Microrheology with optical tweezers: peaks & troughs

Ion-mediated condensation controls the mechanics of mitotic chromosomes

During mitosis in eukaryotic cells, mechanical forces generated by the mitotic spindle pull the sister chromatids into the nascent daughter cells. How do mitotic chromosomes achieve the necessary mechanical stiffness and stability to maintain their integrity under these forces? Here we use optical tweezers to show that ions involved in physiological chromosome condensation are crucial for chromosomal stability, stiffness and viscous dissipation. We combine these experiments with high-salt histone depletion and theory to show that chromosomal elasticity originates from the chromatin fibre behaving as a flexible polymer, whereas energy dissipation can be explained by modelling chromatin loops as an entangled polymer solution. Taken together, we show how collective properties of mitotic chromosomes, a biomaterial of incredible complexity, emerge from molecular properties, and how they are controlled by the physico-chemical environment.

Optical Halo: A Proof of Concept for a New Broadband Microrheology Tool

Microrheology, the study of material flow at micron scales, has advanced significantly since Robert Brown's discovery of Brownian motion in 1827. Mason and Weitz's seminal work in 1995 established the foundation for microrheology techniques, enabling the measurement of viscoelastic properties of complex fluids using light-scattering particles. However, existing techniques face limitations in exploring very slow dynamics, crucial for understanding biological systems. Here, we present a proof of concept for a novel microrheology technique called "Optical Halo", which utilises a ring-shaped Bessel beam created by optical tweezers to overcome existing limitations. Through numerical simulations and theoretical analysis, we demonstrate the efficacy of the Optical Halo in probing viscoelastic properties across a wide frequency range, including low-frequency regimes inaccessible to conventional methods. This innovative approach holds promise for elucidating the mechanical behaviour of complex biological fluids.

3D-printed ultra-small Brownian viscometers

Measuring viscosity in volumes smaller than a microliter is a challenging endeavor. A new type of microscopic viscometers is presented to assess the viscosity of Newtonian liquids. Micron-sized flexible polymer cantilevers are created by two-photon polymerization direct laser writing. Because of the low stiffness and high elasticity of the polymer material the microcantilevers exhibit pronounced Brownian motion when submerged in a liquid medium. By imaging the cantilever's spherically shaped end, these fluctuations can be tracked with high accuracy. The hydrodynamic resistance of the microviscometer is determined by fitting the power spectral density of the measured fluctuations with a theoretical frequency dependence. Validation measurements in water-glycerol mixtures with known viscosities reveal excellent linearity of the hydrodynamic resistance to viscosity, allowing for a simple linear calibration. The stand-alone viscometer structures have a characteristic size of a few tens of microns and only require a very basic external instrumentation in the form of microscopic imaging at moderate framerates (~ 100 fps). Thus, our results point to a practical and simple to use ultra-low volume viscometer that can be integrated into lab-on-a-chip devices.

Micro-tensile rheology of fibrous gels quantifies strain-dependent anisotropy

Semiflexible fiber gels such as collagen and fibrin have unique nonlinear mechanical properties that play an important role in tissue morphogenesis, wound healing, and cancer metastasis. Optical tweezers microrheology has greatly contributed to the understanding of the mechanics of fibrous gels at the microscale, including its heterogeneity and anisotropy. However, the explicit relationship between micromechanical properties and gel deformation has been largely overlooked. We introduce a unique gel-stretching apparatus and employ it to study the relationship between microscale strain and stiffening in fibrin and collagen gels, focusing on the development of anisotropy in the gel. We find that gels stretched by as much as 15 % stiffen significantly both in parallel and perpendicular to the stretching axis, and that the parallel axis is 2-3 times stiffer than the transverse axis. We also measure the stiffening and anisotropy along bands of aligned fibers created by aggregates of cancer cells, and find similar effects as in gels stretched with the tensile apparatus. Our results illustrate that the extracellular microenvironment is highly sensitive to deformation, with implications for tissue homeostasis and pathology. STATEMENT OF SIGNIFICANCE: The inherent fibrous architecture of the extracellular matrix (ECM) gives rise to unique strain-stiffening mechanics. The micromechanics of fibrous networks has been studied extensively, but the deformations involved in its stiffening at the microscale were not quantified. Here we introduce an apparatus that enables measuring the deformations in the gel as it is being stretched while simultaneously using optical tweezers to measure its microscale anisotropic stiffness. We reveal that fibrin and collagen both stiffen dramatically already at ∼10 % deformation, accompanied by the emergence of significant, yet moderate anisotropy. We measure similar stiffening and anisotropy in the matrix remodeled by the tensile apparatus to those found between cancer cell aggregates. Our results emphasize that small strains are enough to introduce substantial stiffening and anisotropy. These have been shown to result in directional cell migration and enhanced force propagation, and possibly control processes like morphogenesis and cancer metastasis.

Fully angularly resolved 3D microrheology with optical tweezers

Microrheology with optical tweezers (MOT) is an all-optical technique that allows the user to investigate a materials' viscoelastic properties at microscopic scales, and is particularly useful for those materials that feature complex microstructures, such as biological samples. MOT is increasingly being employed alongside 3D imaging systems and particle tracking methods to generate maps showing not only how properties may vary between different points in a sample but also how at a single point the viscoelastic properties may vary with direction. However, due to the diffraction limited shape of focussed beams, optical traps are inherently anisotropic in 3D. This can result in a significant overestimation of the fluids' viscosity in certain directions. As such, the rheological properties can only be accurately probed along directions parallel or perpendicular to the axis of trap beam propagation. In this work, a new analytical method is demonstrated to overcome this potential artefact. This is achieved by performing principal component analysis on 3D MOT data to characterise the trap, and then identify the frequency range over which trap anisotropy influences the data. This approach is initially applied to simulated data for a Newtonian fluid where the trap anisotropy induced maximum error in viscosity is reduced from ~ 150% to less than 6%. The effectiveness of the method is corroborated by experimental MOT measurements performed with water and gelatine solutions, thus confirming that the microrheology of a fluid can be extracted reliably across a wide frequency range and in any arbitrary direction. This work opens the door to fully spatially and angularly resolved 3D mapping of the rheological properties of soft materials over a broad frequency range.

Fluorescence lifetime Hong-Ou-Mandel sensing

Fluorescence Lifetime Imaging Microscopy in the time domain is typically performed by recording the arrival time of photons either by using electronic time tagging or a gated detector. As such the temporal resolution is limited by the performance of the electronics to 100's of picoseconds. Here, we demonstrate a fluorescence lifetime measurement technique based on photon-bunching statistics with a resolution that is only dependent on the duration of the reference photon or laser pulse, which can readily reach the 1-0.1 picosecond timescale. A range of fluorescent dyes having lifetimes spanning from 1.6 to 7 picoseconds have been here measured with only ~1 s measurement duration. We corroborate the effectiveness of the technique by measuring the Newtonian viscosity of glycerol/water mixtures by means of a molecular rotor having over an order of magnitude variability in lifetime, thus introducing a new method for contact-free nanorheology. Accessing fluorescence lifetime information at such high temporal resolution opens a doorway for a wide range of fluorescent markers to be adopted for studying yet unexplored fast biological processes, as well as fundamental interactions such as lifetime shortening in resonant plasmonic devices.

Living cells as a biological analog of optical tweezers - a non-invasive microrheology approach

Microrheology, the study of fluids on micron length-scales, promises to reveal insights into cellular biology, including mechanical biomarkers of disease and the interplay between biomechanics and cellular function. Here a minimally-invasive passive microrheology technique is applied to individual living cells by chemically binding a bead to the surface of a cell, and observing the mean squared displacement of the bead at timescales ranging from milliseconds to 100s of seconds. Measurements are repeated over the course of hours, and presented alongside analysis to quantify changes in the cells' low-frequency elastic modulus, G0', and the cell's dynamics over the time window ∼10-2 s to 10 s. An analogy to optical trapping allows verification of the invariant viscosity of HeLa S3 cells under control conditions and after cytoskeletal disruption. Stiffening of the cell is observed during cytoskeletal rearrangement in the control case, and cell softening when the actin cytoskeleton is disrupted by Latrunculin B. These data correlate with conventional understanding that integrin binding and recruitment triggers cytoskeletal rearrangement. This is, to our knowledge, the first time that cell stiffening has been measured during focal adhesion maturation, and the longest time over which such stiffening has been quantified by any means. STATEMENT OF SIGNIFICANCE: Here, we present an approach for studying mechanical properties of live cells without applying external forces or inserting tracers. Regulation of cellular biomechanics is crucial to healthy cell function. For the first time in literature, we can non-invasively and passively quantify cell mechanics during interactions with functionalised surface. Our method can monitor the maturation of adhesion sites on the surface of individual live cells without disrupting the cell mechanics by applying forces to the cell. We observe a stiffening response in cells over tens of minutes after a bead chemically binds. This stiffening reduces the deformation rate of the cytoskeleton, although the internal force generation increases. Our method has potential for applications to study mechanics during cell-surface and cell-vesicle interactions.

OptoRheo: Simultaneous in situ micro-mechanical sensing and imaging of live 3D biological systems

Biomechanical cues from the extracellular matrix (ECM) are essential for directing many cellular processes, from normal development and repair, to disease progression. To better understand cell-matrix interactions, we have developed a new instrument named 'OptoRheo' that combines light sheet fluorescence microscopy with particle tracking microrheology. OptoRheo lets us image cells in 3D as they proliferate over several days while simultaneously sensing the mechanical properties of the surrounding extracellular and pericellular matrix at a sub-cellular length scale. OptoRheo can be used in two operational modalities (with and without an optical trap) to extend the dynamic range of microrheology measurements. We corroborated this by characterising the ECM surrounding live breast cancer cells in two distinct culture systems, cell clusters in 3D hydrogels and spheroids in suspension culture. This cutting-edge instrument will transform the exploration of drug transport through complex cell culture matrices and optimise the design of the next-generation of disease models.

Correlating microscopic viscoelasticity and structure of an aging colloidal gel using active microrheology and cryogenic scanning electron microscopy

Optical tweezers (OTs) can detect pico-Newton range forces operating on a colloidal particle trapped in a medium and have been successfully utilized to investigate complex systems with internal structures. LAPONITE® clay particles in an aqueous medium self-assemble to form microscopic networks over time as electrostatic interactions between the particles gradually evolve in a physical aging process. We investigate the forced movements of an optically trapped micron-sized colloidal probe particle, suspended in an aging LAPONITE® suspension, as the underlying LAPONITE® microstructures gradually develop. Our OT-based oscillatory active microrheology experiments allow us to investigate the mechanical responses of the evolving microstructures in aging aqueous clay suspensions of concentrations ranging from 2.5% w/v to 3.0% w/v and at several aging times between 90 and 150 minutes. We repeat such oscillatory measurements for a range of colloidal probe particle diameters and investigate the effect of probe size on the microrheology of the aging suspensions. Using cryogenic field emission scanning electron microscopy (cryo-FESEM), we examine the average pore areas of the LAPONITE® suspension microstructures for various sample concentrations and aging times. By combining our OT and cryo-FESEM data, we report here for the first time to the best of our knowledge, an inverse correlation between the crossover modulus and the average pore diameter of the aging suspension microstructures for the different suspension concentrations and probe particle sizes studied here.

Photothermal Self-Excitation of a Phase-Controlled Microcantilever for Viscosity or Viscoelasticity Sensing

This work presents a feedback closed-loop platform to be used for viscosity or viscoelasticity sensing of Newtonian or non-Newtonian fluids. The system consists of a photothermally excited microcantilever working in a digital Phase-Locked Loop, in which the phase between the excitation signal to the cantilever and the reference demodulating signals is chosen and imposed in the loop. General analytical models to describe the frequency and amplitude of oscillation of the cantilever immersed in viscous and viscoelastic fluids are derived and validated against experiments. In particular, the sensitivity of the sensor to variations of viscosity of Newtonian fluids, or to variations of elastic/viscous modulus of non-Newtonian fluids, are studied. Interestingly, it is demonstrated the possibility of controlling the sensitivity of the system to variations of these parameters by choosing the appropriate imposed phase in the loop. A working point with maximum sensitivity can be used for real-time detection of small changes of rheological parameters with low-noise and fast-transient response. Conversely, a working point with zero sensitivity to variations of rheological parameters can be potentially used to decouple the effect of simultaneous external factors acting on the resonator.

Exploring cell and tissue mechanics with optical tweezers

Cellular and tissue biosystems emerge from the assembly of their constituent molecules and obtain a set of specific material properties. To measure these properties and understand how they influence cellular function is a central goal of mechanobiology. From a bottoms-up, physics or engineering point-of-view, such systems are a composition of basic mechanical elements. However, the sheer number and dynamic complexity of them, including active molecular machines and their emergent properties, makes it currently intractable to calculate how biosystems respond to forces. Because many diseases result from an aberrant mechanotransduction, it is thus essential to measure this response. Recent advances in the technology of optical tweezers have broadened their scope from single-molecule applications to measurements inside complex cellular environments, even within tissues and animals. Here, we summarize the basic optical trapping principles, implementations and calibration procedures that enable force measurements using optical tweezers directly inside cells of living animals, in combination with complementary techniques. We review their versatility to manipulate subcellular organelles and measure cellular frequency-dependent mechanics in the piconewton force range from microseconds to hours. As an outlook, we address future challenges to fully unlock the potential of optical tweezers for mechanobiology.

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.

A Review of Microfluidic Devices for Rheological Characterisation

The rheological characterisation of liquids finds application in several fields ranging from industrial production to the medical practice. Conventional rheometers are the gold standard for the rheological characterisation; however, they are affected by several limitations, including high costs, large volumes required and difficult integration to other systems. By contrast, microfluidic devices emerged as inexpensive platforms, requiring a little sample to operate and fashioning a very easy integration into other systems. Such advantages have prompted the development of microfluidic devices to measure rheological properties such as viscosity and longest relaxation time, using a finger-prick of volumes. This review highlights some of the microfluidic platforms introduced so far, describing their advantages and limitations, while also offering some prospective for future works.

i-RheoFT: Fourier transforming sampled functions without artefacts

In this article we present a new open-access code named “i-RheoFT” that implements the analytical method first introduced in [PRE, 80, 012501 (2009)] and then enhanced in [New J Phys 14, 115032 (2012)], which allows to evaluate the Fourier transform of any generic time-dependent function that vanishes for negative times, sampled at a finite set of data points that extend over a finite range, and need not be equally spaced. I-RheoFT has been employed here to investigate three important experimental factors: (i) the ‘density of initial experimental points’ describing the sampled function, (ii) the interpolation function used to perform the “virtual oversampling” procedure introduced in [New J Phys 14, 115032 (2012)], and (iii) the detrimental effect of noises on the expected outcomes. We demonstrate that, at relatively high signal-to-noise ratios and density of initial experimental points, all three built-in MATLAB interpolation functions employed in this work (i.e., Spline, Makima and PCHIP) perform well in recovering the information embedded within the original sampled function; with the Spline function performing best. Whereas, by reducing either the number of initial data points or the signal-to-noise ratio, there exists a threshold below which all three functions perform poorly; with the worst performance given by the Spline function in both the cases and the least worst by the PCHIP function at low density of initial data points and by the Makima function at relatively low signal-to-noise ratios. We envisage that i-RheoFT will be of particular interest and use to all those studies where sampled or time-averaged functions, often defined by a discrete set of data points within a finite time-window, are exploited to gain new insights on the systems’ dynamics.

Microrheology reveals microscale viscosity gradients in planktonic systems

At the microscopic scales at which the life of marine microbes unfolds, the physics is dominated by viscosity. Increasing viscosity slows down both the passive transport of solutes and particles and the swimming of motile microorganisms, and thus directly or indirectly affects all aspects of microbial life. Viscosity depends not only on the physical properties of water, but it also varies as a consequence of biological activity, allowing microorganisms some control over their physical landscape. Our use of microrheology allows us to explore how viscosity is structured around phytoplankton cells and marine aggregates and unveils a level of spatial heterogeneity that has implications for the functioning of the microbial food web and hence of marine biogeochemical cycles.

Microbial activity in planktonic systems creates a dynamic and heterogeneous microscale seascape that harbors a diverse community of microorganisms and ecological interactions of global significance. In recent decades great effort has been put into understanding this complex system, particularly focusing on the role of chemical patchiness, while overlooking a physical parameter that governs microbial life and is affected by biological activity: viscosity. Here we reveal spatial heterogeneity of viscosity in planktonic systems by using microrheological techniques that allow measurement of viscosity at length scales relevant to microorganisms. We show the viscous nature and the spatial extent of the phycosphere, the region surrounding phytoplankton. In ∼45% of the phytoplankton cells analyzed we detected increases in viscosity that extended up to 30 µm away from the cell with up to 40 times the viscosity of seawater. We also show how these gradients of viscosity can be amplified around a lysing phytoplankton cell as its viscous contents leak away. Finally, we report conservative estimates of viscosity inside marine aggregates, hotspots of microbial activity, more than an order of magnitude higher than in seawater. Since the diffusivities of dissolved molecules, particles, and microorganisms are inversely related to viscosity, microheterogeneity in viscosity alters the microscale distribution of microorganisms and their resources, with pervasive implications for the functioning of the planktonic ecosystem. Increasing viscosities impacts ecological interactions and processes, such as nutrient uptake, chemotaxis, and particle encounter, that occur at the microscale but influence carbon and nutrient cycles at a global scale.

Optical Tweezers with Integrated Multiplane Microscopy (OpTIMuM): a new tool for 3D microrheology

We introduce a novel 3D microrheology system that combines for the first time Optical Tweezers with Integrated Multiplane Microscopy (OpTIMuM). The system allows the 3D tracking of an optically trapped bead, with ~ 20 nm accuracy along the optical axis. This is achieved without the need for a high precision z-stage, separate calibration sample, nor a priori knowledge of either the bead size or the optical properties of the suspending medium. Instead, we have developed a simple yet effective in situ spatial calibration method using image sharpness and exploiting the fact we image at multiple planes simultaneously. These features make OpTIMuM an ideal system for microrheology measurements, and we corroborate the effectiveness of this novel microrheology tool by measuring the viscosity of water in three dimensions, simultaneously.

What Caging Force Cells Feel in 3D Hydrogels: A Rheological Perspective

It has been established that the mechanical properties of hydrogels control the fate of (stem) cells. However, despite its importance, a one-to-one correspondence between gels' stiffness and cell behavior is still missing from literature. In this work, the viscoelastic properties of poly(ethylene-glycol) (PEG)-based hydrogels are investigated by means of rheological measurements performed at different length scales. The outcomes of this work reveal that PEG-based hydrogels show significant stiffening when subjected to a compressional deformation, implying that conventional bulk rheology measurements may overestimate the stiffness of hydrogels by up to an order of magnitude. It is hypothesized that this apparent stiffening is caused by an induced "tensional state" of the gel network, due to the application of a compressional normal force during sample loading. Moreover, it is shown that the actual stiffness of the hydrogels is instead accurately determined by means of both passive-video-particle-tracking (PVPT) microrheology and nanoindentation measurements, which are inherently performed at the cell's length scale and in absence of any externally applied force in the case of PVPT. These results underpin a methodology for measuring hydrogels' linear viscoelastic properties that are representative of the mechanical constraints perceived by cells in 3D hydrogel cultures.

Helical nanobots as mechanical probes of intra- and extracellular environments

A rheological probe that can measure mechanical properties of biological milieu at well-defined locations with high spatial resolution, on a time scale faster than most biological processes, can further improve our understanding of how living systems operate and behave. Here, we demonstrate nanorobots actively driven in realistic ex vivo biological systems for fast mechanical measurements with high spatial accuracy. In the various demonstrations of magnetic nanobots as mechanical probes, we report the first direct observation of the internalization of probes by a living cell, the accurate measurement of the 'fluid phase' cytoplasmic viscosity of ~200 cP for a HeLa cell, demonstration of intracellular measurements in cells derived from human patients; all of which establish the strength of this novel technique for measurements in both intra- and extracellular environments.

Probing force in living cells with optical tweezers: from single-molecule mechanics to cell mechanotransduction

The invention of optical tweezers more than three decades ago has opened new avenues in the study of the mechanical properties of biological molecules and cells. Quantitative force measurements still represent a challenging task in living cells due to the complexity of the cellular environment. Here, we review different methodologies to quantitatively measure the mechanical properties of living cells, the strength of adhesion/receptor bonds, and the active force produced during intracellular transport, cell adhesion, and migration. We discuss experimental strategies to attain proper calibration of optical tweezers and molecular resolution in living cells. Finally, we show recent studies on the transduction of mechanical stimuli into biomolecular and genetic signals that play a critical role in cell health and disease.