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a thin, flexible film that is placed under tension by external forces and thus exhibits the property of elasticity. A plate, whose elastic properties depend on its material and thickness, should be distinguished from a membrane. Examples of membranes are a skin stretched over a drumhead and the thin metal foil that acts as the moving diaphragm in a condenser microphone. Depending on the shape of the external contour along which the tension is applied, several types of membranes are distinguished: for example, rectangular, circular, and elliptical. The normal modes of vibration of a membrane are represented by systems of standing waves with various types of nodal lines that separate parts of the membrane that vibrate with oppo-site displacements (see Figure 1); the external contour to which the membrane is fastened is always a nodal line if the attachment is such that there is no displacement perpendicular to the plane of the membrane. Different vibration frequencies, the aggregate of which determines the discrete spectrum of the natural frequencies of the membrane, correspond to different systems of standing waves. A membrane undergoes forced vibrations at the external frequency when subjected to concentrated or distributed periodic external forces; when this frequency coincides with one of the natural frequencies of the membrane, resonance occurs.
In engineering, a thin, flexible plate whose flexural rigidity is equal to zero is also called a membrane. A membrane is usually fastened along its contour, with the contour being placed under tension thus ensuring that the membrane will operate as an elastic system. The maximum deflection of a membrane under the action of a uniformly distributed load having an intensity p per unit area W covered by the membrane is determined from the approximate formula z = K (p W/s), where s is the tension applied per unit length of the contour and K is a factor that depends on the shape of the membrane (K = 0.080 for a square membrane, K = 0.078 for a circular membrane, and K = 0.063 for a triangular membrane). Membranes that are to undergo large deflections are designed with longitudinal deformations taken into account; for a circular membrane the maximum deflection is determined from the formula z = Q.665r), where r is the radius of the membrane, E is Young’s modulus for the membrane material, and h is the thickness of the membrane.
A membrane may be made from various materials. Metal membranes (phosphor bronze, beryllium bronze, foil, and chrome-nickel steel) are used in aneroid barometers, measuring instruments that operate at high temperatures, telephone receivers, and sound recorders (dictaphones). Nonmetallic membranes (made of such substances as rubber, leather, cord, plastic, cotton, rubberized fiber, polycaprolactam fiber, and silk fiber) are used as sensing elements that transform pressure variations into linear displacements in differential manometers, automatic pneumatic devices, and diaphragm pumps; nonmetallic membranes are also used as load-carrying elements in the actuating mechanisms of pneumatic control valves.
in plant cells, the nonprotoplasmic component produced by the protoplast. The membrane determines the shape of the cell, protects the protoplast from injury, and participates in transpiration, excretion, and absorption and conduction of matter. It consists predominantly of carbohydrates (polysaccharides). In many fungi it contains chitin; in pollen grains and spores of higher plants it contains the highly stable organic substance sporopollenin. The stroma of the membrane is made up of compact parallel groups of polymerous molecules of cellulose—microfibrils—which are immersed in an amorphous mass (matrix) of pectins and hemicelluloses. The heterogeneity of the structure determines the anisotropy of the membrane and its birefringence.
One differentiates primary, secondary, and, sometimes, tertiary membranes. The thin exterior primary membrane is vitreously transparent, has a loose network of microfibrils, and is capable of stretching. Stretching causes intussusception of new microfibrils in the membrane. The cells of the meristem, mesophyll, and collenchyma have a primary membrane. A middle membrane separates the primary membranes of contiguous cells from the pectins, whose solution causes maceration of the cells. Sometimes the term “middle membrane” is used to designate two primary membranes and the intercellular matter that separates them. The secondary membrane, whose rigidity and elasticity are determined by high cellulose content, lies inside the primary membrane. Thickening of the secondary membrane occurs as a result of the apposition of dense layers of parallel microfibrils. In some conductive elements of the xylem the secondary membrane takes the form of a ring or spiral of twisted ribbons. The thickness of the entire cell wall depends on the thickness of the secondary membrane. In most cells the secondary membrane has pores through which matter is exchanged between cells by means of plasmodesmata, which penetrate the primary membrane and intercellular matter.
Functional specialization of cells is to a large degree associated with changes in the chemical composition of the membrane. Thus, lignification is conditioned by the appearance of lignin in the membrane (especially in the wood and sclerenchyma). The lignin increases the hardness of the membrane, and cell growth ceases. Suberization occurs as a result of infiltration of the membrane by suberin, which is not permeable by fluids and gases. This leads to atrophy of the protoplast (cork cells, exodermis). Cutin causes cutinization of the membrane by forming a film— the cuticle—on the external surface of cells. The cuticle protects the tissue from overheating and evaporation. Accumulation of calcium salts (in red algae, water lilies) or silica (in diatomaceous algae, the epidermis of horsetails and cereals) causes mineralization of the membrane. Conversion of pectins and cellulose to mucilages, which hold back moisture, also occurs. Mucilages occurring on seed coats facilitate sprouting. When there is injury to the surfaces of trunks of cherry, almond, acacia, and other plants, gums are excreted that are chemically similar to mucilages and are used medicinally and in the manufacture of glue.
REFERENCESRazdorskii, V. F. Anatomiia rastenii. Moscow, 1949.
Frey-Wyssling, A., and K. Mülethaler. Ul’trastruktura rastitel’noi kletki. Moscow, 1968. (Translated from English.)
Biokhimiia rastenii. Moscow, 1968. (Translated from English.)
Esau, K. Anatomiia rastenii. Moscow, 1969. (Translated from English.)
L. I. LOTOVA
The membrane of an animal cell is a specialized layer on the cellular surface. It consists of the membrane proper and the plasma membrane, or plasmalemma, which is a submicroscopic structure about 100 Å in thickness. The plasmalemma, which is found in all cells, plays an important role in the exchange of matter between the cell and the external environment (it has selective permeability), in the movement of cells, and in the linkage of cells. It consists of proteins and lipids, and, depending on the nature of the cells and their physiological state, it forms outgrowths (microvilli) and invaginations (pinocytosis). The membrane itself is not present in all animal cells. It is distinguished by great variability: it may perform the function of an external skeleton of the cell (the pellicle of protozoans, the chitin cuticle of arthropods) or play a protective role (the multilayer membrane of egg cells, the wall of a cyst). The membrane contains mainly carbohydrates and their compounds with proteins, lipids, and inorganic substances. It may be secreted by the cell itself or by surrounding cells of the same or other tissue.
T. B. AIZENSHTADT