Thermal fluctuations of fibres at short time scales

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.

Microrheology and structural quantification of hypercoagulable clots

Hypercoagulability is a pathology that remains difficult to explain today in most cases. It is likely due to a modification of the conditions of polymerization of the fibrin, the main clot component. Using passive microrheology, we measured the mechanical properties of clots and correlated them under the same conditions with structural information obtained with confocal microscopy. We tested our approach with known alterations: an excess of fibrinogen and of coagulation Factor VIII. We observed simultaneously a rigidification and densification of the fibrin network, showing the potential of microrheology for hypercoagulability diagnosis.

Passive and Active Microrheology for Biomedical Systems

Microrheology encompasses a range of methods to measure the mechanical properties of soft materials. By characterizing the motion of embedded microscopic particles, microrheology extends the probing length scale and frequency range of conventional bulk rheology. Microrheology can be characterized into either passive or active methods based on the driving force exerted on probe particles. Tracer particles are driven by thermal energy in passive methods, applying minimal deformation to the assessed medium. In active techniques, particles are manipulated by an external force, most commonly produced through optical and magnetic fields. Small-scale rheology holds significant advantages over conventional bulk rheology, such as eliminating the need for large sample sizes, the ability to probe fragile materials non-destructively, and a wider probing frequency range. More importantly, some microrheological techniques can obtain spatiotemporal information of local microenvironments and accurately describe the heterogeneity of structurally complex fluids. Recently, there has been significant growth in using these minimally invasive techniques to investigate a wide range of biomedical systems both in vitro and in vivo. Here, we review the latest applications and advancements of microrheology in mammalian cells, tissues, and biofluids and discuss the current challenges and potential future advances on the horizon.

Damped White Noise Diffusion with Memory for Diffusing Microprobes in Ageing Fibrin Gels

From observations of colloidal tracer particles in fibrin undergoing gelation, we introduce an analytical framework that allows the determination of the probability density function for a stochastic process beyond fractional Brownian motion. Using passive microrheology via videomicroscopy, mean square displacements of tracer particles suspended in fibrin at different ageing times are obtained. The anomalous diffusion is then described by a damped white noise process with memory, with analytical results closely matching experimental plots of mean square displacements and probability density function. We further show that the white noise functional stochastic approach applied to passive microrheology reveals the existence of a gelation parameter μ which elucidates the dynamics of constrained tracer particles embedded in a time-dependent soft material. In addition, we found that microstructural heterogeneity of particle environments decreases as the ageing time increases. This study offers experimental insights on the ageing of fibrin gels while presenting a white noise functional stochastic approach that could be applied to other systems exhibiting non-Markovian diffusive behavior.

Active Modulation of States of Prestress in Self-Assembled Short Peptide Gels

Peptide hydrogels are excellent candidates for medical therapeutics due to their tuneable viscoelastic properties, however, in vivo they will be subject to various osmotic pressures, temperature changes, and biological co-solutes, which could alter their performance. Peptide hydrogels formed from the synthetic peptide I3K have a temperature-induced hardening of their shear modulus by a factor of 2. We show that the addition of uncross-linked poly( N-isopropylacrylamide) chains to the peptide gels increases the gels' temperature sensitivity by 3 orders of magnitude through the control of osmotic swelling and cross-linking. Using machine learning combined with single-molecule fluorescence microscopy, we measured the modulation of states of prestress in the gels on the level of single peptide fibers. A new self-consistent mixture model was developed to simultaneously quantify the energy and the length distributions of the states of prestress. Switching the temperature from 20 to 40 °C causes 6-fold increases in the number of states of prestress. At the higher temperature, many of the fibers experience constrained buckling with characteristic small wavelength oscillations in their curvature.

The flexibility and dynamics of the tubules in the endoplasmic reticulum

The endoplasmic reticulum (ER) is a single organelle in eukaryotic cells that extends throughout the cell and is involved in a large number of cellular functions. Using a combination of fixed and live cells (human MRC5 lung cells) in diffraction limited and super-resolved fluorescence microscopy (STORM) experiments, we determined that the average persistence length of the ER tubules was 3.03 ± 0.24 μm. Removing the branched network junctions from the analysis caused a slight increase in the average persistence length to 4.71 ± 0.14 μm, and provides the tubule's persistence length with a moderate length scale dependence. The average radius of the tubules was 44.1 ± 3.2 nm. The bending rigidity of the ER tubule membranes was found to be 10.9 ± 1.2 kT (17.0 ± 1.3 kT without branch points). We investigated the dynamic behaviour of ER tubules in live cells, and found that the ER tubules behaved like semi-flexible fibres under tension. The majority of the ER tubules experienced equilibrium transverse fluctuations under tension, whereas a minority number of them had active super-diffusive motions driven by motor proteins. Cells thus actively modulate the dynamics of the ER in a well-defined manner, which is expected in turn to impact on its many functions.

Optical detection of nanometric thermal fluctuations to measure the stiffness of rigid superparamagnetic microrods

The rigidity of numerous biological filaments and crafted microrods has been conveniently deduced from the analysis of their thermal fluctuations. However, the difficulty of measuring nanometric displacements with an optical microscope has so far limited such studies to sufficiently flexible rods, of which the persistence length ([Formula: see text]) rarely exceeds 1 m at room temperature. Here, we demonstrate the possibility to probe 10-fold stiffer rods by a combination of superresolutive optical methods and a statistical analysis of the data based on a recent theoretical model that predicts the amplitude of the fluctuations at any location of the rod [Benetatos P, Frey E (2003) Phys Rev E Stat Nonlin Soft Matter Phys 67(5):051108]. Using this approach, we report measures of [Formula: see text] up to 0.5 km. We obtained these measurements on recently designed superparamagnetic [Formula: see text]40-[Formula: see text]m-long microrods containing iron-oxide nanoparticles connected by a polymer mesh. Using their magnetic properties, we provide an alternative proof of validity of these thermal measurements: For each individual studied rod, we performed a second measure of its rigidity by deflecting it with a uniform magnetic field. The agreement between the thermal and the magnetoelastic measures was realized with more than a decade of values of [Formula: see text] from 5.1 m to 129 m, corresponding to a bending modulus ranging from 2.2 to 54 (×[Formula: see text] Jm). Despite the apparent homogeneity of the analyzed microrods, their Young modulus follows a broad distribution from 1.9 MPa to 59 MPa and up to 200 MPa, depending on the size of the nanoparticles.

Advances in the microrheology of complex fluids

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

Foam-like compression behavior of fibrin networks

The rheological properties of fibrin networks have been of long-standing interest. As such there is a wealth of studies of their shear and tensile responses, but their compressive behavior remains unexplored. Here, by characterization of the network structure with synchronous measurement of the fibrin storage and loss moduli at increasing degrees of compression, we show that the compressive behavior of fibrin networks is similar to that of cellular solids. A nonlinear stress-strain response of fibrin consists of three regimes: (1) an initial linear regime, in which most fibers are straight, (2) a plateau regime, in which more and more fibers buckle and collapse, and (3) a markedly nonlinear regime, in which network densification occurs by bending of buckled fibers and inter-fiber contacts. Importantly, the spatially non-uniform network deformation included formation of a moving "compression front" along the axis of strain, which segregated the fibrin network into compartments with different fiber densities and structure. The Young's modulus of the linear phase depends quadratically on the fibrin volume fraction while that in the densified phase depends cubically on it. The viscoelastic plateau regime corresponds to a mixture of these two phases in which the fractions of the two phases change during compression. We model this regime using a continuum theory of phase transitions and analytically predict the storage and loss moduli which are in good agreement with the experimental data. Our work shows that fibrin networks are a member of a broad class of natural cellular materials which includes cancellous bone, wood and cork.

Spatially resolved microrheology of heterogeneous biopolymer hydrogels using covalently bound microspheres

Characterization of the rheological properties of heterogeneous biopolymers is important not only to understand the effect of substrate elasticity on cell behaviors, but also to provide insights into mechanical changes during cellular remodeling of the environment. Conventional particle-tracking microrheology (PTM) techniques are compromised by probe-network slippage and cage-hopping problems, and require a priori knowledge of network mesh size in order to determine a suitable probe size. We demonstrated here the usefulness of covalently bound probes for PTM of biopolymers to overcome the above limitations. We showed that, in a well-defined system like polyacrylamide gels, surface-modified probe particles using a zero-length crosslinker provided more reliable measurements of network mechanics as compared to standard carboxylated probes. We further demonstrated that appropriate surface modification of microspheres for PTM circumvented the requirement of using microspheres larger than the network mesh, an approach typically considered to be ideal. Using the method presented in this study, we found the local network at the leading edge of a typical C6 glioma cell to be stiffer as compared to the side. Our findings established that permanent interaction between the probe and network is crucial to reliably measure the local network mechanics in reconstituted, heterogeneous networks using PTM.

Nanoparticle diffusion measures bulk clot permeability

A clot's function is to achieve hemostasis by resisting fluid flow. Permeability is the measurement of a clot's hemostatic potential. It is sensitive to a wide range of biochemical parameters and pathologies. In this work, we consider the hydrodynamic phenomenon that reduces the mobility of fluid near the fiber surfaces. This no-slip boundary condition both defines the gel's permeability and suppresses nanoparticle diffusion in gel interstices. Here we report that, unlike previous work where steric effects also hindered diffusion, our system-nanoparticles in fibrin gel-was subject exclusively to hydrodynamic diffusion suppression. This result enabled an automated, high-throughput permeability assay that used small clot volumes. Permeability was derived from nanoparticle diffusion using the effective medium theory, and showed one-to-one correlation with measured permeability. This technique measured permeability without quantifying gel structure, and may therefore prove useful for characterizing similar materials (e.g., extracellular matrix) where structure is uncontrolled during polymerization and difficult to measure subsequently. We also report that PEGylation reduced, but did not eliminate, the population of immobile particles. We studied the forces required to pull stuck PEG particles free to confirm that the attachment is a result of neither covalent nor strong electrostatic binding, and discuss the relevance of this force scale to particle transport through physiological clots.

Structural hierarchy governs fibrin gel mechanics

Fibrin gels are responsible for the mechanical strength of blood clots, which are among the most resilient protein materials in nature. Here we investigate the physical origin of this mechanical behavior by performing rheology measurements on reconstituted fibrin gels. We find that increasing levels of shear strain induce a succession of distinct elastic responses that reflect stretching processes on different length scales. We present a theoretical model that explains these observations in terms of the unique hierarchical architecture of the fibers. The fibers are bundles of semiflexible protofibrils that are loosely connected by flexible linker chains. This architecture makes the fibers 100-fold more flexible to bending than anticipated based on their large diameter. Moreover, in contrast with other biopolymers, fibrin fibers intrinsically stiffen when stretched. The resulting hierarchy of elastic regimes explains the incredible resilience of fibrin clots against large deformations.

Biomechanics in hemostasis and thrombosis

See also Liu W, Carlisle CR, Sparks EA, Guthold M. The mechanical properties of single fibrin fibers. This issue, pp 1030-6; Carlisle CR, Sparks EA, Der Loughian C, Guthold M. Strength and failure of fibrin fiber branchpoints. This issue, pp 1135-8.

Stiffening of individual fibrin fibers equitably distributes strain and strengthens networks

As the structural backbone of blood clots, fibrin networks carry out the mechanical task of stemming blood flow at sites of vascular injury. These networks exhibit a rich set of remarkable mechanical properties, but a detailed picture relating the microscopic mechanics of the individual fibers to the overall network properties has not been fully developed. In particular, how the high strain and failure characteristics of single fibers affect the overall strength of the network is not known. Using a combined fluorescence/atomic force microscope nanomanipulation system, we stretched 2-D fibrin networks to the point of failure, while recording the strain of individual fibers. Our results were compared to a pair of model networks: one composed of linearly responding elements and a second of nonlinear, strain-stiffening elements. We find that strain-stiffening of the individual fibers is necessary to explain the pattern of strain propagation throughout the network that we observe in our experiments. Fiber strain-stiffening acts to distribute strain more equitably within the network, reduce strain maxima, and increase network strength. Along with its physiological implications, a detailed understanding of this strengthening mechanism may lead to new design strategies for engineered polymeric materials.