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 varying 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 (cLSEC) and activated hepatic stellate cells (aLX-2) - 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 (ML) model using the dynamic parameters outperforms conventional cell stiffness-based classifiers in assessing cell states, achieving an area under the curve (AUC) 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.

Enhancing liver fibrosis diagnosis and treatment assessment: a novel biomechanical markers-based machine learning approach.

Accurate diagnosis and treatment assessment of liver fibrosis face significant challenges, including inherent limitations in current techniques like sampling errors and inter-observer variability. Addressing this, our study introduces a novel machine learning (ML) framework, which integrates light gradient boosting machine and multivariate imputation by chained equations to enhance liver status assessment using biomechanical markers. Building upon our previously established multiscale mechanical characteristics in fibrotic and treated livers, this framework employs Gaussian Bayesian optimization for post-imputation, significantly improving classification performance. Our findings indicate a marked increase in the precision of liver fibrosis diagnosis and provide a novel, quantitative approach for assessing fibrosis treatment. This innovative combination of multiscale biomechanical markers with advanced ML algorithms represents a transformative step in liver disease diagnostics and treatment evaluation, with potential implications for other areas in medical diagnostics.

Mechanical guidance to self-organization and pattern formation of stem cells.

The self-organization of stem cells (SCs) constitutes the fundamental basis of the development of biological organs and structures. SC-driven patterns are essential for tissue engineering, yet unguided SCs tend to form chaotic patterns, impeding progress in biomedical engineering. Here, we show that simple geometric constraints can be used as an effective mechanical modulation approach that promotes the development of controlled self-organization and pattern formation of SCs. Using the applied SC guidance with geometric constraints, we experimentally uncover a remarkable deviation in cell aggregate orientation from a random direction to a specific orientation. Subsequently, we propose a dynamic mechanical framework, including cells, the extracellular matrix (ECM), and the culture environment, to characterize the specific orientation deflection of guided cell aggregates relative to initial geometric constraints, which agrees well with experimental observation. Based on this framework, we further devise various theoretical strategies to realize complex biological patterns, such as radial and concentric structures. Our study highlights the key role of mechanical factors and geometric constraints in governing SCs' self-organization. These findings yield critical insights into the regulation of SC-driven pattern formation and hold great promise for advancements in tissue engineering and bioactive material design for regenerative application.

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.

Emergence, Pattern, and Frequency of Spontaneous Waves in Spreading Epithelial Monolayers.

A striking phenomenon of collective cell motion is that they can exhibit a spontaneously emerging wave during epithelia expansions. However, the fundamental mechanism, governing the emergence and its crucial characteristics (e.g., the eigenfrequency and the pattern), remains an enigma. By introducing a mechanochemical feedback loop, we develop a highly efficient discrete vertex model to investigate the spatiotemporal evolution of spreading epithelia. We find both numerically and analytically that expanding cell monolayers display a power-law dependence of wave frequency on the local heterogeneities (i.e., cell density) with a scaling exponent of -1/2. Moreover, our study demonstrates the quantitative capability of the proposed model in capturing distinct X-, W-, and V-mode wave patterns. We unveil that the phase transition between these modes is governed by the distribution of active self-propulsion forces. Our work provides an avenue for rigorous quantitative investigations into the collective motion and pattern formation of cell groups.

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.

New Mechanical Markers for Tracking the Progression of Myocardial Infarction.

The mechanical properties of soft tissues can often be strongly correlated with the progression of various diseases, such as myocardial infarction (MI). However, the dynamic mechanical properties of cardiac tissues during MI progression remain poorly understood. Herein, we investigate the rheological responses of cardiac tissues at different stages of MI (i.e., early-stage, mid-stage, and late-stage) with atomic force microscopy-based microrheology. Surprisingly, we discover that all cardiac tissues exhibit a universal two-stage power-law rheological behavior at different time scales. The experimentally found power-law exponents can capture an inconspicuous initial rheological change, making them particularly suitable as markers for early-stage MI diagnosis. We further develop a self-similar hierarchical model to characterize the progressive mechanical changes from subcellular to tissue scales. The theoretically calculated mechanical indexes are found to markedly vary among different stages of MI. These new mechanical markers are applicable for tracking the subtle changes of cardiac tissues during MI progression.

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.

Topological mechanism in the nonlinear power-law relaxation of cell cortex.

Different types of cells exhibit a universal power-law rheology, but the mechanism underneath is still unclear. Based on the exponential distribution of actin filament length, we treat the cell cortex as a collection of chains of crosslinkers with exponentially distributed binding energy, and show that the power-law exponent of its stress relaxation should scale with the chain length. Through this model, we are able to explain how the exponent can be regulated by the crosslinker number and imposed strain during cortex relaxation. Network statistics show that the average length of filament-crosslinker chains decreases with the crosslinker number, which endows a denser network with lower exponent. Due to gradual molecular alignment with the stretch direction, the number of effectively stretched crosslinkers in the network is found to increase with the imposed strain. This effective growth in network density diminishes the exponent under large strain. By incorporating the inclined angle of crosslinkers into the model without in-series structure, we show that the exponent cannot be altered by crosslinker rotation directly, refining our previous conjectures. This work may help to understand cellular mechanics from the molecular perspective.

Network dynamics of the nonlinear power-law relaxation of cell cortex.

Living cells are known to exhibit universal power-law rheological behaviors, but their underlying biomechanical principles are still not fully understood. Here, we present a network dynamics picture to decipher the nonlinear power-law relaxation of cortical cytoskeleton. Under step strains, we present a scaling relation between instantaneous differential stiffness and external stress as a result of chain reorientation. Then, during the relaxation, we show how the scaling law theoretically originates from an exponential form of cortical disorder, with the scaling exponent decreased by the imposed strain or crosslinker density in the nonlinear regime. We attribute this exponent variation to the molecular realignment along the stretch direction or the transition of network structure from in-series to in-parallel modes, both solidifying the network toward our one-dimensional theoretical limit. In addition, the rebinding of crosslinkers is found to be crucial for moderating the relaxation speed under small strains. Together with the disorder nature, we demonstrate that the structural effects of networks provide a unified interpretation for the nonlinear power-law relaxation of cell cortex, and may help to understand cell mechanics from the molecular scale.

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.

A hierarchical cellular structural model to unravel the universal power-law rheological behavior of living cells.

Living cells are a complex soft material with fascinating mechanical properties. A striking feature is that, regardless of their types or states, cells exhibit a universal power-law rheological behavior which to this date still has not been captured by a single theoretical model. Here, we propose a cellular structural model that accounts for the essential mechanical responses of cell membrane, cytoplasm and cytoskeleton. We demonstrate that this model can naturally reproduce the universal power-law characteristics of cell rheology, as well as how its power-law exponent is related to cellular stiffness. More importantly, the power-law exponent can be quantitatively tuned in the range of 0.1 ~ 0.5, as found in most types of cells, by varying the stiffness or architecture of the cytoskeleton. Based on the structural characteristics, we further develop a self-similar hierarchical model that can spontaneously capture the power-law characteristics of creep compliance over time and complex modulus over frequency. The present model suggests that mechanical responses of cells may depend primarily on their generic architectural mechanism, rather than specific molecular properties.

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.

Enumeration-screening method for the design of simple polygonal tensegrities.

Tensegrities, consisting of axially pre-compressed bars and pre-stretched strings, hold broad applications in the design of, for instance, architectures, soft robotics and metamaterials. In this paper, we propose an enumeration-screening method to design planar tensegrities of simple polygonal shapes. In such a polygonal tensegrity, the strings are joined pair-wise to form a simple polygon (a planar shape consisting of straight, non-intersecting line segments) and only one bar is added at each node. The total number of simple polygonal tensegrities designed by this scheme increases exponentially with the number of bars. Moreover, we demonstrate that each of these designed topologies can produce a self-equilibrated and stable tensegrity configuration. This work helps understand the topological features of simple polygonal tensegrities, which can be used as elementary cells to design some novel two- and three-dimensional tensegrity structures.

Unusual Sonochemical Assembly between Carbon Allotropes for High Strain-Tolerant Conductive Nanocomposites.

Facile methods toward strain-tolerant graphene-based electronic components remain scarce. Although being frequently used to disperse low-dimensional carbonaceous materials, ultrasonication (US) has never been reliable for fabricating stretchable carbonaceous nanocomposite (SCNC). Inspired by the unusual sonochemical assembly between graphene oxide (GO) and carbon nanotube (CNT), we verified the roots-like GO-CNT covalent bonding, rather than just π-π conjugation, was formed during US. In addition, the shockwave-induced collision in the binary-component system enables a burst of fragmentation at the early stage, spatially homogeneous hybridization, and time-dependent restoration of graphitic domains. All of the above are distinct from extensive fragmentation of a conventional single-component system and π-π conjugative assembly. The optimized SCNC exhibits conductivity comparable to reduced monolayer GO and outperforms π-π assemblies in retaining electrical conductance at a strain of 160%-among one of the best reported stretchable conductors. Raman analysis and mechanics simulation confirm the dominant role of counterweighing between the intrinsic and external strains on the mechano-response and durability of SCNC. This work suggests the guideline of creating multiple-component sonochemical systems for various functional nanocomposites.

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.