A one-step procedure to probe the viscoelastic properties of cells by Atomic Force Microscopy

Multidepth quantitative analysis of liver cell viscoelastic properties: Fusion of nanoindentation and finite element modeling techniques

Liver cells are the basic functional unit of the liver. However, repeated or sustained injury leads to structural disorders of liver lobules, proliferation of fibrous tissue and changes in structure, thus increasing scar tissue. Cellular fibrosis affects tissue stiffness, shear force, and other cellular mechanical forces. Mechanical force characteristics can serve as important indicators of cell damage and cirrhosis. Atomic force microscopy (AFM) has been widely used to study cell surface mechanics. However, characterization of the deep mechanical properties inside liver cells remains an underdeveloped field. In this work, cell nanoindentation was combined with finite element analysis to simulate and analyze the mechanical responses of liver cells at different depths in vitro and their internal responses and stress diffusion distributions after being subjected to normal stress. The sensitivities of the visco-hyperelastic parameters of the finite element model to the effects of the peak force and equilibrium force were compared. The force curves of alcohol-damaged liver cells at different depths were measured and compared with those of undamaged liver cells. The inverse analysis method was used to simulate the finite element model in vitro. Changes in the parameters of the cell model after injury were explored and analyzed, and their potential for characterizing hepatocellular injury and related treatments was evaluated. RESEARCH HIGHLIGHTS: This study aims to establish an in vitro hyperelastic model of liver cells and analyze the mechanical changes of cells in vitro. An analysis method combining finite element analysis model and nanoindentation was used to obtain the key parameters of the model. The multi-depth mechanical differences and internal structural changes of injured liver cells were analyzed.

Optical Halo: A Proof of Concept for a New Broadband Microrheology Tool

Microrheology, the study of material flow at micron scales, has advanced significantly since Robert Brown's discovery of Brownian motion in 1827. Mason and Weitz's seminal work in 1995 established the foundation for microrheology techniques, enabling the measurement of viscoelastic properties of complex fluids using light-scattering particles. However, existing techniques face limitations in exploring very slow dynamics, crucial for understanding biological systems. Here, we present a proof of concept for a novel microrheology technique called "Optical Halo", which utilises a ring-shaped Bessel beam created by optical tweezers to overcome existing limitations. Through numerical simulations and theoretical analysis, we demonstrate the efficacy of the Optical Halo in probing viscoelastic properties across a wide frequency range, including low-frequency regimes inaccessible to conventional methods. This innovative approach holds promise for elucidating the mechanical behaviour of complex biological fluids.

Investigations of cardiac fibrosis rheology by in vitro cardiac tissue modeling with 3D cellular spheroids

Cardiac fibrosis refers to the abnormal accumulation of extracellular matrix within the cardiac muscle, leading to increased stiffness and impaired heart function. From a rheological standpoint, knowledge about myocardial behavior is still lacking, partially due to a lack of appropriate techniques to investigate the rheology of in vitro cardiac tissue models. 3D multicellular cardiac spheroids are powerful and versatile platforms for modeling healthy and fibrotic cardiac tissue in vitro and studying how their mechanical properties are modulated. In this study, cardiac spheroids were created by co-culturing neonatal rat ventricular cardiomyocytes and fibroblasts in definite ratios using the hanging-drop method. The rheological characterization of such models was performed by Atomic Force Microscopy-based stress-relaxation measurements on the whole spheroid. After strain application, a viscoelastic bi-exponential relaxation was observed, characterized by a fast relaxation time (τ1) followed by a slower one (τ2). In particular, spheroids with higher fibroblasts density showed reduction for both relaxation times comparing to control, with a more pronounced decrement of τ1 with respect to τ2. Such response was found compatible with the increased production of extracellular matrix within these spheroids, which recapitulates the main feature of the fibrosis pathophysiology. These results demonstrate how the rheological characteristics of cardiac tissue vary as a function of cellular composition and extracellular matrix, confirming the suitability of such system as an in vitro preclinical model of cardiac fibrosis.

Numerical simulation of nanoneedle-cell membrane collision: minimum magnetic force and initial kinetic energy for penetration

Aims and objectives: This research aims to develop a kinetic model that accurately captures the dynamics of nanoparticle impact and penetration into cell membranes, specifically in magnetically-driven drug delivery. The primary objective is to determine the minimum initial kinetic energy and constant external magnetic force necessary for successful penetration of the cell membrane.Model Development: Built upon our previous research on quasi-static nanoneedle penetration, the current model development is based on continuum mechanics. The modeling approach incorporates a finite element method and explicit dynamic solver to accurately represent the rapid dynamics involved in the phenomenon. Within the model, the cell is modeled as an isotropic elastic shell with a hemiellipsoidal geometry and a thickness of 200 nm, reflecting the properties of the lipid membrane and actin cortex. The surrounding cytoplasm is treated as a fluid-like Eulerian body.Scenarios and Results: This study explores three distinct scenarios to investigate the penetration of nanoneedles into cell membranes. Firstly, we examine two scenarios in which the particles are solely subjected to either a constant external force or an initial velocity. Secondly, we explore a scenario that considers the combined effects of both parameters simultaneously. In each scenario, we analyze the critical values required to induce membrane puncture and present comprehensive diagrams illustrating the results.Findings and significance: The findings of this research provide valuable insights into the mechanics of nanoneedle penetration into cell membranes and offer guidelines for optimizing magnetically-driven drug delivery systems, supporting the design of efficient and targeted drug delivery strategies.

i-Rheo-optical assay: Measuring the viscoelastic properties of multicellular spheroids

This study introduces a novel mechanobiology assay, named "i-Rheo-optical assay", that integrates rheology with optical microscopy for analysing the viscoelastic properties of multicellular spheroids. These spheroids serve as three-dimensional models resembling tissue structures. The innovative technique enables real-time observation and quantification of morphological responses to applied stress using a cost-effective microscope coverslip for constant compression force application. By bridging a knowledge gap in biophysical research, which has predominantly focused on the elastic properties while only minimally exploring the viscoelastic nature in multicellular systems, the i-Rheo-optical assay emerges as an effective tool. It facilitates the measurement of broadband viscoelastic compressional moduli in spheroids, here derived from cancer (PANC-1) and non-tumoral (NIH/3T3) cell lines during compression tests. This approach plays a crucial role in elucidating the mechanical properties of spheroids and holds potential for identifying biomarkers to discriminate between healthy tissues and their pathological counterparts. Offering comprehensive insights into the biomechanical behaviour of biological systems, i-Rheo-optical assay marks a significant advancement in tissue engineering, cancer research, and therapeutic development.

Atomic Force Microscopy for the Study of Cell Mechanics in Pharmaceutics

Cell mechanics is gaining attraction in drug screening, but the applicable methods have not yet become part of the standardized norm. This review presents the current state of the art for atomic force microscopy, which is the most widely available method. The field is first motivated as a new way of tracking pharmaceutical effects, followed by a basic introduction targeted at pharmacists on how to measure cellular stiffness. The review then moves on to the current state of the knowledge in terms of experimental results and supplementary methods such as fluorescence microscopy that can give relevant additional information. Finally, rheological approaches as well as the theoretical interpretations are presented before ending on additional methods and outlooks.

Emergence of nanoscale viscoelasticity from single cancer cells to established tumors

Tumors are complex materials whose physical properties dictate growth and treatment outcomes. Recent evidence suggests time-dependent physical properties, such as viscoelasticity, are crucial, distinct mechanical regulators of cancer progression and malignancy, yet the genesis and consequences of tumor viscoelasticity are poorly understood. Here, using Wide-bandwidth AFM-based ViscoElastic Spectroscopy (WAVES) coupled with mathematical modeling, we probe the origins of tumor viscoelasticity. From single carcinoma cells to increasingly sized carcinoma spheroids to established tumors, we describe a stepwise evolution of dynamic mechanical properties that create a nanorheological signature of established tumors: increased stiffness, decreased rate-dependent stiffening, and reduced energy dissipation. We dissect this evolution of viscoelasticity by scale, and show established tumors use fluid-solid interactions as the dominant mechanism of mechanical energy dissipation as opposed to fluid-independent intrinsic viscoelasticity. Additionally, we demonstrate the energy dissipation mechanism in spheroids and established tumors is negatively correlated with the cellular density, and this relationship strongly depends on an intact actin cytoskeleton. These findings define an emergent and targetable signature of the physical tumor microenvironment, with potential for deeper understanding of tumor pathophysiology and treatment strategies.

Gold nanoparticle adsorption alters the cell stiffness and cell wall bio-chemical landscape of Candida albicans fungal cells

HYPOTHESIS

Nanomaterials have been extensively investigated for a wide range of biomedical applications, including as antimicrobial agents, drug delivery vehicles, and diagnostic devices. The commonality between these biomedical applications is the necessity for the nanoparticle to interact with or pass through the cellular wall and membrane. Cell-nanomaterial interactions/uptake can occur in various ways, including adhering to the cell wall, forming aggregates on the surface, becoming absorbed within the cell wall itself, or transversing into the cell cytoplasm. These interactions are common to mammalian cells, bacteria, and yeast cells. This variety of interactions can cause changes to the integrity of the cell wall and the cell overall, but the precise mechanisms underpinning such interactions remain poorly understood. Here, we investigate the interaction between commonly investigated gold nanoparticles (AuNPs) and the cell wall/membrane of a model fungal cell to explore the general effects of interaction and uptake.

EXPERIMENTS

The interactions between 100 nm citrate-capped AuNPs and the cell wall of Candida albicans fungal cells were studied using a range of advanced microscopy techniques, including atomic force microscopy, confocal laser scanning microscopy, scanning electron microscopy, transmission electron microscopy, and synchrotron-FTIR micro-spectroscopy.

FINDINGS

In most cases, particles adhered on the cell surface, although instances of particles being up-taken into the cell cytoplasm and localised within the cell wall and membrane were also observed. There was a measurable increase in the stiffness of the fungal cell after AuNPs were introduced. Analysis of the synchrotron-FTIR data showed significant changes in spectral features associated with phospholipids and proteins after exposure to AuNPs.

Methodologies and models for measuring viscoelastic properties of cancer cells: Towards a universal classification

Different methods and several physical models exist to study cell viscoelasticity with the atomic force microscope (AFM). In search of a robust mechanical classification of cells through AFM, in this work, viscoelastic parameters of the cancer cell lines MDA-MB-231, DU-145, and MG-63 are obtained using two methodologies; through force-distance and force-relaxation curves. Four mechanical models were applied to fit the curves. The results show that both methodologies agree qualitatively on the parameters that quantify elasticity but disagree on the parameters that account for energy dissipation. The Fractional Zener (FZ) model represents well the information given by the Solid Linear Standard and Generalized Maxwell models. The Fractional Kelvin (FK) model concentrates the viscoelastic information mainly in two parameters, which could be an advantage over the other models. Therefore, the FZ and FK models are proposed as the basis for the classification of cancer cells. However, more research using these models is needed to obtain a broader view of the meaning of each parameter and to be able to establish a relationship between the parameters and the cellular components.

Compressional stress stiffening & softening of soft hydrogels - how to avoid artefacts in their rheological characterisation

Hydrogels have been successfully employed as analogues of the extracellular matrix to study biological processes such as cells' migration, growth, adhesion and differentiation. These are governed by many factors, including the mechanical properties of hydrogels; yet, a one-to-one correlation between the viscoelastic properties of gels and cell fate is still missing from literature. In this work we provide experimental evidence supporting a possible explanation for the persistence of this knowledge gap. In particular, we have employed common tissues' surrogates such as polyacrylamide and agarose gels to elucidate a potential pitfall occurring when performing rheological characterisations of soft-materials. The issue is related to (i) the normal force applied to the samples prior to performing the rheological measurements, which may easily drive the outcomes of the investigation outside the materials' linear viscoelastic regime, especially when tests are performed with (ii) geometrical tools having unbefitting dimensions (i.e., too small). We corroborate that biomimetic hydrogels can show either compressional stress softening or stiffening, and we provide a simple solution to quench these undesired phenomena, which would likely lead to potentially misleading conclusions if they were not mitigated by a good practice in performing rheological measurements, as elucidated in this work.

Extracting, quantifying, and comparing dynamical and biomechanical properties of living matter through single particle tracking

A panoply of new tools for tracking single particles and molecules has led to an explosion of experimental data, leading to novel insights into physical properties of living matter governing cellular development and function, health and disease. In this Perspective, we present tools to investigate the dynamics and mechanics of living systems from the molecular to cellular scale via single-particle techniques. In particular, we focus on methods to measure, interpret, and analyse complex data sets that are associated with forces, materials properties, transport, and emergent organisation phenomena within biological and soft-matter systems. Current approaches, challenges, and existing solutions in the associated fields are outlined in order to support the growing community of researchers at the interface of physics and the life sciences. Each section focuses not only on the general physical principles and the potential for understanding living matter, but also on details of practical data extraction and analysis, discussing limitations, interpretation, and comparison across different experimental realisations and theoretical frameworks. Particularly relevant results are introduced as examples. While this Perspective describes living matter from a physical perspective, highlighting experimental and theoretical physics techniques relevant for such systems, it is also meant to serve as a solid starting point for researchers in the life sciences interested in the implementation of biophysical methods.

Nanomechanical Characterization of Bacterial Polyhydroxyalkanoates Using Atomic Force Microscopy

Polyhydroxyalkanoates are a promising class of biopolymers that can allow the production of sustainable plastic materials. The mechanical properties of such materials are very important for possible industrial applications, but the amount of polymer required for common mechanical testing can be orders of magnitude more than what is possible to achieve with a lab-scale process. Nanoindentation with the Atomic Force Microscope allows an estimation of the Elastic Modulus that can be used as a preliminary measurement on PHA when only a limited amount of material is available. Poly(hydroxybutyrate-co-hydroxyvalerate) copolymers were analyzed, with moduli ranging from 528 ± 62 MPa to 1623 ± 172 MPa, according to both the composition and the crystallization kinetics.

Viscoelasticity Acts as a Marker for Tumor Extracellular Matrix Characteristics

Biological materials such as extracellular matrix scaffolds, cancer cells, and tissues are often assumed to respond elastically for simplicity; the viscoelastic response is quite commonly ignored. Extracellular matrix mechanics including the viscoelasticity has turned out to be a key feature of cellular behavior and the entire shape and function of healthy and diseased tissues, such as cancer. The interference of cells with their local microenvironment and the interaction among different cell types relies both on the mechanical phenotype of each involved element. However, there is still not yet clearly understood how viscoelasticity alters the functional phenotype of the tumor extracellular matrix environment. Especially the biophysical technologies are still under ongoing improvement and further development. In addition, the effect of matrix mechanics in the progression of cancer is the subject of discussion. Hence, the topic of this review is especially attractive to collect the existing endeavors to characterize the viscoelastic features of tumor extracellular matrices and to briefly highlight the present frontiers in cancer progression and escape of cancers from therapy. Finally, this review article illustrates the importance of the tumor extracellular matrix mechano-phenotype, including the phenomenon viscoelasticity in identifying, characterizing, and treating specific cancer types.

Changes in Cell Morphology and Actin Organization in Embryonic Stem Cells Cultured under Different Conditions

The cellular cytoskeleton provides the cell with a mechanical rigidity that allows mechanical interaction between cells and the extracellular environment. The actin structure plays a key role in mechanical events such as motility or the establishment of cell polarity. From the earliest stages of development, as represented by the ex vivo expansion of naïve embryonic stem cells (ESCs), the critical mechanical role of the actin structure is becoming recognized as a vital cue for correct segregation and lineage control of cells and as a regulatory structure that controls several transcription factors. Naïve ESCs have a characteristic morphology, and the ultrastructure that underlies this condition remains to be further investigated. Here, we investigate the 3D actin cytoskeleton of naïve mouse ESCs using super-resolution optical reconstruction microscopy (STORM). We investigate the morphological, cytoskeletal, and mechanical changes in cells cultured in 2i or Serum/LIF media reflecting, respectively, a homogeneous preimplantation cell state and a state that is closer to embarking on differentiation. STORM imaging showed that the peripheral actin structure undergoes a dramatic change between the two culturing conditions. We also detected micro-rheological differences in the cell periphery between the cells cultured in these two media correlating well with the observed nano-architecture of the ESCs in the two different culture conditions. These results pave the way for linking physical properties and cytoskeletal architecture to cell morphology during early development.

Lopsided Blood-Thinning Drug Increases the Risk of Internal Flow Choking Leading to Shock Wave Generation Causing Asymptomatic Cardiovascular Disease

The discovery of Sanal flow choking in the cardiovascular-system calls for multidisciplinary and global action to develop innovative treatments and to develop new drugs to negate the risk of asymptomatic-cardiovascular-diseases. Herein, it is shown that when blood-pressure-ratio (BPR) reaches the lower-critical-hemorrhage-index (LCHI) internal-flow-choking and shock wave generation can occur in the cardiovascular-system, with sudden expansion/divergence/vasospasm or bifurcation regions, without prejudice to the percutaneous-coronary-intervention (PCI). Analytical findings reveal that the relatively high and the low blood-viscosity are cardiovascular-risk factors. In vitro studies have shown that nitrogen, oxygen, and carbon dioxide gases are dominant in fresh blood samples of humans/guinea pigs at a temperature range of 98.6-104 F. An in silico study demonstrated the Sanal flow choking phenomenon leading to shock-wave generation and pressure-overshoot in the cardiovascular-system. It has been established that disproportionate blood-thinning treatment increases the risk of the internal-flow-choking due to the enhanced boundary-layer-blockage-factor, resulting from an increase in flow-turbulence level in the cardiovascular-system, caused by an increase in Reynolds number as a consequence of low blood-viscosity. The cardiovascular-risk can be diminished by concurrently lessening the viscosity of biofluid/blood and flow-turbulence by raising the thermal-tolerance-level in terms of blood-heat-capacity-ratio (BHCR) and/or by decreasing the systolic-to-diastolic blood-pressure-ratio.

Determination by Relaxation Tests of the Mechanical Properties of Soft Polyacrylamide Gels Made for Mechanobiology Studies

Following the general aim of recapitulating the native mechanical properties of tissues and organs in vitro, the field of materials science and engineering has benefited from recent progress in developing compliant substrates with physical and chemical properties similar to those of biological materials. In particular, in the field of mechanobiology, soft hydrogels can now reproduce the precise range of stiffnesses of healthy and pathological tissues to study the mechanisms behind cell responses to mechanics. However, it was shown that biological tissues are not only elastic but also relax at different timescales. Cells can, indeed, perceive this dissipation and actually need it because it is a critical signal integrated with other signals to define adhesion, spreading and even more complicated functions. The mechanical characterization of hydrogels used in mechanobiology is, however, commonly limited to the elastic stiffness (Young's modulus) and this value is known to depend greatly on the measurement conditions that are rarely reported in great detail. Here, we report that a simple relaxation test performed under well-defined conditions can provide all the necessary information for characterizing soft materials mechanically, by fitting the dissipation behavior with a generalized Maxwell model (GMM). The simple method was validated using soft polyacrylamide hydrogels and proved to be very useful to readily unveil precise mechanical properties of gels that cells can sense and offer a set of characteristic values that can be compared with what is typically reported from microindentation tests.

Evaluation of quasi-static and dynamic nanomechanical properties of bone-metastatic breast cancer cells using a nanoclay cancer testbed

In recent years, there has been increasing interest in investigating the mechanical properties of individual cells to delineate disease mechanisms. Reorganization of cytoskeleton facilitates the colonization of metastatic breast cancer at bone marrow space, leading to bone metastasis. Here, we report evaluation of mechanical properties of two breast cancer cells with different metastatic ability at the site of bone metastases, using quasi-static and dynamic nanoindentation methods. Our results showed that the significant reduction in elastic modulus along with increased liquid-like behavior of bone metastasized MCF-7 cells was induced by depolymerization and reorganization of F-actin to the adherens junctions, whereas bone metastasized MDA-MB-231 cells showed insignificant changes in elastic modulus and F-actin reorganization over time, compared to their respective as-received counterparts. Taken together, our data demonstrate evolution of breast cancer cell mechanics at bone metastases.

A hyperelastic model for simulating cells in flow

In the emerging field of 3D bioprinting, cell damage due to large deformations is considered a main cause for cell death and loss of functionality inside the printed construct. Those deformations, in turn, strongly depend on the mechano-elastic response of the cell to the hydrodynamic stresses experienced during printing. In this work, we present a numerical model to simulate the deformation of biological cells in arbitrary three-dimensional flows. We consider cells as an elastic continuum according to the hyperelastic Mooney-Rivlin model. We then employ force calculations on a tetrahedralized volume mesh. To calibrate our model, we perform a series of FluidFM[Formula: see text] compression experiments with REF52 cells demonstrating that all three parameters of the Mooney-Rivlin model are required for a good description of the experimental data at very large deformations up to 80%. In addition, we validate the model by comparing to previous AFM experiments on bovine endothelial cells and artificial hydrogel particles. To investigate cell deformation in flow, we incorporate our model into Lattice Boltzmann simulations via an Immersed-Boundary algorithm. In linear shear flows, our model shows excellent agreement with analytical calculations and previous simulation data.

Nanomechanical mapping of soft materials with the atomic force microscope: methods, theory and applications

Fast, high-resolution, non-destructive and quantitative characterization methods are needed to develop materials with tailored properties at the nanoscale or to understand the relationship between mechanical properties and cell physiology. This review introduces the state-of-the-art force microscope-based methods to map at high-spatial resolution the elastic and viscoelastic properties of soft materials. The experimental methods are explained in terms of the theories that enable the transformation of observables into material properties. Several applications in materials science, molecular biology and mechanobiology illustrate the scope, impact and potential of nanomechanical mapping methods.

Material-driven fibronectin assembly rescues matrix defects due to mutations in collagen IV in fibroblasts

Basement membranes (BMs) are specialised extracellular matrices that provide structural support to tissues as well as influence cell behaviour and signalling. Mutations in COL4A1/COL4A2, a major BM component, cause a familial form of eye, kidney and cerebrovascular disease, including stroke, while common variants in these genes are a risk factor for intracerebral haemorrhage in the general population. These phenotypes are associated with matrix defects, due to mutant protein incorporation in the BM and/or its absence by endoplasmic reticulum (ER) retention. However, the effects of these mutations on matrix stiffness, the contribution of the matrix to the disease mechanism(s) and its effects on the biology of cells harbouring a collagen IV mutation remain poorly understood. To shed light on this, we employed synthetic polymer biointerfaces, poly(ethyl acrylate) (PEA) and poly(methyl acrylate) (PMA) coated with ECM proteins laminin or fibronectin (FN), to generate controlled microenvironments and investigate their effects on the cellular phenotype of primary fibroblasts harbouring a COL4A2^+/G702D mutation. FN nanonetworks assembled on PEA induced increased deposition and assembly of collagen IV in COL4A2^+/G702D cells, which was associated with reduced ER size and enhanced levels of protein chaperones such as BIP, suggesting increased protein folding capacity of the cell. FN nanonetworks on PEA also partially rescued the reduced stiffness of the deposited matrix and cells, and enhanced cell adhesion through increased actin-myosin contractility, effectively rescuing some of the cellular phenotypes associated with COL4A1/4A2 mutations. The mechanism by which FN nanonetworks enhanced the cell phenotype involved integrin β₁-mediated signalling. Collectively, these results suggest that biomaterials and enhanced integrin signalling via assembled FN are able to shape the matrix and cellular phenotype of the COL4A2^+/G702D mutation in patient-derived cells.

Double power-law viscoelastic relaxation of living cells encodes motility trends

Living cells are constantly exchanging momentum with their surroundings. So far, there is no consensus regarding how cells respond to such external stimuli, although it reveals much about their internal structures, motility as well as the emergence of disorders. Here, we report that twelve cell lines, ranging from healthy fibroblasts to cancer cells, hold a ubiquitous double power-law viscoelastic relaxation compatible with the fractional Kelvin-Voigt viscoelastic model. Atomic Force Microscopy measurements in time domain were employed to determine the mechanical parameters, namely, the fast and slow relaxation exponents, the crossover timescale between power law regimes, and the cell stiffness. These cell-dependent quantities show strong correlation with their collective migration and invasiveness properties. Beyond that, the crossover timescale sets the fastest timescale for cells to perform their biological functions.

i-Rheo: determining the linear viscoelastic moduli of colloidal dispersions from step-stress measurements

We report on the application of a Fourier transform-based method, 'i-Rheo', to evaluate the linear viscoelastic moduli of hard-sphere colloidal dispersions, both in the fluid and glass states, from a direct analysis of raw step-stress (creep) experimental data. We corroborate the efficacy of i-Rheo by comparing the outputs of creep tests performed on homogenous complex fluids to conventional dynamic frequency sweeps. A similar approach is adopted for a number of colloidal suspensions over a broad range of volume fractions. For these systems, we test the limits of the method by varying the applied stress across the materials' linear and non-linear viscoelastic regimes, and we show that the best results are achieved for stress values close to the upper limit of the materials' linear viscoelastic regime, where the signal-to-noise ratio is at its highest and the non-linear phenomena have not appeared yet. We record that, the range of accessible frequencies is controlled at the higher end by the relative weight between the inertia of the instrument and the elasticity of the complex material under investigation; whereas, the lowest accessible frequency is dictated by the extent of the materials' linear viscoelastic regime. Nonetheless, despite these constrains, we confirm the effectiveness of i-Rheo for gaining valuable information on the materials' linear viscoelastic properties even from 'creep ringing' data, confirming its potency and general validity as an accurate method for determining the material's rheological behaviour for a variety of complex systems.

Probing Multidimensional Mechanical Phenotyping of Intracellular Structures by Viscoelastic Spectroscopy

Mechanical phenotyping of complex cellular structures gives insight into the process and function of mechanotransduction in biological systems. Several methods have been developed to characterize intracellular elastic moduli, while direct viscoelastic characterization of intracellular structures is still challenging. Here, we develop a needle tip viscoelastic spectroscopy method to probe multidimensional mechanical phenotyping of intracellular structures during a mini-invasive penetrating process. Viscoelastic spectroscopy is determined by magnetically driven resonant vibration (about 15 kHz) with a tiny amplitude. It not only detects the unique dynamic stiffness, damping, and loss tangent of the cell membrane-cytoskeleton and nucleus-nuclear lamina but also bridges viscoelastic parameters between the mitotic phase and interphase. Self-defined dynamic mechanical ratios of these two phases can identify two malignant cervical cancer cell lines (HeLa-HPV18+, SiHa-HPV16+) whose membrane or nucleus elastic moduli are indistinguishable. This technique provides a quantitative method for studying mechanosensation, mechanotransduction, and mechanoresponse of intracellular structures from a dynamic mechanical perspective. This technique has the potential to become a reliable quantitative measurement method for dynamic mechanical studies of intracellular structures.

A three dimensional model of multicellular aggregate compression

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

Model-Free Rheo-AFM Probes the Viscoelasticity of Tunable DNA Soft Colloids

Atomic force microscopy rheological measurements (Rheo-AFM) of the linear viscoelastic properties of single, charged colloids having a star-like architecture with a hard core and an extended, deformable double-stranded DNA (dsDNA) corona dispersed in aqueous saline solutions are reported. This is achieved by analyzing indentation and relaxation experiments performed on individual colloidal particles by means of a novel model-free Fourier transform method that allows a direct evaluation of the frequency-dependent linear viscoelastic moduli of the system under investigation. The method provides results that are consistent with those obtained via a conventional fitting procedure of the force-relaxation curves based on a modified Maxwell model. The outcomes show a pronounced softening of the dsDNA colloids, which is described by an exponential decay of both the Young's and the storage modulus as a function of the salt concentration within the dispersing medium. The strong softening is related to a critical reduction of the size of the dsDNA corona, down to ≈70% of its size in a salt-free solution. This can be correlated to significant topological changes of the dense star-like polyelectrolyte forming the corona, which are induced by variations in the density profile of the counterions. Similarly, a significant reduction of the stiffness is obtained by increasing the length of the dsDNA chains, which we attribute to a reduction of the DNA density in the outer region of the corona.