Nature's microfluidic transporter: rotational cytoplasmic streaming at high Péclet numbers

Active chiral flows in the separating wall during cell division

Material flow in the actomyosin cortex of a cell, during cell division, has been found to be chiral in nature. It has been attributed to active chiral torques generated in the actomyosin cortex. Here, we explore the possible signature of such chirality during the growth of the intra-cellular membrane partition, which physically divides the cell into two compartments. We use standard hydrodynamic theory of active gel to predict possible chiral flow structures in the growing partition. While the flows in the growing annular-shaped membrane partition is believed to be radial, it can also develop non-zero azimuthal velocity components (rotation) due to chirality. We show that the direction of rotation (clock or anti-clockwise) will not solely be decided by the sign of the active chiral torque but also by the relative strengths of rotational viscosity and flow coupling parameter.

Cytoplasmic stirring by active carpets

Large cells often rely on cytoplasmic flows for intracellular transport, maintaining homeostasis, and positioning cellular components. Understanding the mechanisms of these flows is essential for gaining insights into cell function, developmental processes, and evolutionary adaptability. Here, we focus on a class of self-organized cytoplasmic stirring mechanisms that result from fluid-structure interactions between cytoskeletal elements at the cell cortex. Drawing inspiration from streaming flows in late-stage fruit fly oocytes, we propose an analytically tractable active carpet theory. This model deciphers the origins and three-dimensional spatiotemporal organization of such flows. Through a combination of simulations and weakly nonlinear theory, we establish the pathway of the streaming flow to its global attractor: a cell-spanning vortical twister. Our study reveals the inherent symmetries of this emergent flow, its low-dimensional structure, and illustrates how complex fluid-structure interaction aligns with classical solutions in Stokes flow. This framework can be easily adapted to elucidate a broad spectrum of self-organized, cortex-driven intracellular flows.

Self-organized intracellular twisters

Life in complex systems, such as cities and organisms, comes to a standstill when global coordination of mass, energy, and information flows is disrupted. Global coordination is no less important in single cells, especially in large oocytes and newly formed embryos, which commonly use fast fluid flows for dynamic reorganization of their cytoplasm. Here, we combine theory, computing, and imaging to investigate such flows in the Drosophila oocyte, where streaming has been proposed to spontaneously arise from hydrodynamic interactions among cortically anchored microtubules loaded with cargo-carrying molecular motors. We use a fast, accurate, and scalable numerical approach to investigate fluid-structure interactions of 1000s of flexible fibers and demonstrate the robust emergence and evolution of cell-spanning vortices, or twisters. Dominated by a rigid body rotation and secondary toroidal components, these flows are likely involved in rapid mixing and transport of ooplasmic components.

Helical flow states in active nematics

We show that confining extensile nematics in three-dimensional (3D) channels leads to the emergence of two self-organized flow states with nonzero helicity. The first is a pair of braided antiparallel streams-this double helix occurs when the activity is moderate, anchoring negligible, and reduced temperature high. The second consists of axially aligned counter-rotating vortices-this grinder train arises between spontaneous axial streaming and the vortex lattice. These two unanticipated helical flow states illustrate the potential of active fluids to break symmetries and form complex but organized spatiotemporal structures in 3D fluidic devices.

An update on passive transport in and out of plant cells

Transport across membranes is critical for plant survival. Membranes are the interfaces at which plants interact with their environment. The transmission of energy and molecules into cells provides plants with the source material and power to grow, develop, defend, and move. An appreciation of the physical forces that drive transport processes is thus important for understanding the plant growth and development. We focus on the passive transport of molecules, describing the fundamental concepts and demonstrating how different levels of abstraction can lead to different interpretations of the driving forces. We summarize recent developments on quantitative frameworks for describing diffusive and bulk flow transport processes in and out of cells, with a more detailed focus on plasmodesmata, and outline open questions and challenges.

Getting around the cell: physical transport in the intracellular world

Eukaryotic cells face the challenging task of transporting a variety of particles through the complex intracellular milieu in order to deliver, distribute, and mix the many components that support cell function. In this review, we explore the biological objectives and physical mechanisms of intracellular transport. Our focus is on cytoplasmic and intra-organelle transport at the whole-cell scale. We outline several key biological functions that depend on physically transporting components across the cell, including the delivery of secreted proteins, support of cell growth and repair, propagation of intracellular signals, establishment of organelle contacts, and spatial organization of metabolic gradients. We then review the three primary physical modes of transport in eukaryotic cells: diffusive motion, motor-driven transport, and advection by cytoplasmic flow. For each mechanism, we identify the main factors that determine speed and directionality. We also highlight the efficiency of each transport mode in fulfilling various key objectives of transport, such as particle mixing, directed delivery, and rapid target search. Taken together, the interplay of diffusion, molecular motors, and flows supports the intracellular transport needs that underlie a broad variety of biological phenomena.

Aster swarming by symmetry breaking of cortical dynein transport and coupling kinesins

Microtubule (MT) radial arrays or asters establish the internal topology of a cell by interacting with organelles and molecular motors. We proceed to understand the general pattern forming potential of aster-motor systems using a computational model of multiple MT asters interacting with motors in cellular confinement. In this model dynein motors are attached to the cell cortex and plus-ended motors resembling kinesin-5 diffuse in the cell interior. The introduction of 'noise' in the form of MT length fluctuations spontaneously results in the emergence of coordinated, achiral vortex-like rotation of asters. The coherence and persistence of rotation require a threshold density of both cortical dyneins and coupling kinesins, while the onset is diffusion-limited with relation to the cortical dynein mobility. The coordinated rotational motion emerges due to the resolution of a 'tug-of-war' of multiple cortical dynein motors bound to MTs of the same aster by 'noise' in the form of MT dynamic instability. This transient symmetry breaking is amplified by local coupling by kinesin-5 complexes. The lack of widespread aster rotation across cell types suggests that biophysical mechanisms that suppress such intrinsic dynamics may have evolved. This model is analogous to more general models of locally coupled self-propelled particles (SPP) that spontaneously undergo collective transport in the presence of 'noise' that have been invoked to explain swarming in birds and fish. However, the aster-motor system is distinct from SPP models with regard to the particle density and 'noise' dependence, providing a set of experimentally testable predictions for a novel sub-cellular pattern forming system.

Cyclosis-mediated long distance communications of chloroplasts in giant cells of Characeae

Long-distance communications in giant characean internodal cells involve cytoplasmic streaming as an effective means for transportation of regulatory substances. The local illumination of Chara corallina Klein ex C.L.Willdenow internodal cells with an intense 30s pulse of white light caused a transient increase of modulated chlorophyll fluorescence in cell regions positioned downstream the cytoplasmic flow after a delay whose duration increased with the axial distance from the light source. No changes in fluorescence were observed in cell regions residing upstream of the light spot. The transient increase in actual fluorescence F' in cell areas exposed to constant dim illumination at large distances from the brightly lit area indicates the transmission of photosynthetically active metabolite between chloroplasts separated by 1-5mm distances. The shapes of fluorescence transients were sensitive to retardation of cytoplasmic streaming by cytochalasin D and to variations in cyclosis velocity during gradual recovery of streaming after an instant arrest of cyclosis by elicitation of the action potential. Furthermore, the analysed fluorescence transients were skewed on the ascending or descending fronts depending on the position of light-modulated cytoplasmic package at the moment of streaming cessation with respect to the point of measurements. The observations are simulated in qualitative terms with a simplified streaming-diffusion model.

Fountain streaming contributes to fast tip-growth through regulating the gradients of turgor pressure and concentration in pollen tubes

Fountain streaming is a typical microfluidic pattern in plant cells, especially for cells with a high aspect ratio such as pollen tubes. Although it has been found that fountain streaming plays crucial roles in the transport of nutrients and metabolites, the positioning of organelles and the mixing of cytoplasms, its implications for the fast tip growth of pollen tubes remain a mystery. To address this, based on the observations of asiatic lily Lilium Casablanca, we developed physical models for reverse fountain streaming in pollen tubes and solved the hydrodynamics and advection-diffusion dynamics of viscous Stokes flow in the shank and apical region of pollen tubes. Theoretical and numerical results demonstrated that the gradients of turgor pressure and concentration of wall materials along the length of pollen tubes provide undamped driving force and high-efficiency materials supply, which are supposed to contribute to the fast tip-growth of pollen tubes. The sample experimental results show that the tip-growth will be abnormal when the gradients of turgor pressure change under osmotic stress induced by different concentrations of PEG-6000 (a dehydrant).

Diffusive Promotion by Velocity Gradient of Cytoplasmic Streaming (CPS) in Nitella Internodal Cells

Cytoplasmic streaming (CPS) is well known to assist the movement of nutrients, organelles and genetic material by transporting all of the cytoplasmic contents of a cell. CPS is generated by motility organelles that are driven by motor proteins near a membrane surface, where the CPS has been found to have a flat velocity profile in the flow field according to the sliding theory. There is a consistent mixing of contents inside the cell by CPS if the velocity gradient profile is flattened, which is not assisted by advection diffusion but is only supported by Brownian diffusion. Although the precise flow structure of the cytoplasm has an important role for cellular metabolism, the hydrodynamic mechanism of its convection has not been clarified. We conducted an experiment to visualise the flow of cytoplasm in Nitella cells by injecting tracer fluorescent nanoparticles and using a flow visualisation system in order to understand how the flow profile affects their metabolic system. We determined that the velocity field in the cytosol has an obvious velocity gradient, not a flattened gradient, which suggests that the gradient assists cytosolic mixing by Taylor–Aris dispersion more than by Brownian diffusion.

Efficient mass transport by optical advection

Advection is critical for efficient mass transport. For instance, bare diffusion cannot explain the spatial and temporal scales of some of the cellular processes. The regulation of intracellular functions is strongly influenced by the transport of mass at low Reynolds numbers where viscous drag dominates inertia. Mimicking the efficacy and specificity of the cellular machinery has been a long time pursuit and, due to inherent flexibility, optical manipulation is of particular interest. However, optical forces are relatively small and cannot significantly modify diffusion properties. Here we show that the effectiveness of microparticle transport can be dramatically enhanced by recycling the optical energy through an effective optical advection process. We demonstrate theoretically and experimentally that this new advection mechanism permits an efficient control of collective and directional mass transport in colloidal systems. The cooperative long-range interaction between large numbers of particles can be optically manipulated to create complex flow patterns, enabling efficient and tunable transport in microfluidic lab-on-chip platforms.

A physical perspective on cytoplasmic streaming

Organisms show a remarkable range of sizes, yet the dimensions of a single cell rarely exceed 100 µm. While the physical and biological origins of this constraint remain poorly understood, exceptions to this rule give valuable insights. A well-known counterexample is the aquatic plant Chara, whose cells can exceed 10 cm in length and 1 mm in diameter. Two spiralling bands of molecular motors at the cell periphery drive the cellular fluid up and down at speeds up to 100 µm s(-1), motion that has been hypothesized to mitigate the slowness of metabolite transport on these scales and to aid in homeostasis. This is the most organized instance of a broad class of continuous motions known as 'cytoplasmic streaming', found in a wide range of eukaryotic organisms-algae, plants, amoebae, nematodes and flies-often in unusually large cells. In this overview of the physics of this phenomenon, we examine the interplay between streaming, transport and cell size and discuss the possible role of self-organization phenomena in establishing the observed patterns of streaming.

Drag of the cytosol as a transport mechanism in neurons

Axonal transport is typically divided into two components, which can be distinguished by their mean velocity. The fast component includes steady trafficking of different organelles and vesicles actively transported by motor proteins. The slow component comprises nonmembranous materials that undergo infrequent bidirectional motion. The underlying mechanism of slow axonal transport has been under debate during the past three decades. We propose a simple displacement mechanism that may be central for the distribution of molecules not carried by vesicles. It relies on the cytoplasmic drag induced by organelle movement and readily accounts for key experimental observations pertaining to slow-component transport. The induced cytoplasmic drag is predicted to depend mainly on the distribution of microtubules in the axon and the organelle transport rate.

Cytoplasmic streaming in plant cells emerges naturally by microfilament self-organization

Many cells exhibit large-scale active circulation of their entire fluid contents, a process termed cytoplasmic streaming. This phenomenon is particularly prevalent in plant cells, often presenting strikingly regimented flow patterns. The driving mechanism in such cells is known: myosin-coated organelles entrain cytoplasm as they process along actin filament bundles fixed at the periphery. Still unknown, however, is the developmental process that constructs the well-ordered actin configurations required for coherent cell-scale flow. Previous experimental works on streaming regeneration in cells of Characean algae, whose longitudinal flow is perhaps the most regimented of all, hint at an autonomous process of microfilament self-organization driving the formation of streaming patterns during morphogenesis. Working from first principles, we propose a robust model of streaming emergence that combines motor dynamics with both microscopic and macroscopic hydrodynamics to explain how several independent processes, each ineffectual on its own, can reinforce to ultimately develop the patterns of streaming observed in the Characeae and other streaming species.

Cytoplasmic electric fields and electroosmosis: possible solution for the paradoxes of the intracellular transport of biomolecules

The objective of the paper is to show that electroosmotic flow might play an important role in the intracellular transport of biomolecules. The paper presents two mathematical models describing the role of electroosmosis in the transport of the negatively charged messenger proteins to the negatively charged nucleus and in the recovery of the fluorescence after photobleaching. The parameters of the models were derived from the extensive review of the literature data. Computer simulations were performed within the COMSOL 4.2a software environment. The first model demonstrated that the presence of electroosmosis might intensify the flux of messenger proteins to the nucleus and allow the efficient transport of the negatively charged phosphorylated messenger proteins against the electrostatic repulsion of the negatively charged nucleus. The second model revealed that the presence of the electroosmotic flow made the time of fluorescence recovery dependent on the position of the bleaching spot relative to cellular membrane. The magnitude of the electroosmotic flow effect was shown to be quite substantial, i.e. increasing the flux of the messengers onto the nucleus up to 4-fold relative to pure diffusion and resulting in the up to 3-fold change in the values of fluorescence recovery time, and therefore the apparent diffusion coefficient determined from the fluorescence recovery after photobleaching experiments. Based on the results of the modeling and on the universal nature of the electroosmotic flow, the potential wider implications of electroosmotic flow in the intracellular and extracellular biological processes are discussed. Both models are available for download at ModelDB.

Active chiral processes in thin films

We develop a generic description of thin active films that captures key features of flow and rotation patterns emerging from the activity of chiral motors which introduce torque dipoles. We highlight the role of the spin rotation field and show that fluid flows can occur in two ways: by coupling of the spin rotation rate to the velocity field via a surface or by spatial gradients of the spin rotation rate. We discuss our results in the context of patches of bacteria on solid surfaces and groups of rotating cilia. Our theory could apply to active chiral processes in the cell cytoskeleton and in epithelia.

Cytoplasmic streaming in Drosophila oocytes varies with kinesin activity and correlates with the microtubule cytoskeleton architecture

Cells can localize molecules asymmetrically through the combined action of cytoplasmic streaming, which circulates their fluid contents, and specific anchoring mechanisms. Streaming also contributes to the distribution of nutrients and organelles such as chloroplasts in plants, the asymmetric position of the meiotic spindle in mammalian embryos, and the developmental potential of the zygote, yet little is known quantitatively about the relationship between streaming and the motor activity which drives it. Here we use Particle Image Velocimetry to quantify the statistical properties of Kinesin-dependent streaming during mid-oogenesis in Drosophila. We find that streaming can be used to detect subtle changes in Kinesin activity and that the flows reflect the architecture of the microtubule cytoskeleton. Furthermore, based on characterization of the rheology of the cytoplasm in vivo, we establish estimates of the number of Kinesins required to drive the observed streaming. Using this in vivo data as the basis of a model for transport, we suggest that the disordered character of transport at mid-oogenesis, as revealed by streaming, is an important component of the localization dynamics of the body plan determinant oskar mRNA.

Coupling of active motion and advection shapes intracellular cargo transport

Intracellular cargo transport can arise from passive diffusion, active motor-driven transport along cytoskeletal filament networks, and passive advection by fluid flows entrained by such cargo-motor motion. Active and advective transport are thus intrinsically coupled as related, yet different representations of the same underlying network structure. A reaction-advection-diffusion system is used here to show that this coupling affects the transport and localization of a passive tracer in a confined geometry. For sufficiently low diffusion, cargo localization to a target zone is optimized either by low reaction kinetics and decoupling of bound and unbound states, or by a mostly disordered cytoskeletal network with only weak directional bias. These generic results may help to rationalize subtle features of cytoskeletal networks, for example as observed for microtubules in fly oocytes.

Cytoplasmic streaming in plant cells: the role of wall slip

We present a computer simulation study, via lattice Boltzmann simulations, of a microscopic model for cytoplasmic streaming in algal cells such as those of Chara corallina. We modelled myosin motors tracking along actin lanes as spheres undergoing directed motion along fixed lines. The sphere dimension takes into account the fact that motors drag vesicles or other organelles, and, unlike previous work, we model the boundary close to which the motors move as walls with a finite slip layer. By using realistic parameter values for actin lane and myosin density, as well as for endoplasmic and vacuole viscosity and the slip layer close to the wall, we find that this simplified view, which does not rely on any coupling between motors, cytoplasm and vacuole other than that provided by viscous Stokes flow, is enough to account for the observed magnitude of streaming velocities in intracellular fluid in living plant cells.

Nanoscale spiral flow in a cylindrical channel

We study the behavior of pressure-driven flow in a cylindrical nanochannel patterned with different wettability using molecular dynamics simulations. We consider the flow perpendicular or parallel to the periodic stripes of wetting and nonwetting materials. For both geometries, we observe a sharp increase in the longitudinal velocity of the flow as wetting stripe width decreases, which is clearly distinguishable from the case of shear-driven flow. When the channel wall is spirally patterned with distinct wetting stripes, the transverse velocity of the flow is generated in the channel and its generation depends strongly on the degree of molecular ordering above the wetting stripes, which can be controlled by helical angle, wetting stripe width, the relative area of the wetting region, and the strength of the fluid-wall interaction.

Cytoplasmic streaming enables the distribution of molecules and vesicles in large plant cells

Recent studies of aquatic and land plants show that similar phenomena determine intracellular transport of organelles and vesicles. This suggests that aspects of cell signaling involved in development and response to external stimuli are conserved across species. The movement of molecular motors along cytoskeletal filaments directly or indirectly entrains the fluid cytosol, driving cyclosis (i.e., cytoplasmic streaming) and affecting gradients of molecular species within the cell, with potentially important metabolic implications as a driving force for cell expansion. Research has shown that myosin XI functions in organelle movement driving cytoplasmic streaming in aquatic and land plants. Despite the conserved cytoskeletal machinery propelling organelle movement among aquatic and land plants, the velocities of cyclosis in plant cells varies according to cell types, developmental stage of the cell, and plant species. Here, we synthesize recent insights into cytoplasmic streaming, molecular gradients, cytoskeletal and membrane dynamics, and expand current cellular models to identify important gaps in current research.