Cell and biomolecular mechanics in silico

SimuCell3D: three-dimensional simulation of tissue mechanics with cell polarization

The three-dimensional (3D) organization of cells determines tissue function and integrity, and changes markedly in development and disease. Cell-based simulations have long been used to define the underlying mechanical principles. However, high computational costs have so far limited simulations to either simplified cell geometries or small tissue patches. Here, we present SimuCell3D, an efficient open-source program to simulate large tissues in three dimensions with subcellular resolution, growth, proliferation, extracellular matrix, fluid cavities, nuclei and non-uniform mechanical properties, as found in polarized epithelia. Spheroids, vesicles, sheets, tubes and other tissue geometries can readily be imported from microscopy images and simulated to infer biomechanical parameters. Doing so, we show that 3D cell shapes in layered and pseudostratified epithelia are largely governed by a competition between surface tension and intercellular adhesion. SimuCell3D enables the large-scale in silico study of 3D tissue organization in development and disease at a great level of detail.

Facile Determination of the Poisson's Ratio and Young's Modulus of Polyacrylamide Gels and Polydimethylsiloxane

Polyacrylamide hydrogels (PAH gel) and polydimethylsiloxane (PDMS, an elastomer) are two soft materials often used in cell mechanics and mechanobiology, in manufacturing lab-on-a-chip applications, among others. This is partly due to the ability to tune their elasticity with ease in addition to various chemical modifications. For affine polymeric networks, two (of three) elastic constants, Young's modulus (E), the shear modulus (G), and Poisson's ratio (ν), describe the purely elastic response to external forces. However, the literature addressing the experimental determination of ν for PAH (sometimes called PAA gels in the literature) and the PDMS elastomer is surprisingly limited when compared to the literature that reports values of the elastic moduli, E and G. Here, we present a facile method to obtain the Poisson's ratio and Young's modulus for PAH gel and PDMS elastomer based on static tensile tests. The value of ν obtained from the deformation of the sample is compared to the value determined by comparing E and G via a second independent method that utilizes small amplitude shear rheology. We show that the Poisson's ratio may vary significantly from the value for incompressible materials (ν = 0.5), often assumed in the literature even for soft compressible hydrogels. Surprisingly, we find a high degree of agreement between elastic constants obtained by shear rheology and macroscopic static tension test data for polyacrylamide hydrogels but not for elastomeric PDMS.

Using Adhesive Micropatterns and AFM to Assess Cancer Cell Morphology and Mechanics

The mechanical properties of living cells reflect their physiological and pathological state. In particular, cancer cells undergo cytoskeletal modifications that typically make them softer than healthy cells, a property that could be used as a diagnostic tool. However, this is challenging because cells are complex structures displaying a broad range of morphologies when cultured in standard 2D culture dishes. Here, we use adhesive micropatterns to impose the cell geometry and thus standardize the mechanics and morphologies of cancer cells, which we measure by atomic force microscopy (AFM), mechanical nanomapping, and membrane nanotube pulling. We show that micropatterning cancer cells leads to distinct morphological and mechanical changes for different cell lines. Micropatterns did not systematically lower the variability in cell elastic modulus distribution. These effects emerge from a variable cell spreading rate associated with differences in the organization of the cytoskeleton, thus providing detailed insights into the structure-mechanics relationship of cancer cells cultured on micropatterns. Combining AFM with micropatterns reveals new mechanical and morphological observables applicable to cancer cells and possibly other cell types.

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.

Target Convergence Analysis of Cancer-Inspired Swarms for Early Disease Diagnosis and Targeted Collective Therapy

Sensing and perception is generally a challenging aspect of decision-making. In the nanoscale, however, these processes face further complications due to the physical limitations of devising the nanomachines with more limited perception, more noise, and fewer sensors. There is, hence, higher dependence on swarm sensing and perception of many nanomachines. Here, taking hardware and software bioinspiration, we propose Chemo-Mechanical Cancer-Inspired Swarm Perception (CMCISP) based on online nano fuzzy haptic feedback for early disease diagnosis and targeted therapy. Particularly, we use epithelial cancer cell's scaffold as a carrier, its properties as a distributed perception mechanism, and its motility patterns as the swarm movements such as anti-durotaxis, blebbing, and chemotaxis. We implement the in-silico model of CMCISP using a hybrid computational framework of the cellular Potts model, swarm intelligence, and fuzzy decision-making. Furthermore, the target convergence of CMCISP is analytically proved using swarm control theory. Finally, several numerical experiments and validations for cancer target therapy, cellular stiffness measurement, anti-durotaxis movement, and robustness analysis are also conducted and compared with a mathematical chemotherapy model and authors' previous works on targeted therapy. Results show improvements of up to 57.49% in early cancer detection, 26.64% in target convergence, and 68.01% in increased normoxic cell density. The study also reveals the strategy's robustness to environmental/sensory noise by applying six SNR levels of 0, 2, 5, 10, 30, and 50 dB, with an average diagnosis error of only 0.98% and at most 2.51%.

How Physical Factors Coordinate Virus Infection: A Perspective From Mechanobiology

Pandemics caused by viruses have threatened lives of thousands of people. Understanding the complicated process of viral infection provides significantly directive implication to epidemic prevention and control. Viral infection is a complex and diverse process, and substantial studies have been complemented in exploring the biochemical and molecular interactions between viruses and hosts. However, the physical microenvironment where infections implement is often less considered, and the role of mechanobiology in viral infection remains elusive. Mechanobiology focuses on sensation, transduction, and response to intracellular and extracellular physical factors by tissues, cells, and extracellular matrix. The intracellular cytoskeleton and mechanosensors have been proven to be extensively involved in the virus life cycle. Furthermore, innovative methods based on micro- and nanofabrication techniques are being utilized to control and modulate the physical and chemical cell microenvironment, and to explore how extracellular factors including stiffness, forces, and topography regulate viral infection. Our current review covers how physical factors in the microenvironment coordinate viral infection. Moreover, we will discuss how this knowledge can be harnessed in future research on cross-fields of mechanobiology and virology.

Tunable hydrodynamic focusing with dual-neodymium magnet-based microfluidic separation device

Microfluidic separation technologies are the focus of various biological applications, such as disease diagnostics, single-cell analysis, and therapeutics. Different methods and devices were proposed in the micro-separation field, focusing on minimizing the chemical deformation and physical damage to the particles throughout the separation process; however, it is still a challenge. This paper proposes a hydrodynamic focusing-based microfluidic separation device equipped with a dual-neodymium magnet for positive magnetophoretic microparticles and cell separation. Hydrodynamic focusing is used to help to sort the particles and minimize the damage to the microparticles through the proposed different inlet flow rates between the two focusing channels. The dual magnets help to separate the particles in two stages. The system's novelty is integrating the hydrodynamic focusing with the dual magnetics system, where the hydrodynamic focusing is with variable inlet flow rates. The performance of the proposed microfluidic particle separator is numerically assessed under various operating parameters, including the concentration of the particle in the injected solution and flow rate ratios of high to the low focusing flows on the efficiency of the separation. Following the proposed separation method, it was possible to separate the 16 and 10 [Formula: see text] microparticles with the first-round efficiency of 21% with a quality of 92%, respectively. The developed particle separation system can significantly broaden its applications in a variety of biomedical research studies.

Modeling multicellular dynamics regulated by extracellular-matrix-mediated mechanical communication via active particles with polarized effective attraction

Collective cell migration is crucial to many physiological and pathological processes such as embryo development, wound healing, and cancer invasion. Recent experimental studies have indicated that the active traction forces generated by migrating cells in a fibrous extracellular matrix (ECM) can mechanically remodel the ECM, giving rise to bundlelike mesostructures bridging individual cells. Such fiber bundles also enable long-range propagation of cellular forces, leading to correlated migration dynamics regulated by the mechanical communication among the cells. Motivated by these experimental discoveries, we develop an active-particle model with polarized effective attractions (APPA) to investigate emergent multicellular migration dynamics resulting from ECM-mediated mechanical communications. In particular, the APPA model generalizes the classic active-Brownian-particle (ABP) model by imposing a pairwise polarized attractive force between the particles, which depends on the instantaneous dynamic states of the particles and mimics the effective mutual pulling between the cells via the fiber bundle bridge. The APPA system exhibits enhanced aggregation behaviors compared to the classic ABP system, and the contrast is more apparent at lower particle densities and higher rotational diffusivities. Importantly, in contrast to the classic ABP system where the particle velocities are not correlated for all particle densities, the high-density phase of the APPA system exhibits strong dynamic correlations, which are characterized by the slowly decaying velocity correlation functions with a correlation length comparable to the linear size of the high-density phase domain (i.e., the cluster of particles). The strongly correlated multicellular dynamics predicted by the APPA model is subsequently verified in in vitro experiments using MCF-10A cells. Our studies indicate the importance of incorporating ECM-mediated mechanical coupling among the migrating cells for appropriately modeling emergent multicellular dynamics in complex microenvironments.

Matrix Stiffness Modulates Mechanical Interactions and Promotes Contact between Motile Cells

The mechanical micro-environment of cells and tissues influences key aspects of cell structure and function, including cell motility. For proper tissue development, cells need to migrate, interact, and form contacts. Cells are known to exert contractile forces on underlying soft substrates and sense deformations in them. Here, we propose and analyze a minimal biophysical model for cell migration and long-range cell–cell interactions through mutual mechanical deformations of the substrate. We compute key metrics of cell motile behavior, such as the number of cell-cell contacts over a given time, the dispersion of cell trajectories, and the probability of permanent cell contact, and analyze how these depend on a cell motility parameter and substrate stiffness. Our results elucidate how cells may sense each other mechanically and generate coordinated movements and provide an extensible framework to further address both mechanical and short-range biophysical interactions.

Public-Health-Driven Microfluidic Technologies: From Separation to Detection

Separation and detection are ubiquitous in our daily life and they are two of the most important steps toward practical biomedical diagnostics and industrial applications. A deep understanding of working principles and examples of separation and detection enables a plethora of applications from blood test and air/water quality monitoring to food safety and biosecurity; none of which are irrelevant to public health. Microfluidics can separate and detect various particles/aerosols as well as cells/viruses in a cost-effective and easy-to-operate manner. There are a number of papers reviewing microfluidic separation and detection, but to the best of our knowledge, the two topics are normally reviewed separately. In fact, these two themes are closely related with each other from the perspectives of public health: understanding separation or sorting technique will lead to the development of new detection methods, thereby providing new paths to guide the separation routes. Therefore, the purpose of this review paper is two-fold: reporting the latest developments in the application of microfluidics for separation and outlining the emerging research in microfluidic detection. The dominating microfluidics-based passive separation methods and detection methods are discussed, along with the future perspectives and challenges being discussed. Our work inspires novel development of separation and detection methods for the benefits of public health.

Three-dimensional nonlinear dynamics of prestressed active filaments: Flapping, swirling, and flipping

Initially straight slender elastic filaments or rods with constrained ends buckle and form stable two-dimensional shapes when prestressed by bringing the ends together. Beyond a critical value of this prestress, rods can also deform off plane and form twisted three-dimensional equilibrium shapes. Here, we analyze the three-dimensional instabilities and dynamics of such deformed filaments subject to nonconservative active follower forces and fluid drag. We find that softly constrained filaments that are clamped at one end and pinned at the other exhibit stable two-dimensional planar flapping oscillations when active forces are directed toward the clamped end. Reversing the directionality of the forces quenches the instability. For strongly constrained filaments with both ends clamped, computations reveal an instability arising from the twist-bend-activity coupling. Planar oscillations are destabilized by off-planar perturbations resulting in twisted three-dimensional swirling patterns interspersed with periodic flipping or reversal of the swirling direction. These striking swirl-flip transitions are characterized by two distinct timescales: the time period for a swirl (rotation) and the time between flipping events. We interpret these reversals as relaxation oscillation events driven by accumulation of torsional energy. Each cycle is initiated by a fast jump in torsional deformation with a subsequent slow decrease in net torsion until the next cycle. Our work reveals the rich tapestry of spatiotemporal patterns when weakly inertial strongly damped rods are deformed by nonconservative active forces. Taken together, our results suggest avenues by which prestress, elasticity, and activity may be used to design synthetic macroscale pumps or mixers.

Extensions of the worm-like-chain model to tethered active filaments under tension

Intracellular elastic filaments such as microtubules are subject to thermal Brownian noise and active noise generated by molecular motors that convert chemical energy into mechanical work. Similarly, polymers in living fluids such as bacterial suspensions and swarms suffer bending deformations as they interact with single bacteria or with cell clusters. Often, these filaments perform mechanical functions and interact with their networked environment through cross-links or have other similar constraints placed on them. Here, we examine the mechanical properties-under tension-of such constrained active filaments under canonical boundary conditions motivated by experiments. Fluctuations in the filament shape are a consequence of two types of random forces-thermal Brownian forces and activity derived forces with specified time and space correlation functions. We derive force-extension relationships and expressions for the mean square deflections for tethered filaments under various boundary conditions including hinged and clamped constraints. The expressions for hinged-hinged boundary conditions are reminiscent of the worm-like-chain model and feature effective bending moduli and mode-dependent non-thermodynamic effective temperatures controlled by the imposed force and by the activity. Our results provide methods to estimate the activity by measurements of the force-extension relation of the filaments or their mean square deflections, which can be routinely performed using optical traps, tethered particle experiments, or other single molecule techniques.

Modeling cell migration regulated by cell extracellular-matrix micromechanical coupling

Cell migration in fibrous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response, and cancer progression. During migration, individual cells can generate active pulling forces via actomyosin contraction, which are transmitted to the ECM fibers through focal adhesion complexes, remodel the ECM, and eventually propagate to and can be sensed by other cells in the system. The microstructure and physical properties of the ECM can also significantly influence cell migration, e.g., via durotaxis and contact guidance. Here, we develop a computational model for two-dimensional cell migration regulated by cell-ECM micromechanical coupling. Our model explicitly takes into account a variety of cellular-level processes, including focal adhesion formation and disassembly, active traction force generation and cell locomotion due to actin filament contraction, transmission and propagation of tensile forces in the ECM, as well as the resulting ECM remodeling. We validate our model by accurately reproducing single-cell dynamics of MCF-10A breast cancer cells migrating on collagen gels and show that the durotaxis and contact guidance effects naturally arise as a consequence of the cell-ECM micromechanical interactions considered in the model. Moreover, our model predicts strongly correlated multicellular migration dynamics, which are resulted from the ECM-mediated mechanical coupling among the migrating cell and are subsequently verified in in vitro experiments using MCF-10A cells. Our computational model provides a robust tool to investigate emergent collective dynamics of multicellular systems in complex in vivo microenvironment and can be utilized to design in vitro microenvironments to guide collective behaviors and self-organization of cells.

Buckling instabilities and spatio-temporal dynamics of active elastic filaments

Biological filaments driven by molecular motors tend to experience tangential propulsive forces also known as active follower forces. When such a filament encounters an obstacle, it deforms, which reorients its follower forces and alters its entire motion. If the filament pushes a cargo, the friction on the cargo can be enough to deform the filament, thus affecting the transport properties of the cargo. Motivated by cytoskeletal filament motility assays, we study the dynamic buckling instabilities of a two-dimensional slender elastic filament driven through a dissipative medium by tangential propulsive forces in the presence of obstacles or cargo. We observe two distinct instabilities. When the filament's head is pinned or experiences significant translational but little rotational drag from its cargo, it buckles into a steadily rotating coiled state. When it is clamped or experiences both significant translational and rotational drag from its cargo, it buckles into a periodically beating, overall translating state. Using minimal analytically tractable models, linear stability theory and fully nonlinear computations, we study the onset of each buckling instability, characterize each buckled state, and map out the phase diagram of the system. Finally, we use particle-based Brownian dynamics simulations to show our main results are robust to moderate noise and steric repulsion. Overall, our results provide a unified framework to understand the dynamics of tangentially propelled filaments and filament-cargo assemblies.

A three dimensional model of multicellular aggregate compression

Multicellular aggregates are an excellent model system to explore the role of tissue biomechanics, which has been demonstrated to play a crucial role in many physiological and pathological processes. In this paper, we propose a three-dimensional mechanical model and apply it to the uniaxial compression of a multicellular aggregate in a realistic biological setting. In particular, we consider an aggregate of initially spherical shape and describe both its elastic deformations and the reorganisation of the cells forming the spheroid. The latter phenomenon, understood as remodelling, is accounted for by assuming that the aggregate undergoes plastic-like distortions. The study of the compression of the spheroid, achieved by means of two parallel, compressive plates, needs the formulation of a contact problem between the living spheroid itself and the plates, and is solved with the aid of the augmented Lagrangian method. The results of the performed numerical simulations are in qualitative agreement with the biological observations reported in the literature and can also be used to estimate quantitatively some fundamental aggregate mechanical parameters.

Small asymmetric Brownian objects self-align in nanofluidic channels

Although the self-alignment of asymmetric macro-sized objects of a few tens of microns in size have been studied extensively in experiments and theory, access to much smaller length scales is still hindered by technical challenges. We combine molecular dynamics and stochastic rotation dynamics techniques to investigate the self-orientation phenomenon at different length scales, ranging from the micron to the nano scale by progressively increasing the relative strength of diffusion over convection. To this end, we model an asymmetric dumbbell particle in Hele-Shaw flow and explore a wide range of Péclet numbers (Pe) and different particle shapes, as characterized by the size ratio of the two dumbbell spheres (R[combining tilde]). By independently varying these two parameters we analyse the process of self-orientation and characterize the alignment of the dumbbell with the direction of the fluid flow. We identify three different regimes of strong, weak and no alignment and we map out a state diagram in Pe versus R[combining tilde] plane. Based on these results, we estimate dimensional length scales and flow rates for which these findings would be applicable in experiments. Finally, we find that the characteristic reorientation time of the dumbbell is a monotonically decreasing function of the dumbbell anisotropy.

Cancer cell mechanics with altered cytoskeletal behavior and substrate effects: A 3D finite element modeling study

A robust computational model of a cancer cell is presented using finite element modeling. The model accurately captures nuances of the various components of the cellular substructure. The role of degradation of cytoskeleton on overall elastic properties of the cancer cell is reported. The motivation for degraded cancer cellular substructure, the cytoskeleton is the observation that the innate mechanics of cytoskeleton is disrupted by various anti-cancer drugs as therapeutic treatments for the destruction of the cancer tumors. We report a significant influence on the degradation of the cytoskeleton on the mechanics of cancer cell. Further, a simulations based study is reported where we evaluate mechanical properties of the cancer cell attached to a variety of substrates. The loading of the cancer cell is less influenced by nature of the substrate, but low modulus substrates such as osteoblasts and hydrogels indicate a significant change in unloading behavior and also the plastic deformation. Overall, softer substrates such as osteoblasts and other bone cells result in a much altered unloading response as well as significant plastic deformation. These substrates are relevant to metastasis wherein certain type of cancers such as prostate and breast cancer cells migrate to the bone and colonize through mesenchymal to epithelial transition. The modeling study presented here is an important first step in the development of strong predictive methodologies for cancer progression.

Clogging-free microfluidics for continuous size-based separation of microparticles

In microfluidic filtration systems, one of the leading obstacles to efficient, continuous operation is clogging of the filters. Here, we introduce a lateral flow microfluidic sieving (μ-sieving) technique to overcome clogging and to allow continuous operation of filter based microfluidic separation. A low frequency mechanical oscillation was added to the fluid flow, which made possible the release of aggregated unwanted polystyrene (PS) particles trapped between the larger target PS particles in the filter demonstrating continuous μ-sieving operation. We achieved collection of the target PS particles with 100% separation efficiency. Also, on average, more than 98% of the filtered target particles were retrieved after the filtration showing high retrieval rates. Since the oscillation was applied to the fluid but not to the microfluidic filter system, mechanical stresses to the system was minimized and no additional fabrication procedures were necessary. We also applied the μ-sieving technique to the separation of cancer cells (MDA-MB-231) from whole blood and showed that the fluidic oscillations prevented the filters from being blocked by the filtered cancer cells allowing continuous microfluidic separation with high efficiency.

Modeling the mechanics of cells in the cell-spreading process driven by traction forces

Mechanical properties of cells and their mechanical interaction with the extracellular environments are main factors influencing cellular function, thus indicating the progression of cells in different disease states. By considering the mechanical interactions between cell adhesion molecules and the extracellular environment, we developed a cell mechanical model that can characterize the mechanical changes in cells during cell spreading. A cell model was established that consisted of various main subcellular components, including cortical cytoskeleton, nuclear envelope, actin filaments, intermediate filaments, and microtubules. We demonstrated the structural changes in subcellular components and the changes in spreading areas during cell spreading driven by traction forces. The simulation of nanoindentation tests was conducted by integrating the indenting force to the cell model. The force-indentation curve of the cells at different spreading states was simulated, and the results showed that cell stiffness increased with increasing traction forces, which were consistent with the experimental results. The proposed cell mechanical model provides a strategy to investigate the mechanical interactions of cells with the extracellular environments through the adhesion molecules and to reveal the cell mechanical properties at the subcellular level as cells shift from the suspended state to the adherent state.

Characterization and sorting of cells based on stiffness contrast in a microfluidic channel

This paper reports the characterization and sorting of cells based on stiffness contrast. A microfluidic device with focusing and spacing control for stiffness based sorting of cells is designed, fabricated and demonstrated.

Review of cellular mechanotransduction on micropost substrates

As physical entities, living cells can sense and respond to various stimulations within and outside the body through cellular mechanotransduction. Any deviation in cellular mechanotransduction will not only undermine the orchestrated regulation of mechanical responses, but also lead to the breakdown of their physiological function. Therefore, a quantitative study of cellular mechanotransduction needs to be conducted both in experiments and in computational simulations to investigate the underlying mechanisms of cellular mechanotransduction. In this review, we present an overview of the current knowledge and significant progress in cellular mechanotransduction via micropost substrates. In the aspect of experimental studies, we summarize significant experimental progress and place an emphasis on the coupled relationship among cellular spreading, focal adhesion and contractility as well as the influence of substrate properties on force-involved cellular behaviors. In the other aspect of computational investigations, we outline a coupled framework including the biochemically motivated stress fiber model and thermodynamically motivated adhesion model and present their predicted biomechanical responses and then compare predicted simulation results with experimental observations to further explore the mechanisms of cellular mechanotransduction. At last, we discuss the future perspectives both in experimental technologies and in computational models, as well as facing challenges in the area of cellular mechanotransduction.

A microfluidic device with focusing and spacing control for resistance-based sorting of droplets and cells

This paper reports a novel hydrodynamic technique for sorting of droplets and cells based on size and deformability. The device comprises two modules: a focusing and spacing control module and a sorting module. The focusing and spacing control module enables focusing of objects present in a sample onto one of the side walls of a channel with controlled spacing between them using a sheath fluid. A 3D analytical model is developed to predict the sheath-to-sample flow rate ratio required to facilitate single-file focusing and maintain the required spacing between a pair of adjacent objects. Experiments are performed to demonstrate focusing and spacing control of droplets (size 5-40 μm) and cells (HL60, size 10-25 μm). The model predictions compare well with experimental data in terms of focusing and spacing control within 9%. In the sorting module, the main channel splits into two branch channels (straight and side branches) with the flow into these two channels separated by a "dividing streamline". A sensing channel and a bypass channel control the shifting of the dividing streamline depending on the object size and deformability. While resistance offered by individual droplets of different sizes has been studied in our previous work (P. Sajeesh, M. Doble and A. K. Sen, Biomicrofluidics, 2014, 8, 1-23), here we present resistance of individual cells (HL60) as a function of size. A theoretical model is developed and used for the design of the sorter. Experiments are performed for size-based sorting of droplets (sizes 25 and 40 μm, 10 and 15 μm) and HL60 cells (sizes 11 μm and 19 μm) and deformability-based sorting of droplets (size 10 ± 1.0 μm) and polystyrene microbeads (size 10 ± 0.2 μm). The performance of the device for size- and deformability-based sorting is characterized in terms of sorting efficiency. The proposed device could be potentially used as a diagnostic tool for sorting of larger tumour cells from smaller leukocytes.

Combining AFM and acoustic probes to reveal changes in the elastic stiffness tensor of living cells

Knowledge of how the elastic stiffness of a cell affects its communication with its environment is of fundamental importance for the understanding of tissue integrity in health and disease. For stiffness measurements, it has been customary to quote a single parameter quantity, e.g., Young's modulus, rather than the minimum of two terms of the stiffness tensor required by elasticity theory. In this study, we use two independent methods (acoustic microscopy and atomic force microscopy nanoindentation) to characterize the elastic properties of a cell and thus determine two independent elastic constants. This allows us to explore in detail how the mechanical properties of cells change in response to signaling pathways that are known to regulate the cell's cytoskeleton. In particular, we demonstrate that altering the tensioning of actin filaments in NIH3T3 cells has a strong influence on the cell's shear modulus but leaves its bulk modulus unchanged. In contrast, altering the polymerization state of actin filaments influences bulk and shear modulus in a similar manner. In addition, we can use the data to directly determine the Poisson ratio of a cell and show that in all cases studied, it is less than, but very close to, 0.5 in value.

Single Cell Wall Nonlinear Mechanics Revealed by a Multiscale Analysis of AFM Force-Indentation Curves

Individual plant cells are rather complex mechanical objects. Despite the fact that their wall mechanical strength may be weakened by comparison with their original tissue template, they nevertheless retain some generic properties of the mother tissue, namely the viscoelasticity and the shape of their walls, which are driven by their internal hydrostatic turgor pressure. This viscoelastic behavior, which affects the power-law response of these cells when indented by an atomic force cantilever with a pyramidal tip, is also very sensitive to the culture media. To our knowledge, we develop here an original analyzing method, based on a multiscale decomposition of force-indentation curves, that reveals and quantifies for the first time the nonlinearity of the mechanical response of living single plant cells upon mechanical deformation. Further comparing the nonlinear strain responses of these isolated cells in three different media, we reveal an alteration of their linear bending elastic regime in both hyper- and hypotonic conditions.

Effect of the object 3D shape on the viscoelastic testing in optical tweezers

Viscoelastic testing of biological cells has been performed with the optical tweezers and stretcher. Historically, the cells were modeled by the spring-dashpot network or the power-law models, which can however characterize only the homogeneous, isotropic viscoelastic material, but not the 3D cell itself. Our mechanical and finite element analyses show that the cell elongations are different significantly for different cell 3D shapes in the creep testing. In the dynamic testing the loss tangent, which is measurable directly in the experiment, is not sensitive to the cell shape. However, the stress-strain hysteresis loop still depends on the cell 3D shape.

Cells as liquid motors: mechanosensitivity emerges from collective dynamics of actomyosin cortex

Living cells adapt and respond actively to the mechanical properties of their environment. In addition to biochemical mechanotransduction, evidence exists for a myosin-dependent purely mechanical sensitivity to the stiffness of the surroundings at the scale of the whole cell. Using a minimal model of the dynamics of actomyosin cortex, we show that the interplay of myosin power strokes with the rapidly remodeling actin network results in a regulation of force and cell shape that adapts to the stiffness of the environment. Instantaneous changes of the environment stiffness are found to trigger an intrinsic mechanical response of the actomyosin cortex. Cortical retrograde flow resulting from actin polymerization at the edges is shown to be modulated by the stress resulting from myosin contractility, which in turn, regulates the cell length in a force-dependent manner. The model describes the maximum force that cells can exert and the maximum speed at which they can contract, which are measured experimentally. These limiting cases are found to be associated with energy dissipation phenomena, which are of the same nature as those taking place during the contraction of a whole muscle. This similarity explains the fact that single nonmuscle cell and whole-muscle contraction both follow a Hill-like force-velocity relationship.

The spatial-temporal characteristics of type I collagen-based extracellular matrix

Type I collagen abounds in mammalian extracellular matrix (ECM) and is crucial to many biophysical processes. While previous studies have mostly focused on bulk averaged properties, here we provide a comprehensive and quantitative spatial-temporal characterization of the microstructure of type I collagen-based ECM as the gelation temperature varies. The structural characteristics including the density and nematic correlation functions are obtained by analyzing confocal images of collagen gels prepared at a wide range of gelation temperatures (from 16 °C to 36 °C). As temperature increases, the gel microstructure varies from a "bundled" network with strong orientational correlation between the fibers to an isotropic homogeneous network with no significant orientational correlation, as manifested by the decaying of length scales in the correlation functions. We develop a kinetic Monte-Carlo collagen growth model to better understand how ECM microstructure depends on various environmental or kinetic factors. We show that the nucleation rate, growth rate, and an effective hydrodynamic alignment of collagen fibers fully determines the spatiotemporal fluctuations of the density and orientational order of collagen gel microstructure. Also the temperature dependence of the growth rate and nucleation rate follow the prediction of classical nucleation theory.

Hydrodynamic resistance and mobility of deformable objects in microfluidic channels

This work reports experimental and theoretical studies of hydrodynamic behaviour of deformable objects such as droplets and cells in a microchannel. Effects of mechanical properties including size and viscosity of these objects on their deformability, mobility, and induced hydrodynamic resistance are investigated. The experimental results revealed that the deformability of droplets, which is quantified in terms of deformability index (D.I.), depends on the droplet-to-channel size ratio [Formula: see text] and droplet-to-medium viscosity ratio [Formula: see text]. Using a large set of experimental data, for the first time, we provide a mathematical formula that correlates induced hydrodynamic resistance of a single droplet [Formula: see text] with the droplet size [Formula: see text] and viscosity [Formula: see text]. A simple theoretical model is developed to obtain closed form expressions for droplet mobility [Formula: see text] and [Formula: see text]. The predictions of the theoretical model successfully confront the experimental results in terms of the droplet mobility [Formula: see text] and induced hydrodynamic resistance [Formula: see text]. Numerical simulations are carried out using volume-of-fluid model to predict droplet generation and deformation of droplets of different size ratio [Formula: see text] and viscosity ratio [Formula: see text], which compare well with that obtained from the experiments. In a novel effort, we performed experiments to measure the bulk induced hydrodynamic resistance [Formula: see text] of different biological cells (yeast, L6, and HEK 293). The results reveal that the bulk induced hydrodynamic resistance [Formula: see text] is related to the cell concentration and apparent viscosity of the cells.

A review of the effects of the cell environment physicochemical nanoarchitecture on stem cell commitment

Physicochemical features of a cell nanoenvironment exert important influence on stem cell behavior and include the influence of matrix elasticity and topography on differentiation processes. The presence of growth factors such as TGF-β and BMPs on these matrices provides chemical cues and thus plays vital role in directing eventual stem cell fate. Engineering of functional biomimetic scaffolds that present programmed spatio-temporal physical and chemical signals to stem cells holds great promise in stem cell therapy. Progress in this field requires tacit understanding of the mechanistic aspects of cell-environment nanointeractions, so that they can be manipulated and exploited for the design of sophisticated next generation biomaterials. In this review, we report and discuss the evolution of these processes and pathways in the context of matrix adhesion as they might relate to stemness and stem cell differentiation. Super-resolution microscopy and single-molecule methods for in vitro nano-manipulation are helping to identify and characterize the molecules and mechanics of structural transitions within stem cells and matrices. All these advances facilitate research toward understanding of stem cell niche and consequently to developing new class of biomaterials helping the "used biomaterials" for applications in tissue engineering and regenerative medicine.

Advances in the mechanical modeling of filamentous actin and its cross-linked networks on multiple scales

The protein actin is a part of the cytoskeleton and, therefore, responsible for the mechanical properties of the cells. Starting with the single molecule up to the final structure, actin creates a hierarchical structure of several levels exhibiting a remarkable behavior. The hierarchy spans several length scales and limitations in computational power; therefore, there is a call for different mechanical modeling approaches for the different scales. On the molecular level, we may consider each atom in molecular dynamics simulations. Actin forms filaments by combining the molecules into a double helix. In a model, we replace molecular subdomains using coarse-graining methods, allowing the investigation of larger systems of several atoms. These models on the nanoscale inform continuum mechanical models of large filaments, which are based on worm-like chain models for polymers. Assemblies of actin filaments are connected with cross-linker proteins. Models with discrete filaments, so-called Mikado models, allow us to investigate the dependence of the properties of networks on the parameters of the constituents. Microstructurally motivated continuum models of the networks provide insights into larger systems containing cross-linked actin networks. Modeling of such systems helps to gain insight into the processes on such small scales. On the other hand, they call for verification and hence trigger the improvement of established experiments and the development of new methods.

Nanotechnology in the regulation of stem cell behavior

Stem cells are known for their potential to repair damaged tissues. The adhesion, growth and differentiation of stem cells are likely controlled by the surrounding microenvironment which contains both chemical and physical cues. Physical cues in the microenvironment, for example, nanotopography, were shown to play important roles in stem cell fate decisions. Thus, controlling stem cell behavior by nanoscale topography has become an important issue in stem cell biology. Nanotechnology has emerged as a new exciting field and research from this field has greatly advanced. Nanotechnology allows the manipulation of sophisticated surfaces/scaffolds which can mimic the cellular environment for regulating cellular behaviors. Thus, we summarize recent studies on nanotechnology with applications to stem cell biology, including the regulation of stem cell adhesion, growth, differentiation, tracking and imaging. Understanding the interactions of nanomaterials with stem cells may provide the knowledge to apply to cell-scaffold combinations in tissue engineering and regenerative medicine.

Silicon chips detect intracellular pressure changes in living cells

The ability to measure pressure changes inside different components of a living cell is important, because it offers an alternative way to study fundamental processes that involve cell deformation. Most current techniques such as pipette aspiration, optical interferometry or external pressure probes use either indirect measurement methods or approaches that can damage the cell membrane. Here we show that a silicon chip small enough to be internalized into a living cell can be used to detect pressure changes inside the cell. The chip, which consists of two membranes separated by a vacuum gap to form a Fabry-Pérot resonator, detects pressure changes that can be quantified from the intensity of the reflected light. Using this chip, we show that extracellular hydrostatic pressure is transmitted into HeLa cells and that these cells can endure hypo-osmotic stress without significantly increasing their intracellular hydrostatic pressure.

A multi-structural single cell model of force-induced interactions of cytoskeletal components

Several computational models based on experimental techniques and theories have been proposed to describe cytoskeleton (CSK) mechanics. Tensegrity is a prominent model for force generation, but it cannot predict mechanics of individual CSK components, nor explain the discrepancies from the different single cell stimulating techniques studies combined with cytoskeleton-disruptors. A new numerical concept that defines a multi-structural 3D finite element (FE) model of a single-adherent cell is proposed to investigate the biophysical and biochemical differences of the mechanical role of each cytoskeleton component under loading. The model includes prestressed actin bundles and microtubule within cytoplasm and nucleus surrounded by the actin cortex. We performed numerical simulations of atomic force microscopy (AFM) experiments by subjecting the cell model to compressive loads. The numerical role of the CSK components was corroborated with AFM force measurements on U2OS-osteosarcoma cells and NIH-3T3 fibroblasts exposed to different cytoskeleton-disrupting drugs. Computational simulation showed that actin cortex and microtubules are the major components targeted in resisting compression. This is a new numerical tool that explains the specific role of the cortex and overcomes the difficulty of isolating this component from other networks in vitro. This illustrates that a combination of cytoskeletal structures with their own properties is necessary for a complete description of cellular mechanics.

Multiscale modeling of blood flow: from single cells to blood rheology

Mesoscale simulations of blood flow, where the red blood cells are described as deformable closed shells with a membrane characterized by bending rigidity and stretching elasticity, have made much progress in recent years to predict the flow behavior of blood cells and other components in various flows. To numerically investigate blood flow and blood-related processes in complex geometries, a highly efficient simulation technique for the plasma and solutes is essential. In this review, we focus on the behavior of single and several cells in shear and microcapillary flows, the shear-thinning behavior of blood and its relation to the blood cell structure and interactions, margination of white blood cells and platelets, and modeling hematologic diseases and disorders. Comparisons of the simulation predictions with existing experimental results are made whenever possible, and generally very satisfactory agreement is obtained.

Influence of nanohelical shape and periodicity on stem cell fate

Microenvironments such as protein composition, physical features, geometry, and elasticity play important roles in stem cell lineage specification. The components of the extracellular matrix are known to subsequently assemble into fibrillar networks in vivo with defined periodicity. However, the effect of the most critical parameter, which involves the periodicity of these fibrillar networks, on the stem cell fate is not yet investigated. Here, we show the effect of synthetic fibrillar networks patterned with nanometric periodicities, using bottom-up approaches, on the response of stem cells. We have used helical organic nanoribbons based on self-assemblies of Gemini-type amphiphiles to access chiral silica nanoribbons with two different shapes and periodicities (twisted ribbons and helical ribbons) from the same native self-assembled organic nanostructure. We demonstrate the covalent grafting of these silica nanoribbons onto activated glass substrates and the influence of this programmed isotropically oriented matrix to direct the commitment of human mesenchymal stem cells (hMSCs) into osteoblast lineage in vitro, free of osteogenic-inducing media. The specific periodicity of 63 nm (±5 nm) with helical ribbon shape induces specific cell adhesion through the fibrillar focal adhesion formation and leads to stem cell commitment into osteoblast lineage. In contrast, the matrix of periodicity 100 nm (±15 nm) with twisted ribbon shape does not lead to osteoblast commitment. The inhibition of non-muscle myosin II with blebbistatin is sufficient to block this osteoblast commitment on helical nanoribbon matrix, demonstrating that stem cells interpret the nanohelical shape and periodicity environment physically. These results indicate that hMSCs could interpret nanohelical shape and periodicity in the same way they sense microenvironment elasticity. This provides a promising tool to promote hMSC osteogenic capacity, which can be exploited in a 3D scaffold for bone tissue engineering.

Piezoelectric nanoribbons for monitoring cellular deformations

Methods for probing mechanical responses of mammalian cells to electrical excitations can improve our understanding of cellular physiology and function. The electrical response of neuronal cells to applied voltages has been studied in detail, but less is known about their mechanical response to electrical excitations. Studies using atomic force microscopes (AFMs) have shown that mammalian cells exhibit voltage-induced mechanical deflections at nanometre scales, but AFM measurements can be invasive and difficult to multiplex. Here we show that mechanical deformations of neuronal cells in response to electrical excitations can be measured using piezoelectric PbZr(x)Ti(1-x)O(3) (PZT) nanoribbons, and we find that cells deflect by 1 nm when 120 mV is applied to the cell membrane. The measured cellular forces agree with a theoretical model in which depolarization caused by an applied voltage induces a change in membrane tension, which results in the cell altering its radius so that the pressure remains constant across the membrane. We also transfer arrays of PZT nanoribbons onto a silicone elastomer and measure mechanical deformations on a cow lung that mimics respiration. The PZT nanoribbons offer a minimally invasive and scalable platform for electromechanical biosensing.

Influence of semiflexible structural features of actin cytoskeleton on cell stiffness based on actin microstructural modeling

A new actin cytoskeleton microstructural model based on the semiflexible polymer nature of the actin filament is proposed. The relationship between the stretching force and the mechanical properties of cells was examined. Experiments on deforming hematopoietic cells with distinct primitiveness from normal and leukemic sources were conducted via optical tweezer manipulation at single-cell level. The modeling results were demonstrated to be in good agreement with the experimental data. We characterized how the structural properties of the actin cytoskeleton, such as prestress, density of cross-links, and actin concentration, affect the mechanical behavior of cells based on the proposed model. Increasing prestress, actin concentration, and density of cross-links reduced cell deformation, and the cell also exhibited strain stiffening behavior with an increase in the stretching force. Compared with existing models, the proposed model exhibits a distinct feature in probing the influence of semiflexible polymer nature of the actin filament on cell mechanical behavior.

A power-law rheology-based finite element model for single cell deformation

Physical forces can elicit complex time- and space-dependent deformations in living cells. These deformations at the subcellular level are difficult to measure but can be estimated using computational approaches such as finite element (FE) simulation. Existing FE models predominantly treat cells as spring-dashpot viscoelastic materials, while broad experimental data are now lending support to the power-law rheology (PLR) model. Here, we developed a large deformation FE model that incorporated PLR and experimentally verified this model by performing micropipette aspiration on fibroblasts under various mechanical loadings. With a single set of rheological properties, this model recapitulated the diverse micropipette aspiration data obtained using three protocols and with a range of micropipette sizes. More intriguingly, our analysis revealed that decreased pipette size leads to increased pressure gradient, potentially explaining our previous counterintuitive finding that decreased pipette size leads to increased incidence of cell blebbing and injury. Taken together, our work leads to more accurate rheological interpretation of micropipette aspiration experiments than previous models and suggests pressure gradient as a potential determinant of cell injury.

Beyond-limit light focusing in the intermediate zone

We experimentally verify that a new nanolens of a designed plasmonic aperture can focus visible light to a single line with its width smaller than the limit of half the wavelength in the intermediate zone. The experimental measurement indicates that while the near field plays a role to increase the spot size in the near zone, it is negligible at the beyond-limit focused region; i.e., the focused light is dominated by the radiative fields. The image taken by the optical microscope shows that the fields focused have propagated to the far zone. Besides being of academic interest, the nanolens capable in achieving a lower diffraction limit in the intermediate zone is important for application possibilities.

Substrates for cardiovascular tissue engineering

Cardiovascular tissue engineering aims to find solutions for the suboptimal regeneration of heart valves, arteries and myocardium by creating 'living' tissue replacements outside (in vitro) or inside (in situ) the human body. A combination of cells, biomaterials and environmental cues of tissue development is employed to obtain tissues with targeted structure and functional properties that can survive and develop within the harsh hemodynamic environment of the cardiovascular system. This paper reviews the up-to-date status of cardiovascular tissue engineering with special emphasis on the development and use of biomaterial substrates. Key requirements and properties of these substrates, as well as methods and readout parameters to test their efficacy in the human body, are described in detail and discussed in the light of current trends toward designing biologically inspired microenviroments for in situ tissue engineering purposes.

Cytoskeleton reorganization of spreading cells on micro-patterned islands: a functional model

Predictive numerical models of cellular response to biophysical cues have emerged as a useful quantitative tool for cell biology research. Cellular experiments in silico can augment in vitro and in vivo investigations by filling gaps in what is possible to achieve through 'wet work'. Biophysics-based numerical models can be used to verify the plausibility of mechanisms regulating tissue homeostasis derived from experiments. They can also be used to explore potential targets for therapeutic intervention. In this perspective article we introduce a single cell model developed towards the design of novel biomaterials to elicit a regenerative cellular response for the repair of diseased tissues. The model is governed by basic mechanisms of cell spreading (lamellipodial and filopodial extension, formation of cell-matrix adhesions, actin reinforcement) and is developed in the context of cellular interaction with functionalized substrates that present defined points of potential adhesion. To provide adequate context, we first review the biophysical underpinnings of the model as well as reviewing existing cell spreading models. We then present preliminary benchmarking of the model against published experiments of cell spreading on micro-patterned substrates. Initial results indicate that our mechanistic model may represent a potentially useful approach in a better understanding of cell interactions with the extracellular matrix.

Dynamic modes of red blood cells in oscillatory shear flow

The dynamics of red blood cells (RBCs) in oscillatory shear flow was studied using differential equations of three variables: a shape parameter, the inclination angle θ, and phase angle ϕ of the membrane rotation. In steady shear flow, three types of dynamics occur depending on the shear rate and viscosity ratio. (i) tank-treading (TT): ϕ rotates while the shape and θ oscillate. (ii) tumbling (TB): θ rotates while the shape and ϕ oscillate. (iii) intermediate motion: both ϕ and θ rotate synchronously or intermittently. In oscillatory shear flow, RBCs show various dynamics based on these three motions. For a low shear frequency with zero mean shear rate, a limit-cycle oscillation occurs, based on the TT or TB rotation at a high or low shear amplitude, respectively. This TT-based oscillation well explains recent experiments. In the middle shear amplitude, RBCs show an intermittent or synchronized oscillation. As shear frequency increases, the vesicle oscillation becomes delayed with respect to the shear oscillation. At a high frequency, multiple limit-cycle oscillations coexist. The thermal fluctuations can induce transitions between two orbits at very low shear amplitudes. For a high mean shear rate with small shear oscillation, the shape and θ oscillate in the TT motion but only one attractor exists even at high shear frequencies. The measurement of these oscillatory modes is a promising tool for quantifying the viscoelasticity of RBCs, synthetic capsules, and lipid vesicles.