Filament Rigidity Vies with Mesh Size in Determining Anomalous Diffusion in Cytoskeleton

Disorder-Induced Anomalous Mobility Enhancement in Confined Geometries

Strong, scale-free disorder disrupts typical transport properties like the Stokes-Einstein relation and linear response, leading to anomalous diffusion observed in amorphous materials, glasses, living cells, and other systems. Our study reveals that the combination of scale-free quenched disorder and geometrical constraints induces unconventional single-particle mobility behavior. Specifically, in a two-dimensional channel with width w, under external drive, tighter geometrical constraints (smaller w) enhance mobility. We derive an explicit form of the response to an external force by utilizing the double-subordination approach for the quenched trap model. The observed mobility enhancement occurs in the low-temperature regime where the distribution of localization times is scale-free.

Switchable microscale stress response of actin-vimentin composites emerges from scale-dependent interactions

The mechanical properties of the mammalian cell regulate many cellular functions and are largely dictated by the cytoskeleton, a composite network of protein filaments, including actin, microtubules, and intermediate filaments. Interactions between these distinct filaments give rise to emergent mechanical properties that are difficult to generate synthetically, and recent studies have made great strides in advancing our understanding of the mechanical interplay between actin and microtubule filaments. While intermediate filaments play critical roles in the stress response of cells, their effect on the rheological properties of the composite cytoskeleton remains poorly understood. Here, we use optical tweezers microrheology to measure the linear viscoelastic properties and nonlinear stress response of composites of actin and vimentin with varying molar ratios of actin to vimentin. We reveal a surprising, nearly opposite effect of actin-vimentin network mechanics compared to single-component networks in the linear versus nonlinear regimes. Namely, the linear elastic plateau modulus and zero-shear viscosity are markedly reduced in composites compared to single-component networks of actin or vimentin, whereas the initial response force and stiffness are maximized in composites versus single-component networks in the nonlinear regime. While these emergent trends are indicative of distinct interactions between actin and vimentin, nonlinear stiffening and longtime stress response appear to both be dictated primarily by actin, at odds with previous bulk rheology studies. We demonstrate that these complex, scale-dependent effects arise from the varied contributions of network density, filament stiffness, non-specific interactions, and poroelasticity to the mechanical response at different spatiotemporal scales. Cells may harness this complex behavior to facilitate distinct stress responses at different scales and in response to different stimuli to allow for their hallmark multifunctionality.

Directional change during active diffusion of viral ribonucleoprotein particles through cytoplasm

A mesh of cytoskeletal fibers, consisting of microtubules, intermediate filaments, and fibrous actin, prevents the Brownian diffusion of particles with a diameter larger than 0.10 μm, such as vesicular stomatitis virus ribonucleoprotein (RNP) particles, in mammalian cells. Nevertheless, RNP particles do move in random directions but at a lower rate than Brownian diffusion, which is thermally driven. This nonthermal biological transport process is called "active diffusion" because it is driven by ATP. The ATP powers motor proteins such as myosin II. The motor proteins bend and cross-link actin fibers, causing the mesh to jiggle. Until recently, little was known about how RNP particles get through the mesh. It has been customary to analyze the tracks of particles like RNPs by computing the slope of the ensemble-averaged mean-squared displacement of the particles as a signature of mechanism. Although widely used, this approach "loses information" about the timing of the switches between physical mechanisms. It has been recently shown that machine learning composed of variational Bayesian analysis, Gaussian mixture models, and hidden Markov models can use "all the information" in a single track to reveal that that the positions of RNP particles are spatially clustered. Machine learning assigns a number, called a state, to each cluster. RNP particles remain in one state for 0.2-1.0 s before switching (hopping) to a different state. This earlier work is here extended to analyze the movements of a particle within a state and to determine particle directionality within and between states.

The synergistic effect of multiple organic macromolecules on the formation of calcium oxalate raphides of Musa spp

Needle-like calcium oxalate crystals called raphides are unique structures in the plant kingdom. Multiple biomacromolecules work together in the regulatory and transportation pathways to form raphides; however, the mechanism by which this occurs remains unknown. Using banana (Musa spp.), this study combined in vivo methods including confocal microscopy, transmission electron microscopy, and Q Exactive mass spectrometry to identify the main biomolecules, such as vesicles, together with the compositions of lipids and proteins in the crystal chamber, which is the membrane compartment that surrounds each raphide during its formation. Simulations of the vesicle transportation process and the synthesis of elongated calcium oxalate crystals in vitro were then conducted, and the results suggested that the vesicles carrying amorphous calcium oxalate and proteins embedded in raphides are transported along actin filaments. These vesicles subsequently fuse with the crystal chamber, utilizing the proteins embedded in the raphides as a template for the final formation of the structure. Our findings contribute to the fundamental understanding of the regulation of the diverse biomacromolecules that are crucial for raphide formation. Moreover, the implications of these findings extend to other fields such as materials science, and particularly the synthesis of functionalized materials.

Enzymatic cleaving of entangled DNA rings drives scale-dependent rheological trajectories

DNA, which naturally occurs in linear, ring, and supercoiled topologies, frequently undergoes enzyme-driven topological conversion and fragmentation in vivo, enabling it to perform a variety of functions within the cell. In vitro, highly concentrated DNA polymers form entanglements that yield viscoelastic properties dependent on the topologies and lengths of the DNA. Enzyme-driven alterations of DNA size and shape therefore offer a means of designing active materials with programmable viscoelastic properties. Here, we incorporate multi-site restriction endonucleases into dense DNA solutions to linearize and fragment circular DNA molecules. We pair optical tweezers microrheology with differential dynamic microscopy and single-molecule tracking to measure the linear and nonlinear viscoelastic response and transport properties of entangled DNA solutions over a wide range of spatiotemporal scales throughout the course of enzymatic digestion. We show that, at short timescales, relative to the relaxation timescales of the polymers, digestion of these 'topologically-active' fluids initially causes an increase in elasticity and relaxation times followed by a gradual decrease. Conversely, for long timescales, linear viscoelastic moduli exhibit signatures of increasing elasticity. DNA diffusion, likewise, becomes increasingly slowed, in direct opposition to the short-time behavior. We hypothesize that this scale-dependent rheology arises from the population of small DNA fragments, which increases as digestion proceeds, driving self-association of larger fragments via depletion interactions, giving rise to slow relaxation modes of clusters of entangled chains, interspersed among shorter unentangled fragments. While these slow modes likely dominate at long times, they are presumably frozen out in the short-time limit, which instead probes the faster relaxation modes of the unentangled population.

Mechanisms of active diffusion of vesicular stomatitis virus inclusion bodies and cellular early endosomes in the cytoplasm of mammalian cells

Viral and cellular particles too large to freely diffuse have two different types of mobility in the eukaryotic cell cytoplasm: directed motion mediated by motor proteins moving along cytoskeletal elements with the particle as its load, and motion in random directions mediated by motor proteins interconnecting cytoskeletal elements. The latter motion is referred to as "active diffusion." Mechanisms of directed motion have been extensively studied compared to mechanisms of active diffusion, despite the observation that active diffusion is more common for many viral and cellular particles. Our previous research showed that active diffusion of vesicular stomatitis virus (VSV) ribonucleoproteins (RNPs) in the cytoplasm consists of hopping between traps and that actin filaments and myosin II motors are components of the hop-trap mechanism. This raises the question whether similar mechanisms mediate random motion of larger particles with different physical and biological properties. Live-cell fluorescence imaging and a variational Bayesian analysis used in pattern recognition and machine learning were used to determine the molecular mechanisms of random motion of VSV inclusion bodies and cellular early endosomes. VSV inclusion bodies are membraneless cellular compartments that are the major sites of viral RNA synthesis, and early endosomes are representative of cellular membrane-bound organelles. Like VSV RNPs, inclusion bodies and early endosomes moved from one trapped state to another, but the distance between states was inconsistent with hopping between traps, indicating that the apparent state-to-state movement is mediated by trap movement. Like VSV RNPs, treatment with the actin filament depolymerizing inhibitor latrunculin A increased VSV inclusion body mobility by increasing the size of the traps. In contrast neither treatment with latrunculin A nor depolymerization of microtubules by nocodazole treatment affected the size of traps that confine early endosome mobility, indicating that intermediate filaments are likely major trap components for these cellular organelles.

Motor-driven advection competes with crowding to drive spatiotemporally heterogeneous transport in cytoskeleton composites

The cytoskeleton-a composite network of biopolymers, molecular motors, and associated binding proteins-is a paradigmatic example of active matter. Particle transport through the cytoskeleton can range from anomalous and heterogeneous subdiffusion to superdiffusion and advection. Yet, recapitulating and understanding these properties-ubiquitous to the cytoskeleton and other out-of-equilibrium soft matter systems-remains challenging. Here, we combine light sheet microscopy with differential dynamic microscopy and single-particle tracking to elucidate anomalous and advective transport in actomyosin-microtubule composites. We show that particles exhibit multi-mode transport that transitions from pronounced subdiffusion to superdiffusion at tunable crossover timescales. Surprisingly, while higher actomyosin content increases the range of timescales over which transport is superdiffusive, it also markedly increases the degree of subdiffusion at short timescales and generally slows transport. Corresponding displacement distributions display unique combinations of non-Gaussianity, asymmetry, and non-zero modes, indicative of directed advection coupled with caged diffusion and hopping. At larger spatiotemporal scales, particles in active composites exhibit superdiffusive dynamics with scaling exponents that are robust to changing actomyosin fractions, in contrast to normal, yet faster, diffusion in networks without actomyosin. Our specific results shed important new light on the interplay between non-equilibrium processes, crowding and heterogeneity in active cytoskeletal systems. More generally, our approach is broadly applicable to active matter systems to elucidate transport and dynamics across scales.

Optical-Tweezers-integrating-Differential-Dynamic-Microscopy maps the spatiotemporal propagation of nonlinear strains in polymer blends and composites

How local stresses propagate through polymeric fluids, and, more generally, how macromolecular dynamics give rise to viscoelasticity are open questions vital to wide-ranging scientific and industrial fields. Here, to unambiguously connect polymer dynamics to force response, and map the deformation fields that arise in macromolecular materials, we present Optical-Tweezers-integrating-Differential -Dynamic-Microscopy (OpTiDMM) that simultaneously imposes local strains, measures resistive forces, and analyzes the motion of the surrounding polymers. Our measurements with blends of ring and linear polymers (DNA) and their composites with stiff polymers (microtubules) uncover an unexpected resonant response, in which strain alignment, superdiffusivity, and elasticity are maximized when the strain rate is comparable to the entanglement rate. Microtubules suppress this resonance, while substantially increasing elastic storage, due to varying degrees to which the polymers buildup, stretch and flow along the strain path, and configurationally relax induced stress. More broadly, the rich multi-scale coupling of mechanics and dynamics afforded by OpTiDDM, empowers its interdisciplinary use to elucidate non-trivial phenomena that sculpt stress propagation dynamics-critical to commercial applications and cell mechanics alike.

Multiscale architecture: Mechanics of composite cytoskeletal networks

Different types of biological cells respond differently to mechanical stresses, and these responses are mainly governed by the cytoskeleton. The main components of this biopolymer network are actin filaments, microtubules, and intermediate filaments, whose mechanical and dynamic properties are highly distinct, thus opening up a large mechanical parameter space. Aside from experiments on whole, living cells, "bottom-up" approaches, utilizing purified, reconstituted protein systems, tremendously help to shed light on the complex mechanics of cytoskeletal networks. Such experiments are relevant in at least three aspects: (i) from a fundamental point of view, cytoskeletal networks provide a perfect model system for polymer physics; (ii) in materials science and "synthetic cell" approaches, one goal is to fully understand properties of cellular materials and reconstitute them in synthetic systems; (iii) many diseases are associated with cell mechanics, so a thorough understanding of the underlying phenomena may help solving pressing biomedical questions. In this review, we discuss the work on networks consisting of one, two, or all three types of filaments, entangled or cross-linked, and consider active elements such as molecular motors and dynamically growing filaments. Interestingly, tuning the interactions among the different filament types results in emergent network properties. We discuss current experimental challenges, such as the comparability of different studies, and recent methodological advances concerning the quantification of attractive forces between filaments and their influence on network mechanics.

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Cells can crawl, self-heal, and tune their stiffness due to their remarkably dynamic cytoskeleton. As such, reconstituting networks of cytoskeletal biopolymers may lead to a host of active and adaptable materials. However, engineering such materials with precisely tuned properties requires measuring how the dynamics depend on the network composition and synthesis methods. Quantifying such dynamics is challenged by variations across the time, space, and formulation space of composite networks. The protocol here describes how the Fourier analysis technique, differential dynamic microscopy (DDM), can quantify the dynamics of biopolymer networks and is particularly well suited for studies of cytoskeleton networks. DDM works on time sequences of images acquired using a range of microscopy modalities, including laser-scanning confocal, widefield fluorescence, and brightfield imaging. From such image sequences, one can extract characteristic decorrelation times of density fluctuations across a span of wave vectors. A user-friendly, open-source Python package to perform DDM analysis is also developed. With this package, one can measure the dynamics of labeled cytoskeleton components or of embedded tracer particles, as demonstrated here with data of intermediate filament (vimentin) networks and active actin-microtubule networks. Users with no prior programming or image processing experience will be able to perform DDM using this software package and associated documentation.

Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms

Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.

Subtle changes in crosslinking drive diverse anomalous transport characteristics in actin-microtubule networks

Anomalous diffusion in crowded and complex environments is widely studied due to its importance in intracellular transport, fluid rheology and materials engineering. Specifically, diffusion through the cytoskeleton, a network comprised of semiflexible actin filaments and rigid microtubules that interact both sterically and via crosslinking, plays a principal role in viral infection, vesicle transport and targeted drug delivery. Here, we elucidate the impact of crosslinking on particle diffusion in composites of actin and microtubules with actin-actin, microtubule-microtubule and actin-microtubule crosslinking. We analyze a suite of transport metrics by coupling single-particle tracking and differential dynamic microscopy. Using these complementary techniques, we find that particles display non-Gaussian and non-ergodic subdiffusion that is markedly enhanced by cytoskeletal crosslinking, which we attribute to suppressed microtubule mobility. However, the extent to which transport deviates from normal Brownian diffusion depends strongly on the crosslinking motif - with actin-microtubule crosslinking inducing the most pronounced anomalous characteristics. Our results reveal that subtle changes to actin-microtubule interactions can have complex impacts on particle diffusion in cytoskeleton composites, and suggest that a combination of reduced filament mobility and more variance in actin mobilities leads to more strongly anomalous particle transport.

Myosin-driven actin-microtubule networks exhibit self-organized contractile dynamics

The cytoskeleton is a dynamic network of proteins, including actin, microtubules, and their associated motor proteins, that enables essential cellular processes such as motility, division, and growth. While actomyosin networks are extensively studied, how interactions between actin and microtubules, ubiquitous in the cytoskeleton, influence actomyosin activity remains an open question. Here, we create a network of co-entangled actin and microtubules driven by myosin II. We combine dynamic differential microscopy, particle image velocimetry, and particle tracking to show that both actin and microtubules undergo ballistic contraction with unexpectedly indistinguishable characteristics. This contractility is distinct from faster disordered motion and rupturing that active actin networks exhibit. Our results suggest that microtubules enable self-organized myosin-driven contraction by providing flexural rigidity and enhanced connectivity to actin networks. Beyond the immediate relevance to cytoskeletal dynamics, our results shed light on the design of active materials that can be precisely tuned by the network composition.

Anomalous and heterogeneous DNA transport in biomimetic cytoskeleton networks

The cytoskeleton, a complex network of protein filaments and crosslinking proteins, dictates diverse cellular processes ranging from division to cargo transport. Yet, the role the cytoskeleton plays in the intracellular transport of DNA and other macromolecules remains poorly understood. Here, using single-molecule conformational tracking, we measure the transport and conformational dynamics of linear and relaxed circular (ring) DNA in composite networks of actin and microtubules with variable types of crosslinking. While both linear and ring DNA undergo anomalous, non-Gaussian, and non-ergodic subdiffusion, the detailed dynamics are controlled by both DNA topology (linear vs. ring) and crosslinking motif. Ring DNA swells, exhibiting heterogeneous subdiffusion controlled via threading by cytoskeleton filaments, while linear DNA compacts, exhibiting transport via caging and hopping. Importantly, while the crosslinking motif has little effect on ring DNA, linear DNA in networks with actin-microtubule crosslinking is significantly less ergodic and shows more heterogeneous transport than with actin-actin or microtubule-microtubule crosslinking.

Particle diffusion in extracellular hydrogels

Hyaluronic acid is an abundant polyelectrolyte in the human body that forms extracellular hydrogels in connective tissues. It is essential for regulating tissue biomechanics and cell-cell communication, yet hyaluronan overexpression is associated with pathological situations such as cancer and multiple sclerosis. Due to its enormous molecular weight (in the range of millions of Daltons), accumulation of hyaluronan hinders transport of macromolecules including nutrients and growth factors through tissues and also hampers drug delivery. However, the exact contribution of hyaluronan to tissue penetrability is poorly understood due to the complex structure and molecular composition of tissues. Here we reconstitute biomimetic hyaluronan gels and systematically investigate the effects of gel composition and crosslinking on the diffusion of microscopic tracer particles. We combine ensemble-averaged measurements via differential dynamic microscopy with single-particle tracking. We show that the particle diffusivity depends on the particle size relative to the network pore size and also on the stress relaxation dynamics of the network. We furthermore show that addition of collagen, the other major biopolymer in tissues, causes the emergence of caged particle dynamics. Our findings are useful for understanding macromolecular transport in tissues and for designing biomimetic extracellular matrix hydrogels for drug delivery and tissue regeneration.