Chromosome organization can be modeled using various approaches, ranging from mechanistic bottom-up models to models inferred directly from experimental data. Many such models can recapitulate experimental Hi-C data for pairwise contact probabilities, meaning that these data cannot always be used to distinguish different models. Here, we consider two illustrative example models for bacterial chromosome organization: one a bottom-up model for loop extrusion, the other a data-driven maximum entropy model inferred from Hi-C data. We find that despite predicting similar pairwise contact frequencies, the models predict qualitatively different features on three-point contact maps. We explain these differences by constructing analytical approximations for three-point contact probabilities in each model. Finally, we apply our analytical approximations to previously published experimental multicontact data from human chromosomes, and find that these data are well described by the loop extruder approximation. Our work illustrates how multicontact statistics can be used to compare and test models for chromosome organization. Published by the American Physical Society 2025

The interface of chromosomes enables them to interact with the cell environment and is crucial for their mechanical stability during mitosis. Here, we use Atomic Force Microscopy (AFM) to probe the interface and local micromechanics of the highly condensed and complex chromatin network of native human mitotic chromosomes. Our AFM images provide detailed snapshots of chromatin loops and Sister-Chromatids Intertwines. A scaling analysis of these images reveals that the chromatin surface has fractal nature. AFM-based Force Spectroscopy and microrheology further show that chromosomes can resist severe deformations, elastically recovering their initial shape following two characteristic timescales. Localized indentations over the chromatids reveal that the spatially varying micromechanics of the chromatin network is largely governed by chromatin density. Together, our AFM investigation provides insights into the structure and local mechanics of mitotic chromosomes, offering a toolbox for further characterization of complex biological structures, such as chromosomes, down to the nanoscale.

The migration behavior of colliding cells is critically determined by transient contact-interactions. During these interactions, the motility machinery, including the front-rear polarization of the cell, dynamically responds to surface protein-mediated transmission of forces and biochemical signals between cells. While biomolecular details of such contact-interactions are increasingly well understood, it remains unclear what biophysical interaction mechanisms govern the cell-level dynamics of colliding cells and how these mechanisms vary across cell types. Here, we develop a phenomenological theory based on 14 candidate contact-interaction mechanisms coupling cell position, protrusion, and polarity. Using high-throughput micropattern experiments, we detect which of these phenomenological contact-interactions captures the interaction behaviors of cells. We find that various cell types - ranging from mesenchymal to epithelial cells - are accurately captured by a single model with only two interaction mechanisms: polarity-protrusion coupling and polarity-polarity coupling. The qualitatively different interaction behaviors of distinct cells, as well as cells subject to molecular perturbations of surface protein-mediated signaling, can all be quantitatively captured by varying the strength and sign of the polarity-polarity coupling mechanism. Altogether, our data-driven phenomenological theory of cell-cell interactions reveals polarity-polarity coupling as a versatile and general contact-interaction mechanism, which may underlie diverse collective migration behavior of motile cells.

Bacterial chromosomes are in continual motion as they undergo concurrent transcription, replication, and segregation. Time-course Hi-C experiments hold promise for studying chromosome organization across the cell cycle, but interpreting Hi-C data from dynamic systems remains challenging. Here, we develop a fully data-driven 4D Maximum Entropy approach to extract a model for the dynamic organization of a replicating bacterial chromosome directly from time-course Hi-C and microscopy data. After validating our 4D data-driven model model for Caulobacter crescentus against independent microscopy data, we infer quantitative information about changes in chromosome organization across the bacterial replication cycle. Our model reveals a sustained global linear organization of the C. crescentus chromosome during replication, as well as dynamic patterns of local chromosome extension induced by the replication forks. We use these data-driven inferences to constrain a mechanistic model for a replicating bacterial chromosome. Our model demonstrates that origin-pulling by a ParAB S -like system, together with loop extrusion by condensin, can explain our inferred large-scale chromosome segregation patterns. The inferred replication-induced local changes in chromosome compaction, however, require additional mechanisms, which we attribute to replication-induced NAP unbinding and positive supercoiling. Overall, our work introduces a rigorous data-driven framework for quantitatively interpreting time-course Hi-C data, and offers new mechanistic insights into bacterial chromosome organization across the cell cycle. ### Competing Interest Statement The authors have declared no competing interest.

Many bacterial chromosomes show large-scale linear order, so that a locus's genomic position correlates with its position along the cell. In the model organism E. coli, for instance, the left and right arms of the circular chromosome lie in different cell halves. However, no mechanisms that anchor loci to the cell poles have been identified, and it remains unknown how this so-called ``left-ori-right'' organization arises. Here, we construct a biophysical model that explains how global chromosome order could be established via an active loop extrusion mechanism. Our model assumes that the motor protein complex MukBEF extrudes loops on most of the E. coli chromosome, but is excluded from the terminal region by the protein MatP, giving rise to a partially looped ring polymer structure. Using 3D simulations of loop extrusion on a chromosome, we find that our model can display stable left-ori-right chromosomal order in a parameter regime consistent with prior experiments. We explain this behavior by considering the effect of loop extrusion on the bending rigidity of the chromosome, and derive necessary conditions for left-ori-right order to emerge. Finally, we develop a phase diagram for the system, where order emerges when the loop size is large enough and the looped region is compacted enough. Our work provides a mechanistic explanation for how loop-extruders can establish linear chromosome order in E. coli, and how this order leads to accurate gene positioning within the cell, without locus anchoring. ### Competing Interest Statement The authors have declared no competing interest.

During mitosis in eukaryotic cells, mechanical forces generated by the mitotic spindle pull the sister chromatids into the nascent daughter cells. How do mitotic chromosomes achieve the necessary mechanical stiffness and stability to maintain their integrity under these forces? Here, we use optical tweezers to show that ions involved in physiological chromosome condensation are crucial for chromosomal stability, stiffness and viscous dissipation. We combine these experiments with high-salt histone-depletion and theory to show that chromosomal elasticity originates from the chromatin fiber behaving as a flexible polymer, whereas energy dissipation can be explained by interactions between chromatin loops. Taken together, we show how collective properties of mitotic chromosomes, a biomaterial of incredible complexity, emerge from molecular properties, and how they are controlled by the physico-chemical environment.

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.

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.

The migratory dynamics of cells can be influenced by the complex micro-environment through which they move. It remains unclear how the motility machinery of confined cells responds and adapts to their micro-environment. 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 micro-patterns 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.

Entropic forces have been argued to drive bacterial chromosome segregation during replication. In many bacterial species, how-ever, specifically evolved mechanisms, such as loop-extruding SMC complexes and the ParAB S 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 ParAB S 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.

In the absence of directional motion it is often hard to recognize athermal fluctuations. Probability currents provide such a measure in terms of the rate at which they enclose area in the reduced phase space. We measure this area enclosing rate for trapped colloidal particles, where only one particle is driven. By combining experiment, theory, and simulation, we single out the effect of the different time scales in the system on the measured probability currents. In this controlled experimental setup, particles interact hydrodynamically. These interactions lead to a strong spatial dependence of the probability currents and to a local influence of athermal agitation. In a multiple-particle system, we show that even when the driving acts only on one particle, probability currents occur between other, non-driven particles. This may have significant implications for the interpretation of fluctuations in biological systems containing elastic networks in addition to a suspending fluid.

Advanced breast cancer, as well as ineffective treatments leading to surviving cancer cells, can result in the dissemination of these malignant cells from the primary tumor to distant organs. Recent research has shown that microRNA 200c (miR-200c) can hamper certain steps of the invasion-metastasis cascade. However, it is still unclear whether miR-200c expression alone is sufficient to prevent breast cancer cells from metastasis formation. Hence, we performed a xenograft mouse experiment with inducible miR-200c expression in MDA-MB 231 cells. The ex vivo analysis of metastatic sites in a multitude of organs, including lung, liver, brain, and spleen, revealed a dramatically reduced metastatic burden in mice with miR-200c-expressing tumors. A fundamental prerequisite for metastasis formation is the motility of cancer cells and, therefore, their migration. Consequently, we analyzed the effect of miR-200c on collective- and single-cell migration in vitro, utilizing MDA-MB 231 and MCF7 cell systems with genetically modified miR-200c expression. Analysis of collective-cell migration revealed confluence-dependent motility of cells with altered miR-200c expression. Additionally, scratch assays showed an enhanced predisposition of miR-200c-negative cells to leave cell clusters. The in-between stage of collective- and single-cell migration was validated using transwell assays, which showed reduced migration of miR-200c-positive cells. Finally, to measure migration at the single-cell level, a novel assay on dumbbell-shaped micropatterns was performed, which revealed that miR-200c critically determines confined cell motility. All of these results demonstrate that sole expression of miR-200c impedes metastasis formation in vivo and migration in vitro and highlights miR-200c as a metastasis suppressor in breast cancer.

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.

In the extracellular matrix, eukaryotic cells exert forces that deform their surroundings. By doing so, they can perform mechanosensation: Cells measure the mechanics of their environment, and adapt their behavior accordingly. Extracellular matrices are, however, disordered nonlinear media: How can a mechanosensor at the cellular scale reliably measure the surroundings mechanics through local probing? Here, we develop a model for nonlinear mechanosensation in disordered fiber networks. At low forces, the linear response of the matrix combined with its extreme mechanical heterogeneity precludes reliable mechanosensation. In contrast, we find that this heterogeneity is strongly suppressed in the physiologically relevant nonlinear mechanical regime where fibers buckle. Conceptually, nonlinearity increases the range of mechanosensation, thereby enhancing disorder averaging and providing more accurate nonlinear mechanical measurements. We support our model using microrheology experiments and show theoretically that this nonlinear mechanosensation is generic to all fiber networks. This contrasts with the collagen-specific observation that nonlinear macroscopic elastic moduli are independent of network density, which we show to originate from the fiber's constitutive nonlinearity. Together, our theoretical study disentangles the micro- and macrorheological nonlinearities of fiber networks, and shows how mechanosensors such as cells can take advantage of these nonlinearities to robustly measure their mechanical environment despite heterogeneities.

AbstractAdvanced breast cancer as well as insufficient treatment can lead to the dissemination of malignant cells from the primary tumor to distant organs. Recent research has shown that miR-200c can hamper certain steps of the invasion-metastasis cascade. However, it is still unclear, whether sole miR-200c expression is sufficient to prevent breast cancer cells from metastasis formation. Hence, we performed a xenograft mouse experiment with inducible miR-200c expression in MDA-MB 231 cells. Theex vivoanalysis of metastatic sites in a multitude of organs including lung, liver, brain, and spleen has revealed a dramatically reduced metastatic burden of mice with miR-200c expressing tumors. A fundamental prerequisite for metastasis formation is the motility of cancer cells and, therefore, their migration. Consequently, we analyzed the effect of miR-200c on collective and single cell migrationin vitro, utilizing MDA-MB 231 and MCF7 cell systems with genetically modified miR-200c expression. Analysis of collective cell migration has resulted in confluence dependent motility of cells with altered miR-200c expression. Additionally, scratch assays have shown enhanced predisposition of miR-200c negative cells to leave cell clusters. The in-between stage of collective and single cell migration was validated using transwell assays, which have displayed reduced migration of miR-200c positive cells. Finally, to measure migration on single cell level, a novel assay on dumbbell shaped micropatterns was performed, which revealed that miR-200c critically determines confined cell motility. All of these results demonstrate that exclusive expression of miR-200c impedes metastasis formationin vivoand migrationin vitroand highlight miR-200c as metastatic suppressor in breast cancer.

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.

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.

Time-irreversibility is a distinctive feature of non-equilibrium 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 auto-correlation 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.

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). 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 cadherin-based intercellular contacts sharpen cell boundaries leading to repulsive rather than cohesive interactions between cells, thereby promoting efficient cell spreading during collective migration.