Rheological properties of cells measured by optical tweezers

Exploiting Matrix Stiffness to Overcome Drug Resistance

Drug resistance is arguably one of the biggest challenges facing cancer research today. Understanding the underlying mechanisms of drug resistance in tumor progression and metastasis are essential in developing better treatment modalities. Given the matrix stiffness affecting the mechanotransduction capabilities of cancer cells, characterization of the related signal transduction pathways can provide a better understanding for developing novel therapeutic strategies. In this review, we aimed to summarize the recent advancements in tumor matrix biology in parallel to therapeutic approaches targeting matrix stiffness and its consequences in cellular processes in tumor progression and metastasis. The cellular processes governed by signal transduction pathways and their aberrant activation may result in activating the epithelial-to-mesenchymal transition, cancer stemness, and autophagy, which can be attributed to drug resistance. Developing therapeutic strategies to target these cellular processes in cancer biology will offer novel therapeutic approaches to tailor better personalized treatment modalities for clinical studies.

Viscoelasticity of diverse biological samples quantified by Acoustic Force Microrheology (AFMR)

In the context of soft matter and cellular mechanics, microrheology - the use of micron-sized particles to probe the frequency-dependent viscoelastic response of materials - is widely used to shed light onto the mechanics and dynamics of molecular structures. Here we present the implementation of active microrheology in an Acoustic Force Spectroscopy setup (AFMR), which combines multiplexing with the possibility of probing a wide range of forces ( ~ pN to ~nN) and frequencies (0.01-100 Hz). To demonstrate the potential of this approach, we perform active microrheology on biological samples of increasing complexity and stiffness: collagen gels, red blood cells (RBCs), and human fibroblasts, spanning a viscoelastic modulus range of five orders of magnitude. We show that AFMR can successfully quantify viscoelastic properties by probing many beads with high single-particle precision and reproducibility. Finally, we demonstrate that AFMR to map local sample heterogeneities as well as detect cellular responses to drugs.

Active viscoelastic models for cell and tissue mechanics

Living cells are out of equilibrium active materials. Cell-generated forces are transmitted across the cytoskeleton network and to the extracellular environment. These active force interactions shape cellular mechanical behaviour, trigger mechano-sensing, regulate cell adaptation to the microenvironment and can affect disease outcomes. In recent years, the mechanobiology community has witnessed the emergence of many experimental and theoretical approaches to study cells as mechanically active materials. In this review, we highlight recent advancements in incorporating active characteristics of cellular behaviour at different length scales into classic viscoelastic models by either adding an active tension-generating element or adjusting the resting length of an elastic element in the model. Summarizing the two groups of approaches, we will review the formulation and application of these models to understand cellular adaptation mechanisms in response to various types of mechanical stimuli, such as the effect of extracellular matrix properties and external loadings or deformations.

Brain tissue mechanics is governed by microscale relations of the tissue constituents

Local mechanical tissue properties are a critical regulator of cell function in the central nervous system (CNS) during development and disorder. However, we still don't fully understand how the mechanical properties of individual tissue constituents, such as cell nuclei or myelin, determine tissue mechanics. Here we developed a model predicting local tissue mechanics, which induces non-affine deformations of the tissue components. Using the mouse hippocampus and cerebellum as model systems, we show that considering individual tissue components alone, as identified by immunohistochemistry, is not sufficient to reproduce the local mechanical properties of CNS tissue. Our results suggest that brain tissue shows a universal response to applied forces that depends not only on the amount and stiffness of the individual tissue constituents but also on the way how they assemble. Our model may unify current incongruences between the mechanics of soft biological tissues and the underlying constituents and facilitate the design of better biomedical materials and engineered tissues. To this end, we provide a freely-available platform to predict local tissue elasticity upon providing immunohistochemistry images and stiffness values for the constituents of the tissue.

Photoacoustic based evaluation of viscoelastic properties of Gram-negative and Gram-positive bacterial colonies

Mechanical properties of bacterial colonies are crucial considering both addressing their pathogenic effects and exploring their potential applications. Viscoelasticity is a key mechanical property with major impacts on the cell shapes and functions, which reflects the information about the cell envelope constituents. Hereby, we have proposed the application of photoacoustic viscoelasticity (PAVE) for studying the rheological properties of bacterial colonies. In this regard, we employed an intensity-modulated laser beam as the excitation source followed by the phase delay measurement between the generated PA signal and the reference for the characterization of colonies of two different types of Gram-positive and Gram-negative bacteria. The results of our study show that the colony of Staphylococcus aureus as Gram-positive bacteria has a significantly higher viscoelasticity ratio compared to that value for Acinetobacter baumannii as Gram-negative bacteria (77% difference). This may be due to the differing cell envelope structure between the two species, but we cannot rule out effects of biofilm formation in the colonies. Furthermore, a lumped model has been provided for the mechanical properties of bacterial colonies.

Time-dependent plastic behavior of bacteria leading to rupture

A study of the mechanical response of bacteria is essential in designing an antibacterial surface for implants and food packaging applications. This research evaluated the mechanical response of Escherichia coli under different loading conditions. Indentation and prolonged creep tests were performed to understand their viscoelastic-plastic response. The results indicate that varying loading rates from 1 μm/s to 5 μm/s show an increase in modulus of 182% and 90%, calculated in the loading and unloading cycles, respectively, and a decrease in adhesion force by 42%. However, on varying loads from 5 nN to 25 nN, nominal change is observed in both modulus and adhesion force. The rupture curve at 100 nN load shows elastic and a small plastic deformation accompanied by a sharp peak indicating the cell wall rupture. The rupture force at the peak was found to be 34.38 ± 5.15 nN, irrespective of the loading rate, making it a failure criterion for bacteria rupture. The creep response of bacteria increases (for 6 s) and then remains constant (for 15 s) with time, indicating that a standard linear solid (SLS) model applies to this behavior. This work attempts to evaluate the mechanical properties of E. coli bacteria focusing on its rupture by contact killing mechanism.

Numerical Modeling of Physical Cell Trapping in Microfluidic Chips

Microfluidic methods have proven to be effective in separation and isolation of cells for a wide range of biomedical applications. Among these methods, physical trapping is a label-free isolation approach that relies on cell size as the selective phenotype to retain target cells on-chip for follow-up analysis and imaging. In silico models have been used to optimize the design of such hydrodynamic traps and to investigate cancer cell transmigration through narrow constrictions. While most studies focus on computational fluid dynamics (CFD) analysis of flow over cells and/or pillar traps, a quantitative analysis of mechanical interaction between cells and trapping units is missing. The existing literature centers on longitudinally extended geometries (e.g., micro-vessels) to understand the biological phenomenon rather than designing an effective cell trap. In this work, we aim to make an experimentally informed prediction of the critical pressure for a cell to pass through a trapping unit as a function of cell morphology and trapping unit geometry. Our findings show that a hyperelastic material model accurately captures the stress-related softening behavior observed in cancer cells passing through micro-constrictions. These findings are used to develop a model capable of predicting and extrapolating critical pressure values. The validity of the model is assessed with experimental data. Regression analysis is used to derive a mathematical framework for critical pressure. Coupled with CFD analysis, one can use this formulation to design efficient microfluidic devices for cell trapping and potentially perform downstream analysis of trapped cells.

Advanced Mechanical Testing Technologies at the Cellular Level: The Mechanisms and Application in Tissue Engineering

Mechanics, as a key physical factor which affects cell function and tissue regeneration, is attracting the attention of researchers in the fields of biomaterials, biomechanics, and tissue engineering. The macroscopic mechanical properties of tissue engineering scaffolds have been studied and optimized based on different applications. However, the mechanical properties of the overall scaffold materials are not enough to reveal the mechanical mechanism of the cell-matrix interaction. Hence, the mechanical detection of cell mechanics and cellular-scale microenvironments has become crucial for unraveling the mechanisms which underly cell activities and which are affected by physical factors. This review mainly focuses on the advanced technologies and applications of cell-scale mechanical detection. It summarizes the techniques used in micromechanical performance analysis, including atomic force microscope (AFM), optical tweezer (OT), magnetic tweezer (MT), and traction force microscope (TFM), and analyzes their testing mechanisms. In addition, the application of mechanical testing techniques to cell mechanics and tissue engineering scaffolds, such as hydrogels and porous scaffolds, is summarized and discussed. Finally, it highlights the challenges and prospects of this field. This review is believed to provide valuable insights into micromechanics in tissue engineering.

Trapped-particle microrheology of active suspensions

In microrheology, the local rheological properties of a complex fluid are inferred from the free or forced motion of embedded colloidal probes. Theoretical machinery developed for forced-probe microrheology of colloidal suspensions focused on either constant-force (CF) or constant-velocity (CV) probes while in experiments neither the force nor the kinematics of the probe is fixed. More importantly, the constraint of CF or CV introduces a difficulty in the meaningful quantification of the fluctuations of the probe due to a thermodynamic uncertainty relation. It is known that for a Brownian particle trapped in a harmonic potential well, the product of the standard deviations of the trap force and the particle position is $dk_BT$ in $d$ dimensions with $k_BT$ being the thermal energy. As a result, if the force (position) is not allowed to fluctuate, the position (force) fluctuation becomes infinite. To allow the measurement of fluctuations, we consider a microrheology model in which the probe is dragged along by a moving harmonic potential so that both its position and the trap force are allowed to fluctuate. Starting from the full Smoluchowski equation governing the dynamics of $N$ hard active Brownian particles, we derive a pair equation describing the dynamics of the probe as it interacts with one bath particle in the dilute limit. From this, we determine the mean and the variance (i.e., fluctuation) of the probe position in terms of the pair probability distribution. We then characterize the behavior of the system in the limits of both weak and strong traps.

Exploring cell and tissue mechanics with optical tweezers

Cellular and tissue biosystems emerge from the assembly of their constituent molecules and obtain a set of specific material properties. To measure these properties and understand how they influence cellular function is a central goal of mechanobiology. From a bottoms-up, physics or engineering point-of-view, such systems are a composition of basic mechanical elements. However, the sheer number and dynamic complexity of them, including active molecular machines and their emergent properties, makes it currently intractable to calculate how biosystems respond to forces. Because many diseases result from an aberrant mechanotransduction, it is thus essential to measure this response. Recent advances in the technology of optical tweezers have broadened their scope from single-molecule applications to measurements inside complex cellular environments, even within tissues and animals. Here, we summarize the basic optical trapping principles, implementations and calibration procedures that enable force measurements using optical tweezers directly inside cells of living animals, in combination with complementary techniques. We review their versatility to manipulate subcellular organelles and measure cellular frequency-dependent mechanics in the piconewton force range from microseconds to hours. As an outlook, we address future challenges to fully unlock the potential of optical tweezers for mechanobiology.

Modelling transcranial ultrasound neuromodulation: an energy-based multiscale framework

Several animal and human studies have now established the potential of low intensity, low frequency transcranial ultrasound (TUS) for non-invasive neuromodulation. Paradoxically, the underlying mechanisms through which TUS neuromodulation operates are still unclear, and a consensus on the identification of optimal sonication parameters still remains elusive. One emerging hypothesis based on thermodynamical considerations attributes the acoustic-induced nerve activity alterations to the mechanical energy and/or entropy conversions occurring during TUS action. Here, we propose a multiscale modelling framework to examine the energy states of neuromodulation under TUS. First, macroscopic tissue-level acoustic simulations of the sonication of a whole monkey brain are conducted under different sonication protocols. For each one of them, mechanical loading conditions of the received waves in the anterior cingulate cortex region are recorded and exported into a microscopic cell-level 3D viscoelastic finite element model of neuronal axon embedded extracellular medium. Pulse-averaged elastically stored and viscously dissipated energy rate densities during axon deformation are finally computed under different sonication incident angles and are mapped against distinct combinations of sonication parameters of the TUS. The proposed multiscale framework allows for the analysis of vibrational patterns of the axons and its comparison against the spectrograms of stimulating ultrasound. The results are in agreement with literature data on neuromodulation, demonstrating the potential of this framework to identify optimised acoustic parameters in TUS neuromodulation. The proposed approach is finally discussed in the context of multiphysics energetic considerations, argued here to be a promising avenue towards a scalable framework for TUS in silico predictions. STATEMENT OF SIGNIFICANCE: Low-intensity transcranial ultrasound (TUS) is poised to become a leading neuromodulation technique for the treatment of neurological disorders. Paradoxically, how it operates at the cellular scale remains unknown, hampering progress in personalised treatment. To this end, models of the multiphysics of neurons able to upscale results to the organ scale are required. We propose here to achieve this by considering an axon submitted to an ultrasound wave extracted from a simulation at the organ scale. Doing so, information pertaining to both stored and dissipated axonal energies can be extracted for a given head/brain morphology. This two-scale multiphysics energetic approach is a promising scalable framework for in silico predictions in the context of personalised TUS treatment.

Narrow-Gap Rheometry: A Novel Method for Measuring Cell Mechanics

The viscoelastic properties of a cell cytoskeleton contain abundant information about the state of a cell. Cells show a response to a specific environment or an administered drug through changes in their viscoelastic properties. Studies of single cells have shown that chemical agents that interact with the cytoskeleton can alter mechanical cell properties and suppress mitosis. This envisions using rheological measurements as a non-specific tool for drug development, the pharmacological screening of new drug agents, and to optimize dosage. Although there exists a number of sophisticated methods for studying mechanical properties of single cells, studying concentration dependencies is difficult and cumbersome with these methods: large cell-to-cell variations demand high repetition rates to obtain statistically significant data. Furthermore, method-induced changes in the cell mechanics cannot be excluded when working in a nonlinear viscoelastic range. To address these issues, we not only compared narrow-gap rheometry with commonly used single cell techniques, such as atomic force microscopy and microfluidic-based approaches, but we also compared existing cell monolayer studies used to estimate cell mechanical properties. This review provides insight for whether and how narrow-gap rheometer could be used as an efficient drug screening tool, which could further improve our current understanding of the mechanical issues present in the treatment of human diseases.

Multiscale Mechanobiology in Brain Physiology and Diseases

Increasing evidence suggests that mechanics play a critical role in regulating brain function at different scales. Downstream integration of mechanical inputs into biochemical signals and genomic pathways causes observable and measurable effects on brain cell fate and can also lead to important pathological consequences. Despite recent advances, the mechanical forces that influence neuronal processes remain largely unexplored, and how endogenous mechanical forces are detected and transduced by brain cells into biochemical and genetic programs have received less attention. In this review, we described the composition of brain tissues and their pronounced microstructural heterogeneity. We discuss the individual role of neuronal and glial cell mechanics in brain homeostasis and diseases. We highlight how changes in the composition and mechanical properties of the extracellular matrix can modulate brain cell functions and describe key mechanisms of the mechanosensing process. We then consider the contribution of mechanobiology in the emergence of brain diseases by providing a critical review on traumatic brain injury, neurodegenerative diseases, and neuroblastoma. We show that a better understanding of the mechanobiology of brain tissues will require to manipulate the physico-chemical parameters of the cell microenvironment, and to develop three-dimensional models that can recapitulate the complexity and spatial diversity of brain tissues in a reproducible and predictable manner. Collectively, these emerging insights shed new light on the importance of mechanobiology and its implication in brain and nerve diseases.

"Viscotaxis"- directed migration of mesenchymal stem cells in response to loss modulus gradient

Directed cell migration plays a crucial role in physiological and pathological conditions. One important mechanical cue, known to influence cell migration, is the gradient of substrate elastic modulus (E). However, the cellular microenvironment is viscoelastic and hence the elastic property alone is not sufficient to define its material characteristics. To bridge this gap, in this study, we investigated the influence of the gradient of viscous property of the substrate, as defined by loss modulus (G^″) on cell migration. We cultured human mesenchymal stem cells (hMSCs) on a collagen-coated polyacrylamide gel with constant storage modulus (G^') but with a gradient in the loss modulus (G^″). We found hMSCs to migrate from high to low loss modulus. We have termed this form of directional cellular migration as "Viscotaxis". We hypothesize that the high loss modulus regime deforms more due to creep in the long timescale when subjected to cellular traction. Such differential deformation drives the observed Viscotaxis. To verify our hypothesis, we disrupted the actomyosin contractility with myosin inhibitor blebbistatin and ROCK inhibitor Y27632, and found the directional migration to disappear. Further, such time-dependent creep of the high loss material should lead to lower traction, shorter lifetime of the focal adhesions, and dynamic cell morphology, which was indeed found to be the case. Together, findings in this paper highlight the importance of considering the viscous modulus while preparing stiffness-based substrates for the field of tissue engineering. STATEMENT OF SIGNIFICANCE: While the effect of substrate elastic modulus has been investigated extensively in the context of cell biology, the role of substrate viscoelasticity is poorly understood. This omission is surprising as our body is not elastic, but viscoelastic. Hence, the role of viscoelasticity needs to be investigated at depth in various cellular contexts. One such important context is cell migration. Cell migration is important in morphogenesis, immune response, wound healing, and cancer, to name a few. While it is known that cells migrate when presented with a substrate with a rigidity gradient, cellular behavior in response to viscoelastic gradient has never been investigated. The findings of this paper not only reveal a completely novel cellular taxis or directed migration, it also improves our understanding of cell mechanics significantly.

A Framework for Low-Intensity Low-Frequency Ultrasound Neuromodulation Sonication Parameter Identification from Micromechanical Flexoelectricity Modelling

Low-intensity, low-frequency ultrasound (LILFU) has recently emerged as a promising technique to modulate non-invasively nerve activities at lower cost than other traditional and more-invasive neuromodulation methods. However, there is currently no consensus on the optimum sonication parameters to be used in LILFU applications, and most of the accepted ranges have arisen from trial-and-error approaches. Here we utilise a recently proposed micromechanics model of membrane flexoelectricity, a potential candidate for neuromodulation, and simulate action potentials/membrane polarisation triggered by acoustic pulses of different pulse frequencies, pulse magnitudes and duty cycles. Results reveal that, at constant duty cycles, increasing the transmit frequency increases the thresholds of both the pulse magnitude and the elastic energy rate density required to mechanically trigger an action potential, whereas at constant frequencies, increasing the duty cycle reduces both. The influence of transmit frequency is weakened at lower duty cycles. Our simulation results offer some guidance on the selections of sonication parameters used in LILFU for neurologic disorder treatments in the context of the flexoelectricity hypothesis.

Accurate and practical feature extraction from noisy holograms

Quantitative phase imaging using holographic microscopy is a powerful and non-invasive imaging method, ideal for studying cells and quantifying their features such as size, thickness, and dry mass. However, biological materials scatter little light, and the resulting low signal-to-noise ratio in holograms complicates any downstream feature extraction and hence applications. More specifically, unwrapping phase maps from noisy holograms often fails or requires extensive computational resources. We present a strategy for overcoming the noise limitation: rather than a traditional phase-unwrapping method, we extract the continuous phase values from holograms by using a phase-generation technique based on conditional generative adversarial networks employing a Pix2Pix architecture. We demonstrate that a network trained on random surfaces can accurately generate phase maps for test objects such as dumbbells, spheres, and biconcave discoids. Furthermore, we show that even a rapidly trained network can generate faithful phase maps when trained on related objects. We are able to accurately extract both morphological and quantitative features from the noisy phase maps of human leukemia (HL-60) cells, where traditional phase unwrapping algorithms fail. We conclude that deep learning can decouple noise from signal, expanding potential applications to real-world systems that may be noisy.

Effect of cell geometry in the evaluation of erythrocyte viscoelastic properties

The red blood cell membrane-cytoskeleton is a complex structure mainly responsible for giving the cell rigidity and shape. It also provides the erythrocyte with the ability to pass through narrow capillaries of the vertebrate blood circulatory system. Although the red blood cell viscoelastic properties have been extensively studied, reported experimental data differ by up to three orders of magnitude. This could be attributed to the natural cell variability, to the different techniques employed, and also to the models used for the cell response, which are highly dependent on cell geometry. Here, we use two methodologies based on optical tweezers to investigate the viscoelastic behavior of healthy human red blood cells, one applying small cell deformations (microrheology) and another imposing large deformations (tether extraction). We also establish a defocusing microscopy-based method to characterize the cell geometry and thus the erythrocyte form factor, an essential parameter that allows comparisons among the viscoelastic properties at different conditions. Moreover, for small deformations, a soft glassy rheology model is used to discuss the results, while for large deformations two surface shear moduli and one surface viscosity are determined, together with the surface tension and bending modulus of the erythrocyte membrane lipid component. We also show that F-actin is not detected in tethers, although the erythrocyte membrane has physical properties like those of other adherent cells, known to have tethers containing F-actin inside. Altogether, our results show good agreement with the reported literature and we argue that, to properly compare the viscoelastic properties of red blood cells in different situations, the task of cell geometry characterization must be accomplished. This may be especially important when the influence of agents, like the malaria parasite, induces changes in both the geometry and chemical constituents of the erythrocyte membrane. Together, the new methodologies and procedures used in this study would allow the erythrocyte community to better explore the mechanical behavior of red blood cells and may be useful to characterize erythrocyte viscoelasticity changes in several blood diseases.

Substrate Stiffness Mediates Formation of Novel Cytoskeletal Structures in Fibroblasts during Cell-Microspheres Interaction

It is well known that living cells interact mechanically with their microenvironment. Many basic cell functions, like migration, proliferation, gene expression, and differentiation, are influenced by external forces exerted on the cell. That is why it is extremely important to study how mechanical properties of the culture substrate influence the cellular molecular regulatory pathways. Optical microscopy is one of the most common experimental method used to visualize and study cellular processes. Confocal microscopy allows to observe changes in the 3D organization of the cytoskeleton in response to a precise mechanical stimulus applied with, for example, a bead trapped with optical tweezers. Optical tweezers-based method (OT) is a microrheological technique which employs a focused laser beam and polystyrene or latex beads to study mechanical properties of biological systems. Latex beads, functionalized with a specific protein, can interact with proteins located on the surface of the cellular membrane. Such interaction can significantly affect the cell's behavior. In this work, we demonstrate that beads alone, placed on the cell surface, significantly change the architecture of actin, microtubule, and intermediate filaments. We also show that the observed molecular response to such stimulus depends on the duration of the cell-bead interaction. Application of cytoskeletal drugs: cytochalasin D, jasplakinolide, and docetaxel, abrogates remodeling effects of the cytoskeleton. More important, when cells are plated on elastic substrates, which mimic the mechanical properties of physiological cellular environment, we observe formation of novel, "cup-like" structures formed by the microtubule cytoskeleton upon interaction with latex beads. These results provide new insights into the function of the microtubule cytoskeleton. Based on these results, we conclude that rigidity of the substrate significantly affects the cellular processes related to every component of the cytoskeleton, especially their architecture.

Plasmodium falciparum maturation across the intra-erythrocytic cycle shifts the soft glassy viscoelastic properties of red blood cells from a liquid-like towards a solid-like behavior

The mechanical properties of erythrocytes have been investigated by different techniques. However, there are few reports on how the viscoelasticity of these cells varies during malaria disease. Here, we quantitatively map the viscoelastic properties of Plasmodium falciparum-parasitized human erythrocytes. We apply new methodologies based on optical tweezers to measure the viscoelastic properties and defocusing microscopy to measure the erythrocyte height profile, the overall cell volume, and its form factor, a crucial parameter to convert the complex elastic constant into complex shear modulus. The storage and loss shear moduli are obtained for each stage of parasite maturation inside red blood cells, while the former increase, the latter decrease. Employing a soft glassy rheology model, we obtain the power-law exponent for the storage and loss shear moduli, characterizing the soft glassy features of red blood cells in each parasite maturation stage. Ring forms present a liquid-like behavior, with a slightly lower power-law exponent than healthy erythrocytes, whereas trophozoite and schizont stages exhibit increasingly solid-like behaviors. Finally, the surface elastic shear moduli, low-frequency surface viscosities, and shape recovery relaxation times all increase not only in a stage-dependent manner but also when compared to healthy red blood cells. Overall, the results call attention to the soft glassy characteristics of Plasmodium falciparum-parasitized erythrocyte membrane and may provide a basis for future studies to better understand malaria disease from a mechanobiological perspective.

Nonlinear Elastic and Inelastic Properties of Cells

Mechanical forces play an important role in various physiological processes, such as morphogenesis, cytokinesis, and migration. Thus, in order to illuminate mechanisms underlying these physiological processes, it is crucial to understand how cells deform and respond to external mechanical stimuli. During recent decades, the mechanical properties of cells have been studied extensively using diverse measurement techniques. A number of experimental studies have shown that cells are far from linear elastic materials. Cells exhibit a wide variety of nonlinear elastic and inelastic properties. Such complicated properties of cells are known to emerge from unique mechanical characteristics of cellular components. In this review, we introduce major cellular components that largely govern cell mechanical properties and provide brief explanations of several experimental techniques used for rheological measurements of cell mechanics. Then, we discuss the representative nonlinear elastic and inelastic properties of cells. Finally, continuum and discrete computational models of cell mechanics, which model both nonlinear elastic and inelastic properties of cells, will be described.

Mechanical properties of spinal cord grey matter and white matter in confined compression

To better understand the link between spinal cord impact and the resulting tissue damage, computational models are often used. These models typically simulate the spinal cord as a homogeneous and isotropic material. Recent research suggests that grey and white matter tissue differences and directional differences, i.e. anisotropy, are important to predict spinal cord damage. The objective of this research was to characterize the mechanical properties of spinal cord grey and white matter tissue in confined compression. Spinal cords (n = 12) were harvested immediately following euthanasia from Yorkshire and Yucatan pigs. The spinal cords were flash frozen (60 s at -80 °C) and prepared into four types of test samples: grey matter axial, grey matter transverse, white matter axial, and white matter transverse. Each sample type was thawed, and subsequently tested in confined compression within 6 h of euthanasia. Samples were compressed to 10% strain at a quasi-static strain rate (0.001/sec) and allowed to relax for 120 s. A quasi-linear viscoelastic model combining a first-order exponential with a 1-term Prony series characterized the loading and relaxation responses respectively. The effect of tissue type (grey matter vs. white matter), direction (axial vs. transverse), and their interaction were evaluated with a two-way ANOVA (p < 0.05) with peak stress, aggregate modulus, and relaxation time as dependent variables. This study found grey matter to be 1.6-2 times stiffer than white matter and both grey and white matter were isotropic in compression. These findings should be emphasized when studying SCI biomechanics using computational models.

Short-term angiotensin II treatment regulates cardiac nanomechanics via microtubule modifications

Mechanical properties of single myocytes contribute to the whole heart performance, but the measurement of mechanics in living cells at high resolution with minimal force interaction remains challenging. Angiotensin II (AngII) is a peptide hormone that regulates a number of physiological functions, including heart performance. It has also been shown to contribute to cell mechanics by inducing cell stiffening. Using non-contact high-resolution Scanning Ion Conductance Microscopy (SICM), we determine simultaneously cell topography and membrane transverse Young's modulus (YM) by a constant pressure application through a nanopipette. While applying pressure, the vertical position is recorded and a deformation map is generated from which YM can be calculated and corrected for the uneven geometry. High resolution of this method also allows studying specific membrane subdomains, such as Z-grooves and crests. We found that short-term AngII treatment reduces the transversal YM in isolated adult rat cardiomyocytes acting via an AT1 receptor. Blocking either a TGF-β1 receptor or Rho kinase abolishes this effect. Analysis of the cytoskeleton showed that AngII depletes microtubules by decreasing long-lived detyrosinated and acetylated microtubule populations. Interestingly, in the failing cardiomyocytes, which are stiffer than controls, the short-term AngII treatment also reduces the YM, thus normalizing the mechanical state of cells. This suggests that the short-term softening effect of AngII on cardiac cells is opposite to the well-characterized long-term hypertrophic effect. In conclusion, we generate a precise nanoscale indication map of location-specific transverse cortical YM within the cell and this can substantially advance our understanding of cellular mechanics in a physiological environment, for example in isolated cardiac myocytes.

Membrane Elastic Properties During Neural Precursor Cell Differentiation

Neural precursor cells differentiate into several cell types that display distinct functions. However, little is known about how cell surface mechanics vary during the differentiation process. Here, by precisely measuring membrane tension and bending modulus, we map their variations and correlate them with changes in neural precursor cell morphology along their distinct differentiation fates. Both cells maintained in culture as neural precursors as well as those plated in neurobasal medium reveal a decrease in membrane tension over the first hours of culture followed by stabilization, with no change in bending modulus. During astrocyte differentiation, membrane tension initially decreases and then increases after 72 h, accompanied by consolidation of glial fibrillary acidic protein expression and striking actin reorganization, while bending modulus increases following observed alterations. For oligodendrocytes, the changes in membrane tension are less abrupt over the first hours, but their values subsequently decrease, correlating with a shift from oligodendrocyte marker O4 to myelin basic protein expressions and a remarkable actin reorganization, while bending modulus remains constant. Oligodendrocytes at later differentiation stages show membrane vesicles with similar membrane tension but higher bending modulus as compared to the cell surface. Altogether, our results display an entire spectrum of how membrane elastic properties are varying, thus contributing to a better understanding of neural differentiation from a mechanobiological perspective.

Dynamic indentation reveals differential viscoelastic properties of white matter versus gray matter-derived astrocytes upon treatment with lipopolysaccharide

Astrocytes in white matter (WM) and gray matter (GM) brain regions have been reported to have different morphology and function. Previous single cell biomechanical studies have not differentiated between WM- and GM-derived samples. In this study, we explored the local viscoelastic properties of isolated astrocytes and show that astrocytes from rat brain WM-enriched areas are ~1.8 times softer than astrocytes from GM-enriched areas. Upon treatment with pro-inflammatory lipopolysaccharide, GM-derived astrocytes become significantly softer in the nuclear and the cytoplasmic regions, where the F-actin network appears rearranged, whereas WM-derived astrocytes preserve their initial mechanical features and show no alteration in the F-actin cytoskeletal network. We hypothesize that the flexibility in biomechanical properties of GM-derived astrocytes may contribute to promote regeneration of the brain under neuroinflammatory conditions.

Mechanical characterization of vesicles and cells: A review

Vesicles perform many essential functions in all living organisms. They respond like a transducer to mechanical stress in converting the applied force into mechanical and biological responses. At the same time, both biochemical and biophysical signals influence the vesicular response in bearing mechanical loads. In recent years, liposomes, artificial lipid vesicles, have gained substantial attention from the pharmaceutical industry as a prospective drug carrier which can also serve as an artificial cell-mimetic system. The ability of these vesicles to enter through pores of even smaller size makes them ideal candidates for therapeutic agents to reach the infected sites effectively. Engineering of vesicles with desired mechanical properties that can encapsulate drugs and release as required is the prime challenge in this field. This requirement has led to the modifications of the composition of the bilayer membrane by adding cholesterol, sphingomyelin, etc. In this article, we review the manufacturing and characterization techniques of various artificial/synthetic vesicles. We particularly focus on the electric field-driven characterization techniques to determine different properties of vesicle and its membranes, such as bending rigidity, viscosity, capacitance, conductance, etc., which are indicators of their content and mobility. Similarities and differences between artificial vesicles, natural vesicles, and cells are highlighted throughout the manuscript since most of these artificial vesicles are intended for cell mimetic functions.

Dynamics of hydrodynamically coupled Brownian harmonic oscillators in a Maxwell fluid

It has been shown recently that the coupled dynamics of micro-particles in a viscous fluid has many interesting aspects including motional resonance which can be used to perform two-point micro-rheology. However, it is expected that this phenomenon in a viscoelastic fluid is much more interesting due to the presence of the additional frequency-dependent elasticity of the medium. Thus, a theory describing the equilibrium dynamics of two hydrodynamically coupled Brownian harmonic oscillators in a viscoelastic Maxwell fluid has been derived which appears with new and impressive characteristics. Initially, the response functions have been calculated and then the fluctuation-dissipation theorem has been used to calculate the correlation functions between the coloured noises present on the concerned particles placed in a Maxwell fluid due to the thermal motions of the fluid molecules. These correlation functions appear to be in a linear relationship with the delta-correlated noises in a viscous fluid. Consequently, this reduces the statistical description of a simple viscoelastic fluid to the statistical representation for an extended dynamical system subjected to delta-correlated random forces. Thereupon, the auto and cross-correlation functions in the time domain and frequency domain and the mean-square displacement functions of the particles have been calculated which are perfectly consistent with their corresponding established forms in a viscous fluid and emerge with exceptional features.

The mechanical properties of microbial surfaces and biofilms

Microbes can modify their surface structure as an adaptive mechanism for survival and dissemination in the environment or inside the host. Altering their ability to respond to mechanical stimuli is part of this adaptive process. Since the 1990s, powerful micromanipulation tools have been developed that allow mechanical studies of microbial cell surfaces, exploring little known aspects of their dynamic behavior. This review concentrates on the study of mechanical and rheological properties of bacteria and fungi, focusing on their cell surface dynamics and biofilm formation.

Quantifying the Local Mechanical Properties of Cells in a Fibrous Three-Dimensional Microenvironment

Measurements of the mechanical response of biological cells are critical for understanding injury and disease, for developing diagnostic tools, and for computational models in mechanobiology. Although it is well known that cells are sensitive to the topography of their microenvironment, the current paradigm in mechanical testing of adherent cells is mostly limited to specimens grown on flat two-dimensional substrates. In this study, we introduce a technique in which cellular indentation via optical trapping is performed on cells at a high spatial resolution to obtain their regional mechanical properties while they exist in a more favorable three-dimensional microenvironment. We combine our approach with nonlinear contact mechanics theory to consider the effects of a large deformation. This allows us to probe length scales that are relevant for obtaining overall cell stiffness values. The experimental results herein provide the hyperelastic material properties at both high (∼100 s^-1) and low (∼1-10 s^-1) strain rates of murine central nervous system glial cells. The limitations due to possible misalignment of the indenter in the three-dimensional space are examined using a computational model.

Innovative Tools for Mechanobiology: Unraveling Outside-In and Inside-Out Mechanotransduction

Cells and tissues can sense and react to the modifications of the physico-chemical properties of the extracellular environment (ECM) through integrin-based adhesion sites and adapt their physiological response in a process called mechanotransduction. Due to their critical localization at the cell-ECM interface, transmembrane integrins are mediators of bidirectional signaling, playing a key role in “outside-in” and “inside-out” signal transduction. After presenting the basic conceptual fundamentals related to cell mechanobiology, we review the current state-of-the-art technologies that facilitate the understanding of mechanotransduction signaling pathways. Finally, we highlight innovative technological developments that can help to advance our understanding of the mechanisms underlying nuclear mechanotransduction.

Computational model of the mechanoelectrophysiological coupling in axons with application to neuromodulation

For more than half a century, the action potential (AP) has been considered a purely electrical phenomenon. However, experimental observations of membrane deformations occurring during APs have revealed that this process also involves mechanical features. This discovery has recently fuelled a controversy on the real nature of APs: whether they are mechanical or electrical. In order to examine some of the modern hypotheses regarding APs, we propose here a coupled mechanoelectrophysiological membrane finite-element model for neuronal axons. The axon is modeled as an axisymmetric thin-wall cylindrical tube. The electrophysiology of the membrane is modeled using the classic Hodgkin-Huxley (H-H) equations for the Nodes of Ranvier or unmyelinated axons and the cable theory for the internodal regions, whereas the axonal mechanics is modeled by means of viscoelasticity theory. Membrane potential changes induce a strain gradient field via reverse flexoelectricity, whereas mechanical pulses result in an electrical self-polarization field following the direct flexoelectric effect, in turn influencing the membrane potential. Moreover, membrane deformation also alters the values of membrane capacitance and resistance in the H-H equation. These three effects serve as the fundamental coupling mechanisms between the APs and mechanical pulses in the model. A series of numerical studies was systematically conducted to investigate the consequences of interaction between the APs and mechanical waves on both myelinated and unmyelinated axons. Simulation results illustrate that the AP is always accompanied by an in-phase propagating membrane displacement of ≈1nm, whereas mechanical pulses with enough magnitude can also trigger APs. The model demonstrates that mechanical vibrations, such as the ones arising from ultrasound stimulations, can either annihilate or enhance axonal electrophysiology depending on their respective directionality and frequency. It also shows that frequency of pulse repetition can also enhance signal propagation independently of the amplitude of the signal. This result not only reconciles the mechanical and electrical natures of the APs but also provides an explanation for the experimentally observed mechanoelectrophysiological phenomena in axons, especially in the context of ultrasound neuromodulation.

Laser interference-based technique for dynamic measurement of single cell deformation manipulated by optical tweezers

A laser interference-based method was proposed to measure the deformation response of cell manipulated by optical tweezers. This method was implemented experimentally by integrating a laser illuminating system and optical tweezers with an inverted microscope. Interference fringes generated by the transmitted and reflected lights were recorded by a complementary metal oxide semiconductor camera. From the acquired images, cell height was calculated and cell morphology was constructed. To further validate this method, the morphological analyses of HeLa cells were performed in static state and during detachment process. Subsequently, the dynamic deformation responses of red blood cells were measured during manipulation with optical tweezers. Collectively, this laser interference-based method precludes the requirement of complex optical alignment, allows easy integration with optical tweezers, and enables dynamic measurement of cell deformation response by using a conventional inverted microscope.

Free and confined Brownian motion in viscoelastic Stokes-Oldroyd B fluids

We linearize the Stokes-Oldroyd B model for small perturbations and instantaneous hydrodynamic friction to simulate the environment for a free and confined Brownian particle. We use the standard Green's function approach to determine the viscoelasticity, and show that the expression obtained for the frequency dependent viscosity is similar to that given by the Jeffrey's model, though the latter describes viscoelasticity by the bulk storage and loss moduli that is represented by a complex elastic modulus [Formula: see text] of the fluid concerned. In contrast, we consider the characteristics of the polymer chains and the Newtonian solvent of the complex fluid individually, and determine an expression for frequency-dependent viscosity that would be useful for microrheology performed from Brownian trajectories measured in experiments. Finally, we evaluate the trajectory of a free Brownian particle in a viscoelastic environment using our formalism, and calculate various important parameters quantifying Brownian dynamics, which we then extend to the particle confined in a harmonic potential as provided by optical tweezers.

Advanced and Rationalized Atomic Force Microscopy Analysis Unveils Specific Properties of Controlled Cell Mechanics

The cell biomechanical properties play a key role in the determination of the changes during the essential cellular functions, such as contraction, growth, and migration. Recent advances in nano-technologies have enabled the development of new experimental and modeling approaches to study cell biomechanics, with a level of insights and reliability that were not possible in the past. The use of atomic force microscopy (AFM) for force spectroscopy allows nanoscale mapping of the cell topography and mechanical properties under, nearly physiological conditions. A proper evaluation process of such data is an essential factor to obtain accurate values of the cell elastic properties (primarily Young's modulus). Several numerical models were published in the literature, describing the depth sensing indentation as interaction process between the elastic surface and indenting probe. However, many studies are still relying on the nowadays outdated Hertzian model from the nineteenth century, or its modification by Sneddon. The lack of comparison between the Hertz/Sneddon model with their modern modifications blocks the development of advanced analysis software and further progress of AFM promising technology into biological sciences. In this work, we applied a rationalized use of mechanical models for advanced postprocessing and interpretation of AFM data. We investigated the effect of the mechanical model choice on the final evaluation of cellular elasticity. We then selected samples subjected to different physicochemical modulators, to show how a critical use of AFM data handling can provide more information than simple elastic modulus estimation. Our contribution is intended as a methodological discussion of the limitations and benefits of AFM-based advanced mechanical analysis, to refine the quantification of cellular elastic properties and its correlation to undergoing cellular processes in vitro.

Nanoparticle-Cell Interaction: A Cell Mechanics Perspective

Progress in the field of nanoparticles has enabled the rapid development of multiple products and technologies; however, some nanoparticles can pose both a threat to the environment and human health. To enable their safe implementation, a comprehensive knowledge of nanoparticles and their biological interactions is needed. In vitro and in vivo toxicity tests have been considered the gold standard to evaluate nanoparticle safety, but it is becoming necessary to understand the impact of nanosystems on cell mechanics. Here, the interaction between particles and cells, from the point of view of cell mechanics (i.e., bionanomechanics), is highlighted and put in perspective. Specifically, the ability of intracellular and extracellular nanoparticles to impair cell adhesion, cytoskeletal organization, stiffness, and migration are discussed. Furthermore, the development of cutting-edge, nanotechnology-driven tools based on the use of particles allowing the determination of cell mechanics is emphasized. These include traction force microscopy, colloidal probe atomic force microscopy, optical tweezers, magnetic manipulation, and particle tracking microrheology.

Cell membrane biophysics with optical tweezers

Membrane elastic properties play important roles in regulating cell shape, motility, division and differentiation. Here I review optical tweezer (OT) investigations of membrane surface tension and bending modulus, emphasizing didactic aspects and insights provided for cell biology. OT measurements employ membrane-attached microspheres to extract long cylindrical nanotubes named tethers. The Helfrich-Canham theory yields elastic parameters in terms of tether radius and equilibrium extraction force. It assumes initial point-like microsphere attachment and no cytoskeleton content within tethers. Experimental force-displacement curves reveal violations of those assumptions, and I discuss proposed explanations of such discrepancies, as well as recommended OT protocols. Measurements of elastic parameters for predominant cell types in the central nervous system yield correlations between their values and cell function. Micro-rheology OT experiments extend these correlations to viscoelastic parameters. The results agree with a quasi-universal phenomenological scaling law and are interpreted in terms of the soft glass rheology model. Spontaneously-generated cell nanotube protrusions are also briefly reviewed, emphasizing common features with tethers. Filopodia as well as tunneling nanotubes (TNT), which connect distant cells and allow transfers between their cytoplasms, are discussed, including OT tether pulling from TNTs which mediate communication among bacteria, even of different species. Pathogens, including bacteria, viruses and prions, opportunistically exploit TNTs for cell-to-cell transmission of infection, indicating that TNTs have an ancient evolutionary origin.

Holographic optical tweezers-based in vivo manipulations in zebrafish embryos

Understanding embryonic development requires the characterization of the forces and the mechanical features that shape cells and tissues within the organism. In addition, experimental application of forces on cells and altering cell and organelle shape allows determining the role such forces play in morphogenesis. Here, we present a holographic optical tweezers-based new microscopic platform for in vivo applications in the context of a developing vertebrate embryo that unlike currently used setups allows simultaneous trapping of multiple objects and rapid comparisons of viscoelastic properties in different locations. This non-invasive technique facilitates a dynamic analysis of mechanical properties of cells and tissues without intervening with embryonic development. We demonstrate the application of this platform for manipulating organelle shape and for characterizing the mechanobiological properties of cells in live zebrafish embryos. The method of holographic optical tweezers as described here is of general interest and can be easily transferred to studying a range of developmental processes in zebrafish, thereby establishing a versatile platform for similar investigations in other organisms. Fluorescent beads injected into zebrafish embryos at 1-cell stage are maintained within the embryos and do not affect their development as observed in the presented 1-day old embryo.

A numerical model suggests the interplay between nuclear plasticity and stiffness during a perfusion assay

Cell deformability is a necessary condition for a cell to be able to migrate, an ability that is vital both for healthy and diseased organisms. The nucleus being the largest and stiffest organelle, it often is a barrier to cell migration. It is thus essential to characterize its mechanical behaviour. First, we numerically investigate the visco-elasto-plastic properties of the isolated nucleus during a compression test. This simulation highlights the impact of the mechanical behaviour of the nuclear lamina and the nucleoplasm on the overall plasticity. Second, a whole cell model is developed to simulate a perfusion experiment to study the possible interactions between the cytoplasm and the nucleus. We analyze and discuss the role of the lamina for a wild-type cell model, and a lamin-deficient one, in which the Young's modulus of the lamina is set to 1% of its nominal value. This simulation suggests an interplay between the cytoplasm and the nucleoplasm, especially in the lamin-deficient cell, showing the need of a stiffer nucleoplasm to maintain nuclear plasticity.