A theoretical model of collective cell polarization and alignment

Tensile force field plays a crucial role in local invasion of tumor cells through a mechano-chemical coupling mechanism

Cancer metastasis starts from early local invasion, during which tumor cells detach from the primary tumor, penetrate the extracellular matrix (ECM), and then invade neighboring tissues. However, the cellular mechanics in the detaching and penetrating processes have not been fully understood, and the underlying mechanisms that influence cell polarization and migration in the 3D matrix during tumor invasion remain largely unknown. In this study, we employed a dual tumor-spheroid model to investigate the cellular mechanisms of the tumor invasion. Our results revealed that the tensional force field developed by the active contraction of cells and tissues played a pivotal role in tumor invasion, acting as the driving force for remodeling the collagen fibers during the invasion process. The remodeled collagen fibers promoted cell polarization and migration because of the stiffening of the fiber matrix. The aligned fibers facilitated tumor cell invasion and directed migration from one spheroid to the other. Inhibiting/shielding the cellular contractility abolished matrix remodeling and re-alignment and significantly decreased tumor cell invasion. By developing a coarse-grained cell model that considers the mutual interaction between cells and fibers, we predicted the tensional force field in the fiber network and the associated cell polarization and cell-matrix interaction during cell invasion, which revealed a mechano-chemical coupling mechanism at the cellular level of the tumor invasion process. Our study highlights the roles of cellular mechanics at the early stage of tumor metastasis and may provide new therapeutic strategies for cancer therapy.

Derivation and simulation of a computational model of active cell populations: How overlap avoidance, deformability, cell-cell junctions and cytoskeletal forces affect alignment

Collective alignment of cell populations is a commonly observed phenomena in biology. An important example are aligning fibroblasts in healthy or scar tissue. In this work we derive and simulate a mechanistic agent-based model of the collective behaviour of actively moving and interacting cells, with a focus on understanding collective alignment. The derivation strategy is based on energy minimisation. The model ingredients are motivated by data on the behaviour of different populations of aligning fibroblasts and include: Self-propulsion, overlap avoidance, deformability, cell-cell junctions and cytoskeletal forces. We find that there is an optimal ratio of self-propulsion speed and overlap avoidance that maximises collective alignment. Further we find that deformability aids alignment, and that cell-cell junctions by themselves hinder alignment. However, if cytoskeletal forces are transmitted via cell-cell junctions we observe strong collective alignment over large spatial scales.

Effect of Anisotropic Structural Depth on Orientation and Differentiation Behavior of Skeletal Muscle Cells

Extensive research has been conducted to examine how substrate topological factors are involved in modulating the cell behavior. Among numerous topological factors, the vital influence of the touchable depth of substrates on cell behaviors has already been extensively characterized, but the response of cells to the topological structure at untouchable depth is still elusive. Herein, the influences of substrate depth on myoblast behaviors are systematically investigated using substrates with depths ranging from touchable depth (microgrooved) to untouchable depth (microbridges). The results show that an increase in microgroove depth is accompanied by an inhibited cell spreading, an enhanced elongation, and a more obvious orientation along microgrooves. Interestingly, myoblasts located on microbridges show a more pronounced elongation with increasing culture time but a position-dependent orientation. Myoblasts on the center and parallel boundary of microbridges orient along the bridges, while myoblasts on the vertical boundary align perpendicular to the microbridges. Moreover, the differentiation results of the myoblasts indicate that the differentiated myotubes can maintain this position-dependent orientation. The simulation of the stress field in cell monolayers suggests that the position-dependent orientation is caused by the comprehensive response of myoblasts to the substrate discontinuity and substrate depth. These findings provide valuable insights into the mechanism of cell depth sensing and could inform the design of tissue engineering scaffolds for skeletal muscle and biohybrid actuation.

Molecular-scale substrate anisotropy, crowding and division drive collective behaviours in cell monolayers

The ability of cells to reorganize in response to external stimuli is important in areas ranging from morphogenesis to tissue engineering. While nematic order is common in biological tissues, it typically only extends to small regions of cells interacting via steric repulsion. On isotropic substrates, elongated cells can co-align due to steric effects, forming ordered but randomly oriented finite-size domains. However, we have discovered that flat substrates with nematic order can induce global nematic alignment of dense, spindle-like cells, thereby influencing cell organization and collective motion and driving alignment on the scale of the entire tissue. Remarkably, single cells are not sensitive to the substrate's anisotropy. Rather, the emergence of global nematic order is a collective phenomenon that requires both steric effects and molecular-scale anisotropy of the substrate. To quantify the rich set of behaviours afforded by this system, we analyse velocity, positional and orientational correlations for several thousand cells over days. The establishment of global order is facilitated by enhanced cell division along the substrate's nematic axis, and associated extensile stresses that restructure the cells' actomyosin networks. Our work provides a new understanding of the dynamics of cellular remodelling and organization among weakly interacting cells.

Cellular mechanisms of wound closure under cyclic stretching

Wound closure is a fundamental process in many physiological and pathological processes, but the regulating effects of external force on the closure process are still unclear. Here, we systematically studied the closure process of wounds of different shape under cyclic stretching. We found that the stretching amplitude and direction had significant effect on the healing speed and healing mode. For instance, there was a biphasic dependence of the healing speed on the stretching amplitude. That is, the wound closure was faster under relatively small and large amplitude, while it was slower under intermediate amplitude. At the same time, the stretching could regulate the healing pattern. We showed that the stretching would increase the healing speed along the direction perpendicular to the stretching direction. Specifically, when the stretching was along the major axis of the wound, it accelerated the healing speed along the short axis, which induced a rosette to stitching-line mode transition. In contrast, stretching along the minor axis accelerated the healing speed along the long axis, inducing a stitching-line to rosette mode transition. Our theoretical analyses demonstrated that the wound closure process was coregulated by the mechanical factors including prestress in the cytoskeleton, the protrusion of cells, and the contraction of the actin ring, as well as the geometry of the wound. The cyclic stretch could further modulate the roles of these factors. For example, the stretching changed the stress field in the cell layer, and switched the direction of cell protrusions. This article reveals important cellular mechanisms of the wound healing process under cyclic stretching, and provides an insight into possible approaches of regulating cell collective behaviors via mechanical forces.

Biomimetic Convex Implant for Corneal Regeneration Through 3D Printing

Blindness caused by corneal damage affects millions of people worldwide, and this number continues to rise. However, rapid epithelization and a stable epithelium process are the two biggest challenges for traditional corneal materials. These processes are related to corneal curvature, which is an important factor in determination of the corneal healing process and epithelial behavior during corneal damage. In this study, smooth 3D-printed convex corneal implants based on gelatin methacrylate and collagen are generated. As epithelium distribution and adhesion vary in different regions of the natural cornea, this work separates the surfaces into four regions and studies how cells sense topological cues on curvature. It is found that rabbit corneal epithelial cells (RCECs) seeded on steeper slope gradient surfaces on convex structures result in more aligned cell organization and tighter cell-substrate adhesion, which can also be verified through finite element simulation and signaling pathway analysis. In vivo transplantation of convex implants result in a better fit with adjacent tissue and stronger cell adhesion than flat implants, thereby accelerating corneal epithelialization and promoting collagen fibers and neural regeneration within 180 days. Taken together, printed convex corneal implants that facilitate corneal regeneration may offer a translational strategy for the treatment of corneal damage.

Current strategies for enhancement of the bioactivity of artificial ligaments: A mini-review

Background and objective

Anterior cruciate ligament (ACL) reconstruction calls for artificial ligaments with better bioactivity, however systematic reviews regarding bioactivity enhancement strategies, technologies, and perspectives of artificial ligaments have been rarely found.

Methods

Research papers, reviews, and clinical reports related to artificial ligaments were searched and summarized the current status and research trends of artificial ligaments through a systematic analysis.

Results

Having experienced ups and downs since the very first record of clinical application, artificial ligaments differing in material, and fabrication methods have been reported with different clinical performances. Various manufacturing technologies have developed and realized scaffold- and cell-based strategies. Despite encouraging in-vivo and in-vitro test results, the clinical results of such new designs need further clinical examinations.

Conclusion

As the demand for ACL reconstruction dramatically increases, novel artificial ligaments with better osteoinductivity and mechanical performance are promising.

The translational potential of this article

To develop novel artificial ligaments simultaneously possessing excellent osteoinductivity and satisfactory mechanical performance, it is important to grab a glance at recent research advances. This systematic analysis provides researchers and clinicians with comprehensive and comparable information on artificial ligaments, thus being of clinical translational significance.

Reciprocity of Cell Mechanics with Extracellular Stimuli: Emerging Opportunities for Translational Medicine

Human cells encounter dynamic mechanical cues in healthy and diseased tissues, which regulate their molecular and biophysical phenotype, including intracellular mechanics as well as force generation. Recent developments in bio/nanomaterials and microfluidics permit exquisitely sensitive measurements of cell mechanics, as well as spatiotemporal control over external mechanical stimuli to regulate cell behavior. In this review, the mechanobiology of cells interacting bidirectionally with their surrounding microenvironment, and the potential relevance for translational medicine are considered. Key fundamental concepts underlying the mechanics of living cells as well as the extracelluar matrix are first introduced. Then the authors consider case studies based on 1) microfluidic measurements of nonadherent cell deformability, 2) cell migration on micro/nano-topographies, 3) traction measurements of cells in three-dimensional (3D) matrix, 4) mechanical programming of organoid morphogenesis, as well as 5) active mechanical stimuli for potential therapeutics. These examples highlight the promise of disease diagnosis using mechanical measurements, a systems-level understanding linking molecular with biophysical phenotype, as well as therapies based on mechanical perturbations. This review concludes with a critical discussion of these emerging technologies and future directions at the interface of engineering, biology, and medicine.

Variational methods and deep Ritz method for active elastic solids

Variational methods have been widely used in soft matter physics for both static and dynamic problems. These methods are mostly based on two variational principles: the variational principle of minimum free energy (MFEVP) and Onsager's variational principle (OVP). Our interests lie in the applications of these variational methods to active matter physics. In our former work [H. Wang, T. Qian and X. Xu, Soft Matter, 2021, 17, 3634-3653], we have explored the applications of OVP-based variational methods for the modeling of active matter dynamics. In the present work, we explore variational (or energy) methods that are based on MFEVP for static problems in active elastic solids. We show that MFEVP can be used not only to derive equilibrium equations, but also to develop approximate solution methods, such as the Ritz method, for active solid statics. Moreover, the power of the Ritz-type method can be further enhanced using deep learning methods if we use deep neural networks to construct the trial functions of the variational problems. We then apply these variational methods and the deep Ritz method to study the spontaneous bending and contraction of a thin active circular plate that is induced by internal asymmetric active contraction. The circular plate is found to be bent towards its contracting side. The study of such a simple toy system gives implications for understanding the morphogenesis of solid-like confluent cell monolayers. In addition, we introduce a so-called activogravity length to characterize the importance of gravitational forces relative to internal active contraction in driving the bending of the active plate. When the lateral plate dimension is larger than the activogravity length (about 100 micron), gravitational forces become important. Such gravitaxis behaviors at multicellular scales may play significant roles in the morphogenesis and in the up-down symmetry broken during tissue development.

Nano/Micromotors in Active Matter

Nano/micromotors (NMMs) are tiny objects capable of converting energy into mechanical motion. Recently, a wealth of active matter including synthetic colloids, cytoskeletons, bacteria, and cells have been used to construct NMMs. The self-sustained motion of active matter drives NMMs out of equilibrium, giving rise to rich dynamics and patterns. Alongside the spontaneous dynamics, external stimuli such as geometric confinements, light, magnetic field, and chemical potential are also harnessed to control the movements of NMMs, yielding new application paradigms of active matter. Here, we review the recent advances, both experimental and theoretical, in exploring biological NMMs. The unique dynamical features of collective NMMs are focused on, along with some possible applications of these intriguing systems.

Cellular mechanics of wound formation in single cell layer under cyclic stretching

Wounds can be produced when cells and tissues are subjected to excessive forces, for instance, under pathological conditions or nonphysiological loading. However, the cellular behaviors in the wound formation process are not clear. Here we tested the behaviors of wound formation in the epithelial layer with an in-suit uniaxial stretching device. We found that the wound often nucleates at the position where the cells are dividing. The polarization direction of cells near the wound is preferentially along the wound edge, whereas the cells far from the wound are preferentially perpendicular to the stretching direction. The larger the wound area is, the higher is the aspect ratio of the cells around the wound. Increasing the cell density will strengthen the cell layer. The higher the cell density is, the smaller is the area of the wounds, and the weaker is the effect of stretching on the polarization of the cells. Furthermore, we built a coarse-grained cell model that can explicitly consider the elasticity and viscoelasticity of cells, cell-cell interaction, and cell active stress, by which we simulated the wound formation process and quantitatively analyzed the force and stress fields in the cell layer, particularly around the wound. These analyses reveal the cellular mechanisms of wound formation behaviors in the cell layer under stretching and shed useful light on tissue engineering and regenerative medicine for biomedical applications.

Explicit calculation method for cell alignment in non-circular geometries

The alignment of spindle-shaped cells in two-dimensional geometries induces singular points called topological defects, at which the alignment angle of the cell cannot be defined. To control defects related to biological roles such as cell apoptosis, calculation methods for predicting the defect positions are required. This study proposes an explicit calculation method for predicting cell alignment and defect positions in non-circular geometries. First, a complex potential is introduced to describe the alignment angles of cells, which is used to derive an explicit formula for cell alignment in a unit disc. Then, the derived formula for the unit disc is extended to the case for non-circular geometries using a numerical conformal mapping. Finally, the complex potential allows a calculation of the Frank elastic energy, which can be minimized with respect to the defect positions to predict their equilibrium state in the geometry. The proposed calculation method is used to demonstrate a numerical prediction of multiple defects in circular and non-circular geometries, which are consistent with previous experimental results.

Onsager's variational principle in active soft matter

Onsagers variational principle (OVP) was originally proposed by Lars Onsager in 1931 [L. Onsager, Phys. Rev., 1931, 37, 405]. This fundamental principle provides a very powerful tool for formulating thermodynamically consistent models. It can also be employed to find approximate solutions, especially in the study of soft matter dynamics. In this work, OVP is extended and applied to the dynamic modeling of active soft matter such as suspensions of bacteria and aggregates of animal cells. We first extend the general formulation of OVP to active matter dynamics where active forces are included as external non-conservative forces. We then use OVP to analyze the directional motion of individual active units: a molecular motor walking on a stiff biofilament and a toy two-sphere microswimmer. Next we use OVP to formulate a diffuse-interface model for an active polar droplet on a solid substrate. In addition to the generalized hydrodynamic equations for active polar fluids in the bulk region, we have also derived thermodynamically consistent boundary conditions. Finally, we consider the dynamics of a thin active polar droplet under the lubrication approximation. We use OVP to derive a generalized thin film equation and then employ OVP as an approximation tool to find the spreading laws for the thin active polar droplet. By incorporating the activity of biological systems into OVP, we develop a general approach to construct thermodynamically consistent models for better understanding the emergent behaviors of individual animal cells and cell aggregates or tissues.

Dynamically Re-Organized Collagen Fiber Bundles Transmit Mechanical Signals and Induce Strongly Correlated Cell Migration and Self-Organization

Correlated cell migration in fibrous extracellular matrix (ECM) is important in many biological processes. During migration, cells can remodel the ECM, leading to the formation of mesoscale structures such as fiber bundles. However, how such mesoscale structures regulate correlated single-cells migration remains to be elucidated. Here, using a quasi-3D in vitro model, we investigate how collagen fiber bundles are dynamically re-organized and guide cell migration. By combining laser ablation technique with 3D tracking and active-particle simulations, we definitively show that only the re-organized fiber bundles that carry significant tensile forces can guide strongly correlated cell migration, providing for the first time a direct experimental evidence supporting that matrix-transmitted long-range forces can regulate cell migration and self-organization. This force regulation mechanism can provide new insights for studies on cellular dynamics, fabrication or selection of biomedical materials in tissue repairing, and many other biomedical applications.

Relationship between velocities, tractions, and intercellular stresses in the migrating epithelial monolayer

The relationship between velocities, tractions, and intercellular stresses in the migrating epithelial monolayer are currently unknown. Ten years ago, a method known as monolayer stress microscopy (MSM) was suggested from which intercellular stresses could be computed for a given traction field. The core assumption of MSM is that intercellular stresses within the monolayer obey a linear and passive constitutive law. Examples of these include a Hookean solid (an elastic sheet) or a Newtonian fluid (thin fluid film), which imply a specific relation between the displacements or velocities and the tractions. Due to the lack of independently measured intercellular stresses, a direct validation of the 2D stresses predicted by a linear passive MSM model is presently not possible. An alternative approach, which we give here and denote as the Stokes method, is based on simultaneous measurements of the monolayer velocity field and the cell-substrate tractions. Using the same assumptions as those underlying MSM, namely, a linear and passive constitutive law, the velocity field suffices to compute tractions, from which we can then compare with those measured by traction force microscopy. We find that the calculated tractions and measured tractions are uncorrelated. Since the classical MSM and the Stokes approach both depend on the linear and passive constitutive law, it follows that some serious modification of the underling rheology is needed. One possible modification is the inclusion of an active force. In the special case where this is additive to the linear passive rheology, we have a new relationship between the active force density and the measured velocity (or displacement) field and tractions, which by Newton's laws, must be obeyed.