Orientation by helical motion—III. Microorganisms can orient to stimuli by changing the direction of their rotational velocity

Organisms that move along helical trajectories change their net direction of motion largely by changing the direction, with respect to the body of the organism, of their rotational velocity (Crenshaw and Edelstein-Keshet, 1993,Bull. math. Biol. 55, 213–230). This paper demonstrates that an organism orients to a stimulus field, such as a chemical concentration gradient or a ray of light, if the components of its rotational velocity, with respect to the, body of the organism, are simple functions of the stimulus intensity encountered by the organism. For example, an organism can orient to a chemical concentration gradient if the rate at which it rotates around its anterior-posterior axis is proportional to the chemical concentration it encounters. Such an orientation can be either positive or negative. Furthermore, it is true taxis—orientation of the axis of helical motion is direct. It is neither a kinesis nor a phobic response—there is no random component to this mechanism of orientation.     

Superresolution Imaging of Dynamic MreB Filaments in B. subtilis—A Multiple-Motor-Driven Transport?

The cytoskeletal protein MreB is an essential component of the bacterial cell-shape generation system. Using a superresolution variant of total internal reflection microscopy with structured illumination, as well as three-dimensional stacks of deconvolved epifluorescence microscopy, we found that inside living Bacillus subtilis cells, MreB forms filamentous structures of variable lengths, typically not longer than 1 μm. These filaments move along their orientation and mainly perpendicular to the long bacterial axis, revealing a maximal velocity at an intermediate length and a decreasing velocity with increasing filament length. Filaments move along straight trajectories but can reverse or alter their direction of propagation. Based on our measurements, we provide a mechanistic model that is consistent with all observations. In this model, MreB filaments mechanically couple several motors that putatively synthesize the cell wall, whereas the filaments’ traces mirror the trajectories of the motors. On the basis of our mechanistic model, we developed a mathematical model that can explain the nonlinear velocity length dependence. We deduce that the coupling of cell wall synthesis motors determines the MreB filament transport velocity, and the filament mechanically controls a concerted synthesis of parallel peptidoglycan strands to improve cell wall stability.     

Superresolution Imaging of Dynamic MreB Filaments in B.?subtilis—A Multiple-Motor-Driven Transport?

The cytoskeletal protein MreB is an essential component of the bacterial cell-shape generation system. Using a superresolution variant of total internal reflection microscopy with structured illumination, as well as three-dimensional stacks of deconvolved epifluorescence microscopy, we found that inside living Bacillus subtilis cells, MreB forms filamentous structures of variable lengths, typically not longer than 1 μm. These filaments move along their orientation and mainly perpendicular to the long bacterial axis, revealing a maximal velocity at an intermediate length and a decreasing velocity with increasing filament length. Filaments move along straight trajectories but can reverse or alter their direction of propagation. Based on our measurements, we provide a mechanistic model that is consistent with all observations. In this model, MreB filaments mechanically couple several motors that putatively synthesize the cell wall, whereas the filaments’ traces mirror the trajectories of the motors. On the basis of our mechanistic model, we developed a mathematical model that can explain the nonlinear velocity length dependence. We deduce that the coupling of cell wall synthesis motors determines the MreB filament transport velocity, and the filament mechanically controls a concerted synthesis of parallel peptidoglycan strands to improve cell wall stability.     

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.     

Cargo Transport by Cytoplasmic Dynein Can Center Embryonic Centrosomes

To complete meiosis II in animal cells, the male DNA material needs to meet the female DNA material contained in the female pronucleus at the egg center, but it is not known how the male pronucleus, deposited by the sperm at the periphery of the cell, finds the cell center in large eggs. Pronucleus centering is an active process that appears to involve microtubules and molecular motors. For small and medium-sized cells, the force required to move the centrosome can arise from either microtubule pushing on the cortex, or cortically-attached dynein pulling on microtubules. However, in large cells, such as the fertilized Xenopus laevis embryo, where microtubules are too long to support pushing forces or they do not reach all boundaries before centrosome centering begins, a different force generating mechanism must exist. Here, we present a centrosome positioning model in which the cytosolic drag experienced by cargoes hauled by cytoplasmic dynein on the sperm aster microtubules can move the centrosome towards the cell’s center. We find that small, fast cargoes (diameter ∼100 nm, cargo velocity ∼2 µm/s) are sufficient to move the centrosome in the geometry of the Xenopus laevis embryo within the experimentally observed length and time scales.     

Pressure gradient, not exposure duration, determines the extent of epithelial cell damage in a model of pulmonary airway reopening.

The reduction of tidal volume during mechanical ventilation has been shown to reduce mortality of patients with acute respiratory distress syndrome, but epithelial cell injury can still result from mechanical stresses imposed by the opening of occluded airways. To study these stresses, a fluid-filled parallel-plate flow chamber lined with epithelial cells was used as an idealized model of an occluded airway. Airway reopening was modeled by the progression of a semi-infinite bubble of air through the length of the channel, which cleared the fluid. In our laboratory's prior study, the magnitude of the pressure gradient near the bubble tip was directly correlated to the epithelial cell layer damage (Bilek AM, Dee KC, and Gaver DP III. J Appl Physiol 94: 770-783, 2003). However, in that study, it was not possible to discriminate the stress magnitude from the stimulus duration because the bubble propagation velocity varied between experiments. In the present study, the stress magnitude is modified by varying the viscosity of the occlusion fluid while fixing the reopening velocity across experiments. This approach causes the stimulus duration to be inversely related to the magnitude of the pressure gradient. Nevertheless, cell damage remains directly correlated with the pressure gradient, not the duration of stress exposure. The present study thus provides additional evidence that the magnitude of the pressure gradient induces cellular damage in this model of airway reopening. We explore the mechanism for acute damage and also demonstrate that repeated reopening and closure is shown to damage the epithelial cell layer, even under conditions that would not lead to extensive damage from a single reopening event.     

Determination of the nucleic acids in pig embryonic kidney cells by magnetic cytaphoresis

Gallocyanine-chrome alum-stained pig embryonic kidney cells have paramagnetic properties. They move under the influence of gradient magnetic field (magnetophoresis). The velocity of magnetophoresis is proportional to the content of nucleic acids in cells. This allows to estimate the content of nucleic acids per cell dry weight by magnetophoresis and analytical centrifugation.     

Separation of haemopoietic cells for biochemical investigation. Preparation of erythroid and myeloid cells from human and laboratory-animal bone marrow and the separation of erythroblasts according to their state of maturation.

The separation of haemopoietic bone-marrow cells by centrifugation through discontinuous density gradients of Percoll is described. This method was used to prepare fractions enriched in erythroblasts, myeloid blast cells or reticulocytes from bone marrow of anaemic and non-anaemic rabbits, from the marrow of other anaemic laboratory animals and from human samples. It is a simple, rapid, reproducible and inexpensive technique that can be readily adapted to suit individual requirements. Secondly, a convenient method is presented for the separation of large quantities of bone-marrow cells into fractions enriched in erythroblasts at different stages of maturation, by velocity sedimentation through a linear gradient of 1-2% sucrose at unit gravity. In vitro, erythroblasts adhere together strongly via a mechanism almost certainly involving a beta-galactoside-specific surface lectin termed erythroid developmental agglutinin. Since the efficiency of cell-separation techniques depends heavily on the maintenance of a single cell suspension in which each unit can move independently, the presence of an adhesive molecule at the cell surface is of considerable significance. The effect of washing the marrow with a lactose-containing medium, which has been shown to remove the agglutinin, was therefore investigated in relation to both methods. The separation on Percoll gradients is considerably enhanced by this treatment. In addition, the unit-gravity sedimentation gradient can be loaded with 5-10 times more cells after lactose extraction in comparison with intact marrow. Although enrichment is less, a useful fractionation according to maturation is still obtained.     

Kinesin velocity increases with the number of motors pulling against viscoelastic drag

Although the properties of single kinesin molecular motors are well understood, it is not clear whether multiple motors pulling a single vesicle in a cell cooperate or interfere with one another. To learn how small numbers of motors interact, microtubule gliding assays were carried out with full-length Drosophila kinesin in a novel motility medium containing xanthan, a stiff, water-soluble polysaccharide. At 2 mg/ml xanthan, the zero-shear viscosity of this medium is 1,000 times the viscosity of water, similar to cellular viscosity. To mimic the rheological drag force on the motors when attached to a vesicle in a cell, we attached a 2 μm bead to one end of the microtubule (MT). During gliding assays in our novel medium, the moving bead exerted a drag force of 4–15 pN on the kinesins pulling the MT. The velocity of MTs with an attached bead increased with MT length and with kinesin concentration. The increase with MT length arose because the number of motors is directly proportional to MT length. Our results show that small numbers of kinesins cooperate constructively when pulling against a viscoelastic drag. In the absence of a bead but still in the viscous medium, MT velocity was independent of MT length and kinesin concentration because the thin MT, like a snake moving through grass, was able to move between xanthan molecules with little resistance. A minimal shared-load model in which the number of motors is proportional to MT length fits the observed dependence of gliding velocity on MT length and kinesin concentration.     

Interaction of retinal image and eye velocity in motion perception

When we move our eyes, why does the world look stable even as its image flows across our retinas, and why do afterimages, which are stationary on the retinas, appear to move? Current theories say this is because we perceive motion by summation: if an object slips across the retina at r degrees/s while the eye turns at e degrees/s, the object's perceived velocity in space should be r + e. We show that activity in MT+, the visual-motion complex in human cortex, does reflect a mix of r and e rather than r alone. But we show also that, for optimal perception, r and e should not summate; rather, the signals coding e interact multiplicatively with the spatial gradient of illumination.     

Noise reduction in the intracellular pom1p gradient by a dynamic clustering mechanism

Chemical gradients can generate pattern formation in biological systems. In the fission yeast Schizosaccharomyces pombe, a cortical gradient of pom1p (a DYRK-type protein kinase) functions to position sites of cytokinesis and cell polarity and to control cell length. Here, using quantitative imaging, fluorescence correlation spectroscopy, and mathematical modeling, we study how its gradient distribution is formed. Pom1p gradients exhibit large cell-to-cell variability, as well as dynamic fluctuations in each individual gradient. Our data lead to a two-state model for gradient formation in which pom1p molecules associate with the plasma membrane at cell tips and then diffuse on the membrane while aggregating into and fragmenting from clusters, before disassociating from the membrane. In contrast to a classical one-component gradient, this two-state gradient buffers against cell-to-cell variations in protein concentration. This buffering mechanism, together with time averaging to reduce intrinsic noise, allows the pom1p gradient to specify positional information in a robust manner.     

In chemotaxing fibroblasts, both high-fidelity and weakly biased cell movements track the localization of PI3K signaling

Cell movement biased by a chemical gradient, or chemotaxis, coordinates the recruitment of cells and collective migration of cell populations. During wound healing, chemotaxis of fibroblasts is stimulated by platelet-derived growth factor (PDGF) and certain other chemoattractants. Whereas the immediate PDGF gradient sensing response has been characterized previously at the level of phosphoinositide 3-kinase (PI3K) signaling, the sensitivity of the response at the level of cell migration bias has not yet been studied quantitatively. In this work, we used live-cell total internal reflection fluorescence microscopy to monitor PI3K signaling dynamics and cell movements for extended periods. We show that persistent and properly aligned (i.e., high-fidelity) fibroblast migration does indeed correlate with polarized PI3K signaling; accordingly, this behavior is seen only under conditions of high gradient steepness (>10% across a typical cell length of 50 μm) and a certain range of PDGF concentrations. Under suboptimal conditions, cells execute a random or biased random walk, but nonetheless move in a predictable fashion according to the changing pattern of PI3K signaling. Inhibition of PI3K during chemotaxis is accompanied by loss of both cell-substratum contact and morphological polarity, but after a recovery period, PI3K-inhibited fibroblasts often regain the ability to orient toward the PDGF gradient.     

Different Migration Patterns of Sea Urchin and Mouse Sperm Revealed by a Microfluidic Chemotaxis Device

Chemotaxis refers to a process whereby cells move up or down a chemical gradient. Sperm chemotaxis is known to be a strategy exploited by marine invertebrates such as sea urchins to reach eggs efficiently in moving water. Less is understood about how or whether chemotaxis is used by mammalian sperm to reach eggs, where fertilization takes place within the confinement of a reproductive tract. In this report, we quantitatively assessed sea urchin and mouse sperm chemotaxis using a recently developed microfluidic model and high-speed imaging. Results demonstrated that sea urchin Arbacia punctulata sperm were chemotactic toward the peptide resact with high chemotactic sensitivity, with an average velocity V_x up the chemical gradient as high as 20% of its average speed (238 μm/s), while mouse sperm displayed no statistically significant chemotactic behavior in progesterone gradients, which had been proposed to guide mammalian sperm toward eggs. This work demonstrates the validity of a microfluidic model for quantitative sperm chemotaxis studies, and reveals a biological insight that chemotaxis up a progesterone gradient may not be a universal strategy for mammalian sperm to reach eggs.     

Mechanism of scavenger receptor class B type I-mediated selective uptake of cholesteryl esters from high density lipoprotein to adrenal cells.

Despite extensive studies and characterizations of the high density lipoprotein-cholesteryl ester (HDL-CE)-selective uptake pathway, the mechanisms by which the hydrophobic CE molecules are transferred from the HDL particle to the plasma membrane have remained elusive, until the discovery that scavenger receptor BI (SR-BI) plays an important role. To elucidate the molecular mechanism, we examined the quantitative relationships between the binding of HDL and the selective uptake of its CE in the murine adrenal Y1-BS1 cell line. A comparison of concentration dependences shows that half-maximal high affinity cell association of HDL occurs at 8.7 +/- 4.7 micrograms/ml and the Km of HDL-CE-selective uptake is 4.5 +/- 1.5 micrograms/ml. These values are similar, and there is a very high correlation between these two processes (r2 = 0.98), suggesting that they are linked. An examination of lipid uptake from reconstituted HDL particles of defined composition and size shows that there is a non-stoichiometric uptake of HDL lipid components, with CE being preferred over the major HDL phospholipids, phosphatidylcholine and sphingomyelin. Comparison of the rates of selective uptake of different classes of phospholipid in this system gives the ranking: phosphatidylserine > phosphatidylcholine approximately phosphatidylinositol > sphingomyelin. The rate of CE-selective uptake from donor particles is proportional to the amount of CE initially present in the particles, suggesting a mechanism in which CE moves down its concentration gradient from HDL particles docked on SR-BI into the cell plasma membrane. The activation energy for CE uptake from either HDL3 or reconstituted HDL is about 9 kcal/mol, indicating that HDL-CE uptake occurs via a non-aqueous pathway. HDL binding to SR-BI allows access of CE molecules to a "channel" formed by the receptor from which water is excluded and along which HDL-CE molecules move down their concentration gradient into the cell plasma membrane.     

Precision of sensing cell length via concentration gradients

Unicellular organisms are typically found to have a characteristic cell size. To achieve a homeostatic distribution of cell sizes over many generations requires that cell length is actively sensed and regulated. However, the mechanisms by which cell size is controlled remain poorly understood. Recent experiments in fission yeast have shown that cell length is controlled in part by polar gradients of the protein Pom1 together with localized measurement of concentration at midcell. Dilution as the cell grows leads to a reduction in the midcell protein concentration, which lifts a block on mitosis. Here we analyze the precision of this mechanism for length sensing in the presence of inevitable intrinsic noise in the processes leading to formation and measurement of this gradient. We find that the use of concentration gradients allows for more robust length sensing than a comparable spatially uniform system, and allows for reliable length determination even if the average protein concentration throughout the cell remains constant as the cell grows. Optimal values for the gradient decay length and receptor dissociation constant emerge from maximizing sensitivity while minimizing the impact of density fluctuations.     

Under-agarose folate chemotaxis of Dictyostelium discoideum amoebae in permissive and mechanically inhibited conditions.

Under-agarose chemotaxis has been used previously to assess the ability of neutrophils to respond to gradients of chemoattractant. We have adapted this assay to the chemotactic movement of Dictyostelium amoebae in response to folic acid. Troughs are used instead of wells to increase the area along which the cells can be visualized and to create a uniform front of moving cells. Imaging the transition zone where the cells first encounter the agarose, we find that the cells move perpendicular to the gradient and periodically manage to squeeze under the agarose and move up the gradient. As cells exit the troughs, their cross-sectional area increases as the cells become flattened. Three-dimensional reconstruction of confocal optical sections through GFP-labeled cells demonstrates that the increase in cross-sectional area is due to the flattening of the cells. Since the cells locally deform the agarose and become deformed by it, the concentration of the agarose, and therefore its stiffness, should affect the ability of the cells to migrate. Consistent with this hypothesis, cells in 0.5% agarose move faster and are less flat than cells under 2% agarose. Cells do not exit the troughs and move under 3% agarose at all. Therefore, this assay can be used to compare and quantify the ability of different cell types or mutant cell lines to move in a restrictive environment.     

Modeling of particle dynamics in a thruster

Numerical solutions to the equations describing the process of ion acceleration in a Hall current plasma accelerator (thruster) are studied. The system itself represents a three-component plasma: neutral atoms, free electrons, and singly-ionized atoms. The ions in the acceleration tract move without collisions, i.e., the length of the free path of ions is larger than that of the acceleration tract, while electrons move in a diffusion mode across the magnetic field. It is shown that in case the Poisson equation for an electric field is used the set of dynamic equations does not have an acoustic peculiarity that appears when solving a quasineutral set when the velocity of the ion flow and the ion-acoustic velocity coincide.     

A Maxwell's Demon type of membrane transport: possibility for active transport by ABC-type transporters?

ATP-binding-cassette (or ABC)-type transporters constitute one of the largest family of membrane transporters in nature. Many of its members move substrates "actively", i.e. in an ATP-dependent manner against an electrochemical gradient. No consensus is available about the mechanism. Therefore, a novel class of transport mechanisms is proposed based on Maxwell's demon idea. This transport mechanism consists of a gated pore that selectively opens for substrates from one, but not the other side. Thermoenergy (Brownian motion) would suffice for substrate translocation across the membrane; energy for synchronizing gate opening with substrate arrival would come from ATP hydrolysis. Simulations demonstrate that such a mechanism would be thermodynamically and kinetically feasible. It exhibits "active", unidirectional transport, saturation, and other typical features of protein-catalysed reactions. It also shows pore behavior with charged substrates moving under the influence of electrical potentials. Its efficiency depends on a diffusion time constant of the substrate in solution that is slower than the transit time through the membrane, a situation that can realistically be achieved at millimolar or lower substrate concentrations. Features of the novel mechanism that differ significantly from P- or F-type ATPases are: (1) transport cannot be run in "reverse" to synthesize ATP even if sufficient energy is available in the gradient of the transported solute and (2) unidirectional and net substrate fluxes through the transporter diverge with increasing substrate concentration.     

Temperature dependence of anaphase chromosome velocity and microtubule depolymerization

The time course of chromosome movement and decay of half-spindle birefringence retardation in anaphase have been precisely determined in the endosperm cell of a plant Tilia americana and in the egg of an animal Asterias forbesi. For each species, the anaphase retardation decay rate constant and chromosome velocity are similar exponential functions of temperature. Over the temperature range at which these cells can complete anaphase, chromosome velocity and retardation rate constant yield a positive linear relationship when plotted against each other. At the higher temperatures where the chromosomes move faster, the spindle retardation decays faster, even though the absolute spindle retardation is greater. Chromosome velocity thus parallels the anaphase spindle retardation decay rate, or rate of spindle microtubule depolymerization, rather than absolute spindle retardation, or the amount of microtubules in the spindle. These observations suggest that a common mechanism exists for mitosis in plant and animal cells. The rate of anaphase chromosome movement is associated with an apparent first-order process of spindle fiber disassembly. This process irreversibly prevents spindle fiber subunits from participating in the polymerization equilibrium and removes microtubular subunits from chromosomal spindle fibers.     

Hemolysis by aliphatic alcohols and saponin measured by the coil planet centrifugation method

Using the coil planet centrifugation method, the mechanism of hemolysis by alcohols and saponin was investigated. With this technique, erythrocytes are introduced into a gradient of hemolytic agents in saline, which is prepared in a long coiled polyethylene tube. The tube is centrifuged so that the cells move from a low to a high concentration of hemolytic agent. When the cells lyse, they release hemoglobin which remains stationary, and therefore hemolytic potency can be determined spectrophotometrically by the distance the cells move before lysing. We found that alcohols caused hemolysis at a particular concentration, whereas saponin-induced hemolysis was dependent on the amount of saponin accumulated in the environment of the cell. In addition, alcohols with longer carbon chains were more potent hemolytic agents than those with shorter chains, but each additional carbon group produced less of an increase in hemolysis per mole of alcohol. This chain-length dependency is consistent with a previous study on in vivo alcohol-induced hemolysis. The coil planet centrifugation method is also adaptable to comparative studies on the mechanism of other types of hemolysis, such as immune or drug-induced lysis, and to toxicological studies.