Measuring the viscoelastic creep of soft samples by step response AFM

PyFMLab: Open-source software for atomic force microscopy microrheology data analysis

Background

Atomic force microscopy (AFM) is one of the main techniques used to characterize the mechanical properties of soft biological samples and biomaterials at the nanoscale. Despite efforts made by the AFM community to promote open-source data analysis tools, standardization continues to be a significant concern in a field that requires common analysis procedures. AFM-based mechanical measurements involve applying a controlled force to the sample and measure the resulting deformation in the so-called force-distance curves. These may include simple approach and retract or oscillatory cycles at various frequencies (microrheology). To extract quantitative parameters, such as the elastic modulus, from these measurements, AFM measurements are processed using data analysis software. Although open tools exist and allow obtaining the mechanical properties of the sample, most of them only include standard elastic models and do not allow the processing of microrheology data. In this work, we have developed an open-source software package (called PyFMLab, as of python force microscopy laboratory) capable of determining the viscoelastic properties of samples from both conventional force-distance curves and microrheology measurements.

Methods

PyFMLab has been written in Python, which provides an accessible syntax and sufficient computational efficiency. The software features were divided into separate, self-contained libraries to enhance code organization and modularity and to improve readability, maintainability, testability, and reusability. To validate PyFMLab, two AFM datasets, one composed of simple force curves and another including oscillatory measurements, were collected on HeLa cells.

Results

The viscoelastic parameters obtained on the two datasets analysed using PyFMLab were validated against data processing proprietary software and against validated MATLAB routines developed before obtaining equivalent results.

Conclusions

Its open-source nature and versatility makes PyFMLab an open-source solution that paves the way for standardized viscoelastic characterization of biological samples from both force-distance curves and microrheology measurements.

Multiscale modeling of unfolding and bond dissociation of rubredoxin metalloprotein

Mechanical properties of proteins that have a crucial effect on their operation. This study used a molecular dynamics simulation package to investigate rubredoxin unfolding on the atomic scale. Different simulation techniques were applied, and due to the dissociation of covalent/hydrogen bonds, this protein demonstrates several intermediate states in force-extension behavior. A conceptual model based on the cohesive finite element method was developed to consider the intermediate damages that occur during unfolding. This model is based on force-displacement curves derived from molecular dynamics results. The proposed conceptual model is designed to accurately identify bond rupture points and determine the associated forces. This is achieved by conducting a thorough comparison between molecular dynamics and cohesive finite element results. The utilization of a viscoelastic cohesive zone model allows for the consideration of loading rate effects. This rate-dependent model can be further developed and integrated into the multiscale modeling of large assemblies of metalloproteins, providing a comprehensive understanding of mechanical behavior while maintaining a reduced computational cost.

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.

Xyloglucan deficiency leads to a reduction in turgor pressure and changes in cell wall properties, affecting early seedling establishment

Xyloglucan is believed to play a significant role in cell wall mechanics of dicot plants. Surprisingly, Arabidopsis plants defective in xyloglucan biosynthesis exhibit nearly normal growth and development. We investigated a mutant line, cslc-Δ5, lacking activity in all five Arabidopsis cellulose synthase like-C (CSLC) genes responsible for xyloglucan backbone biosynthesis. We observed that this xyloglucan-deficient line exhibited reduced cellulose crystallinity and increased pectin levels, suggesting the existence of feedback mechanisms that regulate wall composition to compensate for the absence of xyloglucan. These alterations in cell wall composition in the xyloglucan-absent plants were further linked to a decrease in cell wall elastic modulus and rupture stress, as observed through atomic force microscopy (AFM) and extensometer-based techniques. This raised questions about how plants with such modified cell wall properties can maintain normal growth. Our investigation revealed two key factors contributing to this phenomenon. First, measurements of turgor pressure, a primary driver of plant growth, revealed that cslc-Δ5 plants have reduced turgor, preventing the compromised walls from bursting while still allowing growth to occur. Second, we discovered the conservation of elastic asymmetry (ratio of axial to transverse wall elasticity) in the mutant, suggesting an additional mechanism contributing to the maintenance of normal growth. This novel feedback mechanism between cell wall composition and mechanical properties, coupled with turgor pressure regulation, plays a central role in the control of plant growth and is critical for seedling establishment in a mechanically challenging environment by affecting shoot emergence and root penetration.

Viscoelastically tunable substrates elucidate the interface-relaxation-dependent adhesion and assembly behaviors of epithelial cells

Recent progress in mechanobiology sheds light on the regulation of cellular phenotypes by dissipative property of matrices, i.e., viscosity, fluidity, and stress relaxation, in addition to extensively studied elasticity. However, most researches have focused on bulk mechanics, despite cells in 2D culture can only interact with matrix interface directly. Here, we studied the impact of interfacial viscosity as well as elasticity of substrates on the early stage of adhesion behaviors of epithelial cells through new material design and mechanical characterization. The materials are copolymers of ε-caprolactone and d,l-lactide photocrosslinked by benzophenone. The substrate viscoelasticity changes depending on the polymer molecular weight and irradiation time. The interfacial elasticity and relaxation were determined by atomic force microscopy with modes of nanoindentation and tip-dwelling, respectively. MDCK cells changed morphologically, ranging from loose beaded assembly to more compact spheroids and eventual spread monolayer clusters, in response to the interfacial viscoelasticity change. Such morphological changes were mainly determined by substrate interfacial relaxation, rather than interfacial elasticity. Single-cell tracking identified biphasic motility with the minimum speed at intermediate relaxation time (~350 ms), where cells showed transitional morphologies between epithelial and mesenchymal traits. In that relaxation level, partially deformed cells moved around to coalesce with surrounding cells, eventually assembling into compact cellular aggregates. These results highlight, unlike the conventional hanging-drop technique, an appropriate level of interfacial relaxation is critical for efficient cell aggregate maturation on adhesive viscoelastic matrices. This work not only elucidates that the interfacial relaxation as the essential mechanical parameter for epithelial cell adhesion and migration, but also gives useful tips for creating physiologically relevant drug screening platform.

Mechanical Characterization for Cellular Mechanobiology: Current Trends and Future Prospects

Accurate mechanical characterization of adherent cells and their substrates is important for understanding the influence of mechanical properties on cells themselves. Recent mechanobiology studies outline the importance of mechanical parameters, such as stress relaxation and strain stiffening on the behavior of cells. Numerous techniques exist for probing mechanical properties and it is vital to understand the benefits of each technique and how they relate to each other. This mini review aims to guide the reader through the toolbox of mechanical characterization techniques by presenting well-established and emerging methods currently used to assess mechanical properties of substrates and cells.

Recent advances in AFM-based biological characterization and applications at multiple levels

Atomic force microscopy (AFM) has found a wide range of bio-applications in the past few decades due to its ability to measure biological samples in natural environments at a high spatial resolution. AFM has become a key platform in biomedical, bioengineering and drug research fields, enabling mechanical and morphological characterization of live biological systems. Hence, we provide a comprehensive review on recent advances in the use of AFM for characterizing the biomechanical properties of multi-scale biological samples, ranging from molecule, cell to tissue levels. First, we present the fundamental principles of AFM and two AFM-based models for the characterization of biomechanical properties of biological samples, covering key AFM devices and AFM bioimaging as well as theoretical models for characterizing the elasticity and viscosity of biomaterials. Then, we elaborate on a series of new experimental findings through analysis of biomechanics. Finally, we discuss the future directions and challenges. It is envisioned that the AFM technique will enable many remarkable discoveries, and will have far-reaching impacts on bio-related studies and applications in the future.

Rac1 Promotes Cell Motility by Controlling Cell Mechanics in Human Glioblastoma

The failure of existing therapies in treating human glioblastoma (GBM) mostly is due to the ability of GBM to infiltrate into healthy regions of the brain; however, the relationship between cell motility and cell mechanics is not well understood. Here, we used atomic force microscopy (AFM), live-cell imaging, and biochemical tools to study the connection between motility and mechanics in human GBM cells. It was found thatRac1 inactivation by genomic silencing and inhibition with EHT 1864 reduced cell motility, inhibited cell ruffles, and disrupted the dynamics of cytoskeleton organization and cell adhesion. These changes were correlated with abnormal localization of myosin IIa and a rapid suppression of the phosphorylation of Erk1/2. At the same time, AFM measurements of the GBM cells revealed a significant increase in cell elasticity and viscosity following Rac1 inhibition. These results indicate that mechanical properties profoundly affect cell motility and may play an important role in the infiltration of GBM. It is conceivable that the mechanical characters might be used as markers for further surgical and therapeutical interventions.

Measuring viscoelasticity of soft biological samples using atomic force microscopy

Mechanical properties play important roles at different scales in biology. At the level of a single cell, the mechanical properties mediate mechanosensing and mechanotransduction, while at the tissue and organ levels, changes in mechanical properties are closely connected to disease and physiological processes. Over the past three decades, atomic force microscopy (AFM) has become one of the most widely used tools in the mechanical characterization of soft samples, ranging from molecules, cell organoids and cells to whole tissue. AFM methods can be used to quantify both elastic and viscoelastic properties, and significant recent developments in the latter have been enabled by the introduction of new techniques and models for data analysis. Here, we review AFM techniques developed in recent years for examining the viscoelastic properties of cells and soft gels, describe the main steps in typical data acquisition and analysis protocols, and discuss relevant viscoelastic models and how these have been used to characterize the specific features of cellular and other biological samples. We also discuss recent trends and potential directions for this field.

Load-dependent surface nanomechanical properties of poly-HEMA hydrogels in aqueous medium

The mechanical properties of hydrogels are of importance in many applications, including scaffolds and drug delivery vehicles where the release of drugs is controlled by water transport. While the macroscopic mechanical properties of hydrogels have been reported frequently, there are less studies devoted to the equally important nanomechanical response to local load and shear. Scanning probe methods offer the possibility to gain insight on surface nanomechanical properties with high spatial resolution, and thereby provide fundamental insights on local material property variations. In this work, we investigate the local response to load and shear of poly(2-hydroxyethyl methacrylate) hydrogels with two different cross-linking densities submerged in aqueous solution. The response of the hydrogels to purely normal loads, as well as the combined action of load and shear, was found to be complex due to viscoelastic effects. Our results show that the surface stiffness of the hydrogel samples increased with increasing load, while the tip-hydrogel adhesion was strongly affected by the load only when the cross-linking density was low. The combined action of load and shear results in the formation of a temporary sub-micrometer hill in front of the laterally moving tip. As the tip pushes against such hills, a pronounced stick-slip effect is observed for the hydrogel with low cross-linking density. No plastic deformation or permanent wear scar was found under our experimental conditions.

The Effect of Cortical Elasticity and Active Tension on Cell Adhesion Mechanics

We consider a cell as an elastic, contractile shell surrounding a liquid incompressible cytoplasm and with nonspecific adhesion. We perform numerical simulations of this model to study the mechanics of cell-cell separation. By variation of parameters, we are able to recover well-known limits of the Johnson-Kendall-Roberts theory, the Derjaguin-Muller-Toporov model, adhesive vesicles with surface tension (Brochard-Wyart and de Gennes derivation), and thin elastic shells. We further locate biological cells on this parameter space by comparison to existing experiments on S180 cells. Using this model, we show that mechanical parameters can be obtained that are consistent with both dual pipette aspiration and micropipette aspiration, a problem not successfully tackled so far. We estimate a cortex elastic modulus of E_c ≈ 15 kPa, an effective cortex thickness of t_c ≈ 0.3 μm, and an active tension of γ ≈ 0.4 nN/μm. With these parameters, a Johnson-Kendall-Roberts-like scaling of the separation force is recovered. Finally, the change of contact radius with applied force in a pull-off experiment was investigated. For small forces, a scaling similar to both the Brochard-Wyart and de Gennes derivation and the Derjaguin-Muller-Toporov model is found.

Probing cellular mechanics with acoustic force spectroscopy

A large number of studies demonstrate that cell mechanics and pathology are intimately linked. In particular, deformability of red blood cells (RBCs) is key to their function and is dramatically altered in the time course of diseases such as anemia and malaria. Due to the physiological importance of cell mechanics, many methods for cell mechanical probing have been developed. While single-cell methods provide very valuable information, they are often technically challenging and lack the high data throughput needed to distinguish differences in heterogeneous populations, while fluid-flow high-throughput methods miss the accuracy to detect subtle differences. Here we present a new method for multiplexed single-cell mechanical probing using acoustic force spectroscopy (AFS). We demonstrate that mechanical differences induced by chemical treatments of known effect can be measured and quantified. Furthermore, we explore the effect of extracellular vesicles (EVs) uptake on RBC mechanics and demonstrate that EVs uptake increases RBC deformability. Our findings demonstrate the ability of AFS to manipulate cells with high stability and precision and pave the way to further new insights into cellular mechanics and mechanobiology in health and disease, as well as potential biomedical applications.

Mechanical and migratory properties of normal, scar, and Dupuytren's fibroblasts

Mechanical properties of myofibroblasts play a key role in Dupuytren's disease. Here, we used atomic force microscopy to measure the viscoelastic properties of 3 different types of human primary fibroblasts derived from a same patient: normal and scar dermal fibroblasts and palmar fascial fibroblasts from Dupuytren's nodules. Different stiffness hydrogels (soft ~1 kPa and stiff ~ 50 kPa) were used as cell culture matrix to mimic the mechanical properties of the natural tissues, and atomic force microscopy step response force curves were used to discriminate between elastic and viscous properties of cells. Since transforming growth factor-β1 (TGF-β1) is known to induce expression of α-smooth muscle actin positive stress fibers in myofibroblasts, we investigated the behavior of these fibroblasts before and after applying TGF-β1. Finally, we performed an in vitro cell motility test, the wound healing or scratch assay, to evaluate the migratory properties of these fibroblasts. We found that (1) Dupuytren's fibroblasts are stiffer than normal and scar fibroblasts, the elastic modulus E ranging from 4.4, 2.1, to 1.8 kPa, for Dupuytren's, normal and scar fibroblasts, respectively; (2) TGF-β1 enhances the level of α-smooth muscle actin expression and thus cell stiffness in Dupuytren's fibroblasts (E, ~6.2 kPa); (3) matrix stiffness influences cell mechanical properties most prominently in Dupuytren's fibroblasts; and (4) Dupuytren's fibroblasts migrate slower than the other fibroblasts by a factor of 3. Taking together, our results showed that mechanical and migratory properties of fibroblasts might help to discriminate between different pathological conditions, helping to identify and recognize specific cell phenotypes.

3D depth profiling of the interaction between an AFM tip and fluid polymer solutions

In the atomic force microscopy (AFM) investigation of soft polymers and liquids, the tip-sample interaction is dominated by long-range van der Waals forces, capillary forces and adhesion. Furthermore, the tip can indent several tens of nanometres into the surface, and it can pull off a polymer filament from the surface. Therefore, measuring the unperturbed shape of a polymeric fluid can be challenging. Here, we study the tip-sample interaction with polystyrene droplets swollen in chloroform vapour, where we can utilize the solvent vapour concentration to adjust the specimen's mechanical properties from a stiff solid to a fluid film. With the same AFM tip, we use two different AFM force spectroscopy methods to measure three-dimensional (3D) depth profiles of the tip-sample interaction: force-distance (FD) curves and amplitude-phase-distance (APD) curves. The 3D depth profiles reconstructed from FD and APD measurements provide detailed insight into the tip-sample interaction mechanism for a fluid polymer solution. The fluid's intrinsic relaxation time, which we measure with an AFM-based step-strain experiment, is essential for understanding the tip-sample interaction mechanism. Furthermore, measuring 3D depth profiles and using APD data to reconstruct the unperturbed surface comprise a versatile methodology for obtaining accurate dimensional measurements of fluid and gel-like objects on the nanometre scale.

Combining adhesive contact mechanics with a viscoelastic material model to probe local material properties by AFM

Viscoelastic properties are often measured using probe based techniques such as nanoindentation (NI) and atomic force microscopy (AFM). Rarely, however, are these methods verified. In this article, we present a method that combines contact mechanics with a viscoelastic model (VEM) composed of springs and dashpots. We further show how to use this model to determine viscoelastic properties from creep curves recorded by a probe based technique. We focus on using the standard linear solid model and the generalized Maxwell model of order 2. The method operates in the range of 0.01 Hz to 1 Hz. Our approach is suitable for rough surfaces by providing a defined contact area using plastic pre-deformation of the material. The very same procedure is used to evaluate AFM based measurements as well as NI measurements performed on polymer samples made from poly(methyl methacrylate) and polycarbonate. The results of these measurements are then compared to those obtained by tensile creep tests also performed on the same samples. It is found that the tensile test results differ considerably from the results obtained by AFM and NI methods. The similarity between the AFM results and NI results suggests that the proposed method is capable of yielding results comparable to NI but with the advantage of the imaging possibilities of AFM. Furthermore, all three methods allowed a clear distinction between PC and PMMA by means of their respective viscoelastic properties.

Atomic Force Microscopy in Characterizing Cell Mechanics for Biomedical Applications: A Review

Cell mechanics is a novel label-free biomarker for indicating cell states and pathological changes. The advent of atomic force microscopy (AFM) provides a powerful tool for quantifying the mechanical properties of single living cells in aqueous conditions. The wide use of AFM in characterizing cell mechanics in the past two decades has yielded remarkable novel insights in understanding the development and progression of certain diseases, such as cancer, showing the huge potential of cell mechanics for practical applications in the field of biomedicine. In this paper, we reviewed the utilization of AFM to characterize cell mechanics. First, the principle and method of AFM single-cell mechanical analysis was presented, along with the mechanical responses of cells to representative external stimuli measured by AFM. Next, the unique changes of cell mechanics in two types of physiological processes (stem cell differentiation, cancer metastasis) revealed by AFM were summarized. After that, the molecular mechanisms guiding cell mechanics were analyzed. Finally the challenges and future directions were discussed.

Dynamical Modeling and Analysis of Viscoelastic Properties of Single Cells

A single cell can be regarded as a complex network that contains thousands of overlapping signaling pathways. The traditional methods for describing the dynamics of this network are extremely complicated. The mechanical properties of a cell reflect the cytoskeletal structure and composition and are closely related to the cellular biological functions and physiological activities. Therefore, modeling the mechanical properties of single cells provides the basis for analyzing and controlling the cellular state. In this study, we developed a dynamical model with cellular viscoelasticity properties as the system parameters to describe the stress-relaxation phenomenon of a single cell indented by an atomic force microscope (AFM). The system order and parameters were identified and analyzed. Our results demonstrated that the parameters identified using this model represent the cellular mechanical elasticity and viscosity and can be used to classify cell types.