Symmetry and the stationary state behavior of enzyme membranes

An analysis of the stationary state behavior of model enzyme (or catalytic) membranes is considered. In particular, membrane functional symmetry is shown to be of critical importance in deriving a unique set of global linear phenomenological relations from their local counterparts. Indeed the appropriate transformation of the dissipation function, based on the correct identification of the “transport plane” within the membrane, leads to a global analog of the Curie Principle. By extending the argument from the near-equilibrium regime to the pseudo-first-order kinetic regime a set of practical equations can be derived. These make it possible to obtain local transport and reaction parameters from global measurements. The facilitation of transport by reaction is discussed.     

On the stationary state of Kohonen's self-organizing sensory mapping

The stationary state of the self-organizing sensory mapping of Kohonen is investigated. For this purpose the equation for the stationary state is derived for the case of one-dimensional and two-dimensional mappings. The equation can be solved for special cases, including the general one-dimensional case, to yield an explicit expression for the local magnification factor of the map.     

Nernst-planck analog equations and stationary state membrane electric potentials

A set of coupled nonlinear differential equations, determining the concentration profiles and electric potentials valid for isothermal transport of ions and molecules across a diffusion barrier are formulated, using a correction to the limiting expression for chemical potential gradients and the molecular expression for frictional force. These differential equations are similar to Nernst-Planck equations and reduce to these under appropriate approximations. Solutions of these equations valid under specified conditions are presented. Expressions for permeability, concentration profiles of many ion systems are included.     

The vomeronasal epithelia of NMRI mouse

Summary The features of the apical and lateral surfaces of cells of the vomeronasal epithelium were studied in adult male mice by scanning electron microscopy. Supporting cells and receptor cells of the neuroepithelium are covered with microvilli. Microvilli of the sensory cells are longer and thinner than those of the supporting cells. Additionally, the former differ in local distribution, orientation, occurrence of branching and appearance of the cell coat. The receptor-free epithelium consists most likely of one cell type only, which shows different structural modifications including the presence, number and length of microvilli and cilia. In the transitional region, between the neuroepithelium and the receptor-free epithelium, immature receptor cells are present.This paper is dedicated to Prof. A. JinoSupported by grants from the Alexander von Humboldt-Stiftung and the Deutsche Forschungsgemeinschaft (Br. 358/5-1)     

On the stationary state of a network of inhibitory spiking neurons

The background activity of a cortical neural network is modeled by a homogeneous integrate-and-fire network with unreliable inhibitory synapses. For the case of fast synapses, numerical and analytical calculations show that the network relaxes into a stationary state of high attention. The majority of the neurons has a membrane potential just below the threshold; as a consequence the network can react immediately – on the time scale of synaptic transmission- on external pulses. The neurons fire with a low rate and with a broad distribution of interspike intervals. Firing events of the total network are correlated over short time periods. The firing rate increases linearly with external stimuli. In the limit of infinitely large networks, the synaptic noise decreases to zero. Nevertheless, the distribution of interspike intervals remains broad. Action Editor: Misha Tsodyks     

Deviation of the living system from the stationary state during oogenesis

Summary The changes in respiration and glycolysis of whole oocytes and homogenates of oocytes during oogenesis have been studied.The respiration rate of whole oocytes increases during oocyte growth and decreases during oocyte maturation. The respiration rate of homogenates also increases during oocyte growth and does not change during egg maturation. At all oogenesis stages the respiration rate of homogenates is higher than the respiration rate of whole oocytes.Respiration intensity increases during the small growth stage and decreases during the following stages of oogenesis. Respiration intensity of homogenates under optimal conditions changes in a similar way. Respiration intensity under physiological conditions diminishes during oogenesis from 70% at the small growth stage to 42% in unfertilised eggs.The rate of glycolysis in whole oocytes and homogenates of oocytes increases during the growth period of oocytes but does not change during egg maturation.Glycolysis intensity of the whole oocytes increases at the large growth stage—stage of cytoplasmic vacuolisation—and becomes less during the following stages. Glycolysis intensity in homogenates under optimal conditions is much higher than the glycolysis intensity of whole oocytes and it decreases slightly during oogenesis. The efficiency of glycolysis in oocytes under physiological conditions is very low. It increases from the stage of cytoplasmic vacuolisation (3.6%) to the stage at which vitellogenesis starts (20%) and diminishes at the following stages.The data obtained are considered in the light of the Prigogine and Wiame interpretation of a thermodynamic theory of development.     

On the stationary state analysis of reaction-diffusion mechanisms for biological pattern formation

We present a biologically plausible two-variable reaction-diffusion model for the developing vertebrate limb, for which we postulate the existence of a stationary solution. A consequence of this assumption is that the stationary state depends on only a single concentration-variable. Under these circumstances, features of potential biological significance, such as the dependence of the steady-state concentration profile of this variable on parameters such as tissue size and shape, can be studied without detailed information about the rate functions. As the existence and stability of stationary solutions, which must be assumed for any biochemical system governing morphogenesis, cannot be investigated without such information, an analysis is made of the minimal requirements for stable, stationary non-uniform solutions in a general class of reaction-diffusion systems. We discuss the strategy of studying stationary-state properties of systems that are incompletely specified. Where abrupt transitions between successive compartment-sizes occur, as in the developing limb, we argue that it is reasonable to model pattern reorganization as a sequence of independent stationary states.     

The apical plasma membrane of Drosophila embryonic epithelia

The apical plasma membrane of epithelia presents the interface between organs and the external environment. It has biochemical activities distinct from those of the basal and lateral plasma membranes, as it accommodates the production and assembly of ordered apical matrices involved in organ protection and physiology and determines the microenvironment in the apical extracellular milieu. Here, we emphasise the importance of the apical plasma membrane in tissue differentiation, by mainly focussing on the embryo of the fruit fly Drosophila melanogaster, and discuss the principal organisation of the apical plasma membrane into repetitive subdomains of specific topologies and activities essential for epithelial function.     

The conventional short-circuiting technique under-short-circuits most epithelia

Summary The relationships among ion current, membrane potential difference, and resistance of an epithelium are studied. The short-circuit technique introduced by Ussing and Zerahn does not completely short circuit the epithelium if the series resistance parallel to the cell layer between the voltage electrodes is not properly compensated. The residual potential difference across the epithelial cell layer in the short-circuit state is proportional to both the measured short-circuit current and the resistance of the diffusion barriers not compensated. In the conventionally short-circuited small intestinal mucosa the villus and crypt areas are hypo-polarized to different degrees rather than simultaneously hyper- and hypo-polarized. Short-circuiting the whole tissue reduces but does not abolish the passive net ion movement across the tissue. Measurements of the electrical properties of the whole and denuded rat distal small intestine in HCO₃-Ringer solution containing 10mm glucose reveal that the measured short-circuit current has under-estimated approximately 33% of the true short-circuit current and that the passive net Na flux from serosa to mucosa and Cl flux from mucosa to serosa are not negligible in the short-circuit state.     

On the stability of the stationary state of a population growth equation with time-lag

Summary If in the Verhulst equation for population growth the reproduction factor depends on the history then the equilibrium may become unstable and oscillations and even non-constant periodic solutions may occur. It is shown that the equilibrium is unstable if the reproduction factor at time t is, up to a sufficiently large factor, an arbitrary average of the population densities in the interval (t–2, t–1].     

The distribution of blood group antigens in rodent epithelia

Summary The pattern of distribution of antigens cross-reacting with antibodies to human blood group antigens A and B and two precursor molecules was examined by immunofluorescence in the epidermis, oral mucosa and forestomach of rats and mice. Staining for blood group antigen A was negative. In all epithelia examined, blood group antigen B was present at the surface of basal and parabasal cells, and the H antigen at the surface of spinous cells. N-acetyllactosamine was present on the cell membranes in the upper spinous and granular cell layers of epidermis and forestomach epithelium and was not expressed in the oral epithelia except for a limited area in the dorsal tongue epithelium.Thus, the expression of antigen varies both regionally and, as earlier shown in human epithelium, with the stage of maturation of cells within a given epithelium. The observed sequence of expression of these antigens during maturation differs from that of human epithelia, but the present study provides a basis for further experimental studies of the role of cell surface antigens in epithelial homeostasis and maturation.     

Cellular events within peripodial epithelia that accompany evagination of Manduca wing discs: Conversion of cuboidal epithelia to columnar epithelia

In the wing disc of Manduca, a sheet of peripodial epithelium completely covers the apical surface of another epithelium destined to form the wing blade. The cubodial cells of the peripodial epithelium not only are attached to a thick basal lamina but also their lateral and basal surfaces are highly convoluted and stain intensely with ruthenium red (RR). In contrast, the columnar cells of the wing epithelium lack both a basal lamina and RR-positive surfaces. During evagination, the RR-positive material disappears and the extent of lateral cell contact within the peripodial epithelium increases. Concurrently with this lateral “zippering”, the entire peripodial sheet contracts and slides over the wing blade epithelium, thereby exposing the wing to the external surface of the insect. Trypsin treatment of Manduca discs accelerates both evagination and the disappearance of RR-positive material from the surfaces of cells in the peripodial epithelium. Apparently contraction of the peripodial sheet and the increase in its lateral cell contacts is accompanied by the disappearance of acidic glycoproteins from its lateral and basal cell surfaces.     

Terminal differentiation of epithelia

All epithelia form sheets of cells connected by tight and adherent junctions and exhibit polarized distribution of membrane proteins and lipids. During their development, epithelia progress from this 'generic' phenotype to terminally differentiated states characterized by the development of apical structures such as microvilli, apical endocytosis and regulated exocytosis as well as characteristic cell shapes. We have identified an extracellular matrix protein, hensin, which when polymerized into a fiber induces the terminal differentiation of renal cells. Hensin is expressed in most epithelia where it exists in tissue-specific alternately spliced forms. Many epithelial tumors have deletions in the human ortholog of hensin. We propose that hensin mediates terminal differentiation of these epithelia.     

Pathobiology of biliary epithelia

Cholangiocytes are epithelial cells that line the intra- and extrahepatic biliary tree. They serve predominantly to mediate the content of luminal biliary fluid, which is controlled via numerous signaling pathways influenced by endogenous (e.g., bile acids, nucleotides, hormones, neurotransmitters) and exogenous (e.g., microbes/microbial products, drugs etc.) molecules. When injured, cholangiocytes undergo apoptosis/lysis, repair and proliferation. They also become senescent, a form of cell cycle arrest, which may prevent propagation of injury and/or malignant transformation. Senescent cholangiocytes can undergo further transformation to a senescence-associated secretory phenotype (SASP), where they begin secreting pro-inflammatory and pro-fibrotic signals that may contribute to disease initiation and progression. These and other concepts related to cholangiocyte pathobiology will be reviewed herein. This article is part of a Special Issue entitled: Cholangiocytes in Health and Disease edited by Jesus Banales, Marco Marzioni, Nicholas LaRusso and Peter Jansen.