Unbiased retrieval of frequency-dependent mechanical properties from noisy time-dependent signals

The mechanical response of materials to dynamic loading is often quantified by the frequency-dependent complex modulus. Probing materials directly in the frequency domain faces technical challenges such as a limited range of frequencies, long measurement times, or small sample sizes. Furthermore, many biological samples, such as cells or tissues, can change their properties upon repetitive probing at different frequencies. Therefore, it is common practice to extract the material properties by fitting predefined mechanical models to measurements performed in the time domain. This practice, however, precludes the probing of unique and yet unexplored material properties. In this report, we demonstrate that the frequency-dependent complex modulus can be robustly retrieved in a model-independent manner directly from time-dependent stress-strain measurements. While applying a rolling average eliminates random noise and leads to a reliable complex modulus in the lower frequency range, a Fourier transform with a complex frequency helps to recover the material properties at high frequencies. Finally, by properly designing the probing procedure, the recovery of reliable mechanical properties can be extended to an even wider frequency range. Our approach can be used with many state-of-the-art experimental methods to interrogate the mechanical properties of biological and other complex materials

An explicit model to extract viscoelastic properties of cells from AFM force-indentation curves

Atomic force microscopy (AFM) is widely used for quantifying the mechanical properties of soft materials such as cells. AFM force-indentation curves are conventionally fitted with a Hertzian model to extract elastic properties. These properties solely are, however, insufficient to describe the mechanical properties of cells. Here, we expand the analysis capabilities to describe the viscoelastic behavior while using the same force-indentation curves. Our model gives an explicit relation of force and indentation and extracts physically meaningful mechanical parameters. We first validated the model on simulated force-indentation curves. Then, we applied the fitting model to the force-indentation curves of two hydrogels with different crosslinking mechanisms. Finally, we characterized HeLa cells in two cell cycle phases, interphase and mitosis, and showed that mitotic cells have a higher apparent elasticity and a lower apparent viscosity. Our study provides a simple method, which can be directly integrated into the standard AFM framework for extracting the viscoelastic properties of materials

nanite: using machine learning to assess the quality of atomic force microscopy-enabled nano-indentation data

Atomic force microscopy (AFM) allows the mechanical characterization of single cells and live tissue by quantifying force-distance (FD) data in nano-indentation experiments. One of the main problems when dealing with biological tissue is the fact that the measured FD curves can be disturbed. These disturbances are caused, for instance, by passive cell movement, adhesive forces between the AFM probe and the cell, or insufficient attachment of the tissue to the supporting cover slide. In practice, the resulting artifacts are easily spotted by an experimenter who then manually sorts out curves before proceeding with data evaluation. However, this manual sorting step becomes increasingly cumbersome for studies that involve numerous measurements or for quantitative imaging based on FD maps

Compliant Substrates Enhance Macrophage Cytokine Release and NLRP3 Inflammasome Formation During Their Pro-Inflammatory Response

Immune cells process a myriad of biochemical signals but their function and behavior are also determined by mechanical cues. Macrophages are no exception to this. Being present in all types of tissues, macrophages are exposed to environments of varying stiffness, which can be further altered under pathological conditions. While it is becoming increasingly clear that macrophages are mechanosensitive, it remains poorly understood how mechanical cues modulate their inflammatory response. Here we report that substrate stiffness influences the expression of pro-inflammatory genes and the formation of the NLRP3 inflammasome, leading to changes in the secreted protein levels of the cytokines IL-1β and IL-6. Using polyacrylamide hydrogels of tunable elastic moduli between 0.2 and 33.1 kPa, we found that bone marrow-derived macrophages adopted a less spread and rounder morphology on compliant compared to stiff substrates. Upon LPS priming, the expression levels of the gene encoding for TNF-α were higher on more compliant hydrogels. When additionally stimulating macrophages with the ionophore nigericin, we observed an enhanced formation of the NLRP3 inflammasome, increased levels of cell death, and higher secreted protein levels of IL-1β and IL-6 on compliant substrates. The upregulation of inflammasome formation on compliant substrates was not primarily attributed to the decreased cell spreading, since spatially confining cells on micropatterns led to a reduction of inflammasome-positive cells compared to well-spread cells. Finally, interfering with actomyosin contractility diminished the differences in inflammasome formation between compliant and stiff substrates. In summary, we show that substrate stiffness modulates the pro-inflammatory response of macrophages, that the NLRP3 inflammasome is one of the components affected by macrophage mechanosensing, and a role for actomyosin contractility in this mechanosensory response. Thus, our results contribute to a better understanding of how microenvironment stiffness affects macrophage behavior, which might be relevant in diseases where tissue stiffness is altered and might potentially provide a basis for new strategies to modulate inflammatory responses

Combined fluorescence, optical diffraction tomography and Brillouin microscopy

Quantitative measurements of physical parameters become increasingly important for understanding biological processes. Brillouin microscopy (BM) has recently emerged as one technique providing the 3D distribution of viscoelastic properties inside biological samples — so far relying on the implicit assumption that refractive index (RI) and density can be neglected. Here, we present a novel method (FOB microscopy) combining BM with optical diffraction tomography and epi-fluorescence imaging for explicitly measuring the Brillouin shift, RI and absolute density with molecular specificity. We show that neglecting the RI and density might lead to erroneous conclusions. Investigating the cell nucleus, we find that it has lower density but higher longitudinal modulus. Thus, the longitudinal modulus is not merely sensitive to the water content of the sample — a postulate vividly discussed in the field. We demonstrate the further utility of FOB on various biological systems including adipocytes and intracellular membraneless compartments. FOB microscopy can provide unexpected scientific discoveries and shed quantitative light on processes such as phase separation and transition inside living cells

Correlative all-optical quantification of mass density and mechanics of subcellular compartments with fluorescence specificity

Quantitative measurements of physical parameters become increasingly important for understanding biological processes. Brillouin microscopy (BM) has recently emerged as one technique providing the 3D distribution of viscoelastic properties inside biological samples − so far relying on the implicit assumption that refractive index (RI) and density can be neglected. Here, we present a novel method (FOB microscopy) combining BM with optical diffraction tomography and epifluorescence imaging for explicitly measuring the Brillouin shift, RI, and absolute density with specificity to fluorescently labeled structures. We show that neglecting the RI and density might lead to erroneous conclusions. Investigating the nucleoplasm of wild-type HeLa cells, we find that it has lower density but higher longitudinal modulus than the cytoplasm. Thus, the longitudinal modulus is not merely sensitive to the water content of the sample − a postulate vividly discussed in the field. We demonstrate the further utility of FOB on various biological systems including adipocytes and intracellular membraneless compartments. FOB microscopy can provide unexpected scientific discoveries and shed quantitative light on processes such as phase separation and transition inside living cells

Viscoelastic properties of suspended cells measured with shear flow deformation cytometry

Numerous cell functions are accompanied by phenotypic changes in viscoelastic properties, and measuring them can help elucidate higher level cellular functions in health and disease. We present a high-throughput, simple and low-cost microfluidic method for quantitatively measuring the elastic (storage) and viscous (loss) modulus of individual cells. Cells are suspended in a high-viscosity fluid and are pumped with high pressure through a 5.8 cm long and 200 µm wide microfluidic channel. The fluid shear stress induces large, ear ellipsoidal cell deformations. In addition, the flow profile in the channel causes the cells to rotate in a tank-treading manner. From the cell deformation and tank treading frequency, we extract the frequency-dependent viscoelastic cell properties based on a theoretical framework developed by R. Roscoe [1] that describes the deformation of a viscoelastic sphere in a viscous fluid under steady laminar flow. We confirm the accuracy of the method using atomic force microscopy-calibrated polyacrylamide beads and cells. Our measurements demonstrate that suspended cells exhibit power-law, soft glassy rheological behavior that is cell-cycle-dependent and mediated by the physical interplay between the actin filament and intermediate filament networks

De novo identification of universal cell mechanics regulators

Mechanical proprieties determine many cellular functions, such as cell fate specification, migration, or circulation through vasculature. Identifying factors governing cell mechanical phenotype is therefore a subject of great interest. Here we present a mechanomics approach for establishing links between mechanical phenotype changes and the genes involved in driving them. We employ a machine learning-based discriminative network analysis method termed PC-corr to associate cell mechanical states, measured by real-time deformability cytometry (RT-DC), with large-scale transcriptome datasets ranging from stem cell development to cancer progression, and originating from different murine and human tissues. By intersecting the discriminative networks inferred from two selected datasets, we identify a conserved module of five genes with putative roles in the regulation of cell mechanics. We validate the power of the individual genes to discriminate between soft and stiff cell states in silico, and demonstrate experimentally that the top scoring gene, CAV1, changes the mechanical phenotype of cells when silenced or overexpressed. The data-driven approach presented here has the power of de novo identification of genes involved in cell mechanics regulation and paves the way towards engineering cell mechanical properties on demand to explore their impact on physiological and pathological cell functions

An explicit model to extract viscoelastic properties of cells from AFM force-indentation curves

The data and the codes available here are used in the publication: "An explicit model to extract viscoelastic properties of cells from AFM force-indentation curves"THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV

An explicit model to extract viscoelastic properties of cells from AFM force-indentation curves

The data set belongs to theTHIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV