Local motion analysis reveals impact of the dynamic cytoskeleton on intracellular subdiffusion

Forced and spontaneous translocation dynamics of a semiflexible active polymer in two dimensions

Polymer translocation is a fundamental topic in non-equilibrium physics and is crucially important to many biological processes in life. In the present work, we adopt two-dimensional Langevin dynamics simulations to study the forced and spontaneous translocation dynamics of an active filament. The influence of polymer stiffness on the underlying dynamics is explicitly analyzed. For the forced translocation, the results show a robust stiffness-induced inhibition, and the translocation time exhibits a dual-exponent scaling relationship with the bending modulus. Tension propagation (TP) is also examined, where we find prominent modifications in terms of both activity and stiffness. For spontaneous translocation into a pure solvent, the translocation time is almost independent of the polymer stiffness. However, when the polymer is translocated into a porous medium, an intriguing non-monotonic alteration of translocation time with increasing chain stiffness is demonstrated. The semiflexible chain is beneficial for translocation while the rigid chain is not conducive. Stiffness regulation on the diffusion dynamics of the polymer in porous media shows a consistent scenario. The interplay of activity, stiffness, and porous crowding provides a new mechanism for understanding the non-trivial translocation dynamics of an active filament in complex environments.

Anomalous diffusion of E. coli under microfluidic confinement and chemical gradient

We report a two-layer microfluidic device to study the combined effect of confinement and chemical gradient on the motility of wild-type E. coli. We track individual E. coli in 50 μm and 10 μm wide microchannels, with a channel height of 2 μm, to generate quasi-2D conditions. We find that contrary to expectations, bacterial trajectories are superdiffusive even in the absence of a chemical (glucose) gradient. The superdiffusive behaviour becomes more pronounced upon introducing a chemical gradient or strengthening the lateral confinement. Run length distributions for weak lateral confinement in the absence of chemical gradients follow an exponential distribution. Both confinement and chemoattraction induce deviations from this behaviour, with the run length distributions approaching a power-law form under these conditions. Both confinement and chemoattraction suppress large-angle tumbles as well. Our results suggest that wild-type E. coli modulates both its runs and tumbles in a similar manner under physical confinement and chemical gradient. Our findings have implications for understanding how bacteria modulate their motility behaviour in natural habitats.

Passive and active tracer dynamics in polymer solutions with isotropic-to-nematic phase transition

Macromolecular crowding plays a crucial role in determining the dynamics in a living cell. We adopt Langevin dynamics simulations to investigate the anomalous diffusion dynamics of passive and active particles in a solution of polymer chains with tunable stiffness. The solution's anisotropic feature is modulated by changing both the polymer stiffness and volume fraction, where isotropic-to-nematic phase transition is involved. Our results demonstrate the significant impact of polymer flexibility on the dynamics of both passive and active probes. The distinct diffusion mechanism for an active particle is clarified by the interplay between polymer stiffness, crowdedness and activity. Polymer stiffness leads to a global inhibition effect on passive particle diffusion. The diffusion coefficient exhibits an intriguing non-monotonic variation at increasing polymer stiffness, which is due to the fact that the alignment of polymer chains is beneficial for diffusion along the nematic direction but unfavorable for that in the direction perpendicular to it. In sharp contrast, polymer stiffness plays a dominant role in facilitating active particle diffusion. Self-propulsion of the particle can utilize stiffness-induced elastic interactions more efficiently, which promotes its mobility in both directions. Meanwhile, an active particle might have a stronger ability to take advantage of the polymer alignment, contributing substantially enhanced diffusivity. In addition, the diffusion coefficient of an active particle is subject to a tendency of degeneration against varying volume fraction. This counter-intuitive behavior is due to the contrasting factors that increasing crowdedness induces a lower particle speed but a longer persistent motion time.

Impact of neurite alignment on organelle motion

Intracellular transport is pivotal for cell growth and survival. Malfunctions in this process have been associated with devastating neurodegenerative diseases, highlighting the need for a deeper understanding of the mechanisms involved. Here, we use an experimental methodology that leads neurites of differentiated PC12 cells into either one of two configurations: a one-dimensional configuration, where the neurites align along lines, or a two-dimensional configuration, where the neurites adopt a random orientation and shape on a flat substrate. We subsequently monitored the motion of functional organelles, the lysosomes, inside the neurites. Implementing a time-resolved analysis of the mean-squared displacement, we quantitatively characterized distinct motion modes of the lysosomes. Our results indicate that neurite alignment gives rise to faster diffusive and super-diffusive lysosomal motion than the situation in which the neurites are randomly oriented. After inducing lysosome swelling through an osmotic challenge by sucrose, we confirmed the predicted slowdown in diffusive mobility. Surprisingly, we found that the swelling-induced mobility change affected each of the (sub-/super-)diffusive motion modes differently and depended on the alignment configuration of the neurites. Our findings imply that intracellular transport is significantly and robustly dependent on cell morphology, which might in part be controlled by the extracellular matrix.

Modelling the motion of organelles in an elongated cell via the coordination of heterogeneous drift-diffusion and long-range transport

 Cellular distribution of organelles in living cells is achieved via a variety of transport mechanisms, including directed motion, mediated by molecular motors along microtubules (MTs), and diffusion which is predominantly heterogeneous in space. In this paper, we introduce a model for particle transport in elongated cells that couples poleward drift, long-range bidirectional transport and diffusion with spatial heterogeneity in a three-dimensional space. Using stochastic simulations and analysis of a related population model, we find parameter regions where the three-dimensional model can be reduced to a coupled one-dimensional model or even a one-dimensional scalar model. We explore the efficiency with which individual model components can overcome drift towards one of the cell poles to reach an approximately even distribution. In particular, we find that if lateral movement is well mixed, then increasing the binding ability of particles to MTs is an efficient way to overcome a poleward drift, whereas if lateral motion is not well mixed, then increasing the axial diffusivity away from MTs becomes an efficient way to overcome the poleward drift. Our three-dimensional model provides a new tool that will help to understand the mechanisms by which eukaryotic cells organize their organelles in an elongated cell, and in particular when the one-dimensional models are applicable.

Collective intracellular cargo transport by multiple kinesins on multiple microtubules

The transport of intracellular organelles is accomplished by groups of molecular motors, such as kinesin, myosin, and dynein. Previous studies have demonstrated that the cooperation between kinesins on a track is beneficial for long transport. However, within crowded three-dimensional (3D) cytoskeletal networks, surplus motors could impair transport and lead to traffic jams of cargos. Comprehensive understanding of the effects of the interactions among molecular motors, cargo, and tracks on the 3D cargo transport dynamics is still lack. In this work, a 3D stochastic multiphysics model is introduced to study the synergistic and antagonistic motions of kinesin motors walking on multiple mircotubules (MTs). Based on the model, we show that kinesins attaching to a common cargo can interact mechanically through the transient forces in their cargo linkers. Under different environmental conditions, such as different MT topologies and kinesin concentrations, the transient forces in the kinesins, the stepping frequency and the binding and unbinding probabilities of kinesins are changed substantially. Therefore, the macroscopic transport properties, specifically the stall force of the cargo, the transport direction at track intersections, and the mean-square displacement (MSD) of the cargo along the MT bundles vary over the environmental conditions. In general, conditions that improve the synergistic motion of kinesins increase the stall force of the cargo and the capability of maintaining the transport. In contrast, the antagonistic motion of kinesins temporarily traps the cargo and slows down the transport. Furthermore, this study predicts an optimal number of kinesins for the cargo transport at MT intersections and along MT bundles.

Non-Gaussian subdiffusion of single-molecule tracers in a hydrated polymer network

Single molecule tracking experiments inside a hydrated polymer network have shown that the tracer motion is subdiffusive due to the viscoelastic environment inside the gel-like network. This property can be related to the negative autocorrelation of the instantaneous displacements at short times. Although the displacements of the individual tracers exhibit Gaussian statistics, the displacement distribution of all the trajectories combined from different spatial locations of the polymer network exhibits a non-Gaussian distribution. Here, we analyze many individual tracer trajectories to show that the central portion of the non-Gaussian distribution can be well approximated by an exponential distribution that spreads sublinearly with time. We explain all these features seen in the experiment by a generalized Langevin model for an overdamped particle with algebraically decaying correlations. We show that the degree of non-Gaussianity can change with the extent of heterogeneity, which is controlled in our model by the experimentally observed distributions of the motion parameters.

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

The diffusion of microscopic particles through the cell, important to processes such as viral infection, gene delivery, and vesicle transport, is largely controlled by the complex cytoskeletal network, comprised of semiflexible actin filaments and rigid microtubules, that pervades the cytoplasm. By varying the relative concentrations of actin and microtubules, the cytoskeleton can display a host of different structural and dynamic properties that, in turn, impact the diffusion of particles through the composite network. Here, we couple single-particle tracking with differential dynamic microscopy to characterize the transport of microsphere tracers diffusing through composite in vitro networks with varying ratios of actin and microtubules. We analyze multiple complementary metrics for anomalous transport to show that particles exhibit anomalous subdiffusion in all networks, which our data suggest arises from caging by networks. Further, subdiffusive characteristics are markedly more pronounced in actin-rich networks, which exhibit similarly more prominent viscoelastic properties compared to microtubule-rich composites. While the smaller mesh size of actin-rich composites compared to microtubule-rich composites plays an important role in these results, the rigidity of the filaments comprising the network also influences the anomalous characteristics that we observe. Our results suggest that as microtubules in our composites are replaced with actin filaments, the decreasing filament rigidity competes with increasing network connectivity to drive anomalous transport.

Membrane Diffusion Occurs by Continuous-Time Random Walk Sustained by Vesicular Trafficking

Diffusion in cellular membranes is regulated by processes that occur over a range of spatial and temporal scales. These processes include membrane fluidity, interprotein and interlipid interactions, interactions with membrane microdomains, interactions with the underlying cytoskeleton, and cellular processes that result in net membrane movement. The complex, non-Brownian diffusion that results from these processes has been difficult to characterize, and moreover, the impact of factors such as membrane recycling on membrane diffusion remains largely unexplored. We have used a careful statistical analysis of single-particle tracking data of the single-pass plasma membrane protein CD93 to show that the diffusion of this protein is well described by a continuous-time random walk in parallel with an aging process mediated by membrane corrals. The overall result is an evolution in the diffusion of CD93: proteins initially diffuse freely on the cell surface but over time become increasingly trapped within diffusion-limiting membrane corrals. Stable populations of freely diffusing and corralled CD93 are maintained by an endocytic/exocytic process in which corralled CD93 is selectively endocytosed, whereas freely diffusing CD93 is replenished by exocytosis of newly synthesized and recycled CD93. This trafficking not only maintained CD93 diffusivity but also maintained the heterogeneous distribution of CD93 in the plasma membrane. These results provide insight into the nature of the biological and biophysical processes that can lead to significantly non-Brownian diffusion of membrane proteins and demonstrate that ongoing membrane recycling is critical to maintaining steady-state diffusion and distribution of proteins in the plasma membrane.

Heterogeneities Shape Passive Intracellular Transport

A living cell's interior is one of the most complex and intrinsically dynamic systems, providing an elaborate interplay between cytosolic crowding and ATP-driven motion that controls cellular functionality. Here, we investigated two distinct fundamental features of the merely passive, non-biomotor-shuttled material transport within the cytoplasm of Dictyostelium discoideum cells: the anomalous non-linear scaling of the mean-squared displacement of a 150-nm-diameter particle and non-Gaussian distribution of increments. Relying on single-particle tracking data of 320,000 data points, we performed a systematic analysis of four possible origins for non-Gaussian transport: 1) sample-based variability, 2) rarely occurring strong motion events, 3) ergodicity breaking/aging, and 4) spatiotemporal heterogeneities of the intracellular medium. After excluding the first three reasons, we investigated the remaining hypothesis of a heterogeneous cytoplasm as cause for non-Gaussian transport. A, to our knowledge, novel fit model with randomly distributed diffusivities implementing medium heterogeneities suits the experimental data. Strikingly, the non-Gaussian feature is independent of the cytoskeleton condition and lag time. This reveals that efficiency and consistency of passive intracellular transport and the related anomalous scaling of the mean-squared displacement are regulated by cytoskeleton components, whereas cytoplasmic heterogeneities are responsible for the generic, non-Gaussian distribution of increments.

Influence of polymer flexibility on nanoparticle dynamics in semidilute solutions

The hierarchical structure and dynamics of polymer solutions control the transport of nanoparticles (NPs) through them. Here, we perform multi-particle collision dynamics simulations of solutions of semiflexible polymer chains with tunable persistence length lp to investigate the effect of chain stiffness on NP transport. The NPs exhibit two distinct dynamical regimes - subdiffusion on short time scales and diffusion on long time scales. The long-time NP diffusivities are compared with predictions from the Stokes-Einstein relation (SER), mode-coupling theory (MCT), and a recent polymer coupling theory (PCT). Increasing deviations from the SER as the polymer chains become more rigid (i.e. as lp increases) indicate that the NP motions become decoupled from the bulk viscosity of the polymer solution. Likewise, polymer stiffness leads to deviations from PCT, which was developed for fully flexible chains. Independent of lp, however, the long-time diffusion behavior is well-described by MCT, particularly at high polymer concentration. We also observed that the short-time subdiffusive dynamics are strongly dependent on polymer flexibility. As lp is increased, the NP dynamics become more subdiffusive and decouple from the dynamics of the polymer chain center-of-mass. We posit that these effects are due to differences in the segmental mobility of the semiflexible chains.

Strong cytoskeleton activity on millisecond timescales upon particle binding revealed by ROCS microscopy

Cells change their shape within seconds, cellular protrusions even on subsecond timescales enabling various responses to stimuli of approaching bacteria, viruses or pharmaceutical drugs. Typical response patterns are governed by a complex reorganization of the actin cortex, where single filaments and molecules act on even faster timescales. These dynamics have remained mostly invisible due to a superposition of slow and fast motions, but also due to a lack of adequate imaging technology. Whereas fluorescence techniques require too long integration times, novel coherent techniques such as ROCS microscopy can achieve sufficiently high spatiotemporal resolution. ROCS uses rotating back-scattered laser light from cellular structures and generates a consistently high image contrast at 150 nm resolution and frame rates of 100 Hz-without fluorescence or bleaching. Here, we present an extension of ROCS microscopy that exploits the principles of dynamic light scattering for precise localization, visualization and quantification of the cytoskeleton activity of mouse macrophages. The locally observed structural reorganization processes, encoded by dynamic speckle patterns, occur upon distinct mechanical stimuli, such as soft contacts with optically trapped beads. We find that a substantial amount of the near-membrane cytoskeleton activity takes place on millisecond timescales, which is much faster than reported ever before.

Active diffusion and advection in Drosophila oocytes result from the interplay of actin and microtubules

Transport in cells occurs via a delicate interplay of passive and active processes, including diffusion, directed transport and advection. Despite progress in super-resolution microscopy, discriminating and quantifying these processes is a challenge, requiring tracking of rapidly moving, sub-diffraction objects in a crowded, noisy environment. Here we use differential dynamic microscopy with different contrast mechanisms to provide a thorough characterization of the dynamics in the Drosophila oocyte. We study the movement of vesicles and the elusive motion of a cytoplasmic F-actin mesh, a known regulator of cytoplasmic flows. We find that cytoplasmic motility constitutes a combination of directed motion and random diffusion. While advection is mainly attributed to microtubules, we find that active diffusion is driven by the actin cytoskeleton, although it is also enhanced by the flow. We also find that an important dynamic link exists between vesicles and cytoplasmic F-actin motion, as recently suggested in mouse oocytes.

Intracellular transport is facilitated by a combination of processes including directed transport, advection and diffusion. Here the authors microscopically characterise the dynamics of the Drosophila oocyte and find distinct contributions of cytoskeletal components to advection and active diffusion.

Statistical properties of the anomalous scaling exponent estimator based on time-averaged mean-square displacement

The most common way of estimating the anomalous scaling exponent from single-particle trajectories consists of a linear fit of the dependence of the time-averaged mean-square displacement on the lag time at the log-log scale. We investigate the statistical properties of this estimator in the case of fractional Brownian motion (FBM). We determine the mean value, the variance, and the distribution of the estimator. Our theoretical results are confirmed by Monte Carlo simulations. In the limit of long trajectories, the estimator is shown to be asymptotically unbiased, consistent, and with vanishing variance. These properties ensure an accurate estimation of the scaling exponent even from a single (long enough) trajectory. As a consequence, we prove that the usual way to estimate the diffusion exponent of FBM is correct from the statistical point of view. Moreover, the knowledge of the estimator distribution is the first step toward new statistical tests of FBM and toward a more reliable interpretation of the experimental histograms of scaling exponents in microbiology.

Label-free, ultrahigh-speed, 3D observation of bidirectional and correlated intracellular cargo transport by coherent brightfield microscopy

The investigation of intracellular transport at the molecular scale requires measurements at high spatial and temporal resolutions. We demonstrate the label-free, direct imaging and tracking of native cell vesicles in live cells at an ultrahigh spatiotemporal resolution. Using coherent brightfield (COBRI) microscopy, we monitor individual cell vesicles traveling inside the cell with nanometer spatial precision in 3D at 30 000 frames per second. The stepwise directional motion of the vesicle on the cytoskeletal track is clearly resolved. We also observe the repeated switching of the transport direction of the vesicle in a continuous trajectory. Our high-resolution measurement unveils the transient pausing and subtle bidirectional motion of the vesicle, taking place over tens of nanometers in tens of milliseconds. By tracking multiple particles simultaneously, we found strong correlations between the motions of two neighboring vesicles. Our label-free ultrahigh-speed optical imaging provides the opportunity to visualize intracellular cargo transport at the nanoscale in the microsecond timescale with minimal perturbation.

Probing cytoskeletal modulation of passive and active intracellular dynamics using nanobody-functionalized quantum dots

The cytoplasm is a highly complex and heterogeneous medium that is structured by the cytoskeleton. How local transport depends on the heterogeneous organization and dynamics of F-actin and microtubules is poorly understood. Here we use a novel delivery and functionalization strategy to utilize quantum dots (QDs) as probes for active and passive intracellular transport. Rapid imaging of non-functionalized QDs reveals two populations with a 100-fold difference in diffusion constant, with the faster fraction increasing upon actin depolymerization. When nanobody-functionalized QDs are targeted to different kinesin motor proteins, their trajectories do not display strong actin-induced transverse displacements, as suggested previously. Only kinesin-1 displays subtle directional fluctuations, because the subset of microtubules used by this motor undergoes prominent undulations. Using actin-targeting agents reveals that F-actin suppresses most microtubule shape remodelling, rather than promoting it. These results demonstrate how the spatial heterogeneity of the cytoskeleton imposes large variations in non-equilibrium intracellular dynamics.

Fluorescence-tunable Ag-DNA biosensor with tailored cytotoxicity for live-cell applications

DNA-stabilized silver clusters (Ag-DNA) show excellent promise as a multi-functional nanoagent for molecular investigations in living cells. The unique properties of these fluorescent nanomaterials allow for intracellular optical sensors with tunable cytotoxicity based on simple modifications of the DNA sequences. Three Ag-DNA nanoagent designs are investigated, exhibiting optical responses to the intracellular environments and sensing-capability of ions, functional inside living cells. Their sequence-dependent fluorescence responses inside living cells include (1) a strong splitting of the fluorescence peak for a DNA hairpin construct, (2) an excitation and emission shift of up to 120 nm for a single-stranded DNA construct, and (3) a sequence robust in fluorescence properties. Additionally, the cytotoxicity of these Ag-DNA constructs is tunable, ranging from highly cytotoxic to biocompatible Ag-DNA, independent of their optical sensing capability. Thus, Ag-DNA represents a versatile live-cell nanoagent addressable towards anti-cancer, patient-specific and anti-bacterial applications.

Active diffusion and microtubule-based transport oppose myosin forces to position organelles in cells

Even distribution of peroxisomes (POs) and lipid droplets (LDs) is critical to their role in lipid and reactive oxygen species homeostasis. How even distribution is achieved remains elusive, but diffusive motion and directed motility may play a role. Here we show that in the fungus Ustilago maydis ∼95% of POs and LDs undergo diffusive motions. These movements require ATP and involve bidirectional early endosome motility, indicating that microtubule-associated membrane trafficking enhances diffusion of organelles. When early endosome transport is abolished, POs and LDs drift slowly towards the growing cell end. This pole-ward drift is facilitated by anterograde delivery of secretory cargo to the cell tip by myosin-5. Modelling reveals that microtubule-based directed transport and active diffusion support distribution, mobility and mixing of POs. In mammalian COS-7 cells, microtubules and F-actin also counteract each other to distribute POs. This highlights the importance of opposing cytoskeletal forces in organelle positioning in eukaryotes.

The mechanisms underlying the positioning of eukaryotic organelles remain elusive. Here Lin et al. use imaging and a mathematical model to show that microtubule-based transport and active diffusion and actin-based polar drift act together to facilitate even distribution of peroxisomes in filamentous fungi.

Challenges in tissue engineering - towards cell control inside artificial scaffolds

Control of living cells is vital for the survival of organisms. Each cell inside an organism is exposed to diverse external mechano-chemical cues, all coordinated in a spatio-temporal pattern triggering individual cell functions. This complex interplay between external chemical cues and mechanical 3D environments is translated into intracellular signaling loops. Here, we describe how external mechano-chemical cues control cell functions, especially cell migration, and influence intracellular information transport. In particular, this work focuses on the quantitative analysis of (1) intracellular vesicle transport to understand intracellular state changes in response to external cues, (2) cellular sensing of external chemotactic cues, and (3) the cells' ability to migrate in 3D structured environments, artificially fabricated to mimic the 3D environment of tissue in the human body.

Amoeboid movement in protozoan pathogens

Entamoeba histolytica, the causative agent of amoebiasis, is a protozoan parasite characterised by its amoeboid motility, which is essential to its survival and invasion of the human host. Elucidating the molecular mechanisms leading to invasion of human tissues by E. histolytica requires a quantitative understanding of how its cytoskeleton deforms and tailors its mode of migration to the local microenvironment. Here we review the wide range of methods available to extract biophysical information from amoeboid cells, from interventional techniques to computational modelling approaches, and discuss how recent developments in bioimaging and bioimage informatics can complement our understanding of cellular morphodynamics at the intracellular level.

Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic Acanthamoeba castellanii

Acanthamoebae are free-living protists and human pathogens, whose cellular functions and pathogenicity strongly depend on the transport of intracellular vesicles and granules through the cytosol. Using high-speed live cell imaging in combination with single-particle tracking analysis, we show here that the motion of endogenous intracellular particles in the size range from a few hundred nanometers to several micrometers in Acanthamoeba castellanii is strongly superdiffusive and influenced by cell locomotion, cytoskeletal elements, and myosin II. We demonstrate that cell locomotion significantly contributes to intracellular particle motion, but is clearly not the only origin of superdiffusivity. By analyzing the contribution of microtubules, actin, and myosin II motors we show that myosin II is a major driving force of intracellular motion in A. castellanii. The cytoplasm of A. castellanii is supercrowded with intracellular vesicles and granules, such that significant intracellular motion can only be achieved by actively driven motion, while purely thermally driven diffusion is negligible.

Active intracellular transport in metastatic cells studied by spatial light interference microscopy

Spatiotemporal patterns of intracellular transport are very difficult to quantify and, consequently, continue to be insufficiently understood. While it is well documented that mass trafficking inside living cells consists of both random and deterministic motions, quantitative data over broad spatiotemporal scales are lacking. We studied the intracellular transport in live cells using spatial light interference microscopy, a high spatiotemporal resolution quantitative phase imaging tool. The results indicate that in the cytoplasm, the intracellular transport is mainly active (directed, deterministic), while inside the nucleus it is both active and passive (diffusive, random). Furthermore, we studied the behavior of the two-dimensional mass density over 30 h in HeLa cells and focused on the active component. We determined the standard deviation of the velocity distribution at the point of cell division for each cell and compared the standard deviation velocity inside the cytoplasm and the nucleus. We found that the velocity distribution in the cytoplasm is consistently broader than in the nucleus, suggesting mechanisms for faster transport in the cytosol versus the nucleus. Future studies will focus on improving phase measurements by applying a fluorescent tag to understand how particular proteins are transported inside the cell.

Active phase and amplitude fluctuations of flagellar beating

The eukaryotic flagellum beats periodically, driven by the oscillatory dynamics of molecular motors, to propel cells and pump fluids. Small but perceivable fluctuations in the beat of individual flagella have physiological implications for synchronization in collections of flagella as well as for hydrodynamic interactions between flagellated swimmers. Here, we characterize phase and amplitude fluctuations of flagellar bending waves using shape mode analysis and limit-cycle reconstruction. We report a quality factor of flagellar oscillations Q = 38.0 ± 16.7 (mean ± s.e.). Our analysis shows that flagellar fluctuations are dominantly of active origin. Using a minimal model of collective motor oscillations, we demonstrate how the stochastic dynamics of individual motors can give rise to active small-number fluctuations in motor-cytoskeleton systems.

Identifying directional persistence in intracellular particle motion using Hidden Markov Models

Particle tracking is a widely used and promising technique for elucidating complex dynamics of the living cell. The cytoplasm is an active material, in which the kinetics of intracellular structures are highly heterogeneous. Tracer particles typically undergo a combination of random motion and various types of directed motion caused by the activity of molecular motors and other non-equilibrium processes. Random switching between more and less directional persistence of motion generally occurs. We present a method for identifying states of motion with different directional persistence in individual particle trajectories. Our analysis is based on a multi-scale turning angle model to characterize motion locally, together with a Hidden Markov Model with two states representing different directional persistence. We define one of the states by the motion of particles in a reference data set where some active processes have been inhibited. We illustrate the usefulness of the method by studying transport of vesicles along microtubules and transport of nanospheres activated by myosin. We study the results using mean square displacements, durations, and particle speeds within each state. We conclude that the method provides accurate identification of states of motion with different directional persistence, with very good agreement in terms of mean-squared displacement between the reference data set and one of the states in the two-state model.

A Brief Review of the Biophysical Hallmarks of Metastatic Cancer Cells

A hallmark of metastatic cancer cells is their invasion through the basal membrane and endothelial layer, which requires a highly elastic cytoskeleton and nucleus. Therefore, cellular deformability can serve as a universal biophysical marker for detecting a tumor's propensity for invasion, migration, and metastasis. In this review, we define the importance of the biophysical features of cancer cells in tumor metastasis and summarize the state-of-the-art technology for the study of cell biomechanics. This review will serve as a brief introduction to the interdisciplinary character of cancer cell biophysics for cancer biologists, physicists, and engineers.

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

The effect of nanoparticle uptake on cellular behavior: disrupting or enabling functions?

Nanoparticles (NPs) are materials with overall dimensions in the nanoscale range. They have unique physicochemical properties, and have emerged as important players in current research in modern medicine. In the last few decades, several types of NPs and microparticles have been synthesized and proposed for use as contrast agents for diagnostics and imaging and for drug delivery; for example, in cancer therapy. Yet specific targeting that will improve their delivery still represents an unsolved challenge. The mechanism by which NPs enter the cell has important implications not only for their fate but also for their impact on biological systems. Several papers in the literature discuss the potential risks related to NP exposure, and more recently the concept that even sublethal doses of NPs may elicit a cell response has been proposed. In this review, we intend to present an overall view of cell mechanisms that may be perturbed by cell-NP interaction. Published data, in fact, emphasize that NPs should no longer be viewed only as simple carriers for biomedical applications, but that they can also play an active role in mediating biological effects.

Distributions of diffusion measures from a local mean-square displacement analysis

In cell biology, time-resolved fluctuation analysis of tracer particles has recently gained great importance. One such method is the local mean-square displacement (MSD) analysis, which provides an estimate of two parameters as functions of time: the exponent of growth of the MSD and the diffusion coefficient. Here, we study the joint and marginal distributions of these parameters for Brownian motion with Gaussian velocity fluctuations, including the cases of vanishing correlations (overdamped Brownian motion) and of a finite negative velocity correlation (as observed in intracellular motion). Numerically, we demonstrate that a small number of MSD points is optimal for the estimation of the diffusion measures. Motivated by this observation, we derive an analytic approximation for the joint and marginal probability densities of the exponent and diffusion coefficient for the special case of two MSD points. These analytical results show good agreement with numerical simulations for sufficiently large window sizes. Our results might promote better statistical analysis of intracellular motility.

Spatial simulations in systems biology: from molecules to cells

Cells are highly organized objects containing millions of molecules. Each biomolecule has a specific shape in order to interact with others in the complex machinery. Spatial dynamics emerge in this system on length and time scales which can not yet be modeled with full atomic detail. This review gives an overview of methods which can be used to simulate the complete cell at least with molecular detail, especially Brownian dynamics simulations. Such simulations require correct implementation of the diffusion-controlled reaction scheme occurring on this level. Implementations and applications of spatial simulations are presented, and finally it is discussed how the atomic level can be included for instance in multi-scale simulation methods.