells, methods for systematically engineering the physical structure of cells are less developed. Here we consider how coarse-grained models for cellular geometry at the organelle level can be used to build computer-aided design (CAD) tools for cellular structure.

Building the cell: design principles of cellular architecture.

The astounding structural complexity of a cell arises from the action of a relatively small number of genes, raising the question of how this complexity is achieved. Self-organizing processes combined with simple physical constraints seem to have key roles in controlling organelle size, number, shape and position, and these factors then combine to produce the overall cell architecture. By examining how these parameters are controlled in specific cell biological examples we can identify a handful of simple design principles that seem to underlie cellular architecture and assembly.

Microfluidic guillotine for single-cell wound repair studies.

Wound repair is a key feature distinguishing living from nonliving matter. Single cells are increasingly recognized to be capable of healing wounds. The lack of reproducible, high-throughput wounding methods has hindered single-cell wound repair studies. This work describes a microfluidic guillotine for bisecting single Stentor coeruleus cells in a continuous-flow manner. Stentor is used as a model due to its robust repair capacity and the ability to perform gene knockdown in a high-throughput manner. Local cutting dynamics reveals two regimes under which cells are bisected, one at low viscous stress where cells are cut with small membrane ruptures and high viability and one at high viscous stress where cells are cut with extended membrane ruptures and decreased viability. A cutting throughput up to 64 cells per minute-more than 200 times faster than current methods-is achieved. The method allows the generation of more than 100 cells in a synchronized stage of their repair process. This capacity, combined with high-throughput gene knockdown in Stentor, enables time-course mechanistic studies impossible with current wounding methods.

Organelles - understanding noise and heterogeneity in cell biology at an intermediate scale.

Many studies over the years have shown that non-genetic mechanisms for producing cell-to-cell variation can lead to highly variable behaviors across genetically identical populations of cells. Most work to date has focused on gene expression noise as the primary source of phenotypic heterogeneity, yet other sources may also contribute. In this Commentary, we explore organelle-level heterogeneity as a potential secondary source of cellular 'noise' that contributes to phenotypic heterogeneity. We explore mechanisms for generating organelle heterogeneity and present evidence of functional links between organelle morphology and cellular behavior. Given the many instances in which molecular-level heterogeneity has been linked to phenotypic heterogeneity, we posit that organelle heterogeneity may similarly contribute to overall phenotypic heterogeneity and underline the importance of studying organelle heterogeneity to develop a more comprehensive understanding of phenotypic heterogeneity. Finally, we conclude with a discussion of the medical challenges associated with phenotypic heterogeneity and outline how improved methods for characterizing and controlling this heterogeneity may lead to improved therapeutic strategies and outcomes for patients.

Modeling meiotic chromosome pairing: a tug of war between telomere forces and a pairing-based Brownian ratchet leads to increased pairing fidelity.

Meiotic homolog pairing involves associations between homologous DNA regions scattered along the length of a chromosome. When homologs associate, they tend to do so by a processive zippering process, which apparently results from avidity effects. Using a computational model, we show that this avidity-driven processive zippering reduces the selectivity of pairing. When active random forces are applied to telomeres, this drop in selectivity is eliminated in a force-dependent manner. Further simulations suggest that active telomere forces are engaged in a tug-of-war against zippering, which can be interpreted as a Brownian ratchet with a stall force that depends on the dissociation constant of pairing. When perfectly homologous regions of high affinity compete with homeologous regions of lower affinity, the affinity difference can be amplified through this tug of war effect provided the telomere force acts in a range that is strong enough to oppose zippering of homeologs while still permitting zippering of correct homologs. The degree of unzippering depends on the radius of the nucleus, such that complete unzippering of homeologous regions can only take place if the nucleus is large enough to pull the two chromosomes completely apart. A picture of meiotic pairing thus emerges that is fundamentally mechanical in nature, possibly explaining the purpose of active telomere forces, increased nuclear diameter, and the presence of 'Maverick' chromosomes in meiosis.

Inferring cell state by quantitative motility analysis reveals a dynamic state system and broken detailed balance.

Cell populations display heterogeneous and dynamic phenotypic states at multiple scales. Similar to molecular features commonly used to explore cell heterogeneity, cell behavior is a rich phenotypic space that may allow for identification of relevant cell states. Inference of cell state from cell behavior across a time course may enable the investigation of dynamics of transitions between heterogeneous cell states, a task difficult to perform with destructive molecular observations. Cell motility is one such easily observed cell behavior with known biomedical relevance. To investigate heterogenous cell states and their dynamics through the lens of cell behavior, we developed Heteromotility, a software tool to extract quantitative motility features from timelapse cell images. In mouse embryonic fibroblasts (MEFs), myoblasts, and muscle stem cells (MuSCs), Heteromotility analysis identifies multiple motility phenotypes within the population. In all three systems, the motility state identity of individual cells is dynamic. Quantification of state transitions reveals that MuSCs undergoing activation transition through progressive motility states toward the myoblast phenotype. Transition rates during MuSC activation suggest non-linear kinetics. By probability flux analysis, we find that this MuSC motility state system breaks detailed balance, while the MEF and myoblast systems do not. Balanced behavior state transitions can be captured by equilibrium formalisms, while unbalanced switching between states violates equilibrium conditions and would require an external driving force. Our data indicate that the system regulating cell behavior can be decomposed into a set of attractor states which depend on the identity of the cell, together with a set of transitions between states. These results support a conceptual view of cell populations as dynamical systems, responding to inputs from signaling pathways and generating outputs in the form of state transitions and observable motile behaviors.

Diffusion as a Ruler: Modeling Kinesin Diffusion as a Length Sensor for Intraflagellar Transport.

An important question in cell biology is whether cells are able to measure size, either whole cell size or organelle size. Perhaps cells have an internal chemical representation of size that can be used to precisely regulate growth, or perhaps size is just an accident that emerges due to constraint of nutrients. The eukaryotic flagellum is an ideal model for studying size sensing and control because its linear geometry makes it essentially one-dimensional, greatly simplifying mathematical modeling. The assembly of flagella is regulated by intraflagellar transport (IFT), in which kinesin motors carry cargo adaptors for flagellar proteins along the flagellum and then deposit them at the tip, lengthening the flagellum. The rate at which IFT motors are recruited to begin transport into the flagellum is anticorrelated with the flagellar length, implying some kind of communication between the base and the tip and possibly indicating that cells contain some mechanism for measuring flagellar length. Although it is possible to imagine many complex scenarios in which additional signaling molecules sense length and carry feedback signals to the cell body to control IFT, might the already-known components of the IFT system be sufficient to allow length dependence of IFT? Here we investigate a model in which the anterograde kinesin motors unbind after cargo delivery, diffuse back to the base, and are subsequently reused to power entry of new IFT trains into the flagellum. By mathematically modeling and simulating such a system, we are able to show that the diffusion time of the motors can in principle be sufficient to serve as a proxy for length measurement. We found that the diffusion model can not only achieve a stable steady-state length without the addition of any other signaling molecules or pathways, but also is able to produce the anticorrelation between length and IFT recruitment rate that has been observed in quantitative imaging studies.