The diffusive vesicle supply center model for tip growth in fungal hyphae

We propose the diffusive vesicle supply center model for tip growth in fungal hyphae. The model is based on the three-dimensional vesicle supply center (VSC) model [Gierz, G., Bartnicki-García, S., 2001. A three-dimensional model of fungal morphogenesis based on the vesicle supply center concept: J. Theor. Biol. 208, 151-164], but incorporates two aspects of a more realistic vesicle delivery mechanism: vesicle diffusion from the VSC and a finite rate constant for vesicle fusion with the cell membrane. We develop a framework to describe tip growth for a general class of models based on the vesicle supply center concept. Combining this with a method for calculating the steady state distribution of diffusive vesicles we iteratively solve for stationary cell shapes. These show a blunter tip than predicted by the original VSC model, which we attribute to increased forward-directed vesicle delivery via diffusion. The predicted distance between the VSC and the utmost tip of the cell is set by the ratio between the diffusion constant and the rate constant for vesicle exocytosis. Combined with the cell radius, these define the only dimensionless parameter for our model.     

A theoretical model of the pinocytotic vesicular transport process in endothelial cells

A new theoretical model for vesicular transport in single endothelial cells is described using a kinetic molecular approach in which the vesicle diffusion process is coupled with the vesicle attachment/detachment process occurring at the cell plasmalemmal boundaries. Rate constants k^d_i, k_i characterizing a two stage reaction sequence in the attachment/detachment region and the vesicle diffusion coefficient D are obtained by comparison of the theory with the results of tracer studies. For the condition of rapid vesicle loading/discharge of macromolecules it is found that the permeability of endothelial cells to macromolecules tends to be controlled by the vesicular attachment/detachment process rather than the vesicle diffusion process. The rate limiting step in the vesicle attachment/detachment process tends to be the reaction process involving the rate at which a vesicle and the plasmalemmal membrane are brought into/separated from intimate contact rather than that involving the rate of formation/dissolution of the membrane diaphragm of an attached vesicle. Estimated relaxation times for processes occurring in the attachment/detachment region and in the diffusion region, the vesicle transit time in the diffusion region, and the viscosity of the cytoplasm in the diffusion region are deduced. Fair agreement is obtained between the predicted and the observed temperature dependence of the permeability.     

Temporal evolution of the electron diffusion coefficient in electrolyte-filled mesoporous nanocrystalline TiO2 films

Electron transport in electrolyte-filled mesoporous TiO₂-based solar cells is described quantitatively from the perspective of the continuous-time random walk model. An analytical expression is derived for the time-dependent diffusion coefficient of electrons, which transforms at a characteristic (Fermi) time from strongly time-dependent values (dispersive transport) at short times to relatively time-independent values (nondispersive transport) at long times. At short times, the diffusion coefficient displays a power-law behavior with time. The timescale for the diffusion coefficient to reach its steady-state value is substantially longer than the Fermi time. The Fermi time and the steepness of the distribution of waiting times associated with trap sites have a strong influence on both the steady-state diffusion coefficient of electrons and on the dispersiveness of electron transport. At short timescales, ionic drag, associated with the ambipolar effect, slows electron transport through the TiO₂ matrix, whereas at steady state, transport is trap limited. Decreasing the electron density lowers the steady-state limit of the diffusion coefficient and increases the timescale over which transport is dispersive.     

Simultaneous measurements of cytoplasmic viscosity and intracellular vesicle sizes for live human brain cancer cells

Intracellular vesicles, comprised of protein clusters, were individually tracked inside human brain cancer cells and characterized to simultaneously determine the average vesicle size and effective cytoplasmic viscosity. The cells were transfected with a TGF‐β superfamily gene, non‐steroidal anti‐inflammatory drug‐Activated Gene‐1 (NAG‐1) tagged with green fluorescent proteins (GFPs). Using total internal reflection fluorescent microscopy (TIRFM) the individual movements of the vesicles were categorized into either Brownian, caged, or directional type motion. In the near‐field region confined by the evanescent wave field of TIRFM, the hindrance of these vesicles was created by interactions with the glass coverslip and/or sub‐cellular structures. Measured particle motions were compared with theoretical predictions of hindered motion to estimate the unknown size and viscosity parameters using a nonlinear regression technique. For the tested human brain cancer cells, the average vesicle size and effective intracellular fluid viscosity were calculated to be 496 nm and 0.068 Pa s, respectively. This finding suggests that most of the hindrance experienced by vesicles can be due to non‐hydrodynamic interactions with microtubules and other intracellular structures. It should be also noted that this method provides a way to examine changes in vesicle size due to outside stimulus such as drug interaction, cytotoxicity, etc., unlike standard measurement techniques which require fixing the cells themselves. Biotechnol. Bioeng. 2011;108: 2504–2508. © 2011 Wiley Periodicals, Inc.     

Coupled Protein Diffusion and Folding in the Cell

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control''s diffusion coefficient, PGK''s diffusion coefficient is a non-monotonic function of temperature, signaling ‘sticking’ of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates.     

Mechanistic coupling of transport and phosphorylation activity by enzyme IImtl of the Escherichia coli phosphoenolpyruvate-dependent phosphotransferase system

Mannitol bound to enzyme IImtl could be trapped specifically by rapid phosphorylation with P-HPr. The assay was used to demonstrate transport of mannitol across the cytoplasmic membrane with and without phosphorylation of mannitol. The latter was 2-3 orders of magnitude slower. The fraction of bound mannitol molecules that was actually phosphorylated, the efficiency of the trap, was less than 50%. The efficiency was not very different for enzyme IImtl embedded in the membrane of vesicles with an inside-out orientation or solubilized in detergent. Subsequently, it is argued that the fraction of the bound mannitol molecules that was not phosphorylated dissociated into the cytoplasmic space. A model for the catalytic mechanism of enzyme IImtl is proposed on the basis of interpretations of the present experiments. The main features of the model are the following: (i) mechanistically, the coupling between transport and phosphorylation is less than 50%; (ii) in the physiological steady state of mannitol transport and metabolism, the coupling is 100%; (iii) phosphorylated enzyme IImtl catalyzes facilitated diffusion at a high rate; (iv) the state of phosphorylation of the cytoplasmic domain modulates the activity of the translocator domain; (v) the enzyme catalyzes phosphorylation of free cytoplasmic mannitol at least as fast as it catalyzes transport plus phosphorylation of free periplasmic mannitol.     

The plasmalemmal vesicular system in striated muscle capillaries and in pericytes

By ultrathin serial sectioning of frog mesenteric capillaries it was recently demonstrated that the many apparently free vesicles in electron microscope (EM) sections of endothelial cells may be artefacts due to conventional (500–700 Å thick) sectioning (Frøkjaer-Jensen, 1980). The vesicles were found to be part of two sets of invaginations of the cell surfaces; one set connected to the lumen, the other to the interstitium. The present study extends this view to comprise the vesicle organization in frog striated muscle capillaries. By analysis of the three-dimensional organization of the plasmalemmal vesicles in 21 ultrathin serial sections (120–150 Å) of two muscle capillaries it is demonstrated that less than 1% of the about 70% apparently free vesicles seen in conventional thin sections of the same capillaries in fact represent truly free vesicular units. By analysis of 15 conventional EM cross-sections of capillaries from the frog cutaneous-pectoris muscle containing plasmaproteins in high concentration it is furthermore demonstrated that 48% of the total vesicle population connect to the lumen at the time of fixation. This organization of the vesicular system seems incompatible with the concept that macromolecules are transferred across the capillary wall by vesicular transport or by a series of fusions and fissions between individual cytoplasmic vesicles but is compatible with the notion that macromolecules exchange across capillary walls by means of passive processes such as diffusion and convection through rare ‘large pores’. The study emphasizes that any attempts to classify vesicles in conventional thin sections as ‘luminal’, ‘cytoplasmic’ and ‘abluminal’ is impossible and may lead to erroneous interpretations of vesicle involvement in transcapillary exchange of macromolecules. The rare occurrence of transendothelial channels compared to the number of vesicle invaginations suggests that the main function of the vesicular system relates to functions other than transport.     

Parameters of enzyme reactions in microcirculation

It has been shown that time-dependent change in the concentration of enzymic reaction substrate in a microcirculatory channel cell, as well as its steady spatial distribution contain information both about the structure of the microcirculatory channel and about the reaction kinetic parameters. In terms of the hypothesis about the stationary state of the enzyme-substrate complex at selective values of hydrodynamic parameters of the substrate, enzyme, channel correlation between the change in the substrate concentration, its stationary distribution, kinetic parameters and the microcirculation cell structure were estimated.     

How to get to the right place at the right time: Rab/Ypt small GTPases and vesicle transport

Vesicles often must be transported over long distances in a very crowded cytoplasmic environment encumbered by the cytoskeleton and membranes of different origin that provide an important barrier to their free diffusion. In animal cells with specialised tasks, such as neurons or endothelial cells, vesicles that are directed to the cell periphery are linked to the microtubular cytoskeleton tracks via association with motor proteins that allow their vectorial movement. In lower eukaryotes the actin cytoskeleton plays a prominent role in organising vesicle movement during polarised growth and mating. The Ras-like small GTPases of the Rab/Ypt family play an essential role in vesicle trafficking and due to their diversity and specific localisation have long been implicated in the selective delivery of vesicles. Recent evidence has cast doubt on the classical point of view of how this class of proteins acts in vesicle transport and suggests their involvement also in the events that permit vesicle anchoring to the cytoskeleton. Therefore, after a brief review of what is known about how vesicle movement is achieved in mammalian and yeast systems, and how Rab/Ypt proteins regulate the vesicle predocking events, it is discussed how these proteins might participate in the events that lead to vesicle movement through association with the cytoskeleton machinery.     

How to get to the right place at the right time: Rab/Ypt small GTPases and vesicle transport

Summary Vesicles often must be transported over long distances in a very crowded cytoplasmic environment encumbered by the cytoskeleton and membranes of different origin that provide an important barrier to their free diffusion. In animal cells with specialised tasks, such as neurons or endothelial cells, vesicles that are directed to the cell periphery are linked to the microtubular cytoskeleton tracks via association with motor proteins that allow their vectorial movement. In lower eukaryotes the actin cytoskeleton plays a prominent role in organising vesicle movement during polarised growth and mating. The Ras-like small GTPases of the Rab/Ypt family play an essential role in vesicle trafficking and due to their diversity and specific localisation have long been implicated in the selective delivery of vesicles. Recent evidence has cast doubt on the classical point of view of how this class of proteins acts in vesicle transport and suggests their involvement also in the events that permit vesicle anchoring to the cytoskeleton. Therefore, after a brief review of what is known about how vesicle movement is achieved in mammalian and yeast systems, and how Rab/Ypt proteins regulate the vesicle predocking events, it is discussed how these proteins might participate in the events that lead to vesicle movement through association with the cytoskeleton machinery.     

Microfilament Orientation Constrains Vesicle Flow and Spatial Distribution in Growing Pollen Tubes

The dynamics of cellular organelles reveals important information about their functioning. The spatio-temporal movement patterns of vesicles in growing pollen tubes are controlled by the actin cytoskeleton. Vesicle flow is crucial for morphogenesis in these cells as it ensures targeted delivery of cell wall polysaccharides. Remarkably, the target region does not contain much filamentous actin. We model the vesicular trafficking in this area using as boundary conditions the expanding cell wall and the actin array forming the apical actin fringe. The shape of the fringe was obtained by imposing a steady state and constant polymerization rate of the actin filaments. Letting vesicle flux into and out of the apical region be determined by the orientation of the actin microfilaments and by exocytosis was sufficient to generate a flux that corresponds in magnitude and orientation to that observed experimentally. This model explains how the cytoplasmic streaming pattern in the apical region of the pollen tube can be generated without the presence of actin microfilaments.     

Detection and characterization of actin monomers, oligomers, and filaments in solution by measurement of fluorescence photobleaching recovery

Fluorescence photobleaching recovery (FPR) was measured to determine the diffusion coefficient of fluorescein-labeled G-actin in low-salt buffer. The result obtained, 7.15 +/- 0.35 X 10(-7) cm2/s, is in good agreement with that computed from the molecular weight, partial specific volume, and sedimentation coefficient, but is higher than previously obtained values. It is demonstrated from theory that at low ionic strength, the electrostatic contribution to the intrinsic viscosity leads to an overestimate of the hydrodynamic eccentricity of G-actin. Data from FPR, sedimentation, and fluorescence polarization experiments all indicate that the true low-salt form of the actin monomer has an axial ratio less than or equal to 3.0. The G-F transformation of actin was also observed by measurement of FPR during the assembly phase, in the steady state, and in the presence of ligands such as cytochalasin and aldolase. Each FPR record in general yields three data: relative proportion of rapidly and slowly diffusing actin, diffusion coefficient for the high-mobility fraction, and a mean diffusion coefficient for the low-mobility fraction. A relation between the mean low-mobility diffusion coefficient and the number-average filament length is derived and applied to the analysis of FPR data. Under typical conditions, the average filament length was much greater than 10 micron in the steady state. Cytochalasin D was found to decrease filament length and total amount of filament proportionally; total filament number was not greatly affected. In all polymerizations of G-actin, the high-mobility material observed in situ was found to be essentially monomeric actin. Relatively stable oligomers of actin were separated by fractionating G-AF-actin by gel filtration in 50 microM MgCl2 at 4 degrees C. On the basis of the diffusion coefficient, we conclude that monomer and dimer constitute the major particle types present under these conditions. Sedimentation of labeled actin polymerized in 1.0 mM MgCl2 yielded a graded supernatant that contained actin oligomers significantly larger than the monomer.     

Formulation and numerical simulations of a continuum model of avascular tumor growth

In this paper we present a continuum mathematical model for a multicellular spheroid that mimics the micro-environment within avascular tumor growth. The model consists of a coupled system of non-linear convection-diffusion-reaction equations. This system is solved using a previously developed conservative Galerkin characteristics method. In the model considered, there are three cell types: the proliferative cells, the quiescent non-dividing cells which stay in the G₀ phase of the cell cycle and the necrotic cells. The model includes viable cell diffusion, diffusion of cellular material and the removal of necrotic cells. We assume that the nutrients diffuse passively and are consumed by the proliferative and quiescent tumor cells depending on the availability of resources (oxygen, glucose, etc.). The numerical simulations are performed using different sets of parameters, including biologically realistic ones, to explore the effects of each of these model parameters on reaching the steady state. The present results, taken together with those reported earlier, indicate that the removal of necrotic cells and the diffusion of cellular material have significant effects on the steady state, reflecting growth saturation, the number of viable cells, and the spheroid size.     

Calculation of time constants for intracellular diffusion in whole cell patch clamp configuration.

We present a simplified model to identify and analyze the important variables governing the diffusion of substances from pipettes into canine cardiac Purkinje cells in the whole cell patch clamp configuration. We show that diffusion of substances through the pipette is the major barrier for equilibration of the pipette and cellular contents. We solve numerically the one-dimensional diffusion equation for different pipette geometries, and we derive a simple analytic equation which allows one to estimate the time necessary to reach the steady state of intracellular concentration. The time constant of the transient to steady state is given by a pipette geometric factor times the cell volume divided by the diffusion coefficient of the substance of interest. The geometric factor is shown to be given by the ratio of pipette resistance to the resistivity of the filling solution. Additionally from our modeling, we concluded that pipette perfusion at distances greater than 20 microns from the pipette tip would not substantially reduce the time necessary to achieve the steady state.     

A model for de novo synthesis and assembly of tight intercellular junctions. Ultrastructural correlates and experimental verification of the model revealed by freeze-fracture

The structure and function of intercellular tight (occluding) junctions, which constitute the anatomical basis for highly regulated interfaces between tissue compartments such as the blood-testis and blood-brain barriers, are well known. Details of the synthesis and assembly of tight junctions, however, have been difficult to determine primarily because no model for study of these processes has been recognized. Primary cultures of brain capillary endothelial cells are proposed as a model in which events of the synthesis and assembly of tight junctions can be examined by monitoring morphological features of each step in freeze-fracture replicas of the endothelial cell plasma membrane. Examination of replicas of non-confluent monolayers of endothelial cells reveals the following intramembrane structures proposed as 'markers' for the sequential events of synthesis and assembly of zonulae occludentes: development of surface contours consisting of elongate terraces and furrows (valleys) orientated parallel to the axis of cytoplasmic extensions of spreading endothelial cells, appearance of small circular PF face depressions (or volcano-like protrusions on the EF face) that represent cytoplasmic vesicle-plasma membrane fusion sites, which are positioned in linear arrays along the contour furrows, appearance of 13-15 nm intramembrane particles at the perimeter of the vesicle fusion sites, and alignment of these intramembrane particles into the long, parallel, anastomosed strands characteristic of mature tight junctions. These structural features of brain endothelial cells in monolayer culture constitute the morphological expression of: reshaping the cell surface to align future junction-containing regions with those of adjacent cells, delivery and insertion of newly synthesized junctional intramembrane particles into regions of the plasma membrane where tight junctions will form, and aggregation and alignment of tight junction intramembrane particles into the complex interconnected strands of mature zonulae occludentes. The distribution of filipin-sterol complex-free regions on the PF intramembrane fracture face of junction-forming endothelial plasmalemmae corresponds precisely to the furrows, aligned vesicle fusion sites and anastomosed strands of tight junctional elements.(ABSTRACT TRUNCATED AT 400 WORDS)     

On the time dependent diffusion of macromolecules through transient open junctions and their subendothelial spread. 2. Long time model for interaction between leakage sites

In Part 1 of this study (Weinbaum et al., 1988) a short time model has been proposed to describe the initial time dependent leakage of macromolecules at short distances (5 microns or less) from the exit of a transient open junction which the authors have hypothesized as a characteristic feature of endothelial cells in the process of turnover (Weinbaum et al., 1985). This open junction pathway has also been proposed (Weinbaum et al., 1988) to be the primary ultrastructural correlate of the 20 nm diameter large pore suggested by Renkin et al. (1977) using the predictions of cylindrical pore theory. The short time model in (Weinbaum et al., 1988), however, has major limitations in that it neglects the interaction between leakage sites, macromolecular entry through other pathways, the finite thickness of the vessel wall and the curvature of the cell perimeter. The longer time model developed herein will attempt to describe each of these features and also present an improved model and analytic solution for the steady state flux and uptake. In the previous steady state model developed by Weinbaum et al. (1985) the effect of the resistance of the transient open junctions and the non-isotropic diffusion in the underlying tissue due to the internal elastic lamina (IEL) were both neglected. New solutions are first presented which describe the effect of these important model refinements on the steady state macromolecular permeability of the major arteries. Time dependent solutions are then presented to predict the transient longer time labeling following the introduction of tracer macromolecules of varying size. These solutions and the corresponding short time solutions in Weinbaum et al. (1988) are the first solutions to our knowledge to describe the difficult time-dependent boundary value problem to determine how the channel exit concentration and flux at a leaky junction vary with time. This is accomplished by casting the boundary value problem in the form of an integral equation for the unknown flux at the cleft exit and then solving this problem using a specially designed numerical technique. The theoretical predictions are used to interpret the behavior of the localized leaks to HRP and albumin that have been reported in Stemerman et al. (1986) and our own recent experiments (Lin et al., 1988).     

The Time Dependence of Single File Diffusion

The single file diffusion of particles through a narrow pore membrane separating two media is treated as a stochastic birth and death process. A set of differential-difference equations is derived to describe the probability of finding n particles in the pore at any time whose source is the left-hand medium. Explicit time-dependent solutions for an arbitary number of sites are obtained. These can be used to calculate both one-way and net flux as a function of time. Parameters are estimated from steady state permeability data, and the results of some numerical calculations are presented to illustrate the time required to approach a steady state. In many cases, significant time delays can occur.     

Inositol-less death in yeast results in a simultaneous increase in intracellular viscosity.

Inositol auxotrophs of yeast developing on isositol-deficient medium continue protein synthesis for 4-6 h, lose viability rapidly after 6 h, and show an increase in cytoplasmic viscosity as measured by spin label rotational motion. Cycloheximide prevents the rapid loss of cell viability, stops protein synthesis, and simultaneously prevents an increase in cytoplasmic viscosity. From these observations, we infer that intracellular translational diffusion is upset as a consequence of inositol starvation. Cell death may be caused by a modified intracellular diffusion environment.