The cell membrane is an ultrathin film on the surface of a cell or cellular organelle, consisting of a bimolecular layer of lipids with embedded proteins and polysaccharides.

Membrane functions:

• · Barrier - provides regulated, selective, passive and active metabolism with the environment. For example, the peroxisome membrane protects the cytoplasm from peroxides that are dangerous to the cell. Selective permeability means that the permeability of a membrane to different atoms or molecules depends on their size, electrical charge and chemical properties. Selective permeability ensures that the cell and cellular compartments are separated from the environment and supplied with the necessary substances.
• · Transport - transport of substances into and out of the cell occurs through the membrane. Transport through membranes ensures: delivery of nutrients, removal of metabolic end products, secretion of various substances, creation of ion gradients, maintenance of optimal pH and ion concentrations in the cell, which are necessary for the functioning of cellular enzymes. Particles that for any reason are unable to cross the phospholipid bilayer (for example, due to hydrophilic properties, since the membrane inside is hydrophobic and does not allow hydrophilic substances to pass through, or due to their large size), but necessary for the cell, can penetrate the membrane through special carrier proteins (transporters) and channel proteins or by endocytosis. In passive transport, substances cross the lipid bilayer without expending energy along a concentration gradient by diffusion. A variant of this mechanism is facilitated diffusion, in which a specific molecule helps a substance pass through the membrane. This molecule may have a channel that allows only one type of substance to pass through. Active transport requires energy as it occurs against a concentration gradient. There are special pump proteins on the membrane, including ATPase, which actively pumps potassium ions (K +) into the cell and pumps sodium ions (Na +) out of it.
• · matrix - ensures a certain relative position and orientation of membrane proteins, their optimal interaction.
• · mechanical - ensures the autonomy of the cell, its intracellular structures, as well as connection with other cells (in tissues). Cell walls play a major role in ensuring mechanical function, and in animals, the intercellular substance.
• · energy - during photosynthesis in chloroplasts and cellular respiration in mitochondria, energy transfer systems operate in their membranes, in which proteins also participate;
• · receptor - some proteins located in the membrane are receptors (molecules with the help of which the cell perceives certain signals). For example, hormones circulating in the blood act only on target cells that have receptors corresponding to these hormones. Neurotransmitters (chemical substances that ensure the conduction of nerve impulses) also bind to special receptor proteins in target cells.
• · enzymatic - membrane proteins are often enzymes. For example, the plasma membranes of intestinal epithelial cells contain digestive enzymes.
• · implementation of generation and conduction of biopotentials. With the help of the membrane, a constant concentration of ions is maintained in the cell: the concentration of the K + ion inside the cell is much higher than outside, and the concentration of Na + is much lower, which is very important, since this ensures the maintenance of the potential difference on the membrane and the generation of a nerve impulse.
• · cell marking - there are antigens on the membrane that act as markers - “labels” that allow the cell to be identified. These are glycoproteins (that is, proteins with branched oligosaccharide side chains attached to them) that play the role of “antennas”. Because of the myriad configurations of side chains, it is possible to make a specific marker for each cell type. With the help of markers, cells can recognize other cells and act in concert with them, for example, in the formation of organs and tissues. This also allows the immune system to recognize foreign antigens.

Some protein molecules diffuse freely in the plane of the lipid layer; in the normal state, parts of protein molecules emerging on different sides of the cell membrane do not change their position.

The special morphology of cell membranes determines their electrical characteristics, among which the most important are capacitance and conductivity.

Capacitive properties are mainly determined by the phospholipid bilayer, which is impermeable to hydrated ions and at the same time thin enough (about 5 nm) to allow efficient charge separation and storage, and electrostatic interaction of cations and anions. In addition, the capacitive properties of cell membranes are one of the reasons that determine the time characteristics of electrical processes occurring on cell membranes.

Conductivity (g) is the reciprocal of electrical resistance and is equal to the ratio of the total transmembrane current for a given ion to the value that determined its transmembrane potential difference.

Various substances can diffuse through the phospholipid bilayer, and the degree of permeability (P), i.e., the ability of the cell membrane to pass these substances, depends on the difference in concentrations of the diffusing substance on both sides of the membrane, its solubility in lipids and the properties of the cell membrane. The rate of diffusion for charged ions under constant field conditions in a membrane is determined by the mobility of ions, the thickness of the membrane, and the distribution of ions in the membrane. For nonelectrolytes, the permeability of the membrane does not affect its conductivity, since nonelectrolytes do not carry charges, i.e., they cannot carry electric current.

The conductivity of a membrane is a measure of its ionic permeability. An increase in conductivity indicates an increase in the number of ions passing through the membrane.

An important property of biological membranes is fluidity. All cell membranes are mobile fluid structures: most of their constituent lipid and protein molecules are capable of moving quite quickly in the plane of the membrane

It's no secret that all living beings on our planet are made up of cells, these countless "" organic matter. The cells, in turn, are surrounded by a special protective shell - a membrane, which plays a very important role in the life of the cell, and the functions of the cell membrane are not limited to just protecting the cell, but represent a complex mechanism involved in the reproduction, nutrition, and regeneration of the cell.

What is a cell membrane

The word “membrane” itself is translated from Latin as “film,” although a membrane is not just a kind of film in which a cell is wrapped, but a combination of two films connected to each other and having different properties. In fact, the cell membrane is a three-layer lipoprotein (fat-protein) membrane that separates each cell from neighboring cells and the environment, and carries out controlled exchange between cells and the environment, this is the academic definition of what a cell membrane is.

The importance of the membrane is simply enormous, because it not only separates one cell from another, but also ensures the cell’s interaction with both other cells and the environment.

History of cell membrane research

An important contribution to the study of the cell membrane was made by two German scientists Gorter and Grendel back in 1925. It was then that they managed to conduct a complex biological experiment on red blood cells - erythrocytes, during which scientists obtained the so-called “shadows”, empty shells of erythrocytes, which they stacked in one stack and measured the surface area, and also calculated the amount of lipids in them. Based on the amount of lipids obtained, scientists came to the conclusion that they are precisely contained in the double layer of the cell membrane.

In 1935, another pair of cell membrane researchers, this time Americans Daniel and Dawson, after a series of long experiments, established the protein content in the cell membrane. There was no other way to explain why the membrane had such a high surface tension. Scientists have cleverly presented a model of a cell membrane in the form of a sandwich, in which the role of bread is played by homogeneous lipid-protein layers, and between them, instead of oil, there is emptiness.

In 1950, with the advent of electronics, the theory of Daniel and Dawson was confirmed by practical observations - in micrographs of the cell membrane, layers of lipid and protein heads and also the empty space between them were clearly visible.

In 1960, the American biologist J. Robertson developed a theory about the three-layer structure of cell membranes, which for a long time was considered the only true one, but with the further development of science, doubts began to arise about its infallibility. So, for example, from the point of view, it would be difficult and labor-intensive for cells to transport the necessary nutrients through the entire “sandwich”

And only in 1972, American biologists S. Singer and G. Nicholson were able to explain the inconsistencies in Robertson’s theory using a new fluid-mosaic model of the cell membrane. In particular, they found that the cell membrane is not homogeneous in its composition, moreover, it is asymmetrical and filled with liquid. In addition, cells are in constant motion. And the notorious proteins that are part of the cell membrane have different structures and functions.

Properties and functions of the cell membrane

Now let's look at what functions the cell membrane performs:

The barrier function of the cell membrane is the membrane as a real border guard, standing guard over the boundaries of the cell, delaying and not allowing harmful or simply inappropriate molecules to pass through.

Transport function of the cell membrane - the membrane is not only a border guard at the cell gate, but also a kind of customs checkpoint; useful substances are constantly exchanged with other cells and the environment through it.

Matrix function - it is the cell membrane that determines the location relative to each other and regulates the interaction between them.

Mechanical function - is responsible for limiting one cell from another and, at the same time, for correctly connecting cells to each other, for forming them into a homogeneous tissue.

The protective function of the cell membrane is the basis for building the cell's protective shield. In nature, an example of this function can be hard wood, a dense peel, a protective shell, all due to the protective function of the membrane.

Enzymatic function is another important function performed by certain proteins in the cell. For example, thanks to this function, the synthesis of digestive enzymes occurs in the intestinal epithelium.

Also, in addition to all this, cellular exchange occurs through the cell membrane, which can take place in three different reactions:

• Phagocytosis is a cellular exchange in which membrane-embedded phagocyte cells capture and digest various nutrients.
• Pinocytosis is the process of capture by the cell membrane of liquid molecules in contact with it. To do this, special tendrils are formed on the surface of the membrane, which seem to surround a drop of liquid, forming a bubble, which is subsequently “swallowed” by the membrane.
• Exocytosis is a reverse process when a cell releases a secretory functional fluid to the surface through the membrane.

Structure of the cell membrane

There are three classes of lipids in the cell membrane:

• phospholipids (which are a combination of fats and phosphorus),
• glycolipids (a combination of fats and carbohydrates),
• cholesterol.

Phospholipids and glycolipids, in turn, consist of a hydrophilic head, into which two long hydrophobic tails extend. Cholesterol occupies the space between these tails, preventing them from bending; all this, in some cases, makes the membrane of certain cells very rigid. In addition to all this, cholesterol molecules organize the structure of the cell membrane.

But be that as it may, the most important part of the structure of the cell membrane is protein, or rather different proteins that play different important roles. Despite the diversity of proteins contained in the membrane, there is something that unites them - annular lipids are located around all membrane proteins. Annular lipids are special structured fats that serve as a kind of protective shell for proteins, without which they simply would not work.

The structure of the cell membrane has three layers: the basis of the cell membrane is a homogeneous liquid bilipid layer. Proteins cover it on both sides like a mosaic. It is proteins, in addition to the functions described above, that also play the role of peculiar channels through which substances that are unable to penetrate through the liquid layer of the membrane pass through the membrane. These include, for example, potassium and sodium ions; for their penetration through the membrane, nature provides special ion channels in cell membranes. In other words, proteins ensure the permeability of cell membranes.

If we look at the cell membrane through a microscope, we will see a layer of lipids formed by small spherical molecules on which proteins swim as if on the sea. Now you know what substances make up the cell membrane.

Cell membrane video

And finally, an educational video about the cell membrane.

The cell membrane is the structure that covers the outside of the cell. It is also called cytolemma or plasmalemma.

This formation is built from a bilipid layer (bilayer) with proteins built into it. The carbohydrates that make up the plasmalemma are in a bound state.

The distribution of the main components of the plasmalemma is as follows: more than half of the chemical composition is proteins, a quarter is occupied by phospholipids, and a tenth is cholesterol.

Cell membrane and its types

The cell membrane is a thin film, the basis of which is made up of layers of lipoproteins and proteins.

According to localization, membrane organelles are distinguished, which have some features in plant and animal cells:

• mitochondria;
• core;
• endoplasmic reticulum;
• Golgi complex;
• lysosomes;
• chloroplasts (in plant cells).

There is also an inner and outer (plasmolemma) cell membrane.

Structure of the cell membrane

The cell membrane contains carbohydrates that cover it in the form of a glycocalyx. This is a supra-membrane structure that performs a barrier function. The proteins located here are in a free state. Unbound proteins participate in enzymatic reactions, providing extracellular breakdown of substances.

Proteins of the cytoplasmic membrane are represented by glycoproteins. Based on their chemical composition, proteins that are completely included in the lipid layer (along its entire length) are classified as integral proteins. Also peripheral, not reaching one of the surfaces of the plasmalemma.

The former function as receptors, binding to neurotransmitters, hormones and other substances. Insertion proteins are necessary for the construction of ion channels through which the transport of ions and hydrophilic substrates occurs. The latter are enzymes that catalyze intracellular reactions.

Basic properties of the plasma membrane

The lipid bilayer prevents the penetration of water. Lipids are hydrophobic compounds represented in the cell by phospholipids. The phosphate group faces outward and consists of two layers: the outer one, directed to the extracellular environment, and the inner one, delimiting the intracellular contents.

Water-soluble areas are called hydrophilic heads. The fatty acid sites are directed into the cell, in the form of hydrophobic tails. The hydrophobic part interacts with neighboring lipids, which ensures their attachment to each other. The double layer has selective permeability in different areas.

So, in the middle the membrane is impermeable to glucose and urea; hydrophobic substances pass through here freely: carbon dioxide, oxygen, alcohol. Cholesterol is important; the content of the latter determines the viscosity of the plasmalemma.

Functions of the outer cell membrane

The characteristics of the functions are briefly listed in the table:

What is the importance of the cell membrane

The cell membrane is involved in maintaining homeostasis due to the high selectivity of substances entering and exiting the cell (in biology this is called selective permeability).

Outgrowths of the plasmalemma divide the cell into compartments (compartments) responsible for performing certain functions. Specifically designed membranes corresponding to the fluid-mosaic pattern ensure the integrity of the cell.

Cell membranes: their structure and functions

Membranes are extremely viscous and at the same time plastic structures that surround all living cells. Functions of cell membranes:

1. The plasma membrane is a barrier that maintains the different composition of the extra- and intracellular environment.

2. Membranes form specialized compartments inside the cell, i.e. numerous organelles - mitochondria, lysosomes, Golgi complex, endoplasmic reticulum, nuclear membranes.

3. Enzymes involved in energy conversion in processes such as oxidative phosphorylation and photosynthesis are localized in the membranes.

Membrane structure

In 1972, Singer and Nicholson proposed a fluid mosaic model of membrane structure. According to this model, functioning membranes are a two-dimensional solution of globular integral proteins dissolved in a liquid phospholipid matrix. Thus, the basis of the membranes is a bimolecular lipid layer, with an ordered arrangement of molecules.

In this case, the hydrophilic layer is formed by the polar head of phospholipids (a phosphate residue with choline, ethanolamine or serine attached to it) as well as the carbohydrate part of the glycolipids. And the hydrophobic layer is made up of hydrocarbon radicals of fatty acids and sphingosine, phospholipids and glycolipids.

Membrane properties:

1. Selective permeability. The closed bilayer provides one of the main properties of the membrane: it is impermeable to most water-soluble molecules, since they do not dissolve in its hydrophobic core. Gases such as oxygen, CO 2 and nitrogen have the ability to easily penetrate into cells due to the small size of their molecules and weak interaction with solvents. Molecules of a lipid nature, such as steroid hormones, also easily penetrate the bilayer.

2. Liquidity. The lipid bilayer has a liquid crystalline structure, since the lipid layer is generally liquid, but it has areas of solidification, similar to crystalline structures. Although the position of lipid molecules is ordered, they retain the ability to move. Two types of phospholipid movements are possible: somersault (called “flip-flop” in the scientific literature) and lateral diffusion. In the first case, phospholipid molecules opposing each other in the bimolecular layer turn over (or somersault) towards each other and change places in the membrane, i.e. the outer becomes the inner and vice versa. Such jumps involve energy expenditure and occur very rarely. More often, rotations around the axis (rotation) and lateral diffusion are observed - movement within the layer parallel to the surface of the membrane.

3. Membrane asymmetry. The surfaces of the same membrane differ in the composition of lipids, proteins and carbohydrates (transverse asymmetry). For example, phosphatidylcholines predominate in the outer layer, and phosphatidylethanolamines and phosphatidylserines predominate in the inner layer. The carbohydrate components of glycoproteins and glycolipids come to the outer surface, forming a continuous structure called the glycocalyx. There are no carbohydrates on the inner surface. Proteins - hormone receptors are located on the outer surface of the plasma membrane, and the enzymes they regulate - adenylate cyclase, phospholipase C - on the inner surface, etc.

Membrane proteins

Membrane phospholipids act as a solvent for membrane proteins, creating a microenvironment in which the latter can function. The number of different proteins in the membrane varies from 6-8 in the sarcoplasmic reticulum to more than 100 in the plasma membrane. These are enzymes, transport proteins, structural proteins, antigens, including antigens of the major histocompatibility system, receptors for various molecules.

Based on their localization in the membrane, proteins are divided into integral (partially or completely immersed in the membrane) and peripheral (located on its surface). Some integral proteins stitch the membrane multiple times. For example, the retinal photoreceptor and β 2 -adrenergic receptor cross the bilayer 7 times.

Transfer of matter and information across membranes

Cell membranes are not tightly closed partitions. One of the main functions of membranes is the regulation of the transfer of substances and information. The transmembrane movement of small molecules occurs 1) by diffusion, passive or facilitated, and 2) by active transport. Transmembrane movement of large molecules is carried out 1) by endocytosis and 2) by exocytosis. Signal transmission across membranes is carried out using receptors localized on the outer surface of the plasma membrane. In this case, the signal either undergoes transformation (for example, glucagon cAMP), or it is internalized, coupled with endocytosis (for example, LDL - LDL receptor).

Simple diffusion is the penetration of substances into a cell along an electrochemical gradient. In this case, no energy costs are required. The rate of simple diffusion is determined by 1) the transmembrane concentration gradient of the substance and 2) its solubility in the hydrophobic layer of the membrane.

With facilitated diffusion, substances are transported across the membrane also along a concentration gradient, without energy expenditure, but with the help of special membrane carrier proteins. Therefore, facilitated diffusion differs from passive diffusion in a number of parameters: 1) facilitated diffusion is characterized by high selectivity, because the carrier protein has an active center complementary to the substance being transported; 2) the rate of facilitated diffusion can reach a plateau, because the number of carrier molecules is limited.

Some transport proteins simply transfer a substance from one side of the membrane to the other. This simple transfer is called passive uniport. An example of a uniport is GLUT - glucose transporters that transport glucose across cell membranes. Other proteins function as co-transport systems in which the transport of one substance depends on the simultaneous or sequential transport of another substance, either in the same direction, called passive symport, or in the opposite direction, called passive antiport. Translocases of the inner mitochondrial membrane, in particular ADP/ATP translocase, function by the passive antiport mechanism.

During active transport, the transfer of a substance occurs against a concentration gradient and is therefore associated with energy costs. If the transfer of ligands across the membrane is associated with the expenditure of ATP energy, then such transfer is called primary active transport. An example is the Na + K + -ATPase and Ca 2+ -ATPase, localized in the plasma membrane of human cells, and the H + ,K + -ATPase of the gastric mucosa.

Secondary active transport. The transport of some substances against a concentration gradient depends on the simultaneous or sequential transport of Na + (sodium ions) along the concentration gradient. Moreover, if the ligand is transferred in the same direction as Na +, the process is called active symport. According to the mechanism of active symport, glucose is absorbed from the intestinal lumen, where its concentration is low. If the ligand is transferred in the direction opposite to sodium ions, then this process is called active antiport. An example is the Na + ,Ca 2+ exchanger of the plasma membrane.

Cell membrane

Image of a cell membrane. The small blue and white balls correspond to the hydrophobic “heads” of the phospholipids, and the lines attached to them correspond to the hydrophilic “tails”. The figure shows only integral membrane proteins (red globules and yellow helices). Yellow oval dots inside the membrane - cholesterol molecules Yellow-green chains of beads on the outside of the membrane - chains of oligosaccharides forming the glycocalyx

A biological membrane also includes various proteins: integral (penetrating the membrane through), semi-integral (immersed at one end in the outer or inner lipid layer), surface (located on the outer or adjacent to the inner sides of the membrane). Some proteins are the points of contact between the cell membrane and the cytoskeleton inside the cell, and the cell wall (if there is one) outside. Some of the integral proteins function as ion channels, various transporters and receptors.

Functions

• barrier - ensures regulated, selective, passive and active metabolism with the environment. For example, the peroxisome membrane protects the cytoplasm from peroxides that are dangerous to the cell. Selective permeability means that the permeability of a membrane to different atoms or molecules depends on their size, electrical charge and chemical properties. Selective permeability ensures that the cell and cellular compartments are separated from the environment and supplied with the necessary substances.
• transport - transport of substances into and out of the cell occurs through the membrane. Transport through membranes ensures: delivery of nutrients, removal of final metabolic products, secretion of various substances, creation of ion gradients, maintenance of optimal ion concentrations in the cell that are necessary for the functioning of cellular enzymes.
  Particles that for any reason are unable to cross the phospholipid bilayer (for example, due to hydrophilic properties, since the membrane inside is hydrophobic and does not allow hydrophilic substances to pass through, or due to their large size), but necessary for the cell, can penetrate the membrane through special carrier proteins (transporters) and channel proteins or by endocytosis.
  In passive transport, substances cross the lipid bilayer without expending energy along a concentration gradient by diffusion. A variant of this mechanism is facilitated diffusion, in which a specific molecule helps a substance pass through the membrane. This molecule may have a channel that allows only one type of substance to pass through.
  Active transport requires energy as it occurs against a concentration gradient. There are special pump proteins on the membrane, including ATPase, which actively pumps potassium ions (K+) into the cell and pumps sodium ions (Na+) out of it.
• matrix - ensures a certain relative position and orientation of membrane proteins, their optimal interaction.
• mechanical - ensures the autonomy of the cell, its intracellular structures, as well as connection with other cells (in tissues). Cell walls play a major role in ensuring mechanical function, and in animals, the intercellular substance.
• energy - during photosynthesis in chloroplasts and cellular respiration in mitochondria, energy transfer systems operate in their membranes, in which proteins also participate;
• receptor - some proteins located in the membrane are receptors (molecules with the help of which the cell perceives certain signals).
  For example, hormones circulating in the blood act only on target cells that have receptors corresponding to these hormones. Neurotransmitters (chemical substances that ensure the conduction of nerve impulses) also bind to special receptor proteins in target cells.
• enzymatic - membrane proteins are often enzymes. For example, the plasma membranes of intestinal epithelial cells contain digestive enzymes.
• implementation of generation and conduction of biopotentials.
  With the help of the membrane, a constant concentration of ions is maintained in the cell: the concentration of the K+ ion inside the cell is much higher than outside, and the concentration of Na+ is much lower, which is very important, since this ensures the maintenance of the potential difference on the membrane and the generation of a nerve impulse.
• cell marking - there are antigens on the membrane that act as markers - “labels” that allow the cell to be identified. These are glycoproteins (that is, proteins with branched oligosaccharide side chains attached to them) that play the role of “antennas”. Because of the myriad configurations of side chains, it is possible to make a specific marker for each cell type. With the help of markers, cells can recognize other cells and act in concert with them, for example, in the formation of organs and tissues. This also allows the immune system to recognize foreign antigens.

Structure and composition of biomembranes

Membranes are composed of three classes of lipids: phospholipids, glycolipids and cholesterol. Phospholipids and glycolipids (lipids with carbohydrates attached) consist of two long hydrophobic hydrocarbon tails that are connected to a charged hydrophilic head. Cholesterol gives the membrane rigidity by occupying the free space between the hydrophobic tails of lipids and preventing them from bending. Therefore, membranes with a low cholesterol content are more flexible, and those with a high cholesterol content are more rigid and fragile. Cholesterol also serves as a “stopper” that prevents the movement of polar molecules from the cell and into the cell. An important part of the membrane consists of proteins that penetrate it and are responsible for the various properties of membranes. Their composition and orientation differ in different membranes.

Cell membranes are often asymmetrical, that is, the layers differ in lipid composition, the transition of an individual molecule from one layer to another (the so-called flip flop) is difficult.

Membrane organelles

These are closed single or interconnected sections of the cytoplasm, separated from the hyaloplasm by membranes. Single-membrane organelles include the endoplasmic reticulum, Golgi apparatus, lysosomes, vacuoles, peroxisomes; to double membranes - nucleus, mitochondria, plastids. The structure of the membranes of various organelles differs in the composition of lipids and membrane proteins.

Selective permeability

Cell membranes have selective permeability: glucose, amino acids, fatty acids, glycerol and ions slowly diffuse through them, and the membranes themselves, to a certain extent, actively regulate this process - some substances pass through, but others do not. There are four main mechanisms for the entry of substances into the cell or their removal from the cell to the outside: diffusion, osmosis, active transport and exo- or endocytosis. The first two processes are passive in nature, that is, they do not require energy expenditure; the last two are active processes associated with energy consumption.

The selective permeability of the membrane during passive transport is due to special channels - integral proteins. They penetrate the membrane right through, forming a kind of passage. The elements K, Na and Cl have their own channels. Relative to the concentration gradient, the molecules of these elements move in and out of the cell. When irritated, the sodium ion channels open and a sudden influx of sodium ions into the cell occurs. In this case, an imbalance of membrane potential occurs. After which the membrane potential is restored. Potassium channels are always open, allowing potassium ions to slowly enter the cell.

see also

Literature

• Antonov V.F., Smirnova E.N., Shevchenko E.V. Lipid membranes during phase transitions. - M.: Science, 1994.
• Gennis R. Biomembranes. Molecular structure and functions: translation from English. = Biomembranes. Molecular structure and function (by Robert B. Gennis). - 1st edition. - M.: Mir, 1997. - ISBN 5-03-002419-0
• Ivanov V. G., Berestovsky T. N. Lipid bilayer of biological membranes. - M.: Nauka, 1982.
• Rubin A. B. Biophysics, textbook in 2 vols. - 3rd edition, corrected and expanded. - M.: Moscow University Publishing House, 2004. -