Calculation of the force field required for nucleus deformation during cell migration through constrictions

Nuclear deformation and dynamics of migrating cells in 3D confinement reveal adaptation of pulling and pushing forces

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.

Learning dynamical models of single and collective cell migration: a review

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.

Electromechanical interactions between cell membrane and nuclear envelope: Beyond the standard Schwan's model of biological cells

We investigate little-appreciated features of the hierarchical core-shell (CS) models of the electrical, mechanical, and electromechanical interactions between the cell membrane (CM) and nuclear envelope (NE). We first consider a simple model of an individual cell based on a coupled resistor-capacitor (Schwan model (SM)) network and show that the CM, when exposed to ac electric fields, acts as a low pass filter while the NE acts as a wide and asymmetric bandpass filter. We provide a simplified calculation for characteristic time associated with the capacitive charging of the NE and parameterize its range of behavior. We furthermore observe several new features dealing with mechanical analogs of the SM based on elementary spring-damper combinations. The chief merit of these models is that they can predict creep compliance responses of an individual cell under static stress and their effective retardation time constants. Next, we use an alternative and a more accurate CS physical model solved by finite element simulations for which geometrical cell reshaping under electromechanical stress (electrodeformation (ED)) is included in a continuum approach with spatial resolution. We show that under an electric field excitation, the elongated nucleus scales differently compared to the electrodeformed cell.

Subcellular mechano-regulation of cell migration in confined extracellular microenvironment

Cell migration is a highly coordinated cellular event that determines diverse physiological and pathological processes in which the continuous interaction of a migrating cell with neighboring cells or the extracellular matrix is regulated by the physical setting of the extracellular microenvironment. In confined spaces, cell migration occurs differently compared to unconfined open spaces owing to the additional forces that limit cell motility, which create a driving bias for cells to invade the confined space, resulting in a distinct cell motility process compared to what is expected in open spaces. Moreover, cells in confined environments can be subjected to elevated mechanical compression, which causes physical stimuli and activates the damage repair cycle in the cell, including the DNA in the nucleus. Although cells have a self-restoring system to repair damage from the cell membrane to the genetic components of the nucleus, this process may result in genetic and/or epigenetic alterations that can increase the risk of the progression of diverse diseases, such as cancer and immune disorders. Furthermore, there has been a shift in the paradigm of bioengineering from the development of new biomaterials to controlling biophysical cues and fine-tuning cell behaviors to cure damaged/diseased tissues. The external physical cues perceived by cells are transduced along the mechanosensitive machinery, which is further channeled into the nucleus through subcellular molecular linkages of the nucleoskeleton and cytoskeleton or the biochemical translocation of transcription factors. Thus, external cues can directly or indirectly regulate genetic transcriptional processes and nuclear mechanics, ultimately determining cell fate. In this review, we discuss the importance of the biophysical cues, response mechanisms, and mechanical models of cell migration in confined environments. We also discuss the effect of force-dependent deformation of subcellular components, specifically focusing on subnuclear organelles, such as nuclear membranes and chromosomal organization. This review will provide a biophysical perspective on cancer progression and metastasis as well as abnormal cellular proliferation.

Regulation of cellular contractile force, shape and migration of fibroblasts by oncogenes and Histone deacetylase 6

The capacity of cells to adhere to, exert forces upon and migrate through their surrounding environment governs tissue regeneration and cancer metastasis. The role of the physical contractile forces that cells exert in this process, and the underlying molecular mechanisms are not fully understood. We, therefore, aimed to clarify if the extracellular forces that cells exert on their environment and/or the intracellular forces that deform the cell nucleus, and the link between these forces, are defective in transformed and invasive fibroblasts, and to indicate the underlying molecular mechanism of control. Confocal, Epifluorescence and Traction force microscopy, followed by computational analysis, showed an increased maximum contractile force that cells apply on their environment and a decreased intracellular force on the cell nucleus in the invasive fibroblasts, as compared to normal control cells. Loss of HDAC6 activity by tubacin-treatment and siRNA-mediated HDAC6 knockdown also reversed the reduced size and more circular shape and defective migration of the transformed and invasive cells to normal. However, only tubacin-mediated, and not siRNA knockdown reversed the increased force of the invasive cells on their surrounding environment to normal, with no effects on nuclear forces. We observed that the forces on the environment and the nucleus were weakly positively correlated, with the exception of HDAC6 siRNA-treated cells, in which the correlation was weakly negative. The transformed and invasive fibroblasts showed an increased number and smaller cell-matrix adhesions than control, and neither tubacin-treatment, nor HDAC6 knockdown reversed this phenotype to normal, but instead increased it further. This highlights the possibility that the control of contractile force requires separate functions of HDAC6, than the control of cell adhesions, spreading and shape. These data are consistent with the possibility that defective force-transduction from the extracellular environment to the nucleus contributes to metastasis, via a mechanism that depends upon HDAC6. To our knowledge, our findings present the first correlation between the cellular forces that deforms the surrounding environment and the nucleus in fibroblasts, and it expands our understanding of how cells generate contractile forces that contribute to cell invasion and metastasis.

Spatial Heterogeneity in Cytoskeletal Mechanics Response to TGF-β1 and Hypoxia Mediates Partial Epithelial-to-Meshenchymal Transition in Epithelial Ovarian Cancer Cells

Metastatic progression of epithelial ovarian cancer (EOC) involves the partial epithelial-to-mesenchymal transition (EMT) of cancer cells in the primary tumor and dissemination into peritoneal fluid. In part to the high degree of heterogeneity in EOC cells, the identification of EMT in highly epithelial cells in response to differences in matrix mechanics, growth factor signaling, and tissue hypoxia is very difficult. We analyzed different degrees of EMT by tracking changes in cell and nuclear morphology, along with the organization of cytoskeletal proteins. In our analysis, we see a small percentage of individual cells that show dramatic response to TGF-β1 and hypoxia treatment. We demonstrate that EOC cells are spatially aware of their surroundings, with a subpopulation of EOC cells at the periphery of a cell cluster in 2D environments exhibited a greater degree of EMT. These peripheral cancer cells underwent partial EMT, displaying a hybrid of mesenchymal and epithelial characteristics, which often included less cortical actin and more perinuclear cytokeratin expression. Collectively, these data show that tumor-promoting microenvironment conditions can mediate invasive cell behavior in a spatially regulated context in a small subpopulation of highly epithelial clustered cancer cells that maintain epithelial characteristics while also acquiring some mesenchymal traits through partial EMT.

The role of cellular traction forces in deciphering nuclear mechanics

Cellular forces exerted on the extracellular matrix (ECM) during adhesion and migration under physiological and pathological conditions regulate not only the overall cell morphology but also nuclear deformation. Nuclear deformation can alter gene expression, integrity of the nuclear envelope, nucleus-cytoskeletal connection, chromatin architecture, and, in some cases, DNA damage responses. Although nuclear deformation is caused by the transfer of forces from the ECM to the nucleus, the role of intracellular organelles in force transfer remains unclear and a challenging area of study. To elucidate nuclear mechanics, various factors such as appropriate biomaterial properties, processing route, cellular force measurement technique, and micromanipulation of nuclear forces must be understood. In the initial phase of this review, we focused on various engineered biomaterials (natural and synthetic extracellular matrices) and their manufacturing routes along with the properties required to mimic the tumor microenvironment. Furthermore, we discussed the principle of tools used to measure the cellular traction force generated during cell adhesion and migration, followed by recently developed techniques to gauge nuclear mechanics. In the last phase of this review, we outlined the principle of traction force microscopy (TFM), challenges in the remodeling of traction forces, microbead displacement tracking algorithm, data transformation from bead movement, and extension of 2-dimensional TFM to multiscale TFM.

Intermediate filaments: Integration of cell mechanical properties during migration

Cell migration is a vital and dynamic process required for the development of multicellular organisms and for immune system responses, tissue renewal and wound healing in adults. It also contributes to a variety of human diseases such as cancers, autoimmune diseases, chronic inflammation and fibrosis. The cytoskeleton, which includes actin microfilaments, microtubules, and intermediate filaments (IFs), is responsible for the maintenance of animal cell shape and structural integrity. Each cytoskeletal network contributes its unique properties to dynamic cell behaviour, such as cell polarization, membrane protrusion, cell adhesion and contraction. Hence, cell migration requires the dynamic orchestration of all cytoskeleton components. Among these, IFs have emerged as a molecular scaffold with unique mechanical features and a key player in the cell resilience to mechanical stresses during migration through complex 3D environment. Moreover, accumulating evidence illustrates the participation of IFs in signalling cascades and cytoskeletal crosstalk. Teaming up with actin and microtubules, IFs contribute to the active generation of forces required for cell adhesion and mesenchymal migration and invasion. Here we summarize and discuss how IFs integrate mechanical properties and signalling functions to control cell migration in a wide spectrum of physiological and pathological situations.

Quantifying the Probing and Selection of Microenvironmental Pores by Motile Immune Cells

Immune cells are constantly on the move through multicellular organisms to explore and respond to pathogens and other harmful insults. While moving, immune cells efficiently traverse microenvironments composed of tissue cells and extracellular fibers, which together form complex environments of various porosity, stiffness, topography, and chemical composition. In this protocol we describe experimental procedures to investigate immune cell migration through microenvironments of heterogeneous porosity. In particular, we describe micro-channels, micro-pillars, and collagen networks as cell migration paths with alternative pore size choices. Employing micro-channels or micro-pillars that divide at junctions into alternative paths with initially differentially sized pores allows us to precisely (1) measure the cellular translocation time through these porous path junctions, (2) quantify the cellular preference for individual pore sizes, and (3) image cellular components like the nucleus and the cytoskeleton. This reductionistic experimental setup thus can elucidate how immune cells perform decisions in complex microenvironments of various porosity like the interstitium. The setup further allows investigation of the underlying forces of cellular squeezing and the consequences of cellular deformation on the integrity of the cell and its organelles. As a complementary approach that does not require any micro-engineering expertise, we describe the usage of three-dimensional collagen networks with different pore sizes. Whereas we here focus on dendritic cells as a model for motile immune cells, the described protocols are versatile as they are also applicable for other immune cell types like neutrophils and non-immune cell types such as mesenchymal and cancer cells. In summary, we here describe protocols to identify the mechanisms and principles of cellular probing, decision making, and squeezing during cellular movement through microenvironments of heterogeneous porosity. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: Immune cell migration in micro-channels and micro-pillars with defined pore sizes Support Protocol 1: Epoxy replica of generated and/or published micro-structures Support Protocol 2: Dendritic cell differentiation Basic Protocol 2: Immune cell migration in 3D collagen networks of variable pore sizes.