Micropipette force sensors for in vivo force measurements on single cells and multicellular microorganisms

Probing the physical origins of droplet friction using a critically damped cantilever

Previously, we and others have used cantilever-based techniques to measure droplet friction on various surfaces, but typically at low speeds U < 1 mm s-1; at higher speeds, friction measurements become inaccurate because of ringing artefacts. Here, we are able to eliminate the ringing noise using a critically damped cantilever. We measured droplet friction on a superhydrophobic surface over a wide range of speeds U = 10-5-10-1 m s-1 and identified two regimes corresponding to two different physical origins of droplet friction. At low speeds U < 1 cm s-1, the droplet is in contact with the top-most solid (Cassie-Baxter), and friction is dominated by contact-line pinning with Ffric force that is independent of U. In contrast, at high speeds U > 1 cm s-1, the droplet lifts off the surface, and friction is dominated by viscous dissipation in the air layer with Ffric ∝ U2/3 consistent with Landau-Levich-Derjaguin predictions. The same scaling applies for superhydrophobic and underwater superoleophobic surfaces despite their very different surface topographies and chemistries, i.e., the friction scaling law derived here is universal.

Droplet Friction on Superhydrophobic Surfaces Scales With Liquid-Solid Contact Fraction

It is generally assumed that contact angle hysteresis of superhydrophobic surfaces scales with liquid-solid contact fraction, however, its experimental verification has been problematic due to the limited accuracy of contact angle and sliding angle goniometry. Advances in cantilever-based friction probes enable accurate droplet friction measurements down to the nanonewton regime, thus suiting much better for characterizing the wetting of superhydrophobic surfaces than contact angle hysteresis measurements. This work quantifies the relationship between droplet friction and liquid-solid contact fraction, through theory and experimental validation. Well-defined micropillar and microcone structures are used as model surfaces to provide a wide range of different liquid-solid contact fractions. Micropillars are known to be able to hold the water on top of them, and a theoretical analysis together with confocal laser scanning microscopy shows that despite the spiky nature of the microcones droplets do not sink into the conical structure either, rendering a diminishingly small liquid-solid contact fraction. Droplet friction characterization with a micropipette force sensor technique reveals a strong dependence of the droplet friction on the contact fraction, and the dependency is described with a simple physical equation, despite the nearly three-orders-of-magnitude difference in liquid-solid contact fraction between the sparsest cone surface and the densest pillar surface.

Quantifying gliding forces of filamentous cyanobacteria by self-buckling

Filamentous cyanobacteria are one of the oldest and today still most abundant lifeforms on earth, with manifold implications in ecology and economics. Their flexible filaments, often several hundred cells long, exhibit gliding motility in contact with solid surfaces. The underlying force generating mechanism is not yet understood. Here, we demonstrate that propulsion forces and friction coefficients are strongly coupled in the gliding motility of filamentous cyanobacteria. We directly measure their bending moduli using micropipette force sensors, and quantify propulsion and friction forces by analyzing their self-buckling behavior, complemented with analytical theory and simulations. The results indicate that slime extrusion unlikely generates the gliding forces, but support adhesion-based hypotheses, similar to the better-studied single-celled myxobacteria. The critical self-buckling lengths align well with the peaks of natural length distributions, indicating the importance of self-buckling for the organization of their collective in natural and artificial settings.

Measurement Methods for Droplet Adhesion Characteristics and Micrometer-Scale Quantification of Contact Angle on Superhydrophobic Surfaces: Challenges and Opportunities

Inspired by nature, superhydrophobic surfaces have been widely studied. Usually the wettability of a superhydrophobic surface is quantified by the macroscopic contact angle. However, this method has various limitations, especially for precision micro devices with superhydrophobic surfaces, such as biomimetic artificial compound eyes and biomimetic water strider robots. These precision micro devices with superhydrophobic surfaces proposed a higher demand for the quantification of contact angles, requiring contact angle quantification technology to have micrometer-scale measurement capabilities. In this review, it is proposed to achieve micrometer-scale quantification of superhydrophobic surface contact angles through droplet adhesion characteristics (adhesion force and contact radius). Existing contact angle quantification techniques and droplet characteristics' measurement methods were described in detail. The advancement of micrometer-scale quantification technology for the contact angle of superhydrophobic surfaces will enhance our understanding of superhydrophobic surfaces.

Toward vanishing droplet friction on repellent surfaces

Superhydrophobic surfaces are often seen as frictionless materials, on which water is highly mobile. Understanding the nature of friction for such water-repellent systems is central to further minimize resistance to motion and energy loss in applications. For slowly moving drops, contact-line friction has been generally considered dominant on slippery superhydrophobic surfaces. Here, we show that this general rule applies only at very low speed. Using a micropipette force sensor in an oscillating mode, we measure the friction of water drops approaching or even equaling zero contact-line friction. We evidence that dissipation then mainly stems from the viscous shearing of the air film (plastron) trapped under the liquid. Because this force is velocity dependent, it can become a serious drag on surfaces that look highly slippery from quasi-static tests. The plastron thickness is found to be the key parameter that enables the control of this special friction, which is useful information for designing the next generation of ultraslippery water-repellent coatings.

Droplet slipperiness despite surface heterogeneity at molecular scale

Friction determines whether liquid droplets slide off a solid surface or stick to it. Surface heterogeneity is generally acknowledged as the major cause of increased contact angle hysteresis and contact line friction of droplets. Here we challenge this long-standing premise for chemical heterogeneity at the molecular length scale. By tuning the coverage of self-assembled monolayers (SAMs), water contact angles change gradually from about 10° to 110° yet contact angle hysteresis and contact line friction are low for the low-coverage hydrophilic SAMs as well as high-coverage hydrophobic SAMs. Their slipperiness is not expected based on the substantial chemical heterogeneity of the SAMs featuring uncoated areas of the substrate well beyond the size of a water molecule as probed by metal reactants. According to molecular dynamics simulations, the low friction of both low- and high-coverage SAMs originates from the mobility of interfacial water molecules. These findings reveal a yet unknown and counterintuitive mechanism for slipperiness, opening new avenues for enhancing the mobility of droplets.

Buckling of a monolayer of platelike particles trapped at a fluid-fluid interface

Particles trapped at a fluid-fluid interface by capillary forces can form a monolayer that jams and buckles when subject to uniaxial compression. Here we investigate experimentally the buckling mechanics of monolayers of millimeter-sized rigid plates trapped at a planar fluid-fluid interface subject to uniaxial compression in a Langmuir trough. We quantified the buckling wavelength and the associated force on the trough barriers as a function of the degree of compression. To explain the observed buckling wavelength and forces in the two-dimensional (2D) monolayer, we consider a simplified system composed of a linear chain of platelike particles. The chain system enables us to build a theoretical model which is then compared to the 2D monolayer data. Both the experiments and analytical model show that the wavelength of buckling of a monolayer of platelike particles is of the order of the particle size, a different scaling from the one usually reported for monolayers of spheres. A simple model of buckling surface pressure is also proposed, and an analysis of the effect of the bending rigidity resulting from a small overlap between nanosheet particles is presented. These results can be applied to the modeling of the interfacial rheology and buckling dynamics of interfacial layers of 2D nanomaterials.

Fiber-Integrated Force Sensor using 3D Printed Spring-Composed Fabry-Perot Cavities with a High Precision Down to Tens of Piconewton

Developing microscale sensors capable of force measurements down to the scale of piconewtons is of fundamental importance for a wide range of applications. To date, advanced instrumentations such as atomic force microscopes and other specifically developed micro/nano-electromechanical systems face challenges such as high cost, complex detection systems and poor electromagnetic compatibility. Here, it presents the unprecedented design and 3D printing of general fiber-integrated force sensors using spring-composed Fabry-Perot cavities. It calibrates these microscale devices employing varied-diameter μ $\umu$ m-scale silica particles as standard weights. The force sensitivity and resolution reach values of (0.436 ± 0.007) nmnN-1 and (40.0 ± 0.7) pN, respectively, which are the best resolutions among all fiber-based nanomechanical probes so far. It also measured the non-linear airflow force distributions produced from a nozzle with an orifice of 2 μ $\umu$ m, which matches well with the full-sized simulations. With further customization of their geometries and materials, it anticipates the easy-to-use force probe can well extend to many other applications such as air/fluidic turbulences sensing, micro-manipulations, and biological sensing.

Optically Controlled Dissolution Kinetics of Vaterite Microcapsules: Toward Novel Crystal Growth Strategies

Controllable continuous release of functional materials from capsules is one of the unmet functions of theragnosis particles; on this way, understanding cargo-fluid interactions in vitro is an essential milestone. We develop a flexible platform to investigate single particle-fluid interactions utilizing a glass micropipette as a highly localized flow source around an optically trapped particle. In proof-of-concept experiments, this microparticle is sensitive to local microflow distribution, thus serving as a probe. The very same flows are capable of the particle rotating (i.e., vaterite drug cargo) at frequencies dependent on the mutual particle-pipette position. Platform flexibility comes from different interactions of a tweezer (optical forces) and a pipette (mechanical/hydrodynamical) with a microparticle, which makes this arrangement an ideal microtool. We studied the vaterite dissolution kinetics and demonstrated that it can be controlled on demand, providing a wide cargo release dynamic rate. Our results promote the use of inorganic mesoporous nanoparticles as a nanomedicine platform.

Long-term stability of aerophilic metallic surfaces underwater

Aerophilic surfaces immersed underwater trap films of air known as plastrons. Plastrons have typically been considered impractical for underwater engineering applications due to their metastable performance. Here, we describe aerophilic titanium alloy (Ti) surfaces with extended plastron lifetimes that are conserved for months underwater. Long-term stability is achieved by the formation of highly rough hierarchically structured surfaces via electrochemical anodization combined with a low-surface-energy coating produced by a fluorinated surfactant. Aerophilic Ti surfaces drastically reduce blood adhesion and, when submerged in water, prevent adhesion of bacteria and marine organisms such as barnacles and mussels. Overall, we demonstrate a general strategy to achieve the long-term stability of plastrons on aerophilic surfaces for previously unattainable underwater applications.

Measuring Cell Mechanical Properties Using Microindentation

Quantifying cell mechanical properties is of interest to better understand both physiological and pathological cellular processes. Cell mechanical properties are quantified by a finite set of parameters such as the effective Young's modulus or the effective viscosity. These parameters can be extracted by applying controlled forces to a cell and by quantifying the resulting deformation of the cell.Microindentation consists in pressing a cell with a calibrated spring terminated by a rigid tip and by measuring the resulting indentation of the cell. We have developed a microindentation technique that uses a flexible micropipette as a spring. The micropipette has a microbead at its tip, and this spherical geometry allows using analytical models to extract cell mechanical properties from microindentation experiments. We use another micropipette to hold the cell to be indented, which makes this technique well suited to study nonadherent cells, but we also describe how to use this technique on adherent cells.

Single-Cell Quantification of the Mechanical Stability of Cell-Cell Adherens Junction Using Glass Micropipettes

Micropipette-based methods have been widely used for the manipulation of cells and characterization of the mechanical properties at the cell or tissue level. Here, we introduce the glass micropipette-based mechanical assays for the stability of cell-cell adhesion. A probing microbead coated with specific adhesion ligands, captured by a glass micropipette, is manipulated to form the adhesion complexes with the corresponding receptors on a single cell. Once the cell is moving away from the micropipette, forces are generated from 20 pN to 100 nN to the adhesion complexes, which are quantified in real-time based on the bending of the glass micropipette. We specifically emphasize the principle and method to probe the rupturing forces of the adhesion complexes at controlled force loading rates, the ligand coating on the probe microbeads, the force calibration of the glass micropipette, and the applications of the method to probe the E-cadherin-based cell-cell adhesions. The principles can be broadly applied to other cell adhesions such as cell-matrix adhesions, neuronal synapses, and bacterial-cell adhesions.

Advances in the Fabrication and Characterization of Superhydrophobic Surfaces Inspired by the Lotus Leaf

Nature has proven to be a valuable resource in inspiring the development of novel technologies. The field of biomimetics emerged centuries ago as scientists sought to understand the fundamental science behind the extraordinary properties of organisms in nature and applied the new science to mimic a desired property using various materials. Through evolution, living organisms have developed specialized surface coatings and chemistries with extraordinary properties such as the superhydrophobicity, which has been exploited to maintain structural integrity and for survival in harsh environments. The Lotus leaf is one of many examples which has inspired the fabrication of superhydrophobic surfaces. In this review, the fundamental science, supported by rigorous derivations from a thermodynamic perspective, is presented to explain the origin of superhydrophobicity. Based on theory, the interplay between surface morphology and chemistry is shown to influence surface wetting properties of materials. Various fabrication techniques to create superhydrophobic surfaces are also presented along with the corresponding advantages and/or disadvantages. Recent advances in the characterization techniques used to quantify the superhydrophobicity of surfaces is presented with respect to accuracy and sensitivity of the measurements. Challenges associated with the fabrication and characterization of superhydrophobic surfaces are also discussed.

Measuring Laplace pressure and imaging the actin cortex during cytokinesis in cultured cells

Laplace pressure is an important regulator of cell dynamics and behavior during cytokinesis. Here, we provide a protocol to measure Laplace pressure in cultured cells using a micropipette and describe the steps for imaging the actin cortex during cytokinesis. The quantification steps allow tracing dynamic change in Laplace pressure and displaying dynamic response of the actin cortex during cytokinesis in HeLa cells. This protocol can be applied to any cultured cell type during various stages of cell division.

For complete details on the use and execution of this protocol, please refer to Wang et al. (2021).

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Using a micropipette to measure Laplace pressure in cultured cells

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Imaging the dynamic response of actin cortex during cytokinesis

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Correlation of actin cortex dynamics with changes in Laplace pressure during cytokinesis

Biophysical Approaches for Applying and Measuring Biological Forces

Over the past decades, increasing evidence has indicated that mechanical loads can regulate the morphogenesis, proliferation, migration, and apoptosis of living cells. Investigations of how cells sense mechanical stimuli or the mechanotransduction mechanism is an active field of biomaterials and biophysics. Gaining a further understanding of mechanical regulation and depicting the mechanotransduction network inside cells require advanced experimental techniques and new theories. In this review, the fundamental principles of various experimental approaches that have been developed to characterize various types and magnitudes of forces experienced at the cellular and subcellular levels are summarized. The broad applications of these techniques are introduced with an emphasis on the difficulties in implementing these techniques in special biological systems. The advantages and disadvantages of each technique are discussed, which can guide readers to choose the most suitable technique for their questions. A perspective on future directions in this field is also provided. It is anticipated that technical advancement can be a driving force for the development of mechanobiology.

Writhing and hockling instabilities in twisted elastic fibers

The buckling and twisting of slender, elastic fibers is a deep and well-studied field. A slender elastic rod that is twisted with respect to a fixed end will spontaneously form a loop, or hockle, to relieve the torsional stress that builds. Further twisting results in the formation of plectonemes-a helical excursion in the fiber that extends with additional twisting. Here we use an idealized, micron-scale experiment to investigate the energy stored, and subsequently released, by hockles and plectonemes as they are pulled apart, in analogy with force spectroscopy studies of DNA and protein folding. Hysteresis loops in the snapping and unsnapping inform the stored energy in the twisted fiber structures.

Theoretical Thermal-Mechanical Modelling and Experimental Validation of a Three-Dimensional (3D) Electrothermal Microgripper with Three Fingers

This paper presents the theoretical thermal-mechanical modeling and parameter analyses of a novel three-dimensional (3D) electrothermal microgripper with three fingers. Each finger of the microgripper is composed of a bi-directional Z-shaped electrothermal actuator and a 3D U-shaped electrothermal actuator. The bi-directional Z-shaped electrothermal actuator provides the rectilinear motion in two directions. The novel 3D U-shaped electrothermal actuator offers motion with two degrees of freedom (DOFs) in the plane perpendicular to the movement of the Z-shaped actuator. As a result, each finger possesses 3D mobilities with three DOFs. Each beam of the actuators is heated externally with polyimide films. In this work, the static theoretical thermal-mechanical model of the 3D U-shaped electrothermal actuator is established. Finite-element analyses and experimental tests are conducted to verify and validate the model. With this model, parameter analyses are carried out to provide insight and guidance on further improving the 3D U-shaped actuator. Furthermore, a group of micro-manipulation experiments are conducted to demonstrate the flexibility and versality of the 3D microgripper on manipulate different types of small/micro-objects.

Force-Based Wetting Characterization of Stochastic Superhydrophobic Coatings at Nanonewton Sensitivity

Superhydrophobic coatings have extraordinary properties like self-cleaning and staying dry, and have recently appeared on industrial and consumer markets. The stochastic nature of the coating components and coating processes (e.g., spraying, painting) affects the uniformity of the water repellency across the coated substrate. The wetting properties of those coatings are typically quantified on macroscale using contact angle goniometry (CAG). Here, highly sensitive force-based methods, scanning droplet adhesion microscopy (SDAM), and micropipette force sensor (MFS), are used, to quantify the microscale heterogeneity in the wetting properties of stochastic superhydrophobic coatings with irregular surface topography that cannot be investigated by CAG. By mapping the wetting adhesion forces with SDAM and friction forces with MFS, it is demonstrated that even the best coatings on the market are prone to heterogeneities that induce stick-slip motion of droplets. Thus, owing to their high spatial and force resolution, the advantages of these techniques over CAG are demonstrated.

Measuring and upscaling micromechanical interactions in a cohesive granular material

The mechanical properties of a disordered heterogeneous medium depend, in general, on a complex interplay between multiple length scales. Connecting local interactions to macroscopic observables, such as stiffness or fracture, is thus challenging in this type of material. Here, we study the properties of a cohesive granular material composed of glass beads held together by soft polymer bridges. We characterise the mechanical response of single bridges under traction and shear, using a setup based on the deflection of flexible micropipettes. These measurements, along with information from X-ray microtomograms of the granular packings, then inform large-scale discrete element model (DEM) simulations. Although simple, these simulations are constrained in every way by empirical measurement and accurately predict mechanical responses of the aggregates, including details on their compressive failure, and how the material's stiffness depends on the stiffness and geometry of its parts. By demonstrating how to accurately relate microscopic information to macroscopic properties, these results provide new perspectives for predicting the behaviour of complex disordered materials, such as porous rock, snow, or foam.

3D mechanical characterization of single cells and small organisms using acoustic manipulation and force microscopy

Quantitative micromechanical characterization of single cells and multicellular tissues or organisms is of fundamental importance to the study of cellular growth, morphogenesis, and cell-cell interactions. However, due to limited manipulation capabilities at the microscale, systems used for mechanical characterizations struggle to provide complete three-dimensional coverage of individual specimens. Here, we combine an acoustically driven manipulation device with a micro-force sensor to freely rotate biological samples and quantify mechanical properties at multiple regions of interest within a specimen. The versatility of this tool is demonstrated through the analysis of single Lilium longiflorum pollen grains, in combination with numerical simulations, and individual Caenorhabditis elegans nematodes. It reveals local variations in apparent stiffness for single specimens, providing previously inaccessible information and datasets on mechanical properties that serve as the basis for biophysical modelling and allow deeper insights into the biomechanics of these living systems.

Mechanical properties of 2D aggregates of oil droplets as model mono-crystals

We investigate the elastic and yielding properties of two dimensional defect-free mono-crystals made of highly monodisperse droplets. Crystals are compressed between two parallel boundaries of which one acts as a force sensor. As the available space between boundaries is reduced, the crystal goes through successive row-reduction transitions. For small compression forces, the crystal responds elastically until a critical force is reached and the assembly fractures in a single catastrophic global event. Correspondingly there is a peak in the force measurement associated with each row-reduction. The elastic properties of ideal mono-crystal samples are fully captured by a simple analytical model consisting of an assembly of individual capillary springs. The yielding properties of the crystal are captured with a minimal bond breaking model.

Altered N-glycan composition impacts flagella-mediated adhesion in Chlamydomonas reinhardtii

For the unicellular alga Chlamydomonas reinhardtii, the presence of N-glycosylated proteins on the surface of two flagella is crucial for both cell-cell interaction during mating and flagellar surface adhesion. However, it is not known whether only the presence or also the composition of N-glycans attached to respective proteins is important for these processes. To this end, we tested several C. reinhardtii insertional mutants and a CRISPR/Cas9 knockout mutant of xylosyltransferase 1A, all possessing altered N-glycan compositions. Taking advantage of atomic force microscopy and micropipette force measurements, our data revealed that reduction in N-glycan complexity impedes the adhesion force required for binding the flagella to surfaces. This results in impaired polystyrene bead binding and transport but not gliding of cells on solid surfaces. Notably, assembly, intraflagellar transport, and protein import into flagella are not affected by altered N-glycosylation. Thus, we conclude that proper N-glycosylation of flagellar proteins is crucial for adhering C. reinhardtii cells onto surfaces, indicating that N-glycans mediate surface adhesion via direct surface contact.

Continuum Model Applied to Granular Analogs of Droplets and Puddles

We investigate the growth of aggregates made of adhesive frictionless oil droplets, piling up against a solid interface. Monodisperse droplets are produced one by one in an aqueous solution and float upward to the top of a liquid cell where they accumulate and form an aggregate at a flat horizontal interface. Initially, the aggregate grows in 3D until its height reaches a critical value. Beyond a critical height, adding more droplets results in the aggregate spreading in 2D along the interface with a constant height. We find that the shape of such aggregates, despite being granular in nature, is well described by a continuum model. The geometry of the aggregates is determined by a balance between droplet buoyancy and adhesion as given by a single parameter, a "granular" capillary length, analogous to the capillary length of a liquid.

Dynamic force measurements on swimming Chlamydomonas cells using micropipette force sensors

Flagella and cilia are cellular appendages that inherit essential functions of microbial life including sensing and navigating the environment. In order to propel a swimming microorganism they displace the surrounding fluid by means of periodic motions, while precisely timed modulations of their beating patterns enable the cell to steer towards or away from specific locations. Characterizing the dynamic forces, however, is challenging and typically relies on indirect experimental approaches. Here, we present direct in vivo measurements of the dynamic forces of motile Chlamydomonas reinhardtii cells in controlled environments. The experiments are based on partially aspirating a living microorganism at the tip of a micropipette force sensor and optically recording the micropipette's position fluctuations with high temporal and sub-pixel spatial resolution. Spectral signal analysis allows for isolating the cell-generated dynamic forces caused by the periodic motion of the flagella from background noise. We provide an analytic, elasto-hydrodynamic model for the micropipette force sensor and describe how to obtain the micropipette's full frequency response function from a dynamic force calibration. Using this approach, we measure the amplitude of the oscillatory forces during the swimming activity of individual Chlamydomonas reinhardtii cells of 26 ± 5 pN, resulting from the coordinated flagellar beating with a frequency of 49 ± 5 Hz. This dynamic micropipette force sensor technique generalizes the applicability of micropipettes as force sensors from static to dynamic force measurements, yielding a force sensitivity in the piconewton range. In addition to measurements in bulk liquid environment, we study the dynamic forces of the biflagellated microswimmer in the vicinity of a solid/liquid interface. As we gradually decrease the distance of the swimming microbe to the interface, we measure a significantly enhanced force transduction at distances larger than the maximum extent of the beating flagella, highlighting the importance of hydrodynamic interactions for scenarios in which flagellated microorganisms encounter surfaces.

In vivo adhesion force measurements of Chlamydomonas on model substrates

The initial stages of biofilm formation at a surface are triggered by the surface association of individual microorganisms. The biological mechanisms and interfacial interactions underlying microbial adhesion to surfaces have been widely studied for bacteria, while microalgae remained rather unconsidered despite their technological relevance, e.g., in photo-bioreactors. We performed in vivo micropipette force measurements with the model organism Chlamydomonas reinhardtii, a unicellular eukaryotic microalga that dwells in liquid-infused soils and on moist rocks. We characterize the adhesion forces and dissect the influence of intermolecular interactions by probing the adhesion forces of single cells on different model substrates with tailored properties. Our experiments show that the flagella-mediated adhesion of Chlamydomonas to surfaces is largely substrate independent, enabling the cell to adhere to any type of surface. This universal adhesion mechanism allows the microalga to effectively colonize abiotic surfaces in their heterogeneous natural habitats. Our results reveal a dominant contribution of electrostatic interactions governing microalgal adhesion and suggest that flagella membrane processes may cause significant variations of the adhesive properties of the flagella.