Atomic Force Microscopy Nanoindentation Experiments Research Articles

The average Young's modulus as a physical quantity for describing the depth-dependent mechanical properties of cells

Hertzian mechanics is a useful theoretical tool for data processing regarding Atomic Force Microscopy (AFM) nanoindentation experiments on cells and other biological samples. A common approach that is usually followed in the literature is to fit the experimentally obtained data to the equations provided by Hertzian analysis. However, there are many different approaches regarding the selection of the maximum indentation depth even for the same biological sample and many of them depend on the experience of the AFM-user. In addition, the results as provided by different research groups on the same sample (e.g. the same cell type) usually vary significantly. Thus, it is crucial to develop novel user-independent methods for assessing the mechanical properties of cells. In this paper a new approach, based on the work done by the indenter, is proposed for data processing. At first, a hypothetical nanoindentation experiment on an elastic half space is assumed in which the maximum indentation depth and the work done by the indenter are equal to the actual experiment. The Young's modulus of the hypothetical ideal material is the actual sample's average Young's modulus. In addition, the function of the average Young's modulus with respect to the indentation depth is introduced to reveal the depth dependent mechanical properties of biological samples. Secondly, the proposed methodology was applied on experimental data from fibroblasts and H4, A172 human glioma cells. The results showed a ‘softening’ of cells as the indentation depth increases. However, for big indentation depths the average Young's modulus always reaches an asymptotic value (the overall average Young's modulus). Thus, the overall average Young's modulus can be used for comparing the results of AFM nanoindentation experiments on cells between different research groups. In addition, the average Young's modulus function can also reveal the maximum value of the indentation depth that should not be surpassed in order to avoid a substrate effect. The analysis proposed by this paper can be applied to any biological sample using conical or spherical indenters. The great advantage of the proposed by this paper technique is that it does not require a linear elastic response of the sample, thus it is appropriate for the mechanical nano-characterization of highly heterogeneous biological materials.

Molecular deformation mechanism of polycarbonate during nano-indentation: Molecular dynamics simulation and experimentation

Atomic force microscopy (AFM) enables us to evaluate the physical properties of the surface of materials on a nanoscale. Using a coarse-grained molecular dynamics (CG-MD) simulation, this study investigated the molecular deformation mechanisms of polycarbonate (PC) during AFM nano-indentation experiments. By using the coarse-grained (CG) force field of PC, the nano-indentation deformation behavior of PC was simulated. During this process, the AFM tip is used to penetrate the polymer surface and then withdrawn completely; the PC then undergoes local elastoplastic deformation. To investigate the deformation mechanism at a molecular scale, we quantitatively evaluated the variations in the potential energy associated with different molecular deformation modes, such as bond stretching, bending, and torsion. It was found that the bending mode of the molecular chain plays a critical role in the onset of yielding. Furthermore, the spatial variations of the potential energy were investigated. They indicate that the variation of the potential energy of the bending mode is significant when undergoing nano-indentation. The CG-MD simulation results were then compared with the experimental results. They indicate that our computation accurately reproduces the experimental indentation force–displacement curves. Therefore, the present CG-MD simulation can successfully model experimental AFM nano-indentation. This may be useful for the discussion of the molecular deformation mechanisms of PC and related polymer materials.

Effect of cell sample size in atomic force microscopy nanoindentation

Single-cell technologies are powerful tools to evaluate cell characteristics. In particular, Atomic Force Microscopy (AFM) nanoindentation experiments have been widely used to study single cell mechanical properties. One important aspect related to single cell techniques is the need for sufficient statistical power to obtain reliable results. This aspect is often overlooked in AFM experiments were sample sizes are arbitrarily set.The aim of the present work was to propose a tool for sample size estimation in the context of AFM nanoindentation experiments of single cell. To this aim, a retrospective approach was used by acquiring a large dataset of experimental measurements on four bone cell types and by building saturation curves for increasing sample sizes with a bootstrap resampling method.It was observed that the coefficient of variation (CV%) decayed with a function of the form y = axb with similar parameters for all samples tested and that sample sizes of 21 and 83 cells were needed for the specific cells and protocol employed if setting a maximum threshold on CV% of 10% or 5%, respectively. The developed tool is made available as an open-source repository and guidelines are provided for its use for AFM nanoindentation experimental design.

Programmable microscale stiffness pattern of flat polymeric substrates by temperature-memory technology

Temperature-memory technology was utilized to generate flat substrates with a programmable stiffness pattern from cross-linked poly(eth-ylene-co-vinyl acetate) substrates with cylindrical microstructures. Programmed substrates were obtained by vertical compression at temperatures in the range from 60 to 100 °C and subsequent cooling, whereby aflat substrate was achieved by compression at 72 °C, as documented by scanning electron microscopy and atomic force microscopy (AFM). AFM nanoindentation experiments revealed that all programmed substrates exhibited the targeted stiffness pattern. The presented technology for generating polymeric substrates with programmable stiffness pattern should be attractive for applications such as touchpads, optical storage, or cell instructive substrates.

A discussion regarding the approximation of cylindrical and spherical shaped samples as half spaces in AFM nanoindentation experiments

A common assumption of nanoidentation experiments is to consider the sample as an elastic half space due to the simplicity of the analysis regarding the Young’s modulus calculation. However, in the nano—dimensions a sample cannot be considered as a half space and this approximation can lead to significant errors in the analysis. In this paper, the Atomic Force Microscopy (AFM) nanoindentation method on cylindrical and spherical shaped samples is discussed. The purpose of this paper is to investigate the errors that arise under the assumption that a cylindrical/spherical shaped sample is a half space and to provide a simplified methodology to reduce these errors. The new approach can be applied to AFM nanoindentation experiments on cylindrical or spherical biological samples (e.g. collagen fibers and cells).

Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles

The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams) modeling the particle structure. The beams’ deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F)-deformation (X) spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young’s moduli for Hertzian and bending deformations, and the structural damage dependent beams’ survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications.

The role of CD4 on mechanical properties of live cell membrane.

Although much progress has been made in the characterization and identification of CD4 functions, its role in mechanical properties of cell membrane remains largely unknown. Here an atomic force microscopy (AFM) was used to investigate the roles of CD4 in the elasticity of the leukemic human Jurkat (clone E6-1) cell membranes. Analysis of the approach force curves with Hertz model for a completely elastic soft sample measured on the selected CD4+ and CD4- cells showed that CD4+ cell membrane was softer than CD4- one. To confirm that CD4 plays a role in altering cell elasticity, human embryonic kidney 293T cells were transiently transfected with wild type (wt) CD4 plasmid before being used in AFM nanoindentation experiments. The results also demonstrated CD4- membrane was stiffer than CD4+ one suggesting that CD4 integrated into plasma membrane and altered its mechanical properties. The study gives insights into the role of CD4 on cell membrane mechanical characteristics and might be helpful for development of cell biology and medicine.

INFLUENCE OF SPECIFIC THERMAL TREATMENT ON YOUNG'S MODULUS CHANGES IN A NATURAL RUBBER–BASED COMPOUND: STUDY BY AFM NANOINDENTATION

ABSTRACT The determination and study of Young's modulus at the nanometric scale in an efficient and fast way is carried out using atomic force microscopy (AFM) in contact mode. The aim of this study is to evaluate the impact of a specific thermal treatment on Young's modulus changes from the surface toward the bulk of a cured natural rubber (NR)–based compound. The AFM nanoindentation experiments were conducted on a cross-linked NR sample. Following a depth profiling analysis method, AFM deflection distance curves were measured every 40 μm from the oxygen-exposed surface toward the bulk, and then the Hertz's model was applied to force-indentation curves for the calculation of the Young's modulus. Investigations on the thermal-treated samples revealed an overall increase of the Young's modulus along the samples after heating. Moreover, a decrease of Young's modulus values from the surface exposed to oxygen during heating toward the bulk was observed, indicating a stiffening of the sample at the surface.

MRI-based morphological modeling, synthesis and characterization of cardiac tissue-mimicking materials

This study uses standard synthetic methodologies to produce tissue-mimicking materials that match the morphology and emulate the in vivo murine and human cardiac mechanical and imaging characteristics, with dynamic mechanical analysis, atomic force microscopy (AFM), scanning electron microscopy (SEM) and magnetic resonance imaging. In accordance with such aims, poly(glycerol sebacate) (PGS) elastomeric materials were synthesized (at two different glycerol (G)–sebacic (S) acid molar ratios; the first was synthesized using a G:S molar ratio of 2:2, while the second from a 2:5 G:S molar ratio, resulting in PGS2:2 and PGS2:5 elastomers, respectively). Unlike the synthesized PGS2:2 elastomers, the PGS2:5 materials were characterized by an overall mechanical instability in their loading behavior under the three successive loading conditions tested. An oscillatory response in the mechanical properties of the synthesized elastomers was observed throughout the loading cycles, with measured increased storage modulus values at the first loading cycle, stabilizing to lower values at subsequent cycles. These elastomers were characterized at 4 °C and were found to have storage modulus values of 850 and 1430 kPa at the third loading cycle, respectively, in agreement with previously reported values of the rat and human myocardium. SEM of surface topology indicated minor degradation of synthesized materials at 10 and 20 d post-immersion in the PBS buffer solution, with a noted cluster formation on the PGS2:5 elastomers. AFM nanoindentation experiments were also conducted for the measurement of the Young modulus of the sample surface (no bulk contribution). Correspondingly, the PGS2:2 elastomer indicated significantly decreased surface Young's modulus values 20 d post-PBS immersion, compared to dry conditions (Young's modulus = 1160 ± 290 kPa (dry) and 200 ± 120 kPa (20 d)). In addition to the two-dimensional (2D) elastomers, an integrative platform for accurate construction of three-dimensional tissue-mimicking models of cardiac anatomy from 2D MR images using rapid prototyping manufacturing processes was developed. For synthesized elastomers, doping strategies with two different concentrations of the MRI contrast agent Dotarem allowed independent and concurrent control of the imaging characteristics (contrast and relaxivity) during the synthetic process for increased contrast agent absorption, with tremendous potential for non-destructive in vivo use and applications to cardiovascular and cerebrovascular diseases.

Viral Capsid Equilibrium Dynamics Reveals Nonuniform Elastic Properties

The long wavelength, low-frequency modes of motion are the relevant motions for understanding the continuum mechanical properties of biomolecules. By examining these low-frequency modes, in the context of a spherical harmonic basis set, we identify four elastic moduli that are required to describe the two-dimensional elastic behavior of capsids. This is in contrast to previous modeling and theoretical studies on elastic shells, which use only the two-dimensional Young's modulus (Y) and the bending modulus (κ) to describe the system. Presumably, the heterogeneity of the structure and the anisotropy of the biomolecular interactions lead to a deviation from the homogeneous, isotropic, linear elastic shell theory. We assign functional relevance of the various moduli governing different deformation modes, including a mode primarily sensed in atomic force microscopy nanoindentation experiments. We have performed our analysis on the T = 3 cowpea chlorotic mottle virus and our estimate for the nanoindentation modulus is in accord with experimental measurements.

Elucidating the Mechanism behind Irreversible Deformation of Viral Capsids

Atomic force microscopy has recently provided highly precise measurements of mechanical properties of various viruses. However, molecular details underlying viral mechanics remain unresolved. Here we report atomic force microscopy nanoindentation experiments on T=4 hepatitis B virus (HBV) capsids combined with coarse-grained molecular dynamics simulations, which permit interpretation of experimental results at the molecular level. The force response of the indented capsid recorded in simulations agrees with experimental observations. In both experiment and simulation, irreversible capsid deformation is observed for deep indentations. Simulations show the irreversibility to be due to local bending and shifting of capsid proteins, rather than their global rearrangement. These results emphasize the viability of large capsid deformations without significant changes of the mutual positions of HBV capsid proteins, in contrast to the stiffer capsids of other viruses, which exhibit more extensive contacts between their capsid proteins than seen in the case of HBV.

Coarse-grained Simulations and AFM Nanoindentation Experiments on a Hepatitis B Virus Capsid

Mechanical properties of viral capsids are key to the replication cycle of viruses, since a capsid should be stable to protect the virus from the hostile environment outside of host cells, but also needs to disassemble or otherwise release the viral genome during the infection process. Relatively little is known about mechanics of capsids and the underlying molecular mechanisms, however, valuable information is coming from capsid nanoindentation studies employing atomic force microscopy (AFM). The latter provides the force response, in particular, its dependence on the depth of indentation. Details of the corresponding capsid deformation have been studied in recent years through finite-element simulations employing continuous elastic material models. Despite interesting insights, this approach has been limited, since molecular details are not resolved and irreversible structural transitions could not be simulated. On the other hand, detailed atomistic simulations could not handle this problem either, due to the large size of the system and the long time scales involved. We have developed and tested a new shape-based coarse-grained molecular dynamics model that permits us to simulate AFM nanoindentation experiments. We applied the method to the hepatitis B virus capsid. The simulations resolved shapes of individual protein units and allowed us to reach time scales of tens of microseconds. The force response simulated is found in quantitative agreement with experiments. Irreversible deformation (failure) of capsids is observed in repeated rounds of nanoindentation, also in agreement with experiment. The simulations explain observed features of the experimental force-indentation curve, showing which molecular-level events are responsible for specific force responses, and suggesting how the capsid is deformed in the cases of reversible and irreversible indentation.