Intracellular transport of insulin granules is a subordinated random walk

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.

Distinct Sub- to Superdiffuse Insulin Granule Transport Behaviors in β-Cells Are Strongly Affected by Granule Age

Intracellular transport is a complex process that is difficult to describe by a single general model for motion. Here, we study the transport of insulin containing vesicles, termed granules, in live MIN6 cells. We characterize how the observed heterogeneity is affected by different intracellular factors by constructing a MIN6 cell line by CRISPR-CAS9 that constitutively expresses mCherry fused to insulin and is thus packaged in granules. Confocal microscopy imaging and single particle tracking of the granule transport provide long trajectories of thousands of single granule trajectories for statistical analysis. Mean squared displacement (MSD), angle correlation distribution, and step size distribution analysis allowed identifying five distinct granule transport subpopulations, from nearly immobile and subdiffusive to run-pause and superdiffusive. The subdiffusive subpopulation recapitulates the subordinated random walk we reported earlier (Tabei, 2013; ref 18). We show that the transport characteristics of the five subpopulations have a strong dependence on the age of insulin granules. The five subpopulations also reflect the effect of local microtubule and actin networks on transport in different cellular regions. Our results provide robust metrics to clarify the heterogeneity of granule transport and demonstrate the roles of microtubule versus actin networks with granule age since initial packaging in the Golgi.

Intermittent subdiffusion of short nuclear actin rods due to interactions with chromatin

The interior of cellular nuclei, the nucleoplasm, is a crowded fluid that is pervaded by protein-decorated DNA polymers, the chromatin. Due to the complex architecture of chromatin and a multitude of associated nonequilibrium processes, e.g., DNA repair, the nucleoplasm can be expected to feature nontrivial material properties and hence anomalous transport phenomena. Here, we have used single-particle tracking on nuclear actin rods to probe such transport phenomena. Our analysis reveals that short actin rods in the nucleus show an intermittent, antipersistent subdiffusion with clear signatures of fractional Brownian motion. Moreover, the diffusive motion is heterogeneous with clear signatures of an intermittent switching of trajectories between at least two different mobilities, most likely due to transient associations with chromatin. In line with this interpretation, hyperosmotic stress is seen to stall the motion of nuclear actin rods, whereas hypo-osmotic conditions yield a reptationlike motion. Our data highlights the heterogeneity of transport in the nucleoplasm that needs to be taken into account for an understanding of nucleoplasmic organization and the mechanobiology of nuclei.

Fractional Brownian motion with fluctuating diffusivities

Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach of a generalization that incorporates heterogeneities in either the tracers or the environment. This work presents a modification of Lévy's representation of fBm for the case in which the generalized diffusion coefficient is a stochastic process. We derive analytical expressions for the autocovariance function and both ensemble- and time-averaged mean squared displacements. Further, we validate the efficacy of the developed framework in two-state systems, comparing analytical asymptotic expressions with numerical simulations.

Aging and confinement in subordinated fractional Brownian motion

We study the effects of aging properties of subordinated fractional Brownian motion (FBM) with drift and in harmonic confinement, when the measurement of the stochastic process starts a time t_{a}>0 after its original initiation at t=0. Specifically, we consider the aged versions of the ensemble mean-squared displacement (MSD) and the time-averaged MSD (TAMSD), along with the aging factor. Our results are favorably compared with simulations results. The aging subordinated FBM exhibits a disparity between MSD and TAMSD and is thus weakly nonergodic, while strong aging is shown to effect a convergence of the MSD and TAMSD. The information on the aging factor with respect to the lag time exhibits an identical form to the aging behavior of subdiffusive continuous-time random walks (CTRW). The statistical properties of the MSD and TAMSD for the confined subordinated FBM are also derived. At long times, the MSD in the harmonic potential has a stationary value, that depends on the Hurst index of the parental (nonequilibrium) FBM. The TAMSD of confined subordinated FBM does not relax to a stationary value but increases sublinearly with lag time, analogously to confined CTRW. Specifically, short aging times t_{a} in confined subordinated FBM do not affect the aged MSD, while for long aging times the aged MSD has a power-law increase and is identical to the aged TAMSD.

A microrheological examination of insulin-secreting β-cells in healthy and diabetic-like conditions

Pancreatic β-cells regulate glucose homeostasis through glucose-stimulated insulin secretion, which is hindered in type-2 diabetes. Transport of the insulin vesicles is expected to be affected by changes in the viscoelastic and transport properties of the cytoplasm. These are evaluated in situ through particle-tracking measurements using a rat insulinoma β-cell line. The use of inert probes assists in decoupling the material properties of the cytoplasm from the active transport through cellular processes. The effect of glucose-stimulated insulin secretion is examined, and the subsequent remodeling of the cytoskeleton, at constant effects of cell activity, is shown to result in reduced mobility of the tracer particles. Induction of diabetic-like conditions is identified to alter the mean-squared displacement of the passive particles in the cytoplasm and diminish its reaction to glucose stimulation.

A comparative study of the target search of end monomers of real and Rouse chains under spherical confinement

We study the dynamics of the end monomers of a real chain confined in a spherical cavity to search for a small target on the cavity surface using Langevin dynamics simulation. The results are compared and contrasted with those of a Rouse chain to understand the influence of excluded volume interactions on the search dynamics, as characterized by the first passage time (FPT). We analyze how the mean FPT depends on the cavity size Rb, the target size a, and the degree of confinement quantified by Rg/Rb, with Rg being the polymer radius of gyration in free space. As a basic finding, the equilibrium distribution of the end monomers of a real chain in a closed spherical cavity differs from that of a Rouse chain at a given Rg/Rb, which leads to the differences between the mean FPTs of real and Rouse chains. Fitting the survival probability S(t) by a multi-exponential form, we show that the S(t) of real chains exhibits multiple characteristic times at large Rg/Rb. Our simulation results indicate that the search dynamics of a real chain exhibit three characteristic regimes as a function of Rg/Rb, including the transition from the Markovian to non-Markovian process at Rg/Rb ≈ 0.39, along with two distinct regimes at 0.39 < Rg/Rb < 1.0 and Rg/Rb > 1.0, respectively, where S(t) exhibits a single characteristic time and multiple characteristic times.

What determines sub-diffusive behavior in crowded protein solutions?

The aqueous environment inside cells is densely packed. A typical cell has a macromolecular concentration in the range 90-450 g/L, with 5%-40% of its volume being occupied by macromolecules, resulting in what is known as macromolecular crowding. The space available for the free diffusion of metabolites and other macromolecules is thus greatly reduced, leading to so-called excluded volume effects. The slow diffusion of macromolecules under crowded conditions has been explained using transient complex formation. However, sub-diffusion noted in earlier works is not well characterized, particularly the role played by transient complex formation and excluded volume effects. We have used Brownian dynamics simulations to characterize the diffusion of chymotrypsin inhibitor 2 in protein solutions of bovine serum albumin and lysozyme at concentrations ranging from 50 to 300 g/L. The predicted changes in diffusion coefficient as a function of crowder concentration are consistent with NMR experiments. The sub-diffusive behavior observed in the sub-microsecond timescale can be explained in terms of a so-called cage effect, arising from rattling motion in a local molecular cage as a consequence of excluded volume effects. By selectively manipulating the nature of interactions between protein molecules, we determined that excluded volume effects induce sub-diffusive dynamics at sub-microsecond timescales. These findings may help to explain the diffusion-mediated effects of protein crowding on cellular processes.

Multiple diffusive behaviors of the random walk in inhomogeneous environments

Anomalous diffusive behaviors are observed in highly inhomogeneous but relatively stable environments such as intracellular media and are increasingly attracting attention. In this paper we develop a coupled continuous-time random walk model in which the waiting time is power-law coupled with the local environmental diffusion coefficient. We provide two forms of the waiting time density, namely, a heavy-tailed density and an exponential density. For different waiting time densities, anomalous diffusions with the diffusion exponent between 0 and 2 and Brownian yet non-Gaussian diffusion can be realized within the present model. The diffusive behaviors are analyzed and discussed by deriving the mean-squared displacement and probability density function. In addition we derive the effective jump length density corresponding to the decoupled form to help distinguish the diffusion types. Our model unifies two kinds of anomalous diffusive behavior with different characteristics in the same inhomogeneous environment into a theoretical framework. The model interprets the random motion of particles in a complex inhomogeneous environment and reproduces the experimental results of different biological and physical systems.

Non-specific cargo-filament interactions slow down motor-driven transport

Active, motor-based cargo transport is important for many cellular functions and cellular development. However, the cell interior is complex and crowded and could have many weak, non-specific interactions with the cargo being transported. To understand how cargo-environment interactions will affect single motor cargo transport and multi-motor cargo transport, we use an artificial quantum dot cargo bound with few (~ 1) to many (~ 5-10) motors allowed to move in a dense microtubule network. We find that kinesin-driven quantum dot cargo is slower than single kinesin-1 motors. Excitingly, there is some recovery of the speed when multiple motors are attached to the cargo. To determine the possible mechanisms of both the slow down and recovery of speed, we have developed a computational model that explicitly incorporates multi-motor cargos interacting non-specifically with nearby microtubules, including, and predominantly with the microtubule on which the cargo is being transported. Our model has recovered the experimentally measured average cargo speed distribution for cargo-motor configurations with few and many motors, implying that numerous, weak, non-specific interactions can slow down cargo transport and multiple motors can reduce these interactions thereby increasing velocity.

Single-molecule analysis of intracellular insulin granule behavior and its application to analyzing cytoskeletal dependence and pathophysiological implications

Introduction: Mobilization of intracellular insulin granules to the plasma membrane plays a crucial role in regulating insulin secretion. However, the regulatory mechanisms of this mobilization process have been poorly understood due to technical limitations. In this study, we propose a convenient approach for assessing intracellular insulin granule behavior based on single-molecule analysis of insulin granule membrane proteins labeled with Quantum dot fluorescent nanocrystals. Methods: This approach allows us to analyze intracellular insulin granule movement with subpixel accuracy at 33 fps. We tracked two insulin granule membrane proteins, phogrin and zinc transporter 8, fused to HaloTag in rat insulinoma INS-1 cells and, by evaluating the tracks with mean-square displacement, demonstrated the characteristic behavior of insulin granules. Results and discussion: Pharmacological perturbations of microtubules and F-actin affected insulin granule behavior on distinct modalities. Specifically, microtubule dynamics and F-actin positively and negatively regulate insulin granule behavior, respectively, presumably by modulating each different behavioral mode. Furthermore, we observed impaired insulin granule behavior and cytoskeletal architecture under chronic treatment of high concentrations of glucose and palmitate. Our approach provides detailed information regarding intracellular insulin granule mobilization and its pathophysiological implications. This study sheds new light on the regulatory mechanisms of intracellular insulin granule mobilization and has important implications for understanding the pathogenesis of diabetes.

Triggering Gaussian-to-Exponential Transition of Displacement Distribution in Polymer Nanocomposites via Adsorption-Induced Trapping

In many disordered systems, the diffusion of classical particles is described by a displacement distribution P(x, t) that displays exponential tails instead of Gaussian statistics expected for Brownian motion. However, the experimental demonstration of control of this behavior by increasing the disorder strength has remained challenging. In this work, we explore the Gaussian-to-exponential transition by using diffusion of poly(ethylene glycol) (PEG) in attractive nanoparticle-polymer mixtures and controlling the volume fraction of the nanoparticles. In this work, we find "knobs", namely nanoparticle concentration and interaction, which enable the change in the shape of P(x,t) in a well-defined way. The Gaussian-to-exponential transition is consistent with a modified large deviation approach for a continuous time random walk and also with Monte Carlo simulations involving a microscopic model of polymer trapping via reversible adsorption to the nanoparticle surface. Our work bears significance in unraveling the fundamental physics behind the exponential decay of the displacement distribution at the tails, which is commonly observed in soft materials and nanomaterials.

Effects of cytoskeletal network mesh size on cargo transport

Intracellular transport of cargoes in the cell is essential for the organization and functioning cells, especially those that are large and elongated. The cytoskeletal networks inside large cells can be highly complex, and this cytoskeletal organization can have impacts on the distance and trajectories of travel. Here, we experimentally created microtubule networks with varying mesh sizes and examined the ability of kinesin-driven quantum dot cargoes to traverse the network. Using the experimental data, we deduced parameters for cargo detachment at intersections and away from intersections, allowing us to create an analytical theory for the run length as a function of mesh size. We also used these parameters to perform simulations of cargoes along paths extracted from the experimental networks. We find excellent agreement between the trends in run length, displacement, and trajectory persistence length comparing the experimental and simulated trajectories.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Universal to nonuniversal transition of the statistics of rare events during the spread of random walks

Through numerous experiments that analyzed rare event statistics in heterogeneous media, it was discovered that in many cases the probability density function for particle position, P(X,t), exhibits a slower decay rate than the Gaussian function. Typically, the decay behavior is exponential, referred to as Laplace tails. However, many systems exhibit an even slower decay rate, such as power-law, log-normal, or stretched exponential. In this study, we utilize the continuous-time random walk method to investigate the rare events in particle hopping dynamics and find that the properties of the hop size distribution induce a critical transition between the Laplace universality of rare events and a more specific, slower decay of P(X,t). Specifically, when the hop size distribution decays slower than exponential, such as e^{-|x|^{β}} (β>1), the Laplace universality no longer applies, and the decay is specific, influenced by a few large events, rather than by the accumulation of many smaller events that give rise to Laplace tails.

Fractional and scaled Brownian motion on the sphere: The effects of long-time correlations on navigation strategies

We analyze fractional Brownian motion and scaled Brownian motion on the two-dimensional sphere S^{2}. We find that the intrinsic long-time correlations that characterize fractional Brownian motion collude with the specific dynamics (navigation strategies) carried out on the surface giving rise to rich transport properties. We focus our study on two classes of navigation strategies: one induced by a specific set of coordinates chosen for S^{2} (we have chosen the spherical ones in the present analysis), for which we find that contrary to what occurs in the absence of such long-time correlations, nonequilibrium stationary distributions are attained. These results resemble those reported in confined flat spaces in one and two dimensions [Guggenberger et al. New J. Phys. 21, 022002 (2019)1367-263010.1088/1367-2630/ab075f; Vojta et al. Phys. Rev. E 102, 032108 (2020)2470-004510.1103/PhysRevE.102.032108]; however, in the case analyzed here, there are no boundaries that affect the motion on the sphere. In contrast, when the navigation strategy chosen corresponds to a frame of reference moving with the particle (a Frenet-Serret reference system), then the equilibrium distribution on the sphere is recovered in the long-time limit. For both navigation strategies, the relaxation times toward the stationary distribution depend on the particular value of the Hurst parameter. We also show that on S^{2}, scaled Brownian motion, distinguished by a time-dependent diffusion coefficient with a power-scaling, is independent of the navigation strategy finding a good agreement between the analytical calculations obtained from the solution of a time-dependent diffusion equation on S^{2}, and the numerical results obtained from our numerical method to generate ensemble of trajectories.

Anomalous diffusion, nonergodicity, non-Gaussianity, and aging of fractional Brownian motion with nonlinear clocks

How do nonlinear clocks in time and/or space affect the fundamental properties of a stochastic process? Specifically, how precisely may ergodic processes such as fractional Brownian motion (FBM) acquire predictable nonergodic and aging features being subjected to such conditions? We address these questions in the current study. To describe different types of non-Brownian motion of particles-including power-law anomalous, ultraslow or logarithmic, as well as superfast or exponential diffusion-we here develop and analyze a generalized stochastic process of scaled-fractional Brownian motion (SFBM). The time- and space-SFBM processes are, respectively, constructed based on FBM running with nonlinear time and space clocks. The fundamental statistical characteristics such as non-Gaussianity of particle displacements, nonergodicity, as well as aging are quantified for time- and space-SFBM by selecting different clocks. The latter parametrize power-law anomalous, ultraslow, and superfast diffusion. The results of our computer simulations are fully consistent with the analytical predictions for several functional forms of clocks. We thoroughly examine the behaviors of the probability-density function, the mean-squared displacement, the time-averaged mean-squared displacement, as well as the aging factor. Our results are applicable for rationalizing the impact of nonlinear time and space properties superimposed onto the FBM-type dynamics. SFBM offers a general framework for a universal and more precise model-based description of anomalous, nonergodic, non-Gaussian, and aging diffusion in single-molecule-tracking observations.

Unveiling nanoscale optical signatures of cytokine-induced β-cell dysfunction

Pro-inflammatory cytokines contribute to β-cell failure in both Type-1 and Type-2 Diabetes. Data collected so far allowed to dissect the genomic, transcriptomic, proteomic and biochemical landscape underlying cytokine-induced β-cell progression through dysfunction. Yet, no report thus far complemented such molecular information with the direct optical nanoscopy of the β-cell subcellular environment. Here we tackle this issue in Insulinoma 1E (INS-1E) β-cells by label-free fluorescence lifetime imaging microscopy (FLIM) and fluorescence-based super resolution imaging by expansion microscopy (ExM). It is found that 24-h exposure to IL-1β and IFN-γ is associated with a neat modification of the FLIM signature of cell autofluorescence due to the increase of either enzyme-bound NAD(P)H molecules and of oxidized lipid species. At the same time, ExM-based direct imaging unveils neat alteration of mitochondrial morphology (i.e. ~ 80% increase of mitochondrial circularity), marked degranulation (i.e. ~ 40% loss of insulin granules, with mis-localization of the surviving pool), appearance of F-actin-positive membrane blebs and an hitherto unknown extensive fragmentation of the microtubules network (e.g. ~ 37% reduction in the number of branches). Reported observations provide an optical-microscopy framework to interpret the amount of molecular information collected so far on β-cell dysfunction and pave the way to future ex-vivo and in-vivo investigations.

Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift

The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the trapping phase) in a disordered medium is considered in the presence of an external drift. In particular, we consider trapping events whose times follow a scale-free distribution with diverging mean trapping time. We construct this process in terms of fractional Brownian motion with constant forcing in which the trapping effect is introduced by the subordination technique, connecting "operational time" with observable "real time." We derive the statistical properties of this process such as non-Gaussianity and nonergodicity, for both ensemble and single-trajectory (time) averages. We demonstrate nice agreement with extensive simulations for the probability density function, skewness, kurtosis, as well as ensemble and time-averaged mean-squared displacements. We place a specific emphasis on the comparisons between the cases with and without drift.

Glucose-stimulated KIF5B-driven microtubule sliding organizes microtubule networks in pancreatic beta cells

In pancreatic islet beta cells, molecular motors use cytoskeletal polymers microtubules as tracks for intracellular transport of insulin secretory granules. Beta-cell microtubule network has a complex architecture and is non-directional, which provide insulin granules at the cell periphery for rapid secretion response, yet to avoid over-secretion and subsequent hypoglycemia. We have previously characterized a peripheral sub-membrane microtubule array, which is critical for withdrawal of excessive insulin granules from the secretion sites. Microtubules in beta cells originate at the Golgi in the cell interior, and how the peripheral array is formed is unknown. Using real-time imaging and photo-kinetics approaches in clonal mouse pancreatic beta cells MIN6, we now demonstrate that kinesin KIF5B, a motor protein with a capacity to transport microtubules as cargos, slides existing microtubules to the cell periphery and aligns them to each other along the plasma membrane. Moreover, like many physiological beta-cell features, microtubule sliding is facilitated by a high glucose stimulus. These new data, together with our previous report that in high glucose sub-membrane MT array is destabilized to allow for robust secretion, indicate that MT sliding is another integral part of glucose-triggered microtubule remodeling, likely replacing destabilized peripheral microtubules to prevent their loss over time and beta-cell malfunction.

Ensemble heterogeneity mimics ageing for endosomal dynamics within eukaryotic cells

Transport processes of many structures inside living cells display anomalous diffusion, such as endosomes in eukaryotic cells. They are also heterogeneous in space and time. Large ensembles of single particle trajectories allow the heterogeneities to be quantified in detail and provide insights for mathematical modelling. The development of accurate mathematical models for heterogeneous dynamics has the potential to enable the design and optimization of various technological applications, for example, the design of effective drug delivery systems. Central questions in the analysis of anomalous dynamics are ergodicity and statistical ageing which allow for selecting the proper model for the description. It is believed that non-ergodicity and ageing occur concurrently. However, we found that the anomalous dynamics of endosomes is paradoxical since it is ergodic but shows ageing. We show that this behaviour is caused by ensemble heterogeneity that, in addition to space-time heterogeneity within a single trajectory, is an inherent property of endosomal motion. Our work introduces novel approaches for the analysis and modelling of heterogeneous dynamics.

Insulin secretion hot spots in pancreatic β cells as secreting adhesions

Pancreatic β cell secretion of insulin is crucial to the maintenance of glucose homeostasis and prevention of diseases related to glucose regulation, including diabetes. Pancreatic β cells accomplish efficient insulin secretion by clustering secretion events at the cell membrane facing the vasculature. Regions at the cell periphery characterized by clustered secretion are currently termed insulin secretion hot spots. Several proteins, many associated with the microtubule and actin cytoskeletons, are known to localize to and serve specific functions at hot spots. Among these proteins are the scaffolding protein ELKS, the membrane-associated proteins LL5β and liprins, the focal adhesion-associated protein KANK1, and other factors typically associated with the presynaptic active zone in neurons. These hot spot proteins have been shown to contribute to insulin secretion, but many questions remain regarding their organization and dynamics at hot spots. Current studies suggest microtubule- and F-actin are involved in regulation of hot spot proteins and their function in secretion. The hot spot protein association with the cytoskeleton networks also suggests a potential role for mechanical regulation of these proteins and hot spots in general. This perspective summarizes the existing knowledge of known hot spot proteins, their cytoskeletal-mediated regulation, and discuss questions remaining regarding mechanical regulation of pancreatic beta cell hot spots.

Anomalous Dynamical Scaling Determines Universal Critical Singularities

Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at a large argument of the probability density function of rescaled displacement (scaling function) is derived and shown to imply universal singularities in the normalized cumulant generator. Exact calculations for continuous time random walks provide paradigmatic examples connected with singularities of second order phase transitions. In the biased case scaling is restricted to displacements in the drift direction and singularities have no equilibrium analogue.

Extending the analogy between intracellular motion in mammalian cells and glassy dynamics

How molecules, organelles, and foreign objects move within living cells has been studied in organisms ranging from bacteria to human cells. In mammalian cells, in particular, cellular vesicles move across the cell using motor proteins that carry the vesicle down the cytoskeleton to their destination. We have recently noted several similarities between the motion of such vesicles and that in disordered, "glassy", systems, but the generality of this observation remains unclear. Here we follow the motion of mitochondria, the organelles responsible for cell energy production, in mammalian cells over timescales from 50 ms to 70 s. Qualitative observations show that single mitochondria remain within a spatially limited region for extended periods of time, before moving longer distances relatively quickly. The displacement distribution is roughly Gaussian for shorter distances (≲0.05 μm) but exhibits exponentially decaying tails at longer distances (up to 0.40 μm). This behaviour is well-described by a model developed to describe the motion in glassy systems. These observations are extended to in total 3 different objects (mitochondria, lysosomes and nano-sized beads enclosed in vesicles), 3 different mammalian cell types (HEK 293, HeLa, and HT22), from 2 different organisms (human and mouse). Further evidence that supports glass-like characteristics of the motion is a difference between the time it takes to move a longer distance for the first time and subsequent times, as well as a weak ergodicity breaking of the motion. Overall, we demonstrate the ubiquity of glass-like motion in mammalian cells, providing a different perspective on intracellular motion.

Extracting, quantifying, and comparing dynamical and biomechanical properties of living matter through single particle tracking

A panoply of new tools for tracking single particles and molecules has led to an explosion of experimental data, leading to novel insights into physical properties of living matter governing cellular development and function, health and disease. In this Perspective, we present tools to investigate the dynamics and mechanics of living systems from the molecular to cellular scale via single-particle techniques. In particular, we focus on methods to measure, interpret, and analyse complex data sets that are associated with forces, materials properties, transport, and emergent organisation phenomena within biological and soft-matter systems. Current approaches, challenges, and existing solutions in the associated fields are outlined in order to support the growing community of researchers at the interface of physics and the life sciences. Each section focuses not only on the general physical principles and the potential for understanding living matter, but also on details of practical data extraction and analysis, discussing limitations, interpretation, and comparison across different experimental realisations and theoretical frameworks. Particularly relevant results are introduced as examples. While this Perspective describes living matter from a physical perspective, highlighting experimental and theoretical physics techniques relevant for such systems, it is also meant to serve as a solid starting point for researchers in the life sciences interested in the implementation of biophysical methods.

Electro-optical Study of the Anomalous Rotational Diffusion in Polymer Solutions

Brownian diffusion of spherical nanoparticles is usually exploited to ascertain the rheological properties of complex media. However, the behavior of the tracer particles is affected by a number of phenomena linked to the interplay between the dynamics of the particles and polymer coils. For this reason, the characteristic lengths of the dispersed entities, depletion phenomena, and the presence of sticking conditions have been observed to affect the translational diffusion of the probes. On the other hand, the retardation effect of the host fluid on the rotational diffusion of nonspherical particles is less understood. We explore the possibility of studying this phenomenon by analyzing the electro-orientation of the particles in different scenarios in which we vary the ratio between the particle and polymer characteristic size, and the geometry of the particles, including both elongated and oblate shapes. We find that the Stokes-Einstein relation only applies if the radius of gyration of the polymer is much shorter than the particle size and when some repulsive interaction between both is present.

The Fokker-Planck equation of the superstatistical fractional Brownian motion with application to passive tracers inside cytoplasm

By collecting from literature data experimental evidence of anomalous diffusion of passive tracers inside cytoplasm, and in particular of subdiffusion of mRNA molecules inside live Escherichia coli cells, we obtain the probability density function of molecules' displacement and we derive the corresponding Fokker-Planck equation. Molecules' distribution emerges to be related to the Krätzel function and its Fokker-Planck equation to be a fractional diffusion equation in the Erdélyi-Kober sense. The irreducibility of the derived Fokker-Planck equation to those of other literature models is also discussed.

In Silico Studies of Active Probe Dynamics in Crowded Media

Active systems are made of agents, each of which takes energy from the environment and converts it to directed motion. Therefore, by construction, these systems function out of equilibrium and cannot be described using equilibrium statistical mechanics. Though the most studied aspect has been the collective motion of active particles, the motion at the individual particle level in crowded media is also of prime importance. Examples include the motion of bacteria in hydrogels, single cell migration as a way to search for food or escape from toxic agents, and synthetic active agents transporting through soft crowded media. This review presents an overview of our understanding of single active probe dynamics in crowded media from computer simulations. The active probe is a Janus or a dumbbell-shaped particle, and the medium is made of crowders that are either sticky or repulsive to the probe and could be frozen or mobile. The density and the topology of the crowders also play an important role. We hope our in silico studies will help to elucidate the mechanism of activity-driven transport in crowded media in general and design nanomachines for targeted delivery.

Microtubules in Pancreatic β Cells: Convoluted Roadways Toward Precision

Pancreatic islet β cells regulate glucose homeostasis via glucose-stimulated insulin secretion (GSIS). Cytoskeletal polymers microtubules (MTs) serve as tracks for the transport and positioning of secretory insulin granules. MT network in β cells has unique morphology with several distinct features, which support granule biogenesis (via Golgi-derived MT array), net non-directional transport (via interlocked MT mesh), and control availability of granules at secretion sites (via submembrane MT bundle). The submembrane MT array, which is parallel to the plasma membrane and serves to withdraw excessive granules from the secretion hot spots, is destabilized and fragmented downstream of high glucose stimulation, allowing for regulated secretion. The origin of such an unusual MT network, the features that define its functionality, and metabolic pathways that regulate it are still to a large extent elusive and are a matter of active investigation and debate. Besides the MT network itself, it is important to consider the interplay of molecular motors that drive and fine-tune insulin granule transport. Importantly, activity of kinesin-1, which is the major MT-dependent motor in β cells, transports insulin granules, and has a capacity to remodel MT network, is also regulated by glucose. We discuss yet unknown potential avenues toward understanding how MT network and motor proteins provide control for secretion in coordination with other GSIS-regulating mechanisms.

Role of ergodicity, aging, and Gaussianity in resolving the origins of biomolecule subdiffusion

The internal motions of biomolecules are essential to their function. Although biological macromolecules conventionally show subdiffusive dynamics, only recently has subdiffusion been associated with non-ergodicity. These findings have stimulated new questions in biophysics and statistical mechanics. Is non-ergodic subdiffusion a general strategy shared by biomolecules? What underlying mechanisms are responsible for it? Here, we performed extensive molecular dynamics (MD) simulations to characterize the internal dynamics of six different biomolecules, ranging from single or double-stranded DNA, a single domain protein (KRAS), two globular proteins (PGK and SHP2), to an intrinsically disordered protein (SNAP-25). We found that the subdiffusive behavior of these biomolecules falls into two classes. The internal motion of the first three cases is ergodic subdiffusion and can be interpreted by fractional Brownian motion (FBM), while the latter three cases involve non-ergodic subdiffusion and can be modeled by mixed origins of continuous-time random walk (CTRW) and FBM.

Lévy Walk Dynamics in an External Constant Force Field in Non-Static Media

Based on the recognition of the huge change of the transport properties for diffusion particles in non-static media, we consider a Lévy walk model subjected to an external constant force in non-static media. Since the physical and comoving coordinates of non-static media are related by scale factor, we equivalently transfer the process from physical coordinate into comoving coordinate and derive the master equation governing the probability density function of the position of the particles in comoving coordinate. Utilizing the Hermite orthogonal polynomial expansions, some statistical properties are obtained, including the asymptotic behaviors of the first two moments in both coordinates and kurtosis. For some representative types of non-static media and Lévy walks, the striking and interesting phenomena originating from the interplay between non-static media, external force, and intrinsic stochastic motion are observed. The stationary distribution are also analyzed for some cases through numerical simulations.

Transport of a self-propelled tracer through a hairy cylindrical channel: interplay of stickiness and activity

Active transport of biomolecules assisted by motor proteins is imperative for the proper functioning of cellular activities. Inspired by the diffusion of active agents in crowded cellular channels, we computationally investigate the transport of an active tracer through a polymer grafted cylindrical channel by varying the activity of the tracer and stickiness of the tracer to the polymers. Our results reveal that the passive tracer exhibits profound subdiffusion with increasing stickiness by exploring deep into the grafted polymeric zone, while purely repulsive one prefers to diffuse through the pore-like space created along the cylindrical axis of the channel. In contrast, the active tracer shows faster dynamics and intermediate superdiffusion even though the tracer preferentially stays close to the dense polymeric region. This observation is further supported by the sharp peaks in the density profile of the probability of radial displacement of the tracer. We discover that the activity plays an important role in deciding the pathway that the tracer takes through the narrow channel. Interestingly, increasing the activity washes out the effect of stickiness. Adding to this, van-Hove functions manifest that the active tracer dynamics deviates from Gaussianity, and the degree of deviation grows with the activity. Our work has direct implications on how effective transportation and delivery of cargo can be achieved through a confined medium where activity, interactions, and crowding are interplaying. Looking ahead, these factors will be crucial for understanding the mechanism of artificial self-powered machines navigating through the cellular channels and performing in vivo challenging tasks.

Organization and dynamics of the cortical complexes controlling insulin secretion in β-cells

Insulin secretion in pancreatic β-cells is regulated by cortical complexes that are enriched at the sites of adhesion to extracellular matrix facing the vasculature. Many components of these complexes, including bassoon, RIM, ELKS and liprins, are shared with neuronal synapses. Here, we show that insulin secretion sites also contain the non-neuronal proteins LL5β (also known as PHLDB2) and KANK1, which, in migrating cells, organize exocytotic machinery in the vicinity of integrin-based adhesions. Depletion of LL5β or focal adhesion disassembly triggered by myosin II inhibition perturbed the clustering of secretory complexes and attenuated the first wave of insulin release. Although previous analyses in vitro and in neurons have suggested that secretory machinery might assemble through liquid–liquid phase separation, analysis of endogenously labeled ELKS in pancreatic islets indicated that its dynamics is inconsistent with such a scenario. Instead, fluorescence recovery after photobleaching and single-molecule imaging showed that ELKS turnover is driven by binding and unbinding to low-mobility scaffolds. Both the scaffold movements and ELKS exchange were stimulated by glucose treatment. Our findings help to explain how integrin-based adhesions control spatial organization of glucose-stimulated insulin release.

Summary: Characterization of the composition of cortical complexes controlling insulin secretion, showing that their dynamics is inconsistent with assembly through liquid–liquid phase separation.

Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models

How does a systematic time-dependence of the diffusion coefficient $D (t)$ affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we examine how the behavior of the...

Non-ergodicity of a globular protein extending beyond its functional timescale

Internal motions of folded proteins have been assumed to be ergodic, i.e., that the dynamics of a single protein molecule averaged over a very long time resembles that of an ensemble. Here, by performing single-molecule fluorescence resonance energy transfer (smFRET) experiments and molecular dynamics (MD) simulations of a multi-domain globular protein, cytoplasmic protein-tyrosine phosphatase (SHP2), we demonstrate that the functional inter-domain motion is observationally non-ergodic over the time spans 10⁻¹² to 10⁻⁷ s and 10⁻¹ to 10² s. The difference between observational non-ergodicity and simple non-convergence is discussed. In comparison, a single-strand DNA of similar size behaves ergodically with an energy landscape resembling a one-dimensional linear chain. The observed non-ergodicity results from the hierarchical connectivity of the high-dimensional energy landscape of the protein molecule. As the characteristic time for the protein to conduct its dephosphorylation function is ∼10 s, our findings suggest that, due to the non-ergodicity, individual, seemingly identical protein molecules can be dynamically and functionally different.

Internal motions of folded proteins have been assumed to be ergodic, i.e., that the dynamics of a single protein molecule averaged over a very long time resembles that of an ensemble.

β-Cell Pathophysiology: A Review of Advanced Optical Microscopy Applications

β-cells convert glucose (input) resulting in the controlled release of insulin (output), which in turn has the role to maintain glucose homeostasis. β-cell function is regulated by a complex interplay between the metabolic processing of the input, its transformation into second-messenger signals, and final mobilization of insulin-containing granules towards secretion of the output. Failure at any level in this process marks β-cell dysfunction in diabetes, thus making β-cells obvious potential targets for therapeutic purposes. Addressing quantitatively β-cell (dys)function at the molecular level in living samples requires probing simultaneously the spatial and temporal dimensions at the proper resolution. To this aim, an increasing amount of research efforts are exploiting the potentiality of biophysical techniques. In particular, using excitation light in the visible/infrared range, a number of optical-microscopy-based approaches have been tailored to the study of β-cell-(dys)function at the molecular level, either in label-free mode (i.e., exploiting intrinsic autofluorescence of cells) or by the use of organic/genetically-encoded fluorescent probes. Here, relevant examples from the literature are reviewed and discussed. Based on this, new potential lines of development in the field are drawn.

Aging power spectrum of membrane protein transport and other subordinated random walks

Single-particle tracking offers detailed information about the motion of molecules in complex environments such as those encountered in live cells, but the interpretation of experimental data is challenging. One of the most powerful tools in the characterization of random processes is the power spectral density. However, because anomalous diffusion processes in complex systems are usually not stationary, the traditional Wiener-Khinchin theorem for the analysis of power spectral densities is invalid. Here, we employ a recently developed tool named aging Wiener-Khinchin theorem to derive the power spectral density of fractional Brownian motion coexisting with a scale-free continuous time random walk, the two most typical anomalous diffusion processes. Using this analysis, we characterize the motion of voltage-gated sodium channels on the surface of hippocampal neurons. Our results show aging where the power spectral density can either increase or decrease with observation time depending on the specific parameters of both underlying processes.

Fingerprints of viscoelastic subdiffusion in random environments: Revisiting some experimental data and their interpretations

Many experimental studies revealed subdiffusion of various nanoparticles in diverse polymer and colloidal solutions, cytosol and plasma membrane of biological cells, which are viscoelastic and, at the same time, highly inhomogeneous randomly fluctuating environments. The observed subdiffusion often combines features of ergodic fractional Brownian motion (reflecting viscoelasticity) and nonergodic jumplike non-Markovian diffusional processes (reflecting disorder). Accordingly, several theories were proposed to explain puzzling experimental findings. Below we show that some of the significant and profound published experimental results are better rationalized within the viscoelastic subdiffusion approach in random environments, which is based on generalized Langevin dynamics in random potentials, than some earlier proposed theories.

Spatiotemporal Correlation Spectroscopy Reveals a Protective Effect of Peptide-Based GLP-1 Receptor Agonism against Lipotoxicity on Insulin Granule Dynamics in Primary Human β-Cells

Glucagon-like peptide-1 receptor (GLP-1R) agonists are being used for the treatment of type 2 diabetes (T2D) and may have beneficial effects on the pancreatic β-cells. Here, we evaluated the effects of GLP-1R agonism on insulin secretory granule (ISG) dynamics in primary β-cells isolated from human islets exposed to palmitate-induced lipotoxic stress. Islets cells were exposed for 48 h to 0.5 mM palmitate (hereafter, ‘Palm’) with or without the addition of a GLP-1 agonist, namely 10 nM exendin-4 (hereafter, ‘Ex-4’). Dissociated cells were first transfected with syncollin-EGFP in order to fluorescently mark the ISGs. Then, by applying a recently established spatiotemporal correlation spectroscopy technique, the average structural (i.e., size) and dynamic (i.e., the local diffusivity and mode of motion) properties of ISGs are extracted from a calculated imaging-derived Mean Square Displacement (iMSD) trace. Besides defining the structural/dynamic fingerprint of ISGs in human cells for the first time, iMSD analysis allowed to probe fingerprint variations under selected conditions: namely, it was shown that Palm affects ISGs dynamics in response to acute glucose stimulation by abolishing the ISGs mobilization typically imparted by glucose and, concomitantly, by reducing the extent of ISGs active/directed intracellular movement. By contrast, co-treatment with Ex-4 normalizes ISG dynamics, i.e., re-establish ISG mobilization and ability to perform active transport in response to glucose stimulation. These observations were correlated with standard glucose-stimulated insulin secretion (GSIS), which resulted in being reduced in cells exposed to Palm but preserved in cells concomitantly exposed to 10 nM Ex-4. Our data support the idea that GLP-1R agonism may exert its beneficial effect on human β-cells under metabolic stress by maintaining ISGs’ proper intracellular dynamics.

Imaging therapeutic peptide transport across intestinal barriers

Oral delivery is a highly preferred method for drug administration due to high patient compliance. However, oral administration is intrinsically challenging for pharmacologically interesting drug classes, in particular pharmaceutical peptides, due to the biological barriers associated with the gastrointestinal tract. In this review, we start by summarizing the pharmacological performance of several clinically relevant orally administrated therapeutic peptides, highlighting their low bioavailabilities. Thus, there is a strong need to increase the transport of peptide drugs across the intestinal barrier to realize future treatment needs and further development in the field. Currently, progress is hampered by a lack of understanding of transport mechanisms that govern intestinal absorption and transport of peptide drugs, including the effects of the permeability enhancers commonly used to mediate uptake. We describe how, for the past decades, mechanistic insights have predominantly been gained using functional assays with end-point read-out capabilities, which only allow indirect study of peptide transport mechanisms. We then focus on fluorescence imaging that, on the other hand, provides opportunities to directly visualize and thus follow peptide transport at high spatiotemporal resolution. Consequently, it may provide new and detailed mechanistic understanding of the interplay between the physicochemical properties of peptides and cellular processes; an interplay that determines the efficiency of transport. We review current methodology and state of the art in the field of fluorescence imaging to study intestinal barrier transport of peptides, and provide a comprehensive overview of the imaging-compatible in vitro, ex vivo, and in vivo platforms that currently are being developed to accelerate this emerging field of research.

Microtubules and Gαo-signaling modulate the preferential secretion of young insulin secretory granules in islet β cells via independent pathways

For sustainable function, each pancreatic islet β cell maintains thousands of insulin secretory granules (SGs) at all times. Glucose stimulation induces the secretion of a small portion of these SGs and simultaneously boosts SG biosynthesis to sustain this stock. The failure of these processes, often induced by sustained high-insulin output, results in type 2 diabetes. Intriguingly, young insulin SGs are more likely secreted during glucose-stimulated insulin secretion (GSIS) for unknown reasons, while older SGs tend to lose releasability and be degraded. Here, we examine the roles of microtubule (MT) and Gαo-signaling in regulating the preferential secretion of young versus old SGs. We show that both MT-destabilization and Gαo inactivation results in more SGs localization near plasma membrane (PM) despite higher levels of GSIS and reduced SG biosynthesis. Intriguingly, MT-destabilization or Gαo-inactivation results in higher secretion probabilities of older SGs, while combining both having additive effects on boosting GSIS. Lastly, Gαo inactivation does not detectably destabilize the β-cell MT network. These findings suggest that Gαo and MT can modulate the preferential release of younger insulin SGs via largely parallel pathways.

Characterizing stochastic resonance in a triple cavity

Many biological systems possess confined structures, which produce novel influences on the dynamics. Here, stochastic resonance (SR) in a triple cavity that consists of three units and is subjected to noise, periodic force and vertical constance force is studied, by calculating the spectral amplification η numerically. Meanwhile, SR in the given triple cavity and differences from other structures are explored. First, it is found that the cavity parameters can eliminate or regulate the maximum of η and the noise intensity that induces this maximum. Second, compared to a double cavity with similar maximum/minimum widths and distances between two maximum widths as the triple cavity, η in the triple one shows a larger maximum. Next, the conversion of the natural boundary in the pure potential to the reflection boundary in the triple cavity will create the necessity of a vertical force to induce SR and lead to a decrease in the maximum of η. In addition, η monotonically decreases with the increase of the vertical force and frequency of the periodic force, while it presents several trends when increasing the periodic force's amplitude for different noise intensities. Finally, our studies are extended to the impact of fractional Gaussian noise excitations. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Anomalous diffusion in a bench-scale pulsed fluidized bed

We present our analysis on microrheology of a bench-scale pulsed fluidized bed, which represents a weakly confined system. Nonlinear gas-particle and particle-particle interactions resulting from pulsed flow are associated with harmonic and subharmonic modes. While periodic structured bubble patterns are observed at the mesoscale, particle-scale measurements reveal anomalous diffusion in the driven granular medium. We use single-particle tracks to analyze ergodicity and ageing properties at two pulsing frequencies having remarkably different mesoscale features. The scaling of ensemble-averaged mean-squared displacement is not unique. The distribution of time-averaged mean-squared displacements is non-Gaussian, asymmetric, and has a finite trivial contribution from particles in crowded quasistatic surroundings. Results indicate weak ergodicity breaking, which along with ageing characterizes the nonstationary and out-of-equilibrium dynamics.

Intrinsic fractional noise in nanopores: The effect of reservoirs

Fluctuations affect nanoporous transport in complex and intricate ways, making optimization of the signal-to-noise ratio in artificial designs challenging. Here, we focus on the simplest nanopore system, where non-interacting particles diffuse through a pore separating reservoirs. We find that the concentration difference between both sides (akin to the osmotic pressure drop) exhibits fractional noise in time t with mean square average that grows as t^1/2. This originates from the diffusive exchange of particles from one region to another. We fully rationalize this effect, with particle simulations and analytic solutions. We further infer the parameters (pore radius and pore thickness) that control this exotic behavior. As a consequence, we show that the number of particles within the pore also exhibits fractional noise. Such fractional noise is responsible for noise spectral density scaling as 1/f^3/2 with frequency f, and we quantify its amplitude. Our theoretical approach is applicable to more complex nanoporous systems (for example, with adsorption within the pore) and drastically simplifies both particle simulations and analytic calculus.

ZIGIR, a Granule-Specific Zn2+ Indicator, Reveals Human Islet α Cell Heterogeneity

Numerous mammalian cells contain abundant Zn²⁺ in their secretory granules, yet available Zn²⁺ sensors lack the desired specificity and sensitivity for imaging granular Zn²⁺. We developed a fluorescent zinc granule indicator, ZIGIR, that possesses numerous desired properties for live cell imaging, including >100-fold fluorescence enhancement, membrane permeability, and selective enrichment to acidic granules. The combined advantages endow ZIGIR with superior sensitivity and specificity for imaging granular Zn²⁺. ZIGIR enables separation of heterogenous β cells based on their insulin content and sorting of mouse islets into pure α cells and β cells. In human islets, ZIGIR facilitates sorting of endocrine cells into highly enriched α cells and β cells, reveals unexpectedly high Zn²⁺ activity in the somatostatin granule of some δ cells, and uncovers variation in the glucagon content among human α cells. We expect broad applications of ZIGIR for studying Zn²⁺ biology and Zn²⁺-rich secretory granules and for engineering β cells with high insulin content for treating diabetes.

Glass-like characteristics of intracellular motion in human cells

The motion in the cytosol of microorganisms such as bacteria and yeast has been observed to undergo a dramatic slowing down upon cell energy depletion. These observations have been interpreted as the motion being "glassy," but whether this notion is useful also for active, motor-protein-driven transport in eukaryotic cells is less clear. Here, we use fluorescence microscopy of beads in human (HeLa) cells to probe the motion of membrane-surrounded structures that are carried along the cytoskeleton by motor proteins. Evaluating several hallmarks of glassy dynamics, we show that at short length scales, the motion is heterogeneous, is nonergodic, is well described by a model for the displacement distribution in glassy systems, and exhibits a decoupling of the exchange and persistence times. Overall, these results suggest that the short length scale behavior of objects that can be transported actively by motor proteins in human cells shares features with the motion in glassy systems.

Lévy walk dynamics in mixed potentials from the perspective of random walk theory

Lévy walk process is one of the most effective models to describe superdiffusion, which underlies some important movement patterns and has been widely observed in micro- and macrodynamics. From the perspective of random walk theory, here we investigate the dynamics of Lévy walks under the influences of the constant force field and the one combined with harmonic potential. Utilizing Hermite polynomial approximation to deal with the spatiotemporally coupled analysis challenges, some striking features are detected, including non-Gaussian stationary distribution, faster diffusion, still strongly anomalous diffusion, etc.

Measurements and characterization of the dynamics of tracer particles in an actin network

The underlying physics governing the diffusion of a tracer particle in a viscoelastic material is a topic of some dispute. The long-term memory in the mechanical response of such materials should induce diffusive motion with a memory kernel, such as fractional Brownian motion (fBM). This is the reason that microrheology is able to provide the shear modulus of polymer networks. Surprisingly, the diffusion of a tracer particle in a network of a purified protein, actin, was found to conform to the continuous time random walk type (CTRW). We set out to resolve this discrepancy by studying the tracer particle diffusion using two different tracer particle sizes, in actin networks of different mesh sizes. We find that the ratio of tracer particle size to the characteristic length scale of a bio-polymer network plays a crucial role in determining the type of diffusion it performs. We find that the diffusion of the tracer particles has features of fBm when the particle is large compared to the mesh size, of normal diffusion when the particle is much smaller than the mesh size, and of the CTRW in between these two limits. Based on our findings, we propose and verify numerically a new model for the motion of the tracer in all regimes. Our model suggests that diffusion in actin networks consists of fBm of the tracer particle coupled with caging events with power-law distributed escape times.

Anomalous nanoparticle surface diffusion in LCTEM is revealed by deep learning-assisted analysis

The motion of nanoparticles near surfaces is of fundamental importance in physics, biology, and chemistry. Liquid cell transmission electron microscopy (LCTEM) is a promising technique for studying motion of nanoparticles with high spatial resolution. Yet, the lack of understanding of how the electron beam of the microscope affects the particle motion has held back advancement in using LCTEM for in situ single nanoparticle and macromolecule tracking at interfaces. Here, we experimentally studied the motion of a model system of gold nanoparticles dispersed in water and moving adjacent to the silicon nitride membrane of a commercial LC in a broad range of electron beam dose rates. We find that the nanoparticles exhibit anomalous diffusive behavior modulated by the electron beam dose rate. We characterized the anomalous diffusion of nanoparticles in LCTEM using a convolutional deep neural-network model and canonical statistical tests. The results demonstrate that the nanoparticle motion is governed by fractional Brownian motion at low dose rates, resembling diffusion in a viscoelastic medium, and continuous-time random walk at high dose rates, resembling diffusion on an energy landscape with pinning sites. Both behaviors can be explained by the presence of silanol molecular species on the surface of the silicon nitride membrane and the ionic species in solution formed by radiolysis of water in presence of the electron beam.