Mathematical theory of biological periodicities II. Effect of active transport

A previous study (Bull. Math. Biophysics,30, 735–749) is generalized to the case of active transport, which acts together in general with ordinary diffusion. The basic results obtained are the same except for an additional important conclusion. In principle it is possible to obtain sustained oscillations even when the secretions of the different glands do not affect the rates of formation or decay of each other at all, but affect the “molecular pumps,” which are responsible for the active transports in various parts of the system. Thus no biochemical interactions need necessarily take place between then-metabolites to make sustained oscillations possible in principle. This is an addition to a previous finding (Bull. Math. Biophysics,30, 751–760) that due to effects of the secreted hormones on target organs, non-linearity of biochemical interactions is not needed for production of sustained oscillations.     

Effect of tubular inhomogeneities on filter properties of thick ascending limb of Henle's loop

We used a simple mathematical model of rat thick ascending limb (TAL) of the loop of Henle to predict the impact of spatially inhomogeneous NaCl permeability, spatially inhomogeneous NaCl active transport, and spatially inhomogeneous tubular radius on luminal NaCl concentration when sustained, sinusoidal perturbations were superimposed on steady-state TAL flow. A mathematical model previously devised by us that used homogeneous TAL transport and fixed TAL radius predicted that such perturbations result in TAL luminal fluid NaCl concentration profiles that are standing waves. That study also predicted that nodes in NaCl concentration occur at the end of the TAL when the tubular fluid transit time equals the period of a periodic perturbation, and that, for non-nodal periods, sinusoidal perturbations generate non-sinusoidal oscillations (and thus a series of harmonics) in NaCl concentration at the TAL end. In the present study we find that the inhomogeneities transform the standing waves and their associated nodes into approximate standing waves and approximate nodes. The impact of inhomogeneous NaCl permeability is small. However, for inhomogeneous active transport or inhomogeneous radius, the oscillations for non-nodal periods tend to be less sinusoidal and more distorted than in the homogeneous case and to thus have stronger harmonics. Both the homogeneous and non-homogeneous cases predict that the TAL, in its transduction of flow oscillations into concentration oscillations, acts as a low-pass filter, but the inhomogeneities result in a less effective filter that has accentuated non-linearities.     

Effects of biocide treatment and backflow pressure on the permeability of microbially fouled model cores

Summary Sintered glass bead cores were plugged until the permeability was reduced to 1% or less of the original permeability by the injection of a slime-producing bacterium isolated from produced water. Scanning electron microscopy of fractured core sections showed that the bacteria were predominantly located in the uppermost sections, around the core inlet. Killing the bacterial cells in the plugging biofilm, using a biocide, had little effect on core permeability. The dead cells were only removed when backflow pressure, simulated by inversion of the test core followed by fluid injection, was applied and maintained at 55–69 kPa. Backflow of plugged cores containing live bacteria produced transient pressure-dependent increases in permeability that were proportional to the backflow pressure applied. We conclude that only sustained backflow procedures reduced permeability: such operations are not effective for oil recovery in field conditions.     

Epithelial water transport in a balanced gradient system.

The relationship between epithelial fluid transport, standing osmotic gradients, and standing hydrostatic pressure gradients has been investigated using a perturbation expansion of the governing equations. The assumptions used in the expansion are: (a) the volume of lateral intercellular space per unit volume of epithelium is small; (b) the membrane osmotic permeability is much larger than the solute permeability. We find that the rate of fluid reabsorption is set by the rate of active solute transport across lateral membranes. The fluid that crosses the lateral membranes and enters the intercellular cleft is driven longitudinally by small gradients in hydrostatic pressure. The small hydrostatic pressure in the intercellular space is capable of causing significant transmembrane fluid movement, however, the transmembrane effect is countered by the presence of a small standing osmotic gradient. Longitudinal hydrostatic and osmotic gradients balance such that their combined effect on transmembrane fluid flow is zero, whereas longitudinal flow is driven by the hydrostatic gradient. Because of this balance, standing gradients within intercellular clefts are effectively uncoupled from the rate of fluid reabsorption, which is driven by small, localized osmotic gradients within the cells. Water enters the cells across apical membranes and leaves across the lateral intercellular membranes. Fluid that enters the intercellular clefts can, in principle, exit either the basal end or be secreted from the apical end through tight junctions. Fluid flow through tight junctions is shown to depend on a dimensionless parameter, which scales the resistance to solute flow of the entire cleft relative to that of the junction. Estimates of the value of this parameter suggest that an electrically leaky epithelium may be effectively a tight epithelium in regard to fluid flow.     

Oscillations in stomatal conductance and plant functioning associated with stomatal conductance: Observations and a model

Summary Measurements of transpiration, leaf water content, and flux of water in a cotton plant exhibiting sustained oscillations, in stomatal conductance are presented, and a model of the mechanism causing this behaviour is developed. The dynamic elements, of the model are capacitors—representing the change of water content with water potential in mesophyll, subsidiary and guard cells—interconnected by resistances representing flow paths in the plant. Increase of water potential in guard cells causes an increase in stomatal conductance. Increase of water potential in the subsidiary cells has the opposite effect and provides the positive feed-back which can cause stomatal conductance to oscillate. The oscillations are shown to have many of the characteristics of free-running oscillations in real plants. The behaviour of the model has been examined, using an analogue computer, with constraints and perturbations representing some of those which could be applied to real plants in physiological experiments. Aspects of behaviour which have been simulated are (a) opening and closing of stomata under the influence of changes in illumination, (b) transient responses due to step changes in potential transpiration, root permeability and potential of water surrounding the roots, (c) the influence of these factors on the occurrence and shape of spontaneous oscillations, and (d) modulation of sustained oscillations due to a circadian rhythm in the permeability of roots.     

Influence of apical fluid volume on the development of functional intercellular junctions in the human epithelial cell line 16HBE14o-: implications for the use of this cell line as an in vitro model for bronchial drug absorption studies

Air-interfaced culture (AIC) versus liquid-covered culture (LCC) conditions are known to have different effects on the differentiated phenotype of several cell types, including lung epithelial cells. We report the influence of culture conditions such as apical medium volume on the development of intercellular junctions in the human epithelial cell line 16HBE14o-. Immunofluorescence staining of the tight-junctional protein, ZO-1, has revealed its presence in cells grown in both AIC and LCC. However, only LCC-grown cells exhibit protein ZO-1 localized as a zonula-occludens-like regular belt connecting neighboring cells. The presence of typical tight junctions has been confirmed by electron microscopy. Immunostaining for occludin, claudin-1, connexin43, and E-cadherin has demonstrated intercellular junction structures only in the cells in LCC. These morphological findings have been paralleled by higher transepithelial electrical resistance values and similar fluxes of the hydrophilic permeability marker, fluorescein-Na, under LCC compared with AIC conditions. We conclude that the formation of functional 16HBE14o- cell layers requires the presence of an apical fluid volume, in contrast to other culture conditions for airway epithelial cells.     

Anti-phase calcium oscillations in astrocytes via inositol (1, 4, 5)-trisphosphate regeneration

Observations in cultured mouse astrocytes suggest anti-phase synchronization of cytosolic calcium concentrations in nearest neighbor cells that are coupled through gap junctions. A mathematical model is used to investigate physiologic conditions under which diffusion of the second messenger inositol (1, 4, 5)-trisphosphate (IP(3)) through gap junctions can facilitate synchronized anti-phase Ca(2+) oscillations. Our model predicts anti-phase oscillations in both cytosolic calcium and IP(3) concentrations if (a) the gap junction permeability is within a window of values and (b) IP(3) is regenerated in the astrocytes via, e.g. phospholipase C(delta). This result sheds new light on the current dispute on the mechanism of intercellular calcium signaling. It provides indirect evidence for a partially regenerative mechanism as the model excludes anti-phase synchrony in the absence of IP(3) regeneration.     

Evidence that short-term regulation of nodule permeability does not occur in the inner cortex

Regulation of nodule permeability in response to short-term changes in environmental and physiological conditions is thought to occur by occlusion of intercellular spaces in the nodule inner cortex. To test this hypothesis, the permeability of legume nodules was altered by adapting them to either 20 or 80% O₂ over a 2.5-h period. The nodules were then rapidly frozen, cryo-planed and examined under cryo-scanning electron microscopy for differences in the number, area or shape factor of intercellular spaces. Comparisons were made between whole nodules and specific nodule zones (outer cortex, middle cortex, inner cortex and central zone) in each treatment. Gas analysis measurements indicated that nodules equilibrated at 20% O₂ had a 6.6-fold higher permeability than those equilibrated at 80% O₂ However, no significant differences were observed between pO₂ treatments in the number of open intercellular spaces, the cross-sectional area of those spaces, or the proportion of the tissue area present as open space in whole nodules or any nodule zone. Also, although nodules in both treatments possessed a boundary layer of tightly packed cells in the inner cortex, the total area of intercellular spaces between cells bordering this layer did not differ between treatments. Together these observations do not support the currently favored hypothesis that nodule permeability is regulated by opening or occlusion of intercellular spaces in the nodule inner cortex. Highly significant differences (P= 0.0006) were observed between O₂ treatments in the shape factor of the open intercellular spaces in all nodule zones. Nodules equilibrated at 80% O₂ had significantly more isodiametric spaces while those equilibrated at 20% O₂ had more long, narrow spaces. This observation suggests that the critical step in the regulation of nodule permeability to O₂ may be localized in the central, infected zone and involve changes in the ratio of the surface area of the intercellular space to the volume of the infected cell.     

Temperature-dependent changes in fluid transport across goldfish gallbladder

Summary The temperature dependence of fluid transport acrossin vitro preparations of goldfish gallbladder was measured using a gravimetric technique. Fluid transport showed a direct dependence on incubation temperature when the adaptation temperature was kept constant. For constant incubation temperature, transport fell as the adaptation temperature rose. The width of intercellular channels varied with incubation and adaptation temperature as expected if fluid were to cross the tissue by this route. The structure of the gallbladder was otherwise unaffected by changes of temperature. Intracellular concentrations of Na, K and Cl also depended on the environmental temperature of the fish. The levels of Na and Cl increased and the level of K decreased, at constant incubation temperature, as the adaptation temperature rose from 8 to 30°C. These changes took two to three weeks to become apparent while fluid transport regulated within 20 hours of raising the environmental temperature. The osmotic permeability of the gallbladder remained independent of both incubation and adaptation temperature.The outcome of adaptation was to maintain constant both the ionic composition of the epithelium and the rate at which it could transport fluid, when these parameters were measured at incubation temperatures equal to the previous environmental temperature of the fish. The significance of these findings is discussed and a mechanism for regulation postulated which involves an initial regulation of salt entry into the mucosa followed by long term changes in the pumping ability of newly synthesized cells.     

Transduction of intracellular and intercellular dynamics in yeast glycolytic oscillations

Under certain well-defined conditions, a population of yeast cells exhibits glycolytic oscillations that synchronize through intercellular acetaldehyde. This implies that the dynamic phenomenon of the oscillation propagates within and between cells. We here develop a method to establish by which route dynamics propagate through a biological reaction network. Application of the method to yeast demonstrates how the oscillations and the synchronization signal can be transduced. That transduction is not so much through the backbone of glycolysis, as via the Gibbs energy and redox coenzyme couples (ATP/ADP, and NADH/NAD), and via both intra- and intercellular acetaldehyde.     

Water pathways across a reconstituted epithelial barrier formed by caco-2 cells: Effects of medium hypertonicity

Caco-2 cells, originated in a human colonic cancer, are currently used as model systems to study transepithelial transports. To further characterize their water permeability properties, clone P1 Caco-2 cells were cultured on permeable supports. At confluence, the transepithelial net water movement (J _W), mannitol permeability (P _s), and electrical resistance (R) were simultaneously measured. The observed results were correlated with transmission and freeze-fracture electron microscopy studies and compared with those obtained, in similar experimental conditions, in a typical mammalian epithelial barrier: the rabbit rectum. When the serosal solution was made hypertonic (50 mm polyethylene glycol-PEG), the spontaneously observed secretory J _w rapidly reversed, became absorptive and then stabilized. Simultaneously, the R values dropped and P _s went up. In the case of the rabbit rectal epithelium, a similar treatment did not elicit significant changes in the water permeability during the first 20 min following the osmotic challenge while there was a significant increase in the transepithelial resistance. After exposure to serosal hypertonicity, several morphological modifications developed in the Caco-2 cells: Localized dilations in the intercellular spaces and vacuoles in the cytoplasm appeared. Nevertheless, most cells remained in contact and no evidence of cell shrinking was observed. Simultaneously, the tight-junction structure was more or less disorganized. The filament network lost its sharpness and omega figures appeared, bordering the intercellular spaces. In some cases the tight-junction network was completely disrupted. In the case of the rabbit rectum the structural modifications were completely different: Serosal hypertonicity rapidly induced cell shrinking and the opening of the intercellular spaces, with no noticeable change in the tight-junction structure. These results suggest that Caco-2-P1 cell membranes, contrary to the case of the basolateral membrane of rabbit rectal cells, have no water channels and that a paracellular route could play a central role in the water movements across this epithelial barrier.     

Dynamics of chemostat in which one microbial population grows on multiple complementary nutrients

The equations of a chemostat in which one microbial population grows on multiple rate-limiting nutrients are formulated. The dynamics of a chemostat involving growth on complementary nutrients is studied through stability analysis of the system of equations. Some conditions are derived that relate the dynamic behavior of the chemostat to its operating conditions and can be applied to any model for the specific growth rate of the population. It is shown that, if maintenance of the population is neglected, the system exhibits no sustained or damped oscillations. If maintenance of the population is considered, damped oscillations are observed for some operating conditions.     

Observations on the permeability of the choriocapillaris of the eye

Summary The choriocapillaris is a fenestrated capillary bed located posterior to the retinal pigment epithelium. It serves as the main source of supply to the photoreceptors, retinal pigment epithelium, and other cells of the outer retina. The permeability of these capillaries to intravenously injected ferritin (MW — approx. 480,000; mol. diam. 11 nm) was examined in the mouse, rabbit, and guinea pig, each of which is characterized by a different type of retinal vascularization. In all three species, the bulk of the ferritin remained in the capillary lumina, where it appeared to be blocked at the level of the diaphragmed fenestrae. Some ferritin was present in endothelial cell vacuoles. The results confirm previous work on the rat choriocapillaris and indicate that the barrier function of the choriocapillary endothelium is present even among species in which the retinal circulation differs significantly.Supported by NIH grant EY03418     

Membrane junctions between salivary gland cells ofChironomus thummi

Summary Cells ofChironomus salivary glands communicate through intercellular connections of high permeability. Electron micrographs of salivary glands show two kinds of junctions between the membranes of adjacent cells, which may be responsible for cell coupling: septate junctions and close membrane junctions.A large fraction of lateral cell surfaces is occupied by septate junctions, while the area of close membrane junctions appears to be very small. Consequently septate junctions have been considered as likely sites for intercellular coupling. There are however some indications that intercellular communication is provided by structures which seem to be unstable. As osmotic effects are among the factors which can disrupt cellular communications, we have tried to eliminate possible effects of the fixing solutions on the ultrastructure of intercellular connections by using isoosmotic fixatives. Under these conditions large regions of close membrane junctions of the nexus kind have been observed to occur between gland cells. They are of similar size as septate junctions. It seems to be possible that as in other communicating cell systems nexus could be the sites for intercellular coupling of salivary gland cells.The authors would like to thank Prof. Dr. H. Leonhardt, Institut für Anatomie I, Homburg, for the use of his electron microscope (Zeiss EM 9-DFG grant LE 69–8) during part of this work and Prof. Dr. H. Kroeger, Institut für Genetik, Saarbrücken for the supply withChironomus larvae.     

A model of smooth muscle cell synchronization in the arterial wall

Vasomotion is a rhythmic variation in microvascular diameter. Although known for more than 150 years, the cellular processes underlying the initiation of vasomotion are not fully understood. In the present study a model of a single cell is extended by coupling a number of cells into a tube. The simulated results point to a permissive role of cGMP in establishing intercellular synchronization. In sufficient concentration, cGMP may activate a cGMP-sensitive calcium-dependent chloride channel, causing a tight spatiotemporal coupling between release of sarcoplasmic reticulum calcium, membrane depolarization, and influx of extracellular calcium. Low [cGMP] is associated only with unsynchronized waves. At intermediate concentrations, cells display either waves or whole cell oscillations, but these remain unsynchronized between cells. Whole cell oscillations are associated with rhythmic variation in membrane potential and flow of current through gap junctions. The amplitude of these oscillations in potential grows with increasing [cGMP], and, past a certain threshold, they become strong enough to entrain all cells in the vascular wall, thereby initiating sustained vasomotion. In this state there is a rhythmic flow of calcium through voltage-sensitive calcium channels into the cytoplasm, making the frequency of established vasomotion sensitive to membrane potential. It is concluded that electrical coupling through gap junctions is likely to be responsible for the rapid synchronization across a large number of cells. Gap-junctional current between cells is due to the appearance of oscillations in the membrane potential that again depends on the entrainment of sarcoplasmic reticulum and plasma membrane within the individual cell.     

Intercellular communication: role of gap junctions in establishing the pattern of ATP-elicited Ca2+ oscillations and Ca2+-dependent currents in freshly isolated aortic smooth muscle cells

Cytosolic-free [Ca2+] was evaluated in freshly dissociated smooth muscle cells from mouse thoracic aorta by the ratio of Fura Red and Fluo 4 emitted fluorescence using confocal microscopy. The role of intercellular communication in forming and shaping ATP-elicited responses was demonstrated. Extracellular ATP (250 microM) elicited [Ca2+]i transient responses, sustained [Ca2+]i rise, periodic [Ca2+]i oscillations and aperiodic repetitive [Ca2+]i transients. Quantity of smooth muscle cells in the preparation responding to ATP with periodical [Ca2+]i oscillations depended on the density of isolated cells on the cover slip. ATP-elicited bursts of [Ca2+]i spikes in 66+/-7% of cells in dense and in 33+/-8.5% of cells in non-dense preparations. The number of cells responding to ATP with bursts of [Ca2+]i spikes decreased from 55+/-5% (n=84) to 14+/-3% (n=141) in dense preparations pretreated with carbenoxolone. Simultaneous measurement of [Ca2+]i and ion currents revealed a correlation between [Ca2+]i and current oscillations. ATP-elicited bursts of current spikes in 76% of cells regrouped in small clusters and in 9% of isolated cells. Clustered cells responding to ATP with current oscillations had higher membrane capacity than clustered cells with transient and sustained ATP-elicited responses. Lucifer Yellow (1% in 130 mM KCl) injected into one of clustered cells was transferred to the neighboring cell only when ATP-elicited oscillations. Fast application of carbenoxolone (100 microM) inhibited ATP (250 microM) elicited Ca2+-dependent current oscillations. Taken together these results suggest that the probability of ATP (250 microM) triggered cytosolic [Ca2+]i oscillations accompanied with K+ and Cl- current oscillations increased with the coupling of smooth muscle cells.     

The effect of chemical stress on the polypeptide composition of the intercellular fluid of barley leaves

The effect of chemical stress on the polypeptide composition of the intercellular fluid of barley (Hordeum vulgare L.) and tomato (Lycopersicon esculentum Mill.) leaves has been studied. In some dicotyledonous plant species, including tomato, exposure to chemical stress leads to the denovo synthesis of intercellular proteins known as pathogenesis-related proteins which have been implicated to be part of a defence mechanism. In barley, however, no such changes in the polypeptide composition of the intercellular fluid could be detected. On the other hand, similar stress conditions induce in barley a strong accumulation of mRNA encoding leaf-specific thionins. These barley thionins represent a novel class of cell-wall proteins toxic to phytopathogenic fungi and are possibly involved in the defence mechanism. These proteins could not be detected in tomato plants. In contrast to the pathogenesis-related proteins of dicotyledonous plants, the leaf-specific thionins of barley are not present in the intercellular fluid of leaves. These results indicate that barley may have evolved a different mechanism to cope with the presence of stress.Abbreviations PAGE polyacrylamide gel electrophoresis - PR pathogenesis-related - SDS sodium dodecyl sulfate     

The permeability of nonhuman primate vaginal epithelium: a freeze-fracture and tracer-perfusion study

The lining of the vaginal mucosa in primates is a keratinized stratified squamous epithelium. As in other structurally similar epithelia, one function of the vaginal epithelium is to provide a barrier between the external environment and the underlying tissues. The vaginal lining is aglandular and the source of true vaginal fluid has been suggested to be the intercellular channels of the epithelium. On the other hand, other structurally similar epithelia have been shown to have a barrier to the movement of water-soluble molecules through these channels. In the present study, we have examined the permeability of rhesus monkey vaginal epithelium to lanthanum and horseradish peroxidase. Both tracer molecules penetrated the intercellular channels in the lower layers of the epithelium, but were excluded from the channels at and above the granular layer. Neither tracer penetrated significantly between cells at the free surface of the epithelium and usually did not penetrate between cells in the upper layers to any degree from the cut edges of the biopsy. These results are consistent with tracer studies in other structurally similar epithelia and strongly suggest that the upper layers of vaginal epithelium present a barrier to the movement of water-soluble molecules through the intercellular channel system. Freeze-fracture analysis of the epithelium revealed gap junctions and desmosomes between cells in the lower layers, but the former disappear in the upper layers. Unlike other keratinizing epithelia that have been described, random intramembranous particles do not disappear from the plasma membranes of the fully differentiated cells. Fracture planes through the upper layers reveal particle-free lamellae in the intercellular spaces, supporting the idea that intercellular lipids may be one of the components that limits the permeability of the intercellular spaces in this epithelium.     

Fine structure of supporting cells in the lateral-line canal-organ of Fundulus

Phase and electron microscopic studies have revealed that the supporting cells of the lateral-line canal-organ of Fundulus heteroclitus have a fine structure characterized by (1) mitochondria and vacuoles in the apical zone, (2) granular endoplasmic reticulum surrounding a core of Golgi complex in the middle zone, and (3) an indented nucleus in the basal zone. In the middle and basal zones, wide intercellular spaces separate the adjacent supporting cells, whose plasma membranes form long flap-like interdigitations across the intercellular spaces. Secretion of subcupular fluid and cupula, metabolic regulation through the intercellular spaces, and rigid support for the organ are discussed as possible metabolic and mechanical functions of the supporting cells essential for the lateral-line canal-organ.     

Frequency Spectrum of Transepithelial Potential Difference Reveals Transport-Related Oscillations

How epithelia transport fluid is a fundamental issue that is unresolved. Explanations offered include molecular engines, local transcellular osmosis, local paracellular osmosis, and paracellular fluid transport. On the basis of experimental and theoretical work done on corneal endothelium, a fluid transporting epithelium, we suggest electroosmotic coupling at the level of the intercellular junctions driven by the transendothelial electrical potential difference as an explanation of paracellular fluid transport. We collect frequency spectra of that potential difference in real-time. For what we believe is the first time for any epithelium, we report that, unexpectedly, the potential difference displays oscillations at many characteristic frequencies. We also show that on both stimulating cell activity and inhibiting ion transport mechanisms, there are corresponding changes in the oscillations amplitudes that mirror changes known previously in rates of fluid transport. We believe these findings provide a novel tool to study the kinetics of electrogenic elements such as channels and transporters, which from this evidence would give rise to current oscillations with characteristic periods going from 150 ms to 8 s.