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Eukaryotic cells show an astounding ability to remodel their shape and cytoskeleton and to migrate through pores and constrictions smaller than their nuclear diameter. However, the relation of nuclear deformation and migration dynamics in confinement remains unclear. Here, we study the mechanics and dynamics of mesenchymal cancer cell nuclei transitioning through three-dimensional compliant hydrogel channels. We find a biphasic dependence of migration speed and transition frequency on channel width, peaking at widths comparable to the nuclear diameter. Using confocal imaging and hydrogel bead displacement, we determine nuclear deformations and corresponding forces during confined migration. The nucleus deforms reversibly with a reduction in volume during confinement. With decreasing channel width, the nuclear shape during transmigration changes biphasically, concomitant with the transitioning dynamics. Our proposed physical model explains the observed nuclear shapes and transitioning dynamics in terms of the cytoskeletal force generation adapting from purely pulling-based to a combined pulling- and pushing-based mechanism with increasing nuclear confinement.
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Movimiento Celular , Núcleo Celular , Humanos , Núcleo Celular/metabolismo , Citoesqueleto/metabolismo , Hidrogeles/química , Línea Celular Tumoral , Fenómenos BiomecánicosRESUMEN
Entropic forces have been argued to drive bacterial chromosome segregation during replication. In many bacterial species, however, specifically evolved mechanisms, such as loop-extruding SMC complexes and the ParABS origin segregation system, contribute to or are even required for chromosome segregation, suggesting that entropic forces alone may be insufficient. The interplay between and the relative contributions of these segregation mechanisms remain unclear. Here, we develop a biophysical model showing that purely entropic forces actually inhibit bacterial chromosome segregation until late replication stages. By contrast, our model reveals that loop-extruders loaded at the origins of replication, as observed in many bacterial species, alter the effective topology of the chromosome, thereby redirecting and enhancing entropic forces to enable accurate chromosome segregation during replication. We confirm our model predictions with polymer simulations: purely entropic forces do not allow for concurrent replication and segregation, whereas entropic forces steered by specifically loaded loop-extruders lead to robust, global chromosome segregation during replication. Finally, we show how loop-extruders can complement locally acting origin separation mechanisms, such as the ParABS system. Together, our results illustrate how changes in the geometry and topology of the polymer, induced by DNA-replication and loop-extrusion, impact the organization and segregation of bacterial chromosomes.
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Segregación Cromosómica , Cromosomas Bacterianos , Replicación del ADN , Entropía , Cromosomas Bacterianos/genética , Proteínas Bacterianas/metabolismo , Proteínas Bacterianas/genética , Origen de Réplica , Escherichia coli/genéticaRESUMEN
The interplay between bacterial chromosome organization and functions such as transcription and replication can be studied in increasing detail using novel experimental techniques. Interpreting the resulting quantitative data, however, can be theoretically challenging. In this minireview, we discuss how connecting experimental observations to biophysical theory and modeling can give rise to new insights on bacterial chromosome organization. We consider three flavors of models of increasing complexity: simple polymer models that explore how physical constraints, such as confinement or plectoneme branching, can affect bacterial chromosome organization; bottom-up mechanistic models that connect these constraints to their underlying causes, for instance, chromosome compaction to macromolecular crowding, or supercoiling to transcription; and finally, data-driven methods for inferring interpretable and quantitative models directly from complex experimental data. Using recent examples, we discuss how biophysical models can both deepen our understanding of how bacterial chromosomes are structured and give rise to novel predictions about bacterial chromosome organization.
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Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.
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Desarrollo Embrionario , Modelos Biológicos , Movimiento Celular/fisiologíaRESUMEN
The migratory dynamics of cells can be influenced by the complex microenvironment through which they move. It remains unclear how the motility machinery of confined cells responds and adapts to their microenvironment. Here, we propose a biophysical mechanism for a geometry-dependent coupling between cellular protrusions and the nucleus that leads to directed migration. We apply our model to geometry-guided cell migration to obtain insights into the origin of directed migration on asymmetric adhesive micropatterns and the polarization enhancement of cells observed under strong confinement. Remarkably, for cells that can choose between channels of different size, our model predicts an intricate dependence for cellular decision making as a function of the two channel widths, which we confirm experimentally.
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Extensiones de la Superficie Celular , Movimiento CelularRESUMEN
Nonlinear stiffening is a ubiquitous property of major types of biopolymers that make up the extracellular matrices (ECM) including collagen, fibrin, and basement membrane. Within the ECM, many types of cells such as fibroblasts and cancer cells have a spindle-like shape that acts like two equal and opposite force monopoles, which anisotropically stretch their surroundings and locally stiffen the matrix. Here, we first use optical tweezers to study the nonlinear force-displacement response to localized monopole forces. We then propose an effective-probe scaling argument that a local point force application can induce a stiffened region in the matrix, which can be characterized by a nonlinear length scale R* that increases with the increasing force magnitude; the local nonlinear force-displacement response is a result of the nonlinear growth of this effective probe that linearly deforms an increasing portion of the surrounding matrix. Furthermore, we show that this emerging nonlinear length scale R* can be observed around living cells and can be perturbed by varying matrix concentration or inhibiting cell contractility.
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Colágeno , Matriz Extracelular , Elasticidad , Biopolímeros , FibrinaRESUMEN
The multicellular organization of diverse systems, including embryos, intestines, and tumors relies on coordinated cell migration in curved environments. In these settings, cells establish supracellular patterns of motion, including collective rotation and invasion. While such collective modes have been studied extensively in flat systems, the consequences of geometrical and topological constraints on collective migration in curved systems are largely unknown. Here, we discover a collective mode of cell migration in rotating spherical tissues manifesting as a propagating single-wavelength velocity wave. This wave is accompanied by an apparently incompressible supracellular flow pattern featuring topological defects as dictated by the spherical topology. Using a minimal active particle model, we reveal that this collective mode arises from the effect of curvature on the active flocking behavior of a cell layer confined to a spherical surface. Our results thus identify curvature-induced velocity waves as a mode of collective cell migration, impacting the dynamical organization of 3D curved tissues.
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Movimiento Celular , RotaciónRESUMEN
In preparation for mitotic cell division, the nuclear DNA of human cells is compacted into individualized, X-shaped chromosomes1. This metamorphosis is driven mainly by the combined action of condensins and topoisomerase IIα (TOP2A)2,3, and has been observed using microscopy for over a century. Nevertheless, very little is known about the structural organization of a mitotic chromosome. Here we introduce a workflow to interrogate the organization of human chromosomes based on optical trapping and manipulation. This allows high-resolution force measurements and fluorescence visualization of native metaphase chromosomes to be conducted under tightly controlled experimental conditions. We have used this method to extensively characterize chromosome mechanics and structure. Notably, we find that under increasing mechanical load, chromosomes exhibit nonlinear stiffening behaviour, distinct from that predicted by classical polymer models4. To explain this anomalous stiffening, we introduce a hierarchical worm-like chain model that describes the chromosome as a heterogeneous assembly of nonlinear worm-like chains. Moreover, through inducible degradation of TOP2A5 specifically in mitosis, we provide evidence that TOP2A has a role in the preservation of chromosome compaction. The methods described here open the door to a wide array of investigations into the structure and dynamics of both normal and disease-associated chromosomes.
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Cromosomas Humanos , Cromosomas , Cromosomas/genética , Cromosomas/metabolismo , Cromosomas Humanos/metabolismo , ADN/química , ADN-Topoisomerasas de Tipo II/genética , Humanos , Mitosis , Óptica y FotónicaRESUMEN
Upscaling motor protein activity to perform work in man-made devices has long been an ambitious goal in bionanotechnology. The use of hierarchical motor assemblies, as realized in sarcomeres, has so far been complicated by the challenges of arranging sufficiently high numbers of motor proteins with nanoscopic precision. Here, we describe an alternative approach based on actomyosin cortex-like force production, allowing low complexity motor arrangements in a contractile meshwork that can be coated onto soft objects and locally activated by ATP. The design is reminiscent of a motorized exoskeleton actuating protein-based robotic structures from the outside. It readily supports the connection and assembly of micro-three-dimensional printed modules into larger structures, thereby scaling up mechanical work. We provide an analytical model of force production in these systems and demonstrate the design flexibility by three-dimensional printed units performing complex mechanical tasks, such as microhands and microarms that can grasp and wave following light activation.
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Procedimientos Quirúrgicos Robotizados , Robótica , Humanos , Impresión TridimensionalRESUMEN
Time irreversibility is a distinctive feature of nonequilibrium dynamics and several measures of irreversibility have been introduced to assess the distance from thermal equilibrium of a stochastically driven system. While the dynamical noise is often approximated as white, in many real applications the time correlations of the random forces can actually be significantly long-lived compared to the relaxation times of the driven system. We analyze the effects of temporal correlations in the noise on commonly used measures of irreversibility and demonstrate how the theoretical framework for white-noise-driven systems naturally generalizes to the case of colored noise. Specifically, we express the autocorrelation function, the area enclosing rates, and mean phase space velocity in terms of solutions of a Lyapunov equation and in terms of their white-noise limit values.
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Cell dispersion from a confined area is fundamental in a number of biological processes, including cancer metastasis. To date, a quantitative understanding of the interplay of single-cell motility, cell proliferation, and intercellular contacts remains elusive. In particular, the role of E- and N-cadherin junctions, central components of intercellular contacts, is still controversial. Combining theoretical modeling with in vitro observations, we investigate the collective spreading behavior of colonies of human cancer cells (T24). The spreading of these colonies is driven by stochastic single-cell migration with frequent transient cell-cell contacts. We find that inhibition of E- and N-cadherin junctions decreases colony spreading and average spreading velocities, without affecting the strength of correlations in spreading velocities of neighboring cells. Based on a biophysical simulation model for cell migration, we show that the behavioral changes upon disruption of these junctions can be explained by reduced repulsive excluded volume interactions between cells. This suggests that in cancer cell migration, cadherin-based intercellular contacts sharpen cell boundaries leading to repulsive rather than cohesive interactions between cells, thereby promoting efficient cell spreading during collective migration.
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Cadherinas , Neoplasias , Adhesión Celular , Comunicación Celular , Movimiento Celular , Proliferación Celular , HumanosRESUMEN
A long-standing puzzle in the rheology of living cells is the origin of the experimentally observed long-time stress relaxation. The mechanics of the cell is largely dictated by the cytoskeleton, which is a biopolymer network consisting of transient crosslinkers, allowing for stress relaxation over time. Moreover, these networks are internally stressed due to the presence of molecular motors. In this work we propose a theoretical model that uses a mode-dependent mobility to describe the stress relaxation of such prestressed transient networks. Our theoretical predictions agree favorably with experimental data of reconstituted cytoskeletal networks and may provide an explanation for the slow stress relaxation observed in cells.
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The spatiotemporal organization of bacterial cells is crucial for the active segregation of replicating chromosomes. In several species, including Caulobacter crescentus, the ATPase ParA binds to DNA and forms a gradient along the long cell axis. The ParB partition complex on the newly replicated chromosome translocates up this ParA gradient, thereby contributing to chromosome segregation. A DNA-relay mechanism-deriving from the elasticity of the fluctuating chromosome-has been proposed as the driving force for this cargo translocation, but a mechanistic theoretical description remains elusive. Here, we propose a minimal model to describe force generation by the DNA-relay mechanism over a broad range of operational conditions. Conceptually, we identify four distinct force-generation regimes characterized by their dependence on chromosome fluctuations. These relay force regimes arise from an interplay of the imposed ParA gradient, chromosome fluctuations, and an emergent friction force due to chromosome-cargo interactions.
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ADN Bacteriano/metabolismo , Modelos Biológicos , Adenosina Trifosfatasas/genética , Adenosina Trifosfatasas/metabolismo , Transporte Biológico , Caulobacter crescentus/genética , Caulobacter crescentus/metabolismo , Segregación Cromosómica , Cromosomas Bacterianos , ADN Primasa/química , ADN Primasa/genética , ADN Primasa/metabolismo , ADN Bacteriano/química , ADN Bacteriano/genéticaRESUMEN
Regulation of growth and cell size is crucial for the optimization of bacterial cellular function. So far, single bacterial cells have been found to grow predominantly exponentially, which implies the need for tight regulation to maintain cell size homeostasis. Here, we characterize the growth behavior of the apically growing bacterium Corynebacterium glutamicum using a novel broadly applicable inference method for single-cell growth dynamics. Using this approach, we find that C. glutamicum exhibits asymptotically linear single-cell growth. To explain this growth mode, we model elongation as being rate-limited by the apical growth mechanism. Our model accurately reproduces the inferred cell growth dynamics and is validated with elongation measurements on a transglycosylase deficient ΔrodA mutant. Finally, with simulations we show that the distribution of cell lengths is narrower for linear than exponential growth, suggesting that this asymptotically linear growth mode can act as a substitute for tight division length and division symmetry regulation.
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Ciclo Celular , Corynebacterium glutamicum/crecimiento & desarrollo , Análisis de la Célula IndividualRESUMEN
The order and variability of bacterial chromosome organization, contained within the distribution of chromosome conformations, are unclear. Here, we develop a fully data-driven maximum entropy approach to extract single-cell 3D chromosome conformations from Hi-C experiments on the model organism Caulobacter crescentus. The predictive power of our model is validated by independent experiments. We find that on large genomic scales, organizational features are predominantly present along the long cell axis: chromosomal loci exhibit striking long-ranged two-point axial correlations, indicating emergent order. This organization is associated with large genomic clusters we term Super Domains (SuDs), whose existence we support with super-resolution microscopy. On smaller genomic scales, our model reveals chromosome extensions that correlate with transcriptional and loop extrusion activity. Finally, we quantify the information contained in chromosome organization that may guide cellular processes. Our approach can be extended to other species, providing a general strategy to resolve variability in single-cell chromosomal organization.
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Caulobacter crescentus/genética , Cromosomas Bacterianos/genética , Modelos Moleculares , Conformación Molecular , Algoritmos , Sitios de Unión , Caulobacter crescentus/citología , Caulobacter crescentus/metabolismo , Segregación Cromosómica/genética , Cromosomas Bacterianos/metabolismo , Regulación Bacteriana de la Expresión Génica , Genoma Bacteriano/genética , Genómica/métodos , Modelos GenéticosRESUMEN
The migratory dynamics of cells in physiological processes, ranging from wound healing to cancer metastasis, rely on contact-mediated cell-cell interactions. These interactions play a key role in shaping the stochastic trajectories of migrating cells. While data-driven physical formalisms for the stochastic migration dynamics of single cells have been developed, such a framework for the behavioral dynamics of interacting cells still remains elusive. Here, we monitor stochastic cell trajectories in a minimal experimental cell collider: a dumbbell-shaped micropattern on which pairs of cells perform repeated cellular collisions. We observe different characteristic behaviors, including cells reversing, following, and sliding past each other upon collision. Capitalizing on this large experimental dataset of coupled cell trajectories, we infer an interacting stochastic equation of motion that accurately predicts the observed interaction behaviors. Our approach reveals that interacting noncancerous MCF10A cells can be described by repulsion and friction interactions. In contrast, cancerous MDA-MB-231 cells exhibit attraction and antifriction interactions, promoting the predominant relative sliding behavior observed for these cells. Based on these experimentally inferred interactions, we show how this framework may generalize to provide a unifying theoretical description of the diverse cellular interaction behaviors of distinct cell types.
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Comunicación Celular , Movimiento Celular , Línea Celular , Línea Celular Tumoral , Humanos , Modelos Teóricos , Análisis Espacio-Temporal , Procesos EstocásticosRESUMEN
Time-lapse microscopy imaging provides direct access to the dynamics of soft and living systems. At mesoscopic scales, such microscopy experiments reveal intrinsic thermal and non-equilibrium fluctuations. These fluctuations, together with measurement noise, pose a challenge for the dynamical analysis of these Brownian movies. Traditionally, methods to analyze such experimental data rely on tracking embedded or endogenous probes. However, it is in general unclear, especially in complex many-body systems, which degrees of freedom are the most informative about their non-equilibrium nature. Here, we introduce an alternative, tracking-free approach that overcomes these difficulties via an unsupervised analysis of the Brownian movie. We develop a dimensional reduction scheme selecting a basis of modes based on dissipation. Subsequently, we learn the non-equilibrium dynamics, thereby estimating the entropy production rate and time-resolved force maps. After benchmarking our method against a minimal model, we illustrate its broader applicability with an example inspired by active biopolymer gels.
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Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into the physical laws governing the system. Here, we derive a principled framework to infer the dynamics of underdamped stochastic systems from realistic experimental trajectories, sampled at discrete times and subject to measurement errors. This framework yields an operational method, Underdamped Langevin Inference, which performs well on experimental trajectories of single migrating cells and in complex high-dimensional systems, including flocks with Viscek-like alignment interactions. Our method is robust to experimental measurement errors, and includes a self-consistent estimate of the inference error.