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Measurement of force on a micro- or nano-Newton scale is important when exploring the mechanical properties of materials in the biophysics and nanomechanical fields. The atomic force microscope (AFM) is widely used in microforce measurement. The cantilever probe works as an AFM force sensor, and the spring constant of the cantilever is of great significance to the accuracy of the measurement results. This paper presents a normal spring constant calibration method with the combined use of an electromagnetic balance and a homemade AFM head. When the cantilever presses the balance, its deflection is detected through an optical lever integrated in the AFM head. Meanwhile, the corresponding bending force is recorded by the balance. Then the spring constant can be simply calculated using Hooke’s law. During the calibration, a feedback loop is applied to control the deflection of the cantilever. Errors that may affect the stability of the cantilever could be compensated rapidly. Five types of commercial cantilevers with different shapes, stiffness, and operating modes were chosen to evaluate the performance of our system. Based on the uncertainty analysis, the expanded relative standard uncertainties of the normal spring constant of most measured cantilevers are believed to be better than 2%.

Dynamic operation modes of scanning force microscopy based on probe resonance frequency detection are very successful methods to study force-related properties of surfaces with high spatial resolution. There are well-recognized approaches to measure vertical force components as well as setups sensitive to lateral force components. Here, we report on a concept of bidirectional force gradient microscopy that enables a direct, fast, and quantitative real space mapping of force component derivatives in both the perpendicular and a lateral direction. It relies solely on multiple-mode flexural cantilever oscillations related to vertical probe excitation and vertical deflection sensing. Exploring this concept we present a cantilever-based sensor setup and corresponding quantitative measurements employing magnetostatic interactions with emphasis on the calculation of mode-dependent spring constants that are the foundation of quantitative force gradient studies.

In this paper, the effect of Magneto Hydro-Dynamics (MHD) on a polymer chain in the micro channel is studied by employing the Dissipative Particle Dynamics simulation (DPD) method. First, in a simple symmetric micro-channel, the results are evaluated and validated for different values of Hartmann (Ha) Number. The difference between the simulation and analytical solution is below 10%. Then, two types of polymer chain including short and long polymer chain are examined in the channel and the effective parameters such as Ha number, the harmony bond coefficient or spring constant (K), and the length of the polymer chain (N) are studied in the MHD flow. It is shown that by increasing harmony bond constant to 10 times with Ha = 20, the reduction of about 80% in radius of gyration squared, and half in polymer length compared to Ha = 1 would occur for both test cases. For short and long length of polymer, proper transfer of a polymer chain through MHD particles flow is observed with less perturbations (80%) and faster polymer transfer in the symmetric micro-channel.

PIEZO1 is a mechanosensitive channel that converts applied force into electrical signals. Partial molecular structures show that PIEZO1 is a bowl-shaped trimer with extended arms. Here we use cryo-electron microscopy to show that PIEZO1 adopts different degrees of curvature in lipid vesicles of different sizes. We also use high-speed atomic force microscopy to analyse the deformability of PIEZO1 under force in membranes on a mica surface, and show that PIEZO1 can be flattened reversibly into the membrane plane. By approximating the absolute force applied, we estimate a range of values for the mechanical spring constant of PIEZO1. Both methods of microscopy demonstrate that PIEZO1 can deform its shape towards a planar structure. This deformation could explain how lateral membrane tension can be converted into a conformation-dependent change in free energy to gate the PIEZO1 channel in response to mechanical perturbations. Cryo-electron microscopy and high-speed atomic force microscopy reveal that PIEZO1 can reversibly deform its shape towards a planar structure, which may explain how the PIEZO1 channel is gated in response to mechanical stimulation.

The article analyzes a pile frame composed of two bored piles with a diameter of 40 cm. The frame is subjected to a horizontal force. Calculations in three different method are conducted – subgrade reaction approach, 2D plaxis and 3D plaxis, after which a comparison was made between the results of the individual methods. The aim is to see under what conditions a subgrade reaction method is suitable for use without moving away from sure side. Results were also obtained for the distribution of the value of the spring constant by depth, as well as values for the ratio between the resistance of the second and first pile. A proposal has been made for obtaining a p-curve that can be applied to any of the linear approximation methods.

Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator’s material properties has remained elusive. Here we show a method for determining the Young’s modulus of suspended 2D material membranes from their nonlinear dynamic response. To demonstrate the method, we perform measurements on graphene and MoS 2 nanodrums electrostatically driven into the nonlinear regime at multiple driving forces. We show that a set of frequency response curves can be fitted using only the cubic spring constant as a fit parameter, which we then relate to the Young’s modulus of the material using membrane theory. The presented method is fast, contactless, and provides a platform for high-frequency characterization of the mechanical properties of 2D materials. The mechanical resonances of atomically thin membranes show nonlinear responses at driving forces in the picoNewton range. Here, the authors develop a contactless method to extract the Young’s modulus of 2D materials from the nonlinear dynamic response of these nanomechanical resonators.

Simulating chromatin is crucial for predicting genome organization and dynamics. Although coarse-grained bead-spring polymer models are commonly used to describe chromatin, the relevant bead dimensions, elastic properties, and the nature of inter-bead potentials are unknown. Using nucleosome-resolution contact probability (Micro-C) data, we systematically coarse-grain chromatin and predict quantities essential for polymer representation of chromatin. We compute size distributions of chromatin beads for different coarse-graining scales, quantify fluctuations and distributions of bond lengths between neighboring regions, and derive effective spring constant values. Unlike the prevalent notion, our findings argue that coarse-grained chromatin beads must be considered as soft particles that can overlap, and we derive an effective inter-bead soft potential and quantify an overlap parameter. We also compute angle distributions giving insights into intrinsic folding and local bendability of chromatin. While the nucleosome-linker DNA bond angle naturally emerges from our work, we show two populations of local structural states. The bead sizes, bond lengths, and bond angles show different mean behavior at Topologically Associating Domain (TAD) boundaries and TAD interiors. We integrate our findings into a coarse-grained polymer model and provide quantitative estimates of all model parameters, which can serve as a foundational basis for all future coarse-grained chromatin simulations. Here the authors provide a quantitative description of chromatin as bead-spring polymers. The study predicts the 3D size of chromatin beads given the genomic length and computes how stretchable and bendable chromatin is and how soft chromatin beads are.

The spatial resolution of atomic force microscopy (AFM) can be drastically increased by terminating the tip with a single carbon monoxide (CO) molecule. However, the CO molecule is not stiff, and lateral forces, such as those around the sides of molecules, distort images. This issue begs a larger question of how AFM can probe structures that are laterally weak. Lateral force microscopy (LFM) can probe lateral stiffnesses that are not accessible to normal-force AFM, resulting in higher spatial resolution. With LFM, we determined the torsional spring constant of a CO-terminated tip molecule to be 0.24 newtons per meter. This value is less than that of a surface molecule and an example of a system whose stiffness is a product not only of bonding partners but also local environment.

Cell migration plays a major role in many fundamental biological processes, such as morphogenesis, tumor metastasis, and wound healing. As they anchor and pull on their surroundings, adhering cells actively probe the stiffness of their environment. Current understanding is that traction forces exerted by cells arise mainly at mechanotransduction sites, called focal adhesions, whose size seems to be correlated to the force exerted by cells on their underlying substrate, at least during their initial stages. In fact, our data show by direct measurements that the buildup of traction forces is faster for larger substrate stiffness, and that the stress measured at adhesion sites depends on substrate rigidity. Our results, backed by a phenomenological model based on active gel theory, suggest that rigidity-sensing is mediated by a large-scale mechanism originating in the cytoskeleton instead of a local one. We show that large-scale mechanosensing leads to an adaptative response of cell migration to stiffness gradients. In response to a step boundary in rigidity, we observe not only that cells migrate preferentially toward stiffer substrates, but also that this response is optimal in a narrow range of rigidities. Taken together, these findings lead to unique insights into the regulation of cell response to external mechanical cues and provide evidence for a cytoskeleton-based rigidity-sensing mechanism.