Beyond stiffness: Multiscale viscoelastic features as biomechanical markers for assessing cell types and states.

Cell mechanics are pivotal in regulating cellular activities, diseases progression, and cancer development. However, the understanding of how cellular viscoelastic properties vary in physiological and pathological stimuli remains scarce. Here, we develop a hybrid self-similar hierarchical theory-microrheology approach to accurately and efficiently characterize cellular viscoelasticity. Focusing on two key cell types associated with livers fibrosis-the capillarized liver sinusoidal endothelial cells and activated hepatic stellate cells-we uncover a universal two-stage power-law rheology characterized by two distinct exponents, αshort and αlong. The mechanical profiles derived from both exponents exhibit significant potential for discriminating among diverse cells. This finding suggests a potential common dynamic creep characteristic across biological systems, extending our earlier observations in soft tissues. Using a tailored hierarchical model for cellular mechanical structures, we discern significant variations in the viscoelastic properties and their distribution profiles across different cell types and states from the cytoplasm (elastic stiffness E1 and viscosity η), to a single cytoskeleton fiber (elastic stiffness E2), and then to the cell level (transverse expansion stiffness E3). Importantly, we construct a logistic-regression-based machine-learning model using the dynamic parameters that outperforms conventional cell-stiffness-based classifiers in assessing cell states, achieving an area under the curve of 97% vs. 78%. Our findings not only advance a robust framework for monitoring intricate cell dynamics but also highlight the crucial role of cellular viscoelasticity in discerning cell states across a spectrum of liver diseases and prognosis, offering new avenues for developing diagnostic and therapeutic strategies based on cellular viscoelasticity.

Local Mechanical Modulation-Driven Evagination in Invaginated Epithelia.

Local cells can actively create reverse bending (evagination) in invaginated epithelia, which plays a crucial role in the formation of elaborate organisms. However, the precise physical mechanism driving the evagination remains elusive. Here, we present a three-dimensional vertex model, incorporating the intrinsic cell polarity, to explore the complex morphogenesis induced by local mechanical modulations. We find that invaginated tissues can spontaneously generate local reverse bending due to the shift of the apicobasal polarity. Their exact shapes can be analytically determined by the local apicobasal differential tension and the internal stress. Our continuum theory exhibits three regions in a phase diagram controlled by these two parameters, showing curvature transitions from ordered to disordered states. Additionally, we delve into epithelial curvature transition induced by the nucleus repositioning, revealing its active contribution to the apicobasal force generation. The uncovered mechanical principles could potentially guide more studies on epithelial folding in diverse systems.

Anisotropic power-law viscoelasticity of living cells is dominated by cytoskeletal network structure.

During physiological and pathological processes, cells experience significant morphological alterations with the re-arrangement of cytoskeletal filaments, resulting in anisotropic viscoelasticity. Here, a structure-based cell model is proposed to study the anisotropic viscoelastic mechanical behaviors of living cells. We investigate how cell shape affects its creep responses in longitudinal and perpendicular directions. It is shown that cells exhibit power-law rheological behavior in both longitudinal and perpendicular directions under step stress, with a more solid-like behavior along the longitudinal direction. We reveal that the cell volume and cytoskeletal filament orientation, which have been neglected in most existing models, play a critical role in regulating cellular anisotropic viscoelasticity. The stiffness of the cell in both directions increases linearly with increasing its aspect ratio, due to the decrease of cell volume. Moreover, the increase in the cell's aspect ratio produces the aggregation of cytoskeletal filaments along the longitudinal direction, resulting in higher stiffness in this direction. It is also shown that the increase in cell's aspect ratio corresponds to a process of cellular ordering, which can be quantitatively characterized by the orientational entropy of cytoskeletal filaments. In addition, we present a simple yet robust method to establish the relationship between cell's aspect ratio and cell volume, thus providing a theoretical framework to capture the anisotropic viscoelastic behavior of cells. This study suggests that the structure-based cell models may be further developed to investigate cellular rheological responses to external mechanical stimuli and may be extended to the tissue scale. STATEMENT OF SIGNIFICANCE: The viscoelastic behaviors of cells hold significant importance in comprehending the roles of mechanical forces in embryo development, invasion, and metastasis of cancer cells. Here, a structure-based cell model is proposed to study the anisotropic viscoelastic mechanical behaviors of living cells. Our study highlights the crucial role of previously neglected factors, such as cell volume and cytoskeletal filament orientation, in regulating cellular anisotropic viscoelasticity. We further propose an orientational entropy of cytoskeletal filaments to quantitatively characterize the ordering process of cells with increasing aspect ratios. Moreover, we derived the analytical interrelationships between cell aspect ratio, cell stiffness, cell volume, and cytoskeletal fiber orientation. This study provides a theoretical framework to describe the anisotropic viscoelastic mechanical behavior of cells.

Viscoelastic Multiscale Mechanical Indexes for Assessing Liver Fibrosis and Treatment Outcomes.

Understanding liver tissue mechanics, particularly in the context of liver pathologies like fibrosis, cirrhosis, and carcinoma, holds pivotal significance for assessing disease severity and prognosis. Although the static mechanical properties of livers have been gradually studied, the intricacies of their dynamic mechanics remain enigmatic. Here, we characterize the dynamic creep responses of healthy, fibrotic, and mesenchymal stem cells (MSCs)-treated fibrotic lives. Strikingly, we unearth a ubiquitous two-stage power-law rheology of livers across different time scales with the exponents and their distribution profiles highly correlated to liver status. Moreover, our self-similar hierarchical theory effectively captures the delicate changes in the dynamical mechanics of livers. Notably, the viscoelastic multiscale mechanical indexes (i.e., power-law exponents and elastic stiffnesses of different hierarchies) and their distribution characteristics prominently vary with liver fibrosis and MSCs therapy. This study unveils the viscoelastic characteristics of livers and underscores the potential of proposed mechanical criteria for assessing disease evolution and prognosis.

Size-induced motion mode transitions in collective cell invasion toward free spaces.

Collective cell migration plays a vital role in various physiological and pathological processes, such as embryonic development and tumor metastasis. Recent experiments have shown that different from isolated cells, the moving cell groups exhibit rich emerging motion modes in response to external geometrical constraints. By considering the interactions between neighboring cells and internal biomechanical processes of each cell (i.e., cell sociality and cell individuality), we develop an active vertex model to investigate the emerging modes of collective cell migration in microchannels. Single-cell polarization is propelled by continuous protrusion of its leading edge and retraction of the rear. We here introduce the contribution of continuous protrusions and retractions of lamellipodia, named the protrusion alignment mechanism, to the cell individuality. Using the present model, it is found that altering the width of channels can trigger the motion mode transitions of cell groups. When cells move in narrow channels, the protrusion alignment mechanism brings neighboring groups of coordinated cells into conflicts and in turn induces the caterpillar-like motion mode. As the channel width increases, local swirls spanning the channel in width first appear as long as the channel width is smaller than the intrinsic correlation length of cell groups. Then, only local swirls with a maximum diameter of the intrinsic correlation length are formed, when the channel is sufficiently wider. These rich dynamical modes of collective cells originate from the competition between cell individuality and sociality. In addition, the velocity of the cell sheet invading free spaces varies with the channel size-induced transitions of migration modes. Our predictions are in broad agreement with many experiments and may shed light on the spatiotemporal dynamics of active matter.

Frequency-dependent transition in power-law rheological behavior of living cells.

Living cells are active viscoelastic materials exhibiting diverse mechanical behaviors at different time scales. However, dynamical rheological characteristics of cells in frequency range spanning many orders of magnitude, especially in high frequencies, remain poorly understood. Here, we show that a self-similar hierarchical model can capture cell's power-law rheological characteristics in different frequency scales. In low-frequency scales, the storage and loss moduli exhibit a weak power-law dependence on frequency with same exponent. In high-frequency scales, the storage modulus becomes a constant, while the loss modulus shows a power-law dependence on frequency with an exponent of 1.0. The transition between low- and high-frequency scales is defined by a transition frequency based on cell's mechanical parameters. The cytoskeletal differences of different cell types or states can be characterized by changes in mechanical parameters in the model. This study provides valuable insights into potentially using mechanics-based markers for cell classification and cancer diagnosis.

Cell chirality regulates coherent angular motion on small circular substrates.

Collective cell migration occurs in a wide range of physiological and pathological processes, such as wound healing and tumor metastasis. Experiments showed that many types of cells confined in circular islands can perform coherent angular rotation, yet the underlying mechanisms remain unclear. Here we propose a biomechanical model, including the membrane, microtubules, and nucleus, to study the spatiotemporal evolutions of small cell clusters in confined space. We show that cells can spontaneously transfer from "radial pattern" to "chiral pattern" due to fluctuations. For a pair of cells with identical chiral orientation, the cluster rotates in the opposite direction of the chiral orientation, and the fluctuations can reverse the cluster's rotational direction. Interestingly, during the persistent rotation, each cell rotates around its own centroid while it is revolving around the island center and shows a constant side to the island center, as tidal locking in astronomy. Furthermore, for a few more cells, coherent angular rotation also appears, and the emergence of a central cell can accelerate the cluster rotation. These findings shed light on collective cell migration in life processes and help to understand the spatiotemporal dynamics of active matter.

A Bionic-Homodimerization Strategy for Optimizing Modulators of Protein-Protein Interactions: From Statistical Mechanics Theory to Potential Clinical Translation.

Emerging protein-protein interaction (PPI) modulators have brought out exciting ability as therapeutics in human diseases, but its clinical translation has been greatly hampered by the limited affinity. Inspired by the homodimerize structure of antibody, the homodimerization contributes hugely to generating the optimized affinity is conjectured. Herein, a statistical-mechanics-theory-guided method is established to quantize the affinity of ligands with different topologies through analyzing the change of enthalpy and the loss of translational and rotational entropies. A peptide modulator for p53-MDM2 termed CPAP is used to homodimerize connecting, and this simple homodimerization can significantly increase the affinity. To realize the cellular internalization and tumor accumulation, Dimer CPAP and Mono CPAP are nanoengineered into gold(I)-CPAP supermolecule by the aurophilic interaction-driven self-assembly. Nano-Dimer CPAP potently suppressed tumor growth in lung cancer allograft model and a patient-derived xenograft model in more action than Nano-Mono CPAP, while keeping a favorable drug safety profile. This work not only presents a physico-mechanical method for calculating the affinity of PPI modulators, but also provides a simple yet robust homodimerization strategy to optimize the affinity of PPI modulators.

Mesoscopic dynamic model of epithelial cell division with cell-cell junction effects.

Cell division is central for embryonic development, tissue morphogenesis, and tumor growth. Experiments have evidenced that mitotic cell division is manipulated by the intercellular cues such as cell-cell junctions. However, it still remains unclear how these cortical-associated cues mechanically affect the mitotic spindle machinery, which determines the position and orientation of the cell division. In this paper, a mesoscopic dynamic cell division model is established to explore the integrated regulations of cortical polarity, microtubule pulling forces, cell deformability, and internal osmotic pressure. We show that the distributed pulling forces of astral microtubules play a key role in encoding the instructive cortical cues to orient and position the spindle of a dividing cell. The present model can not only predict the spindle orientation and position, but also capture the morphological evolution of cell rounding. The theoretical results agree well with relevant experiments both qualitatively and quantitatively. This work sheds light on the mechanical linkage between cell cortex and mitotic spindle, and holds potential in regulating cell division and sculpting tissue morphology.

Stress-driven cell extrusion can maintain homeostatic cell density in response to overcrowding.

Epithelial tissues can become overcrowded during proliferation and growth, in which case excessive cells need to be constantly removed. Here, we employed a vertex dynamics model to explore the microscopic mechanisms that govern homeostasis in an overcrowded monolayer of epithelial cells. It is demonstrated that the monolayer under mechanical compression can maintain a constant cell density and an optimal stress level through cell extrusion. Interestingly, cells are always extruded at sites of stress singularity in the monolayer, which may be spontaneously generated through random movements of cell groups near the extruding cells, and the fluctuation of protein molecules aggregating along the cell surface facilitates the restoration of the monolayer to its equilibrium state. Our results provide a foundation to interpret recent experiments as well as shed light on the mechanisms that underlie epithelial development and maintenance.

Three-dimensional collective cell motions in an acinus-like lumen.

Collective cell migration is an essential process in embryo development, wound healing, inflammatory response, and cancer invasion. Although cell motions in two-dimensional (2D) monolayers have been studied previously, three-dimensional (3D) collective cell migration, which constantly occurs during embryogenesis such as the establishment of ducts and acini in vivo, remains elusive. In this paper, we develop a cell-based model incorporating cell mechanics and cell motility to address coherent cell motions in a spherical acinus-like lumen with different cell populations. It is found that the interplays between cell persistence, random fluctuation, and geometrical confinement may engender rich and novel migratory modes. In a 3D spherical lumen, two cells may undergo stripe-like or cross-circular coherent rotations, whereas multiple cells can form dynamic twisting or circulating bands, leaving sparse cells at the center or even a hollow cavity in the cell aggregate. The cell density is found to profoundly influence the collective cell migration modes. Our model can reproduce the fundamental features observed in experiments and highlight the role of mechanics in steering 3D collective cell dynamics during mammary acinar morphogenesis.

Dynamic Migration Modes of Collective Cells.

Collective cell migration occurs in a diversity of physiological processes such as wound healing, cancer metastasis, and embryonic morphogenesis. In the collective context, cohesive cells may move as a translational solid, swirl as a fluid, or even rotate like a disk, with scales ranging from several to dozens of cells. In this work, an active vertex model is presented to explore the regulatory roles of social interactions of neighboring cells and environmental confinements in collective cell migration in a confluent monolayer. It is found that the competition between two kinds of intercellular social interactions-local alignment and contact inhibition of locomotion-drives the cells to self-organize into various dynamic coherent structures with a spatial correlation scale. The interplay between this intrinsic length scale and the external confinement dictates the migration modes of collective cells confined in a finite space. We also show that the local alignment-contact inhibition of locomotion coordination can induce giant density fluctuations in a confluent cell monolayer without gaps, which triggers the spontaneous breaking of orientational symmetry and leads to phase separation.

Orientations of Cells on Compliant Substrates under Biaxial Stretches: A Theoretical Study.

Mechanical cues from the microenvironments play a regulating role in many physiological and pathological processes, such as stem cell differentiation and cancer cell metastasis. Experiments showed that cells adhered on a compliant substrate may change orientation with an externally applied strain in the substrate. By accounting for actin polymerization, actin retrograde flow, and integrin binding dynamics, here we develop a mechanism-based tensegrity model to study the orientations of polarized cells on a compliant substrate under biaxial stretches. We show that the cell can actively regulate its mechanical state by generating different traction force levels along its polarized direction. Under static or ultralow-frequency cyclic stretches, stretching a softer substrate leads to a higher increase in the traction force and induces a narrower distribution of cell alignment. Compared to static loadings, high-frequency cyclic loadings have a more significant influence on cell reorientation on a stiff substrate. In addition, the width of the cellular angular distribution scales inversely with the stretch amplitude under both static and cyclic stretches. Our results are in agreement with a wide range of experimental observations, and provide fundamental insights into the functioning of cellular mechanosensing systems.

Impact of lipid rafts on the T-cell-receptor and peptide-major-histocompatibility-complex interactions under different measurement conditions.

The interactions between T-cell receptor (TCR) and peptide-major-histocompatibility complex (pMHC), which enable T-cell development and initiate adaptive immune responses, have been intensively studied. However, a central issue of how lipid rafts affect the TCR-pMHC interactions remains unclear. Here, by using a statistical-mechanical membrane model, we show that the binding affinity of TCR and pMHC anchored on two apposing cell membranes is significantly enhanced because of the lipid raft-induced signaling protein aggregation. This finding may provide an alternative insight into the mechanism of T-cell activation triggered by very low densities of pMHC. In the case of cell-substrate adhesion, our results indicate that the loss of lateral mobility of the proteins on the solid substrate leads to the inhibitory effect of lipid rafts on TCR-pMHC interactions. Our findings help to understand why different experimental methods for measuring the impact of lipid rafts on the receptor-ligand interactions have led to contradictory conclusions.

Collective dynamics of cancer cells confined in a confluent monolayer of normal cells.

Tumorigenesis often involves specific changes in cell motility and intercellular adhesion. Understanding the collective cancer cell behavior associated with these specific changes could facilitate the detection of malignant characteristics during tumor growth and invasion. In this study, a cellular vertex model is developed to investigate the collective dynamics of a disk-like aggregate of cancer cells confined in a confluent monolayer of normal cells. The effects of intercellular adhesion and cell motility on tumor progression are examined. It is found that the stresses in both the cancer cells and the normal cells increase with tumor growth, resulting in a crowded environment and enhanced cell apoptosis. The intercellular adhesion between cancer cells and normal cells is revealed to promote tumor growth and invasion. The tumor invasion dynamics hinges on the motility of cancer cells. The cancer cells could orchestrate into different collective migration modes, e.g., directional migration and rotational oscillations, dictated by the competition between cell persistence and local coordination. Phase diagrams are established to reveal the competitive mechanisms. This work highlights the role of mechanics in regulating tumor growth and invasion.

A Tensegrity Model of Cell Reorientation on Cyclically Stretched Substrates.

Deciphering the mechanisms underlying the high sensitivity of cells to mechanical microenvironments is crucial for understanding many physiological and pathological processes, e.g., stem cell differentiation and cancer cell metastasis. Here, a cytoskeletal tensegrity model is proposed to study the reorientation of polarized cells on a substrate under biaxial cyclic deformation. The model consists of four bars, representing the longitudinal stress fibers and lateral actin network, and eight strings, denoting the microfilaments. It is found that the lateral bars in the tensegrity, which have been neglected in most of the existing models, can play a vital role in regulating the cellular orientation. The steady orientation of cells can be quantitatively determined by the geometric dimensions and elastic properties of the tensegrity elements, as well as the frequency and biaxial ratio of the cyclic stretches. It is shown that this tensegrity model can reproduce all available experimental observations. For example, the dynamics of cell reorientation is captured by an exponential scaling law with a characteristic time that is independent of the loading frequency at high frequencies and scales inversely with the square of the strain amplitude. This study suggests that tensegrity type models may be further developed to understand cellular responses to mechanical microenvironments and provide guidance for engineering delicate cellular mechanosensing systems.

The glycocalyx promotes cooperative binding and clustering of adhesion receptors.

Cell adhesion plays a pivotal role in various biological processes, e.g., immune responses, cancer metastasis, and stem cell differentiation. The adhesion behaviors depend subtly on the binding kinetics of receptors and ligands restricted at the cell-substrate interfaces. Although much effort has been directed toward investigating the kinetics of adhesion molecules, the role of the glycocalyx, anchored on cell surfaces as an exterior layer, is still unclear. In this paper, we propose a theoretical approach to study the collective binding kinetics of a few and a large number of binders in the presence of the glycocalyx, representing the cases of initial and mature adhesions of cells, respectively. The analytical results are validated by finding good agreement with our Monte Carlo simulations. In the force loading case, the on-rate and affinity increase as more bonds form, whereas this cooperative effect is not observed in the displacement loading case. The increased thickness and stiffness of the glycocalyx tend to decrease the affinity for a few bonds, while they have less influence on the affinity for a large number of bonds. Moreover, for a flexible membrane with thermally-excited shape fluctuations, the glycocalyx is exhibited to promote the formation of bond clusters, mainly due to the cooperative binding of binders. This study helps to understand the cooperative kinetics of adhesion receptors under physiologically relevant loading conditions and sheds light on the novel role of the glycocalyx in cell adhesion.

Oriented cell division affects the global stress and cell packing geometry of a monolayer under stretch.

Cell division plays a vital role in tissue morphogenesis and homeostasis, and the division plane is crucial for cell fate. For isolated cells, extensive studies show that the orientation of divisions is sensitive to cell shape and the direction of extrinsic mechanical forces. However, it is poorly understood that how the cell divides within a cell monolayer and how the local stress change, due to the division, affects the global stress of epithelial monolayers. Here, we use the vertex dynamics models to investigate the effects of division orientation on the configurations and mechanics of a cell monolayer under stretch. We examine three scenarios of the divisions: dividing along the stretch axis, dividing along the geometric long axis of cells, and dividing at a random angle. It is found that the division along the long cell axis can induce the minimal energy difference, and the global stress of the monolayer after stretch releases more rapidly in this case. Moreover, the long-axis division can result in more random cell orientations and more isotropic cell shapes within the monolayer, comparing with other two cases. This study helps understand the division orientation of cells within a monolayer under mechanical stimuli, and may shed light on linking individual cell's behaviors to the global mechanics and patterns of tissues.

How do changes at the cell level affect the mechanical properties of epithelial monolayers?

Epithelial monolayers play a vital role in gastrulation, tumor metastasis and wound healing, and protect the tissue from pathogens. During these processes, the monolayers sense, generate, and exert mechanical forces to perform their biological functions, but their mechanical properties are rarely known. Here, we use the vertex dynamics models to investigate the mechanical behaviors of an epithelial monolayer and the configurations of the cells within the monolayer during stretch. It was found that the epithelial monolayer exhibited elastic and plastic properties, due to the geometric extension of cells and cell division, respectively. Moreover, the elasticity of monolayers was increased by enhancing the cell adhesion or by reducing the active contractility of actin-myosin rings. This study furthers our understanding of the relationship between the mechanical properties of individual cells and of their monolayers, and may shed light on linking cell behavior to the patterning and morphogenesis of tissues.

Controlled release and assembly of drug nanoparticles via pH-responsive polymeric micelles: a theoretical study.

Tumor tissues often have a pH value lower than normal tissues, and this difference suggests a promising way of targeted cancer therapy by using pH-controlled drug delivery systems. On the basis of the mean-field theory, we present a theoretical methodology to predict the self-assembly and disassembly of pH-responsive polymers and nanoparticles in an ionic solution. It is found that vesicles, cylindrical, and spherical micelles can rapidly disassemble and release contained nanoparticles in a narrow pH range. The model is further used to study the controlled assembly of pH-sensitive drug with significantly improved encapsulation efficiency. This method is also applicable for the design of controlled delivery nanodevices for various biomedical applications.