Mechanics of living cells measured by laser tracking microrheology

A microrheological examination of insulin-secreting β-cells in healthy and diabetic-like conditions

Pancreatic β-cells regulate glucose homeostasis through glucose-stimulated insulin secretion, which is hindered in type-2 diabetes. Transport of the insulin vesicles is expected to be affected by changes in the viscoelastic and transport properties of the cytoplasm. These are evaluated in situ through particle-tracking measurements using a rat insulinoma β-cell line. The use of inert probes assists in decoupling the material properties of the cytoplasm from the active transport through cellular processes. The effect of glucose-stimulated insulin secretion is examined, and the subsequent remodeling of the cytoskeleton, at constant effects of cell activity, is shown to result in reduced mobility of the tracer particles. Induction of diabetic-like conditions is identified to alter the mean-squared displacement of the passive particles in the cytoplasm and diminish its reaction to glucose stimulation.

A Simulation of the Mechanical Testing of the Cell Membrane and Cytoskeleton

Cell models play a crucial role in analyzing the mechanical response of cells and quantifying cellular damage incurred during micromanipulation. While traditional models can capture the overall mechanical behavior of cells, they often lack the ability to discern among distinct cellular components. Consequently, by employing dissipative particle dynamics, this study constructed a triangular network-like representation of the cell membrane along with cross-linked cytoskeletal chains. The mechanical properties of both the membrane and cytoskeleton were then analyzed through a series of simulated mechanical tests, validated against real-world experiments. The investigation utilized particle-tracking rheology to monitor changes in the mean square displacements of membrane particles over time, facilitating the analysis of the membrane's storage and loss moduli. Additionally, the cytoskeletal network's storage and loss moduli were examined via a double-plate oscillatory shear experiment. The simulation results revealed that both the membrane and cytoskeleton exhibit viscoelastic behavior, as evidenced by the power-law dependency of their storage and loss moduli on frequency. Furthermore, indentation and microinjection simulations were conducted to examine the overall mechanical properties of cells. In the indentation experiments, an increase in the shear modulus of the membrane's WLCs correlated with a higher Young's modulus for the entire cell. Regarding the microinjection experiment, augmenting the microinjection speed resulted in reduced deformation of the cell at the point of membrane rupture and a lower percentage of high strain.

Shining Light in Mechanobiology: Optical Tweezers, Scissors, and Beyond

Mechanobiology helps us to decipher cell and tissue functions by looking at changes in their mechanical properties that contribute to development, cell differentiation, physiology, and disease. Mechanobiology sits at the interface of biology, physics and engineering. One of the key technologies that enables characterization of properties of cells and tissue is microscopy. Combining microscopy with other quantitative measurement techniques such as optical tweezers and scissors, gives a very powerful tool for unraveling the intricacies of mechanobiology enabling measurement of forces, torques and displacements at play. We review the field of some light based studies of mechanobiology and optical detection of signal transduction ranging from optical micromanipulation-optical tweezers and scissors, advanced fluorescence techniques and optogenentics. In the current perspective paper, we concentrate our efforts on elucidating interesting measurements of forces, torques, positions, viscoelastic properties, and optogenetics inside and outside a cell attained when using structured light in combination with optical tweezers and scissors. We give perspective on the field concentrating on the use of structured light in imaging in combination with tweezers and scissors pointing out how novel developments in quantum imaging in combination with tweezers and scissors can bring to this fast growing field.

Studying fluctuating trajectories of optically confined passive tracers inside cells provides familiar active forces

In recent years, there has been a growing interest in studying the trajectories of microparticles inside living cells. Among other things, such studies are useful in understanding the spatio-temporal properties of a cell. In this work, we study the stochastic trajectories of a passive microparticle inside a cell using experiments and theory. Our theory is based on modeling the microparticle inside a cell as an active particle in a viscoelastic medium. The activity is included in our model from an additional stochastic term with non-zero persistence in the Langevin equation describing the dynamics of the microparticle. Using this model, we are able to predict the power spectral density (PSD) measured in the experiment and compute active forces. This caters to the situation where a tracer particle is optically confined and then yields a PSD for positional fluctuations. The low frequency part of the PSD yields information about the active forces that the particle feels. The fit to the model extracts such active force. Thus, we can conclude that trapping the particle does not affect the values of the forces extracted from the active fits if accounted for appropriately by proper theoretical models. In addition, the fit also provides system properties and optical tweezers trap stiffness.

Ultra-wideband optical coherence elastography from acoustic to ultrasonic frequencies

Visualizing viscoelastic waves in materials and tissues through noninvasive imaging is valuable for analyzing their mechanical properties and detecting internal anomalies. However, traditional elastography techniques have been limited by a maximum wave frequency below 1-10 kHz, which hampers temporal and spatial resolution. Here, we introduce an optical coherence elastography technique that overcomes the limitation by extending the frequency range to MHz. Our system can measure the stiffness of hard materials including bones and extract viscoelastic shear moduli for polymers and hydrogels in conventionally inaccessible ranges between 100 Hz and 1 MHz. The dispersion of Rayleigh surface waves across the ultrawide band allowed us to profile depth-dependent shear modulus in cartilages ex vivo and human skin in vivo with sub-mm anatomical resolution. This technique holds immense potential as a noninvasive measurement tool for material sciences, tissue engineering, and medical diagnostics.

A fluorescent probe for detecting mitochondrial viscosity and its application in distinguishing human breast cancer cells from normal ones

Mitochondrial viscosity is closely associated with intracellular physiological activities yet their abnormality will result in various diseases. In particular, viscosity in cancer cells is different from that in normal cells, which is thought to be an indicator for cancer diagnosis. However, there were few fluorescent probes able to distinguish homologous cancer and normal cells by detecting mitochondrial viscosity. Herein, we designed a viscosity-sensitive fluorescent probe (named NP) based on the twisting intramolecular charge transfer (TICT) mechanism. NP exhibited exquisite sensitivity to viscosity and selectivity to mitochondria and excellent photophysical properties, such as large Stokes shift and high molar extinction coefficient, which enables wash-free, high-fidelity and fast imaging mitochondria. Moreover, it was capable of detecting mitochondrial viscosity in living cells and tissue, as well as monitoring apoptosis process. Significantly, considering numerous breast cancer cases in every country of the world, NP was successfully applied to distinguish human breast cancer cells (MCF-7) from normal cells (MCF-10A) by difference in fluorescence intensity originated from abnormality in mitochondrial viscosity. All the results indicated that NP could serve as a robust tool for effectively detecting mitochondrial viscosity changes in-situ.

Kappa-Carrageenan/Chitosan/Gelatin Scaffolds Provide a Biomimetic Microenvironment for Dentin-Pulp Regeneration

This study aims to investigate the impact of kappa-carrageenan on dental pulp stem cells (DPSCs) behavior in terms of biocompatibility and odontogenic differentiation potential when it is utilized as a component for the production of 3D sponge-like scaffolds. For this purpose, we prepared three types of scaffolds by freeze-drying (i) kappa-carrageenan/chitosan/gelatin enriched with KCl (KCG-KCl) as a physical crosslinker for the sulfate groups of kappa-carrageenan, (ii) kappa-carrageenan/chitosan/gelatin (KCG) and (iii) chitosan/gelatin (CG) scaffolds as a control. The mechanical analysis illustrated a significantly higher elastic modulus of the cell-laden scaffolds compared to the cell-free ones after 14 and 28 days with values ranging from 25 to 40 kPa, showing an increase of 27-36%, with the KCG-KCl scaffolds indicating the highest and CG the lowest values. Cell viability data showed a significant increase from days 3 to 7 and up to day 14 for all scaffold compositions. Significantly increasing alkaline phosphatase (ALP) activity has been observed over time in all three scaffold compositions, while the KCG-KCl scaffolds indicated significantly higher calcium production after 21 and 28 days compared to the CG control. The gene expression analysis of the odontogenic markers DSPP, ALP and RunX2 revealed a two-fold higher upregulation of DSPP in KCG-KCl scaffolds at day 14 compared to the other two compositions. A significant increase of the RunX2 expression between days 7 and 14 was observed for all scaffolds, with a significantly higher increase of at least twelve-fold for the kappa-carrageenan containing scaffolds, which exhibited an earlier ALP gene expression compared to the CG. Our results demonstrate that the integration of kappa-carrageenan in scaffolds significantly enhanced the odontogenic potential of DPSCs and supports dentin-pulp regeneration.

How do cells stiffen?

Cell stiffness is an important characteristic of cells and their response to external stimuli. In this review, we survey methods used to measure cell stiffness, summarize stimuli that alter cell stiffness, and discuss signaling pathways and mechanisms that control cell stiffness. Several pathological states are characterized by changes in cell stiffness, suggesting this property can serve as a potential diagnostic marker or therapeutic target. Therefore, we consider the effect of cell stiffness on signaling and growth processes required for homeostasis and dysfunction in healthy and pathological states. Specifically, the composition and structure of the cell membrane and cytoskeleton are major determinants of cell stiffness, and studies have identified signaling pathways that affect cytoskeletal dynamics both directly and by altered gene expression. We present the results of studies interrogating the effects of biophysical and biochemical stimuli on the cytoskeleton and other cellular components and how these factors determine the stiffness of both individual cells and multicellular structures. Overall, these studies represent an intersection of the fields of polymer physics, protein biochemistry, and mechanics, and identify specific mechanisms involved in mediating cell stiffness that can serve as therapeutic targets.

Passive and Active Microrheology for Biomedical Systems

Microrheology encompasses a range of methods to measure the mechanical properties of soft materials. By characterizing the motion of embedded microscopic particles, microrheology extends the probing length scale and frequency range of conventional bulk rheology. Microrheology can be characterized into either passive or active methods based on the driving force exerted on probe particles. Tracer particles are driven by thermal energy in passive methods, applying minimal deformation to the assessed medium. In active techniques, particles are manipulated by an external force, most commonly produced through optical and magnetic fields. Small-scale rheology holds significant advantages over conventional bulk rheology, such as eliminating the need for large sample sizes, the ability to probe fragile materials non-destructively, and a wider probing frequency range. More importantly, some microrheological techniques can obtain spatiotemporal information of local microenvironments and accurately describe the heterogeneity of structurally complex fluids. Recently, there has been significant growth in using these minimally invasive techniques to investigate a wide range of biomedical systems both in vitro and in vivo. Here, we review the latest applications and advancements of microrheology in mammalian cells, tissues, and biofluids and discuss the current challenges and potential future advances on the horizon.

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.

Foregut organ progenitors and their niche display distinct viscoelastic properties in vivo during early morphogenesis stages

Material properties of living matter play an important role for biological function and development. Yet, quantification of material properties of internal organs in vivo, without causing physiological damage, remains challenging. Here, we present a non-invasive approach based on modified optical tweezers for quantifying sub-cellular material properties deep inside living zebrafish embryos. Material properties of cells within the foregut region are quantified as deep as 150 µm into the biological tissue through measurements of the positions of an inert tracer. This yields an exponent, α, which characterizes the scaling behavior of the positional power spectra and the complex shear moduli. The measurements demonstrate differential mechanical properties: at the time when the developing organs undergo substantial displacements during morphogenesis, gut progenitors are more elastic (α = 0.57 ± 0.07) than the neighboring yolk (α = 0.73 ± 0.08), liver (α = 0.66 ± 0.06) and two mesodermal (α = 0.68 ± 0.06, α = 0.64 ± 0.06) progenitor cell populations. The higher elasticity of gut progenitors correlates with an increased cellular concentration of microtubules. The results infer a role of material properties during morphogenesis and the approach paves the way for quantitative material investigations in vivo of embryos, explants, or organoids.

Here, the authors present a method based on optical tweezers to measure mechanical properties of cells inside living zebrafish embryos. The measurement reveals spatiotemporally distinct mechanical properties, linking cell mechanics and morphogenesis.

Pervasive cytoquakes in the actomyosin cortex across cell types and substrate stiffness

The actomyosin cytoskeleton enables cells to resist deformation, crawl, change their shape and sense their surroundings. Despite decades of study, how its molecular constituents can assemble together to form a network with the observed mechanics of cells remains poorly understood. Recently, it has been shown that the actomyosin cortex of quiescent cells can undergo frequent, abrupt reconfigurations and displacements, called cytoquakes. Notably, such fluctuations are not predicted by current physical models of actomyosin networks, and their prevalence across cell types and mechanical environments has not previously been studied. Using micropost array detectors, we have performed high-resolution measurements of the dynamic mechanical fluctuations of cells' actomyosin cortex and stress fiber networks. This reveals cortical dynamics dominated by cytoquakes-intermittent events with a fat-tailed distribution of displacements, sometimes spanning microposts separated by 4 μm, in all cell types studied. These included 3T3 fibroblasts, where cytoquakes persisted over substrate stiffnesses spanning the tissue-relevant range of 4.3 kPa-17 kPa, and primary neonatal rat cardiac fibroblasts and myofibroblasts, human embryonic kidney cells and human bone osteosarcoma epithelial (U2OS) cells, where cytoquakes were observed on substrates in the same stiffness range. Overall, these findings suggest that the cortex self-organizes into a marginally stable mechanical state whose physics may contribute to cell mechanical properties, active behavior and mechanosensing.

Active gels, heavy tails, and the cytoskeleton

The eukaryotic cell's cytoskeleton is a prototypical example of an active material: objects embedded within it are driven by molecular motors acting on the cytoskeleton, leading to anomalous diffusive behavior. Experiments tracking the behavior of cell-attached objects have observed anomalous diffusion with a distribution of displacements that is non-Gaussian, with heavy tails. This has been attributed to "cytoquakes" or other spatially extended collective effects. We show, using simulations and analytical theory, that a simple continuum active gel model driven by fluctuating force dipoles naturally creates heavy power-law tails in cytoskeletal displacements. We predict that this power law exponent should depend on the geometry and dimensionality of where force dipoles are distributed through the cell; we find qualitatively different results for force dipoles in a 3D cytoskeleton and a quasi-two-dimensional cortex. We then discuss potential applications of this model both in cells and in synthetic active gels.

In Vitro Measurements of Cellular Forces and their Importance in the Lung-From the Sub- to the Multicellular Scale

Throughout life, the body is subjected to various mechanical forces on the organ, tissue, and cellular level. Mechanical stimuli are essential for organ development and function. One organ whose function depends on the tightly connected interplay between mechanical cell properties, biochemical signaling, and external forces is the lung. However, altered mechanical properties or excessive mechanical forces can also drive the onset and progression of severe pulmonary diseases. Characterizing the mechanical properties and forces that affect cell and tissue function is therefore necessary for understanding physiological and pathophysiological mechanisms. In recent years, multiple methods have been developed for cellular force measurements at multiple length scales, from subcellular forces to measuring the collective behavior of heterogeneous cellular networks. In this short review, we give a brief overview of the mechanical forces at play on the cellular level in the lung. We then focus on the technological aspects of measuring cellular forces at many length scales. We describe tools with a subcellular resolution and elaborate measurement techniques for collective multicellular units. Many of the technologies described are by no means restricted to lung research and have already been applied successfully to cells from various other tissues. However, integrating the knowledge gained from these multi-scale measurements in a unifying framework is still a major future challenge.

Multi-frequency passive and active microrheology with optical tweezers

Optical tweezers have attracted significant attention for microrheological applications, due to the possibility of investigating viscoelastic properties in vivo which are strongly related to the health status and development of biological specimens. In order to use optical tweezers as a microrheological tool, an exact force calibration in the complex system under investigation is required. One of the most promising techniques for optical tweezers calibration in a viscoelastic medium is the so-called active–passive calibration, which allows determining both the trap stiffness and microrheological properties of the medium with the least a-priori knowledge in comparison to the other methods. In this manuscript, we develop an optimization of the active–passive calibration technique performed with a sample stage driving, whose implementation is more straightforward with respect to standard laser driving where two different laser beams are required. We performed microrheological measurements over a broad frequency range in a few seconds implementing an accurate multi-frequency driving of the sample stage. The optical tweezers-based microrheometer was first validated by measuring water, and then exemplarily applied to more viscous medium and subsequently to a viscoelastic solution of methylcellulose in water. The described method paves the way to microrheological precision metrology in biological samples with high temporal- and spatial-resolution allowing for investigation of even short time-scale phenomena.

Viscoelastic Properties in Cancer: From Cells to Spheroids

AFM-based rheology methods enable the investigation of the viscoelastic properties of cancer cells. Such properties are known to be essential for cell functions, especially for malignant cells. Here, the relevance of the force modulation method was investigated to characterize the viscoelasticity of bladder cancer cells of various invasiveness on soft substrates, revealing that the rheology parameters are a signature of malignancy. Furthermore, the collagen microenvironment affects the viscoelastic moduli of cancer cell spheroids; thus, collagen serves as a powerful proxy, leading to an increase of the dynamic moduli vs. frequency, as predicted by a double power law model. Taken together, these results shed new light on how cancer cells and tissues adapt their viscoelastic properties depending on their malignancy and the microenvironment. This method could be an attractive way to control their properties in the future, based on the similarity of spheroids with in vivo tumor models.

The Cell as Matter: Connecting Molecular Biology to Cellular Functions

Viewing cell as matter to understand the intracellular biomolecular processes and multicellular tissue behavior represents an emerging research area at the interface of physics and biology. Cellular material displays various physical and mechanical properties, which can strongly affect both intracellular and multicellular biological events. This review provides a summary of how cells, as matter, connect molecular biology to cellular and multicellular scale functions. As an impact in molecular biology, we review recent progresses in utilizing cellular material properties to direct cell fate decisions in the communities of immune cells, neurons, stem cells, and cancer cells. Finally, we provide an outlook on how to integrate cellular material properties in developing biophysical methods for engineered living systems, regenerative medicine, and disease treatments.

Intracellular motor-driven transport of rodlike smooth organelles along microtubules

Molecular motors are fascinating proteins that use the energy of ATP hydrolysis to drive vesicles and organelles along cytoskeleton filaments toward their final destination within the cell. Several copies of these proteins bind to the cargo and take turns transporting the cargo attaching to and detaching from the track stochastically. Despite the relevance of molecular motors to cell physiology, key aspects of their collective functioning are still unknown. In this work we propose a one-dimensional model for the transport of extensive and smooth organelles driven by molecular motors. We ran numerical simulations to study the behavior of the cargo for different motor configurations, focusing on the transport properties observable in the experiments, e.g., average speed of the organelle and variations in length. We found that active motors drive the cargo using two different mechanisms: Either they locate in front of the cargo and pull the organelle or they situate at the cargo lagging edge and push. Variations in the organelle length is in close relation with the fraction of motors in each configuration, which depends on the resisting load. The results of this model were contrasted with experimental data obtained from the tracking of rodlike mitochondria during active transport in Xenopus laevis melanophores.

Tumor cell nuclei soften during transendothelial migration

During cancer metastasis, tumor cells undergo significant deformation in order to traverse through endothelial cell junctions in the walls of blood vessels. As cells pass through narrow gaps, smaller than the nuclear diameter, the spatial configuration of chromatin must change along with the distribution of nuclear enzymes. Nuclear stiffness is an important determinant of the ability of cells to undergo transendothelial migration, yet no studies have been conducted to assess whether tumor cell cytoskeletal or nuclear stiffness changes during this critical process in order to facilitate passage. To address this question, we employed two non-contact methods, Brillouin confocal microscopy (BCM) and confocal reflectance quantitative phase microscopy (QPM), to track the changes in mechanical properties of live, transmigrating tumor cells in an in vitro collagen gel platform. Using these two imaging modalities to study transmigrating MDA-MB-231, A549, and A375 cells, we found that both the cells and their nuclei soften upon extravasation and that the nuclear membranes remain soft for at least 24 h. These new data suggest that tumor cells adjust their mechanical properties in order to facilitate extravasation.

Diffusion of kinesin motors on cargo can enhance binding and run lengths during intracellular transport

Cellular cargoes, including lipid droplets and mitochondria, are transported along microtubules using molecular motors such as kinesins. Many experimental and computational studies focused on cargoes with rigidly attached motors, in contrast to many biological cargoes that have lipid surfaces that may allow surface mobility of motors. We extend a mechanochemical three-dimensional computational model by adding coupled-viscosity effects to compare different motor arrangements and mobilities. We show that organizational changes can optimize for different objectives: Cargoes with clustered motors are transported efficiently but are slow to bind to microtubules, whereas those with motors dispersed rigidly on their surface bind microtubules quickly but are transported inefficiently. Finally, cargoes with freely diffusing motors have both fast binding and efficient transport, although less efficient than clustered motors. These results suggest that experimentally observed changes in motor organization may be a control point for transport.

Glass-like characteristics of intracellular motion in human cells

The motion in the cytosol of microorganisms such as bacteria and yeast has been observed to undergo a dramatic slowing down upon cell energy depletion. These observations have been interpreted as the motion being "glassy," but whether this notion is useful also for active, motor-protein-driven transport in eukaryotic cells is less clear. Here, we use fluorescence microscopy of beads in human (HeLa) cells to probe the motion of membrane-surrounded structures that are carried along the cytoskeleton by motor proteins. Evaluating several hallmarks of glassy dynamics, we show that at short length scales, the motion is heterogeneous, is nonergodic, is well described by a model for the displacement distribution in glassy systems, and exhibits a decoupling of the exchange and persistence times. Overall, these results suggest that the short length scale behavior of objects that can be transported actively by motor proteins in human cells shares features with the motion in glassy systems.

Getting around the cell: physical transport in the intracellular world

Eukaryotic cells face the challenging task of transporting a variety of particles through the complex intracellular milieu in order to deliver, distribute, and mix the many components that support cell function. In this review, we explore the biological objectives and physical mechanisms of intracellular transport. Our focus is on cytoplasmic and intra-organelle transport at the whole-cell scale. We outline several key biological functions that depend on physically transporting components across the cell, including the delivery of secreted proteins, support of cell growth and repair, propagation of intracellular signals, establishment of organelle contacts, and spatial organization of metabolic gradients. We then review the three primary physical modes of transport in eukaryotic cells: diffusive motion, motor-driven transport, and advection by cytoplasmic flow. For each mechanism, we identify the main factors that determine speed and directionality. We also highlight the efficiency of each transport mode in fulfilling various key objectives of transport, such as particle mixing, directed delivery, and rapid target search. Taken together, the interplay of diffusion, molecular motors, and flows supports the intracellular transport needs that underlie a broad variety of biological phenomena.

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.

Mapping cellular-scale internal mechanics in 3D tissues with thermally responsive hydrogel probes

Local tissue mechanics play a critical role in cell function, but measuring these properties at cellular length scales in living 3D tissues can present considerable challenges. Here we present thermoresponsive, smart material microgels that can be dispersed or injected into tissues and optically assayed to measure residual tissue elasticity after creep over several weeks. We first develop and characterize the sensors, and demonstrate that internal mechanical profiles of live multicellular spheroids can be mapped at high resolutions to reveal broad ranges of rigidity within the tissues, which vary with subtle differences in spheroid aggregation method. We then show that small sites of unexpectedly high rigidity develop in invasive breast cancer spheroids, and in an in vivo mouse model of breast cancer progression. These focal sites of increased intratumoral rigidity suggest new possibilities for how early mechanical cues that drive cancer cells towards invasion might arise within the evolving tumor microenvironment.

Multiple particle tracking analysis in isolated nuclei reveals the mechanical phenotype of leukemia cells

The nucleus is fundamentally composed by lamina and nuclear membranes that enclose the chromatin, nucleoskeletal components and suspending nucleoplasm. The functional connections of this network integrate external stimuli into cell signals, including physical forces to mechanical responses of the nucleus. Canonically, the morphological characteristics of the nucleus, as shape and size, have served for pathologists to stratify and diagnose cancer patients; however, novel biophysical techniques must exploit physical parameters to improve cancer diagnosis. By using multiple particle tracking (MPT) technique on chromatin granules, we designed a SURF (Speeded Up Robust Features)-based algorithm to study the mechanical properties of isolated nuclei and in living cells. We have determined the apparent shear stiffness, viscosity and optical density of the nucleus, and how the chromatin structure influences on these biophysical values. Moreover, we used our MPT-SURF analysis to study the apparent mechanical properties of isolated nuclei from patients of acute lymphoblastic leukemia. We found that leukemia cells exhibited mechanical differences compared to normal lymphocytes. Interestingly, isolated nuclei from high-risk leukemia cells showed increased viscosity than their counterparts from normal lymphocytes, whilst nuclei from relapsed-patient's cells presented higher density than those from normal lymphocytes or standard- and high-risk leukemia cells. Taken together, here we presented how MPT-SURF analysis of nuclear chromatin granules defines nuclear mechanical phenotypic features, which might be clinically relevant.

Spatial Nanomechanical Communications Based on State Transitions

In this paper, we present a novel framework of a nanomechanical communication (NMC) system where nanomechanical (NM) systems can communicate using mechanical movements to encode and transfer information between a transmitter (TX) nanomachine and a receiver (RX) nanomachine. First, some unique features of the envisioned NMC system have been presented in contrast to traditional communications systems. It is demonstrated that the encoding of distinct repeatable movements or motions is the key to information transfer in an NMC system. Using a state transition framework, we identify rest states (RSs) and motional degrees of freedom (MDoF) as the two essential concepts that determine the transmission rate of an NMC system in the spatial domain in two different modes, namely, synchronous and asynchronous transmissions. While the synchronous transmission is found to achieve much higher transmission rate compared to the asynchronous transmission in the noise-free case, the asynchronous mode is less restrictive and may have wider applicability. A stochastic model is considered to incorporate the influence of thermal noise in the system. A closed-form expression of the symbol error rate (SER) and its bounds have been derived for a particular symbol of a synchronous sliding motion NMC system with MDoF = 2. Numerical results show a promising SER performance in support of developing an NMC system model for nanoscale communications networks.

Impact of global structure on diffusive exploration of organelle networks

We investigate diffusive search on planar networks, motivated by tubular organelle networks in cell biology that contain molecules searching for reaction partners and binding sites. Exact calculation of the diffusive mean first-passage time on a spatial network is used to characterize the typical search time as a function of network connectivity. We find that global structural properties — the total edge length and number of loops — are sufficient to largely determine network exploration times for a variety of both synthetic planar networks and organelle morphologies extracted from living cells. For synthetic networks on a lattice, we predict the search time dependence on these global structural parameters by connecting with percolation theory, providing a bridge from irregular real-world networks to a simpler physical model. The dependence of search time on global network structural properties suggests that network architecture can be designed for efficient search without controlling the precise arrangement of connections. Specifically, increasing the number of loops substantially decreases search times, pointing to a potential physical mechanism for regulating reaction rates within organelle network structures.

Filament Rigidity Vies with Mesh Size in Determining Anomalous Diffusion in Cytoskeleton

The diffusion of microscopic particles through the cell, important to processes such as viral infection, gene delivery, and vesicle transport, is largely controlled by the complex cytoskeletal network, comprised of semiflexible actin filaments and rigid microtubules, that pervades the cytoplasm. By varying the relative concentrations of actin and microtubules, the cytoskeleton can display a host of different structural and dynamic properties that, in turn, impact the diffusion of particles through the composite network. Here, we couple single-particle tracking with differential dynamic microscopy to characterize the transport of microsphere tracers diffusing through composite in vitro networks with varying ratios of actin and microtubules. We analyze multiple complementary metrics for anomalous transport to show that particles exhibit anomalous subdiffusion in all networks, which our data suggest arises from caging by networks. Further, subdiffusive characteristics are markedly more pronounced in actin-rich networks, which exhibit similarly more prominent viscoelastic properties compared to microtubule-rich composites. While the smaller mesh size of actin-rich composites compared to microtubule-rich composites plays an important role in these results, the rigidity of the filaments comprising the network also influences the anomalous characteristics that we observe. Our results suggest that as microtubules in our composites are replaced with actin filaments, the decreasing filament rigidity competes with increasing network connectivity to drive anomalous transport.

Microfluidic Cytometry for High-Throughput Characterization of Single Cell Cytoplasmic Viscosity Using Crossing Constriction Channels

This article presents an approach of microfluidic flow cytometry capable of continuously characterizing cytoplasmic viscosities of single cells. The microfluidic system consists of a major constriction channel and a side constriction channel perpendicularly crossing each other. Cells are forced to rapidly travel through the major channel and are partially aspirated into the side channel when passing the channel junction. Numerical simulations were conducted to model the time dependence of the aspiration length into the side channel, which enables the measurement of cytoplasmic viscosity by fitting the model results to experimental data. As a demonstration for high-throughput measurement, the cytoplasmic viscosities of HL-60 cells that were native or treated by N-Formylmethionine-leucyl-phenylalanine (fMLP) were quantified with sample sizes as large as thousands of cells. Both the average and median cytoplasmic viscosities of native HL-60 cells were found to be about 10% smaller than those of fMLP-treated HL-60 cells, consistent with previous observations that fMLP treatment can increase the rigidity of white blood cells. Furthermore, the microfluidic system was used to process granulocytes from three donors (sample size >1,000 cells for each donor). The results revealed that the cytoplasmic viscosity of granulocytes from one donor was significantly higher than the other two, which may result from the fact that this donor just recovered from an inflammation. In summary, the developed microfluidic system can collect cytoplasmic viscosities from thousands of cells and may function as an enabling tool in the field of single-cell analysis. © 2019 International Society for Advancement of Cytometry.

Sticky, active microrheology: Part 1. Linear-response

Attractive colloidal-scale forces between macromolecules in biological fluids are suspected to play a role in important system dynamics, including association times, spatially heterogeneous viscosity, and anomalous diffusion. Passive and active microrheology provide a natural connection between observable particle motion and viscosity in such systems via generalized Stokes-Einstein and Stokes' drag law relations. While such models are robust for purely repulsive colloidal-scale interactions, no such theory exists to model the effects of attractive forces. Here we present such a model for the linear-response regime, where a Brownian probe particle is driven gently through a complex fluid by an external force that weakly augments thermal fluctuations. As the probe moves through the bath, hard-sphere repulsion results in an accumulation of particles on its upstream face and a trailing depletion zone, producing particle drag that slows the probe. Linear-response viscosity can be inferred constitutively from this speed reduction. One expects attractive forces to make the suspension more viscous, but surprisingly, weak attractions exerted by upstream particles actively pull the probe forward, giving it a "hypoviscous" environment through which it slides more easily. As attractions grow stronger, particles join to the probe in a long-lasting doublet, extracting particles from the upstream region and depositing them behind the probe. At a critical value of the second virial coefficient common to all potentials we studied, the distorted structure reverses direction, and continued growth of attraction strength causes the probe to drag a cluster of density along, dramatically increasing viscosity. But at this transition, the structure is neutral under the balance of attraction and repulsion, allowing the probe to "cloak" itself and move through the bath undetected and unhindered relative to hard-sphere dispersions. This poses an intriguing mechanism by which proteins or other macromolecules may change their surface chemistry in order to alter the viscosity of the surrounding medium to speed their own motion, or simply to pass undetected through a cell.

Distribution of active forces in the cell cortex

In this work, we study in detail the distribution of stochastic forces generated by the molecular motors activity, in the actin cortex of pre-muscular cells. By combining active and passive rheology experiments, performed on the same micro-bead bound to the actin network through membrane adhesive receptors, we measure the auto-correlation function C_ff(τ) of the average force pulling on the bead. As for any out-of-equilibrium system, the force distribution differs from the thermodynamical equilibrium one, especially at long time scale τ⪆ 1 s where the bead motion becomes partially directed. Thus the fluctuation-dissipation theorem does not apply and one can measure the distance from equilibrium through its violation. We investigate the influence of different parameters on the force distribution, focusing particularly on the role of ligand density: a detailed study shows how the amplitude of active forces increases when the bead is more tightly attached to the cortex. We introduce and study a model, which takes into account the number of bonds between the bead and the cytoskeleton, as well as the viscoelastic properties of the medium. This model faithfully accounts for the experimental observations. Also, it is shown that the amplitude of active forces increases with temperature. Finally, our data confirm that ATP depletion in the cell, or partial inhibition of the actomyosin activity, leads to a decrease of the amplitude of the force distribution. Altogether, we propose a consistent and quantitative description for the motion of a micrometric probe interacting with the actin network, and for the amplitude of the stochastic forces generated by molecular motors in the cortex surrounding this probe.

Dissecting fat-tailed fluctuations in the cytoskeleton with active micropost arrays

The ability of animal cells to crawl, change their shape, and respond to applied force is due to their cytoskeleton: A dynamic, cross-linked network of actin protein filaments and myosin motors. How these building blocks assemble to give rise to cells' mechanics and behavior remains poorly understood. Using active micropost array detectors containing magnetic actuators, we have characterized the mechanics and fluctuations of cells' actomyosin cortex and stress fiber network in detail. Here, we find that both structures display remarkably consistent power law viscoelastic behavior along with highly intermittent fluctuations with fat-tailed distributions of amplitudes. Notably, this motion in the cortex is dominated by occasional large, step-like displacement events, with a spatial extent of several micrometers. Overall, our findings for the cortex appear contrary to the predictions of a recent active gel model, while suggesting that different actomyosin contractile units act in a highly collective and cooperative manner. We hypothesize that cells' actomyosin components robustly self-organize into marginally stable, plastic networks that give cells' their unique biomechanical properties.

Measuring local properties inside a cell-mimicking structure using rotating optical tweezers

Exploring the rheological properties of intracellular materials is essential for understanding cellular and subcellular processes. Optical traps have been widely used for physical manipulation of micro and nano objects within fluids enabling studies of biological systems. However, experiments remain challenging as it is unclear how the probe particle's mobility is influenced by the nearby membranes and organelles. We use liposomes (unilamellar lipid vesicles) as a simple biomimetic model of living cells, together with a trapped particle rotated by optical tweezers to study mechanical and rheological properties inside a liposome both theoretically and experimentally. Here, we demonstrate that this system has the capacity to predict the hydrodynamic interaction between three-dimensional spatial membranes and internal probe particles within submicron distances, and it has the potential to aid in the design of high resolution optical micro/nanorheology techniques to be used inside living cells.

Translation of a Coated Rigid Spherical Inclusion in an Elastic Matrix: Exact Solution, and Implications for Mechanobiology

The displacement of relatively rigid beads within a relatively compliant, elastic matrix can be used to measure the mechanical properties of the matrix. For example, in mechanobiological studies, magnetic or reflective beads can be displaced with a known external force to estimate the matrix modulus. Although such beads are generally rigid compared to the matrix, the material surrounding the beads typically differs from the matrix in one or two ways. The first case, as is common in mechanobiological experimentation, is the situation in which the bead must be coated with materials such as protein ligands that enable adhesion to the matrix. These layers typically differ in stiffness relative to the matrix material. The second case, common for uncoated beads, is the situation in which the beads disrupt the structure of the hydrogel or polymer, leading to a region of enhanced or reduced stiffness in the neighborhood of the bead. To address both cases, we developed the first analytical solution of the problem of translation of a coated, rigid spherical inclusion displaced within an isotropic elastic matrix by a remotely applied force. The solution is applicable to cases of arbitrary coating stiffness and size of the coating. We conclude by discussing applications of the solution to mechanobiology.

Mapping the creep compliance of living cells with scanning ion conductance microscopy reveals a subcellular correlation between stiffness and fluidity

Living cells exhibit complex material properties, which play a crucial role in many aspects of cell function in health and disease, including migration, proliferation, differentiation, and apoptosis. Various techniques exist to probe the viscoelastic material properties of living cells and a frequent observation is a cell-to-cell correlation between average stiffness and fluidity in populations of cells. However, the origin of this correlation is still under discussion. Here, we introduce an imaging technique based on the scanning ion conductance microscope (SICM) to measure the creep compliance of soft samples, which allowed us to generate images of viscoelastic material properties of living cells with high spatial and temporal resolution. We observe a strong subcellular correlation between the local stiffness and fluidity across the individual living cell: stiff regions exhibit lower fluidity while soft regions exhibit higher fluidity. We find that this subcellular correlation is identical to the previously observed cell-to-cell correlation. The subcellular correlation reversibly vanishes after drug-induced disruption of the cytoskeleton, indicating that the subcellular correlation is a property of the intact cytoskeleton of the living cell.

Active Mechanics Reveal Molecular-Scale Force Kinetics in Living Oocytes

Active diffusion of intracellular components is emerging as an important process in cell biology. This process is mediated by complex assemblies of molecular motors and cytoskeletal filaments that drive force generation in the cytoplasm and facilitate enhanced motion. The kinetics of molecular motors have been precisely characterized in vitro by single molecule approaches, but their in vivo behavior remains elusive. Here, we study the active diffusion of vesicles in mouse oocytes, where this process plays a key role in nuclear positioning during development, and combine an experimental and theoretical framework to extract molecular-scale force kinetics (force, power stroke, and velocity) of the in vivo active process. Assuming a single dominant process, we find that the nonequilibrium activity induces rapid kicks of duration τ ∼ 300 μs resulting in an average force of F ∼ 0.4 pN on vesicles in in vivo oocytes, remarkably similar to the kinetics of in vitro myosin-V. Our results reveal that measuring in vivo active fluctuations allows extraction of the molecular-scale activity in agreement with single-molecule studies and demonstrates a mesoscopic framework to access force kinetics.

Complex nearly immotile behaviour of enzymatically driven cargos

We report a minimal microtubule-based motile system displaying signatures of unconventional diffusion. The system consists of a single model cargo driven by an ensemble of N340K NCD motors along a single microtubule. Despite the absence of cytosolic or cytoskeleton complexity, the system shows complex behavior, characterized by sub-diffusive motion for short time lag scales and linear mean squared displacement dependence for longer time lags. The latter is also shown to have non-Gaussian character and cannot be ascribed to a canonical diffusion process. We use single particle tracking and analysis at varying temperatures and motor concentrations to identify the origin of these behaviors as enzymatic activity of mutant NCD. Our results show that signatures of non-Gaussian diffusivities can arise as a result of an active process and suggest that some immotility of cargos observed in cells may reflect the ensemble workings of mechanochemical enzymes and need not always reflect the properties of the cytoskeletal network or the cytosol.

Phosphoethanolamine cellulose enhances curli-mediated adhesion of uropathogenic Escherichia coli to bladder epithelial cells

Uropathogenic Escherichia coli (UPEC) are the major causative agents of urinary tract infections, employing numerous molecular strategies to contribute to adhesion, colonization, and persistence in the bladder niche. Identifying strategies to prevent adhesion and colonization is a promising approach to inhibit bacterial pathogenesis and to help preserve the efficacy of available antibiotics. This approach requires an improved understanding of the molecular determinants of adhesion to the bladder urothelium. We designed experiments using a custom-built live cell monolayer rheometer (LCMR) to quantitatively measure individual and combined contributions of bacterial cell surface structures [type 1 pili, curli, and phosphoethanolamine (pEtN) cellulose] to bladder cell adhesion. Using the UPEC strain UTI89, isogenic mutants, and controlled conditions for the differential production of cell surface structures, we discovered that curli can promote stronger adhesive interactions with bladder cells than type 1 pili. Moreover, the coproduction of curli and pEtN cellulose enhanced adhesion. The LCMR enables the evaluation of adhesion under high-shear conditions to reveal this role for pEtN cellulose which escaped detection using conventional tissue culture adhesion assays. Together with complementary biochemical experiments, the results support a model wherein cellulose serves a mortar-like function to promote curli association with and around the bacterial cell surface, resulting in increased bacterial adhesion strength at the bladder cell surface.

Creeping motion of a solid particle inside a spherical elastic cavity⋆

On the basis of the linear hydrodynamic equations, we present an analytical theory for the low-Reynolds-number motion of a solid particle moving inside a larger spherical elastic cavity which can be seen as a model system for a fluid vesicle. In the particular situation where the particle is concentric with the cavity, we use the stream function technique to find exact analytical solutions of the fluid motion equations on both sides of the elastic cavity. In this particular situation, we find that the solution of the hydrodynamic equations is solely determined by membrane shear properties and that bending does not play a role. For an arbitrary position of the solid particle within the spherical cavity, we employ the image solution technique to compute the axisymmetric flow field induced by a point force (Stokeslet). We then obtain analytical expressions of the leading-order mobility function describing the fluid-mediated hydrodynamic interactions between the particle and the confining elastic cavity. In the quasi-steady limit of vanishing frequency, we find that the particle self-mobility function is higher than that predicted inside a rigid no-slip cavity. Considering the cavity motion, we find that the pair-mobility function is determined only by membrane shear properties. Our analytical predictions are supplemented and validated by fully resolved boundary integral simulations where a very good agreement is obtained over the whole range of applied forcing frequencies.

Supramolecular polymeric biomaterials

Polymeric chains crosslinked through supramolecular interactions-directional and reversible non-covalent interactions-compose an emerging class of modular and tunable biomaterials. The choice of chemical moiety utilized in the crosslink affords different thermodynamic and kinetic parameters of association, which in turn illustrate the connectivity and dynamics of the system. These parameters, coupled with the choice of polymeric architecture, can then be engineered to control environmental responsiveness, viscoelasticity, and cargo diffusion profiles, yielding advanced biomaterials which demonstrate rapid shear-thinning, self-healing, and extended release. In this review we examine the relationship between supramolecular crosslink chemistry and biomedically relevant macroscopic properties. We then describe how these properties are currently leveraged in the development of materials for drug delivery, immunology, regenerative medicine, and 3D-bioprinting (253 references).

Broken detailed balance and non-equilibrium dynamics in living systems: a review

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Compressive Force Spectroscopy: From Living Cells to Single Proteins

One of the most successful applications of atomic force microscopy (AFM) in biology involves monitoring the effect of force on single biological molecules, often referred to as force spectroscopy. Such studies generally entail the application of pulling forces of different magnitudes and velocities upon individual molecules to resolve individualistic unfolding/separation pathways and the quantification of the force-dependent rate constants. However, a less recognized variation of this method, the application of compressive force, actually pre-dates many of these "tensile" force spectroscopic studies. Further, beyond being limited to the study of single molecules, these compressive force spectroscopic investigations have spanned samples as large as living cells to smaller, multi-molecular complexes such as viruses down to single protein molecules. Correspondingly, these studies have enabled the detailed characterization of individual cell states, subtle differences between seemingly identical viral structures, as well as the quantification of rate constants of functionally important, structural transitions in single proteins. Here, we briefly review some of the recent achievements that have been obtained with compressive force spectroscopy using AFM and highlight exciting areas of its future development.

Cellular and Nuclear Forces: An Overview

Biological cells sample their surrounding microenvironments using nanoscale force sensors on the cell surfaces. These surface-based force and stress sensors generate physical and chemical responses inside the cell. The inherently well-connected cytoskeleton and its physical contacts with the force elements on the nuclear membrane lead these physicochemical responses to cascade all the way inside the cell nucleus, physically altering the nuclear state. These physical alterations of the cell nucleus, through yet-unknown complex steps elicit physical and functional response from the chromatin in the form of altered gene expression profiles. This mechanism of force/stress sensing by the cell and then its nuclear response has been shown to play a vital role in maintaining robust cellular homeostasis, controlling gene expression profiles during developmental phases as well as cell differentiation. Over the last few years, there has been appreciable progress toward identification of the molecular players responsible for force sensing. However, the actual sensing mechanism of cell surface bound force sensors and more importantly cascading of the signals, both physical (via cytosolic force sensing elements such as microtubule and actin framework) and chemical (cascade of biochemical signaling from cell surface to nuclear surface and further to the chromatin), inside the cell is poorly understood. In this chapter, we present a review of the currently known molecular players in cellular as well as nuclear force sensing repertoire and their possible mechanistic aspects. We also introduce various biophysical concepts that are used to describe the force/stress sensing and response of a cell. We hope this will help asking clearer questions and designing pointed experiments for better understanding of the force-dependent design principles of the cell surface, nuclear surface, and gene expression.

Dynamic Light Scattering Microrheology Reveals Multiscale Viscoelasticity of Polymer Gels and Precious Biological Materials

The development of experimental techniques capable of probing the viscoelasticity of soft materials over a broad range of time scales is essential to uncovering the physics that governs their behavior. In this work, we develop a microrheology technique that requires only 12 μL of sample and is capable of resolving dynamic behavior ranging in time scales from 10^-6 to 10 s. Our approach, based on dynamic light scattering in the single-scattering limit, enables the study of polymer gels and other soft materials over a vastly larger hierarchy of time scales than macrorheology measurements. Our technique captures the viscoelastic modulus of polymer hydrogels with a broad range of stiffnesses from 10 to 10⁴ Pa. We harness these capabilities to capture hierarchical molecular relaxations in DNA and to study the rheology of precious biological materials that are impractical for macrorheology measurements, including decellularized extracellular matrices and intestinal mucus. The use of a commercially available benchtop setup that is already available to a variety of soft matter researchers renders microrheology measurements accessible to a broader range of users than existing techniques, with the potential to reveal the physics that underlies complex polymer hydrogels and biological materials.