Statistical modeling of mRNP transport in dendrites: A comparative analysis of ß-actin and Arc mRNP dynamics.

Localization of messenger RNA (mRNA) in dendrites is crucial for regulating gene expression during long-term memory formation. mRNA binds to RNA-binding proteins (RBPs) to form messenger ribonucleoprotein (mRNP) complexes that are transported by motor proteins along microtubules to their target synapses. However, the dynamics by which mRNPs find their target locations in the dendrite have not been well understood. Here, we investigated the motion of endogenous ß-actin and Arc mRNPs in dissociated mouse hippocampal neurons using the MS2 and PP7 stem-loop systems, respectively. By evaluating the statistical properties of mRNP movement, we found that the aging Lévy walk model effectively describes both ß-actin and Arc mRNP transport in proximal dendrites. A critical difference between ß-actin and Arc mRNPs was the aging time, the time lag between transport initiation and measurement initiation. The longer mean aging time of ß-actin mRNP (~100 s) compared with that of Arc mRNP (~30 s) reflects the longer half-life of constitutively expressed ß-actin mRNP. Furthermore, our model also permitted us to estimate the ratio of newly generated and pre-existing ß-actin mRNPs in the dendrites. This study offers a robust theoretical framework for mRNP transport, which provides insight into how mRNPs locate their targets in neurons.

Stochastic chromatin packing of 3D mitotic chromosomes revealed by coherent X-rays.

DNA molecules are atomic-scale information storage molecules that promote reliable information transfer via fault-free repetitions of replications and transcriptions. Remarkable accuracy of compacting a few-meters-long DNA into a micrometer-scale object, and the reverse, makes the chromosome one of the most intriguing structures from both physical and biological viewpoints. However, its three-dimensional (3D) structure remains elusive with challenges in observing native structures of specimens at tens-of-nanometers resolution. Here, using cryogenic coherent X-ray diffraction imaging, we succeeded in obtaining nanoscale 3D structures of metaphase chromosomes that exhibited a random distribution of electron density without characteristics of high-order folding structures. Scaling analysis of the chromosomes, compared with a model structure having the same density profile as the experimental results, has discovered the fractal nature of density distributions. Quantitative 3D density maps, corroborated by molecular dynamics simulations, reveal that internal structures of chromosomes conform to diffusion-limited aggregation behavior, which indicates that 3D chromatin packing occurs via stochastic processes.

Nonequilibrium diffusion of active particles bound to a semiflexible polymer network: Simulations and fractional Langevin equation.

In a viscoelastic environment, the diffusion of a particle becomes non-Markovian due to the memory effect. An open question concerns quantitatively explaining how self-propulsion particles with directional memory diffuse in such a medium. Based on simulations and analytic theory, we address this issue with active viscoelastic systems where an active particle is connected with multiple semiflexible filaments. Our Langevin dynamics simulations show that the active cross-linker displays superdiffusive and subdiffusive athermal motion with a time-dependent anomalous exponent α. In such viscoelastic feedback, the active particle always exhibits superdiffusion with α = 3/2 at times shorter than the self-propulsion time (τA). At times greater than τA, the subdiffusive motion emerges with α bounded between 1/2 and 3/4. Remarkably, active subdiffusion is reinforced as the active propulsion (Pe) is more vigorous. In the high Pe limit, athermal fluctuation in the stiff filament eventually leads to α = 1/2, which can be misinterpreted with the thermal Rouse motion in a flexible chain. We demonstrate that the motion of active particles cross-linking a network of semiflexible filaments can be governed by a fractional Langevin equation combined with fractional Gaussian noise and an Ornstein-Uhlenbeck noise. We analytically derive the velocity autocorrelation function and mean-squared displacement of the model, explaining their scaling relations as well as the prefactors. We find that there exist the threshold Pe (Pe∗) and crossover times (τ∗ and τ†) above which active viscoelastic dynamics emerge on timescales of τ∗≲ t ≲ τ†. Our study may provide theoretical insight into various nonequilibrium active dynamics in intracellular viscoelastic environments.

Fractal and Knot-Free Chromosomes Facilitate Nucleoplasmic Transport.

Chromosomes in the nucleus assemble into hierarchies of 3D domains that, during interphase, share essential features with a knot-free condensed polymer known as the fractal globule (FG). The FG-like chromosome likely affects macromolecular transport, yet its characteristics remain poorly understood. Using computer simulations and scaling analysis, we show that the 3D folding and macromolecular size of the chromosomes determine their transport characteristics. Large-scale subdiffusion occurs at a critical particle size where the network of accessible volumes is critically connected. Condensed chromosomes have connectivity networks akin to simple Bernoulli bond percolation clusters, regardless of the polymer models. However, even if the network structures are similar, the tracer's walk dimension varies. It turns out that the walk dimension depends on the network topology of the accessible volume and dynamic heterogeneity of the tracer's hopping rate. We find that the FG structure has a smaller walk dimension than other random geometries, suggesting that the FG-like chromosome structure accelerates macromolecular diffusion and target-search.

Anomalous diffusion of active Brownian particles cross-linked to a networked polymer: Langevin dynamics simulation and theory.

Quantitatively understanding the dynamics of an active Brownian particle (ABP) interacting with a viscoelastic polymer environment is a scientific challenge. It is intimately related to several interdisciplinary topics such as the microrheology of active colloids in a polymer matrix and the athermal dynamics of the in vivo chromosomes or cytoskeletal networks. Based on Langevin dynamics simulation and analytic theory, here we explore such a viscoelastic active system in depth using a star polymer of functionality f with the center cross-linker particle being ABP. We observe that the ABP cross-linker, despite its self-propelled movement, attains an active subdiffusion with the scaling ΔR2(t) ∼ tα with α ≤ 1/2, through the viscoelastic feedback from the polymer. Counter-intuitively, the apparent anomaly exponent α becomes smaller as the ABP is driven by a larger propulsion velocity, but is independent of functionality f or the boundary conditions of the polymer. We set forth an exact theory and show that the motion of the active cross-linker is a Gaussian non-Markovian process characterized by two distinct power-law displacement correlations. At a moderate Péclet number, it seemingly behaves as fractional Brownian motion with a Hurst exponent H = α/2, whereas, at a high Péclet number, the self-propelled noise in the polymer environment leads to a logarithmic growth of the mean squared displacement (∼ln t) and a velocity autocorrelation decaying as -t-2. We demonstrate that the anomalous diffusion of the active cross-linker is precisely described by a fractional Langevin equation with two distinct random noises.

Fluctuations of random walks in critical random environments.

Percolation networks have been widely used in the description of porous media but are now found to be relevant to understand the motion of particles in cellular membranes or the nucleus of biological cells. Random walks on the infinite cluster at criticality of a percolation network are asymptotically ergodic. On any finite size cluster of the network stationarity is reached at finite times, depending on the cluster's size. Despite of this we here demonstrate by combination of analytical calculations and simulations that at criticality the disorder and cluster size average of the ensemble of clusters leads to a non-vanishing variance of the time averaged mean squared displacement, regardless of the measurement time. Fluctuations of this relevant experimental quantity due to the disorder average of such ensembles are thus persistent and non-negligible. The relevance of our results for single particle tracking analysis in complex and biological systems is discussed.

Geometry controlled anomalous diffusion in random fractal geometries: looking beyond the infinite cluster.

We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T(-h) with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.

Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion.

Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is 〈x(2)(t)〉 ≃ 2K(t)t with K(t) ≃ t(α-1) for 0 < α < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellular compartments or when optical tweezers tracking methods are used.

Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking.

Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.

An effective mesoscopic model of double-stranded DNA.

Watson and Crick's epochal presentation of the double helix structure in 1953 has paved the way to intense exploration of DNA's vital functions in cells. Also, recent advances of single molecule techniques have made it possible to probe structures and mechanics of constrained DNA at length scales ranging from nanometers to microns. There have been a number of atomistic scale quantum chemical calculations or molecular level simulations, but they are too computationally demanding or analytically unfeasible to describe the DNA conformation and mechanics at mesoscopic levels. At micron scales, on the other hand, the wormlike chain model has been very instrumental in describing analytically the DNA mechanics but lacks certain molecular details that are essential in describing the hybridization, nano-scale confinement, and local denaturation. To fill this fundamental gap, we present a workable and predictive mesoscopic model of double-stranded DNA where the nucleotides beads constitute the basic degrees of freedom. With the inter-strand stacking given by an interaction between diagonally opposed monomers, the model explains with analytical simplicity the helix formation and produces a generalized wormlike chain model with the concomitant large bending modulus given in terms of the helical structure and stiffness. It also explains how the helical conformation undergoes overstretch transition to the ladder-like conformation at a force plateau, in agreement with the experiment.

Pedicled abdominal flap using deep inferior epigastric artery perforators for forearm reconstruction: A case report.

BACKGROUND: Pedicled abdominal flaps are a widely used surgical technique for forearm reconstruction in patients with soft tissue defects. However, some drawbacks include restricted flap size, partial flap loss, and donor-site morbidity. To address these concerns, we present a case of a pedicled abdominal flap using the deep inferior epigastric artery perforators (DIEP) for forearm reconstruction in a patient with a large soft tissue defect. CASE SUMMARY: A 46-year-old male patient was admitted to our hospital with forearm injury caused by a pressing machine. A 15 cm × 10 cm soft tissue defect with complete rupture of the ulnar side structures of the forearm was found. One week after orthopedic management of the neurovascular injury and fractures using the first stage of Masquelet technique, the patient was referred to the plastic and reconstructive surgery department for wound coverage. Surgical debridement and negative-pressure wound therapy revealed a 20 cm × 15 cm soft tissue defect. A pedicle abdominal flap with the DIEP was used to cover the defect. Three weeks later, the flap was detached from the abdomen, and the abdominal defect was directly closed. Subsequently, the second stage of Masquelet technique was performed at the fracture site at week 10. Finally, all donor and recipient sites healed without complications, such as flap dehiscence, infection, hematoma, or necrosis. Fracture site osteosynthesis was achieved without complications. CONCLUSION: Pedicled abdominal flap using the DIEP provides a reliable option for forearm reconstruction in patients with large soft tissue defects.

Noisy continuous time random walks.

Experimental studies of the diffusion of biomolecules within biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here, we consider subdiffusive continuous time random walks that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time random walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time random walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, such noisy continuous time random walks may appear ergodic, while the bare continuous time random walk exhibits weak ergodicity breaking. Detailed knowledge of this behavior will be useful for the truthful physical analysis of experimentally observed subdiffusion.

A machine learning approach to discover migration modes and transition dynamics of heterogeneous dendritic cells.

Dendritic cell (DC) migration is crucial for mounting immune responses. Immature DCs (imDCs) reportedly sense infections, while mature DCs (mDCs) move quickly to lymph nodes to deliver antigens to T cells. However, their highly heterogeneous and complex innate motility remains elusive. Here, we used an unsupervised machine learning (ML) approach to analyze long-term, two-dimensional migration trajectories of Granulocyte-macrophage colony-stimulating factor (GMCSF)-derived bone marrow-derived DCs (BMDCs). We discovered three migratory modes independent of the cell state: slow-diffusive (SD), slow-persistent (SP), and fast-persistent (FP). Remarkably, imDCs more frequently changed their modes, predominantly following a unicyclic SD→FP→SP→SD transition, whereas mDCs showed no transition directionality. We report that DC migration exhibits a history-dependent mode transition and maturation-dependent motility changes are emergent properties of the dynamic switching of the three migratory modes. Our ML-based investigation provides new insights into studying complex cellular migratory behavior.

Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins.

Combining extensive molecular dynamics simulations of lipid bilayer systems of varying chemical compositions with single-trajectory analyses, we systematically elucidate the stochastic nature of the lipid motion. We observe subdiffusion over more than 4 orders of magnitude in time, clearly stretching into the submicrosecond domain. The lipid motion depends on the lipid chemistry, the lipid phase, and especially the presence of cholesterol. We demonstrate that fractional Langevin equation motion universally describes the lipid motion in all phases, including the gel phase, and in the presence of cholesterol. The results underline the relevance of anomalous diffusion in lipid bilayers and the strong effects of the membrane composition.

Formation of cellular close-ended tunneling nanotubes through mechanical deformation.

Membrane nanotubes or tunneling nanotubes (TNTs) that connect cells have been recognized as a previously unidentified pathway for intercellular transport between distant cells. However, it is unknown how this delicate structure, which extends over tens of micrometers and remains robust for hours, is formed. Here, we found that a TNT develops from a double filopodial bridge (DFB) created by the physical contact of two filopodia through helical deformation of the DFB. The transition of a DFB to a close-ended TNT is most likely triggered by disruption of the adhesion of two filopodia by mechanical energy accumulated in a twisted DFB when one of the DFB ends is firmly attached through intercellular cadherin-cadherin interactions. These studies pinpoint the mechanistic questions about TNTs and elucidate a formation mechanism.

In vivo anomalous diffusion and weak ergodicity breaking of lipid granules.

Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion.

Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking.

Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is connected with non-ergodic behaviour. In such cases the time averages remain random variables and hence irreproducible. Here we present a detailed analysis of the time averaged mean squared displacement for systems governed by anomalous diffusion, considering both unconfined and restricted (corralled) motion. We discuss the behaviour of the time averaged mean squared displacement for two prominent stochastic processes, namely, continuous time random walks and fractional Brownian motion. We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristics even for short time series. Recently, velocity correlation functions were suggested to distinguish between these processes. We here present analytical expressions for the velocity correlation functions. The knowledge of the results presented here is expected to be relevant for the correct interpretation of single particle trajectory data in complex systems.

Cleavage of HSP90ß induced by histone deacetylase inhibitor and proteasome inhibitor modulates cell growth and apoptosis.

HSP90, one of the molecular chaperones, contributes to protein stability in most living organisms. Previously, we found cleavage of HSP90 by caspase 10 in response to treatment with histone deacetylase inhibitor or proteasome inhibitor in leukemic cell lines. In this study, we investigated this phenomenon in various cell lines and found that HSP90 was cleaved by treatment with SAHA or MG132 in 6 out of 16 solid tumor cell lines. To further investigate the effects of HSP90 cleavage on cells, we introduced mutations to the potential cleavage sites of HSP90ß and found that the 294th aspartic acid residue of the protein was mainly cleaved. In the K562 and Mia-PaCa-2 cell lines expressing HSP90ß D294A, the cleavage of HSP90 by the treatment with SAHA or MG132 was reduced compared with the K562 and Mia-PaCa-2 cell lines expressing HSP90ß WT. Accordingly, cell growth and survival were enhanced by HSP90ß D294A expression. Therefore, we suggest that HSP90 cleavage widely occurs in several cell lines, and cleavage of HSP90 may have a potential for one of the mechanisms involved in the anti-tumor effects of known drugs and novel anti-tumor drug candidates.

Objective comparison of methods to decode anomalous diffusion.

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.

Supercoiling induces denaturation bubbles in circular DNA.

We present a theoretical framework for the thermodynamic properties of supercoiling-induced denaturation bubbles in circular double-stranded DNA molecules. We explore how DNA supercoiling, ambient salt concentration, and sequence heterogeneity impact on the bubble occurrence. An analytical derivation of the probability distribution to find multiple bubbles is derived and the relevance for supercoiled DNA discussed. We show that in vivo sustained DNA bubbles are likely to occur due to partial twist release in regions rich in weaker AT base pairs. Single DNA plasmid imaging experiments clearly demonstrate the existence of bubbles in free solution.