An improved method to investigate staining kinetics in single cells

Summary A new method to analyze staining processes in single cells of histochemical and cytochemical specimens in situ is described. The combination of a microscope photometer with a perfusion cuvette developed in our laboratory allows the continuous observation of a cell during the staining process. The flow rate dependence of the staining process has been examined demonstrating the strong suppression of the diffusional boundary layer adjacent to the cell surface by sufficiently high flow rates. Experiments to find optimal conditions for the kinetic analysis of the staining reaction of nuclei in lymphocytes, neutrophile granulocytes and monkey kidney cells with thionin are described. Half-staining times of the binding of monomer dye molecules and aggregates to nuclei have been calculated; they depend on the pretreatment of the cells. The addition of electrolytes decreases the rate of staining. The formation of aggregates obeys approximately a first-order reaction law and the binding of monomers provides an order of reaction of n=0.5.     

An improved method to investigate staining kinetics in single cells

A new method to analyze staining processes in single cells of histochemical and cytochemical specimens in situ is described. The combination of a microscope photometer with a perfusion cuvette developed in our laboratory allows the continuous observation of a cell during the staining process. The flow rate dependence of the staining process has been examined demonstrating the strong suppression of the diffusional boundary layer adjacent to the cell surface by sufficiently high flow rates. Experiments to find optimal conditions for the kinetic analysis of the staining reaction of nuclei in lymphocytes, neutrophile granulocytes and monkey kidney cells with thionin are described. Half-staining times of the binding of monomer dye molecules and aggregates to nuclei have been calculated; they depend on the pretreatment of the cells. The addition of electrolytes decreases the rate of staining. The formation of aggregates obeys approximately a first-order reaction law and the binding of monomers provides an order of reaction of n = 0.5.     

Use of a membrane-bound fluorophore to characterize diffusion boundary layers around human erythrocytes.

A novel method is used to demonstrate the presence of diffusion boundary layers around erythrocytes following rapid mixing in a stopped-flow spectrophotometer and to estimate the apparent dimensions of the diffusion boundary layers. Pink erythrocyte ghosts labeled on their external surfaces with tetramethyl rhodamine isothiocyanate (TRITC) were mixed in a stopped-flow apparatus with 50 mM NaI in Ringer's solutions. I- is an effective collisional quencher of TRITC fluorescence. TRITC fluorescence after flow stopped decreased monoexponentially with time. The concentration of I- at the cell surface as a function of time was estimated from the dependence of TRITC fluorescence on I- concentration in steady-state experiments. The kinetics of the increase in I- concentration at the cell surface was fit to two diffusional models: a planar erythrocyte ghost bounded by planar diffusion boundary layer and a spherical erythrocyte surrounded by a spherical shell diffusion boundary layer. The planar model best fits the experimental data with a diffusion boundary layer 4.68 microns thick. Using the spherical model the experimental data is best fit by a 6.9 microns diffusion boundary layer.     

Hindered transport of macromolecules in isolated glomeruli. I. Diffusion across intact and cell-free capillaries.

The filtrate formed by renal glomerular capillaries must pass through a layer of endothelial cells, the glomerular basement membrane (GBM), and a layer of epithelial cells, arranged in series. To elucidate the relative resistances of the GBM and cell layers to movement of uncharged macromolecules, we measured the diffusional permeabilities of intact and cell-free capillaries to narrow fractions of Ficoll with Stokes-Einstein radii ranging from 3.0 to 6.2 nm. Glomeruli were isolated from rat kidneys, and diffusion of fluorescein-labeled Ficoll across the walls of single capillary loops was monitored with a confocal microscopy technique. In half of the experiments the glomeruli were treated first to remove the cells, leaving skeletons that retained the general shape of the glomerulus and consisted almost entirely of GBM. The diffusional permeability of cell-free capillaries to Ficoll was approximately 10 to 20 times that of intact capillaries, depending on molecular size. Taking into account the blockage of much of the GBM surface by cells, the contribution of the GBM to the diffusional resistance of the intact barrier was calculated to be 13% to 26% of the total, increasing with molecular size. Thus, the GBM contribution, although smaller than that of the cells, was not negligible. The structure that is most likely to be responsible for the cellular part of the diffusional resistance is the slit diaphragm, which spans the filtration slit between epithelial foot processes. A novel hydrodynamic model was developed to relate the diffusional resistance of the slit diaphragm to its structure, which was idealized as a single layer of cylindrical fibers in a ladder-like arrangement.     

Hydrodynamic and Thermal Slip Effect on Double-Diffusive Free Convective Boundary Layer Flow of a Nanofluid Past a Flat Vertical Plate in the Moving Free Stream

The effects of hydrodynamic and thermal slip boundary conditions on the double-diffusive free convective flow of a nanofluid along a semi-infinite flat solid vertical plate are investigated numerically. It is assumed that free stream is moving. The governing boundary layer equations are non-dimensionalized and transformed into a system of nonlinear, coupled similarity equations. The effects of the controlling parameters on the dimensionless velocity, temperature, solute and nanofluid concentration as well as on the reduced Nusselt number, reduced Sherwood number and the reduced nanoparticle Sherwood number are investigated and presented graphically. To the best of our knowledge, the effects of hydrodynamic and thermal slip boundary conditions have not been investigated yet. It is found that the reduced local Nusselt, local solute and the local nanofluid Sherwood numbers increase with hydrodynamic slip and decrease with thermal slip parameters.     

The nature of the fluid boundary layer and the selection of parameters for benthic ecology

1. The nature of flow structure close to a river bed is reviewed and suggestions made as to appropriate equations to apply to given hydrodynamic regimes. 2. It is emphasized that in natural rivers the laminar sublayer observed immediately above the bed in some experimental studies is completely disrupted for flows characterized by high turbulence levels. 3. Instead of resorting to direct topographical measurement of bed undulations, the roughness of the river bed also can be quantified using hydraulic data obtained from velocity profiles. 4. Ambuhl's experimental findings of 1959 underpin modern ecological research into the nature of the benthic boundary layer. Common misconceptions concerning Ambuhl's contribution are corrected and it is shown that his results only apply to certain prescribed hydrodynamic conditions. 5. The adoption of a consistent approach to describing the benthic boundary layer is to be preferred, so that diverse studies can be usefully compared.     

Mechanical filtering by the boundary layer and fluid–structure interaction in the superficial neuromast of the fish lateral line system

A great diversity of aquatic animals detects water flow with ciliated mechanoreceptors on the body's surface. In order to understand how these receptors mechanically filter signals, we developed a theoretical model of the superficial neuromast in the fish lateral line system. The cupula of the neuromast was modeled as a cylindrical beam that deflects in response to an oscillating flow field. Its accuracy was verified by comparison with prior measurements of cupular deflection in larval zebrafish (Danio rerio). The model predicts that the boundary layer of flow over the body attenuates low-frequency stimuli. The fluid-structure interaction between this flow and the cupula attenuates high-frequency stimuli. The number and height of hair cell kinocilia and the dimensions of the cupular matrix determine the range of intermediate frequencies to which a neuromast is sensitive. By articulating the individual mechanical contributions of the boundary layer and the components of cupular morphology, this model provides the theoretical framework for understanding how a hydrodynamic receptor filters flow signals.     

Passive Asymmetric Transport through Biological Membranes

The magnitude of passive diffusional solute transfer through artificial membranes is usually considered to be independent of the direction of the concentration gradient driving force. It can be shown, however, that a composite membrane, having as one component a membrane with a chemical reaction-facilitated diffusion transport mechanism, can result in an asymmetrical flux. An asymmetric flux caused by this type of structural heterogeneity may be one mechanism contributing to the asymmetric properties of biological membranes. Similar vectorial fluxes can be generated in interfacial solute transfer through membranes if hydrodynamic boundary layers occur at the membrane interface and reversible chemical reactions with the permeant species are involved in either phase.     

Three-dimensional rotational plasma flows near solid surfaces in an axial magnetic field

A rotational flow of a conducting viscous medium near an extended dielectric disk in a uniform axial magnetic field is analyzed in the magnetohydrodynamic (MHD) approach. An analytical solution to the system of nonlinear differential MHD equations of motion in the boundary layer for the general case of different rotation velocities of the disk and medium is obtained using a modified Slezkin–Targ method. A particular case of a medium rotating near a stationary disk imitating the end surface of a laboratory device is considered. The characteristics of a hydrodynamic flow near the disk surface are calculated within the model of a finite-thickness boundary layer. The influence of the magnetic field on the intensity of the secondary flow is studied. Calculations are performed for a weakly ionized dense plasma flow without allowance for the Hall effect and plasma compressibility. An MHD flow in a rotating cylinder bounded from above by a retarding cap is considered. The results obtained can be used to estimate the influence of the end surfaces on the main azimuthal flow, as well as the intensities of circulating flows in various devices with rotating plasmas, in particular, in plasma centrifuges and laboratory devices designed to study instabilities of rotating plasmas.     

A New Proposal for the Action of Vasopressin, Based on Studies of a Complex Synthetic Membrane

The total osmotic flow of water across cell membranes generally exceeds diffusional flow measured with labeled water. The ratio of osmotic to diffusional flow has been widely used as a basis for the calculation of the radius of pores in the membrane, assuming Poiseuille flow of water through the pores. An important assumption underlying this calculation is that both osmotic and diffusional flow are rate-limited by the same barrier in the membrane. Studies employing a complex synthetic membrane show, however, that osmotic flow can be limited by one barrier (thin, dense barrier), and the rate of diffusion of isotopic water by a second (thick, porous) barrier in series with the first. Calculation of a pore radius is meaningless under these conditions, greatly overestimating the size of the pores determining osmotic flow. On the basis of these results, the estimation of pore radius in biological membranes is reassessed. It is proposed that vasopressin acts by greatly increasing the rate of diffusion of water across an outer barrier of the membrane, with little or no accompanying increase in pore size.     

Hydrodynamic modes of arbitrarily shaped flexible macromolecules: Influence on dynamic light scattering

The diffusional motions of flexible macromolecules are analyzed with an increasingly realistic Rouse–Zimm model, i.e., by modeling the molecule as an arbitrary set of spheres connected by nearly harmonic springs. New features include (1) nearly arbitrary arrangements of spheres, (2) arbitrary arrangements of translational and torsional springs, (3) significant anharmonic corrections to the elastic potential surface, and (4) inclusion of torsional damping and various hydrodynamic cross-coupling effects (including two types of translational-rotational coupling) with no additional fitted parameters. The hydrodynamic interactions [R. F. Goldstein (1985) Journal of Chemical Physics, Vol. 83, pp. 2390–2397] contain no adjustable parameters other than temperature, viscosity, and the radii and positions of the spheres. These hydrodynamic interactions allow accurate calculations of rigid body diffusion as well as flexible motions. Given the positions, radii, and spring constant matrix, one can calculate a full set of three-dimensional diffusional modes. Because one uses an off-diagonal hydrodynamic resistance matrix instead of a diagonal mass matrix, the diffusional modes are different in structure from vacuum normal modes, and give rise to different rms motions in the laboratory frame. These hydrodynamic modes include the effects of vibrational-translational cross-coupling (i.e., motion along a vibrational coordinate may give rise to a translational force, and vice versa). The diffusional modes are used to simulate dynamic light scattering (DLS). I examine various molecules with different shapes, flexibilities, and with different scattering vectors. Radial and angular motions influence DLS decays differently. These effects are dependent upon the molecular shape (straight, bent, or curved) and type of flexibility (stretching or bending). Furthermore, small cubic corrections to the potential surface can be significant for DLS of certain geometries such as straight rods and semicircles. © 1993 John Wiley & Sons, Inc.     

Wall shear stress estimates in coronary artery constrictions.

Wall shear stress estimates from laminar boundary layer theory were found to agree fairly well with the magnitude of shear stress levels along coronary artery constrictions obtained from solutions of the Navier Stokes equations for both steady and pulsatile flow. The relatively simple method can be used for in vivo estimates of wall shear stress in constrictions by using a vessel shape function determined from a coronary angiogram, along with a knowledge of the flow rate.     

Motion of nanobeads proximate to plasma membranes during single particle tracking

Drag and torque on nanobeads translating within the pericellular layer while attached to glycolipids of the plasma membrane are calculated by a novel hydrodynamic model. The model considers a bead that translates proximate to a rigid planar interface that separates two distinct Brinkman media. The hydrodynamic resistance is calculated numerically by a modified boundary integral equation formulation, where the pertinent boundary conditions result in a hybrid system of Fredholm integrals of the first and second kinds. The hydrodynamic resistance on the translating bead is calculated for different combinations of the Brinkman screening lengths in the two layers, and for different viscosity ratios. Depending on the bead-membrane separation and on the hydrodynamic properties of both the plasma membrane and the pericellular layer, the drag on the bead may be affected by the properties of the plasma membrane. The Stokes-Einstein relation is applied for calculating the diffusivity of probes (colloidal gold nanobeads attached to glycolipids) in the plasma membrane. This approach provides an alternative way for the interpretation of in vitro observations during single particle tracking procedure, and predicts new properties of the plasma membrane structure.     

Mathematical simulation of a biofilm process

A mathematical model has been developed for a fixed-film biological process (film flow over a flat plate) that describes bulk liquid transport, diffusional transport of oxygen and organics across a stagnant film, diffusional transport of oxygen and organics into the biofilm, biochemical reactions by the individual cells within the biofilm, biofilm growth, and cell density changes within the biofilm due to cellular decay. Simulation studies are presented to show how contact time and diffusion layer thickness affect process performance.     

Gaseous diffusive properties of soybean nodules cultured with non-ambient pO2

Measurements of the short-term response of nodulated roots of soybean ( Glycine max L. Merr, cv. Harosoy: Bradyrhizobium japonicum USDA 16) to rapid changes in surrounding pO₂ indicate that their ability to reversibly adjust gaseous diffusive resistance is retained whether plants are cultured in rhizospheres of very low (2.8%) or very high (61.2%) pO₂. Thus the capacity for reversible short-term diffusion adjustment is additional to structural changes in the fixed diffusional barriers of nodules which allow their continued fixation of N₂ in unfavourably high or low external pO₂. Anatomical evidence, involving quantitative measurement of intercellular spaces in the cortical tissues using electron microscopy of thin sections, indicates that the major fixed diffusional barrier is a boundary layer of cells in the inner cortex which may be as small as one cell thick in nodules from 2.8% O₂ to 5 or 6 cells thick, and almost completely devoid of intercellular spaces, in those from 61.2% O₂. The data are interpreted to indicate that the variable diffusion harrier is distinct from the boundary layer and is most likely to be a property of cells and/or intercellular spaces inside the boundary layer of the nodule cortex.     

Diffusion of the Reaction Boundary of Rapidly Interacting Macromolecules in Sedimentation Velocity

Sedimentation velocity analytical ultracentrifugation combines relatively high hydrodynamic resolution of macromolecular species with the ability to study macromolecular interactions, which has great potential for studying dynamically assembled multiprotein complexes. Complicated sedimentation boundary shapes appear in multicomponent mixtures when the timescale of the chemical reaction is short relative to the timescale of sedimentation. Although the Lamm partial differential equation rigorously predicts the evolution of concentration profiles for given reaction schemes and parameter sets, this approach is often not directly applicable to data analysis due to experimental and sample imperfections, and/or due to unknown reaction pathways. Recently, we have introduced the effective particle theory, which explains quantitatively and in a simple physical picture the sedimentation boundary patterns arising in the sedimentation of rapidly interacting systems. However, it does not address the diffusional spread of the reaction boundary from the cosedimentation of interacting macromolecules, which also has been of long-standing interest in the theory of sedimentation velocity analytical ultracentrifugation. Here, effective particle theory is exploited to approximate the concentration gradients during the sedimentation process, and to predict the overall, gradient-average diffusion coefficient of the reaction boundary. The analysis of the heterogeneity of the sedimentation and diffusion coefficients across the reaction boundary shows that both are relatively uniform. These results support the application of diffusion-deconvoluting sedimentation coefficient distributions c(s) to the analysis of rapidly interacting systems, and provide a framework for the quantitative interpretation of the diffusional broadening and the apparent molar mass values of the effective sedimenting particle in dynamically associating systems.     

Reduction of barnacle recruitment on micro‐textured surfaces: Analysis of effective topographic characteristics and evaluation of skin friction

This study investigates five designed micro‐textured surfaces and their effects on barnacle fouling and hydrodynamic drag. Three of the micro‐textures were developed in the present study and evaluated together with two commercial riblet films. All micro‐structures were arranged as longitudinal grooves with different profile depths, widths and angles of inclination. In field tests the recruitment of the barnacle Balanus improvisus on micro‐textured surfaces and smooth controls was evaluated. All micro‐textured surfaces reduced recruitment, and the most efficient texture reduced recruitment by 98%. For some micro‐textures the reduction of recruitment declined as settlement intensity increased. In a correlative analysis, the trigonometric inclination of the micro‐structures explained most of the recruitment reduction. The steepest angle of inclination caused a massive reduction in barnacle settlement. Surface micro‐structures may affect the boundary‐layer flow and the hydrodynamic drag (skin friction) of the surface. The skin friction was empirically measured in a flow channel using a sub‐set of the tested micro‐textures. The measurements of skin friction showed that the orientation of the microstructures is important, with a minimum friction when the grooves are parallel to the flow. For one of the micro‐textures the skin friction was ca 10% lower compared to a hydraulically smooth surface. It is concluded that, depending on the flow speed, micro‐textures will not significantly increase skin friction when arranged parallel to the flow, even at moderate protrusion through the viscous sub‐layer.     

Photosynthetic rate and dynamic environment. * Kazutoshi Yabuki, 2004. * Dordrecht/Boston/London: Kluwer Academic Publishers. * {euro}50 (hardback). 130 pp.

In photosynthesis, CO₂ enters theleaf from the atmosphere and moves to the active site of thecarboxylating enzyme, to be bound in an organic compound. Theprocess is largely diffusional and the pathway, although complicatedin detail, is usually split into sections related to differentanatomic structures, such as chloroplasts, cell walls, intercellularair space, stomatal pores and, finally the leaf boundary layer.Biologists have mainly been concerned with those sections thatare embedded within the leaf, considering the boundary layeras something external, not under the control by biological processes.Well, light is also not controlled     

Shear modulation of intercellular contact area between two deformable cells colliding under flow

Shear rate has been shown to critically affect the kinetics and receptor specificity of cell-cell interactions. In this study, the collision process between two modeled cells interacting in a linear shear flow is numerically investigated. The two identical biological or artificial cells are modeled as deformable capsules composed of an elastic membrane. The cell deformation and trajectories are computed using the immersed boundary method (IBM) for shear rates of 100-400s(-1). As the two cells collide under hydrodynamic shear, large local cell deformations develop. The effective contact area between the two cells is modulated by the shear rate, and reaches a maximum value at intermediate levels of shear. At relatively low shear rate, the contact area is an enclosed region. As the shear rate increases, dimples form on the membrane surface, and the contact region becomes annular. The nonmonotonic increase of the contact area with the increase of shear rate from computational results implies that there is a maximum effective receptor-ligand binding area for cell adhesion. This finding suggests the existence of possible hydrodynamic mechanism that could be used to interpret the observed maximum leukocyte aggregation in shear flow. The critical shear rate for maximum intercellular contact area is shown to vary with cell properties such as radius and membrane elastic modulus.