Plastic. Carbohydrates are formed in plants during the process of photosynthesis and serve as the starting material for the synthesis of all other organic substances;
Structural. This role is played by cellulose or fiber, pectin substances, hemicellulose;
Storage. Spare nutrients: starch, inulin, sucrose...
Protective. Sucrose is the main protective nutrient in wintering plants.
Energy. Carbohydrates are the main substrate of respiration. When 1 g of carbohydrates is oxidized, 17 kJ of energy is released.
2.2. Proteins (B).
Proteins, or proteins, are high-molecular compounds built from amino acids.
Among organic substances, in terms of quantity in plants, the first place is not proteins, but carbohydrates and fats. But it is B. that play a decisive role in metabolism.
Functions of proteins in plants.
Structural. In the cytoplasm of cells, the proportion of proteins is 2/3 of the total mass. Proteins are an integral part of membranes;
Storage. Plants contain less protein than animal organisms, but quite a lot. So, in cereal seeds - 10-20% of dry weight, in seeds of legumes and oilseeds - 20-40%;
Energy. Oxidation of 1 g of protein gives 17 kJ;
Catalytic. Cell enzymes that perform a catalytic function are protein substances;
Transport. Transport substances through membranes;
Protective. Proteins are like antibodies.
Proteins perform a number of other specific functions.
2.2.1. Amino acids (A),
A are the basic structural units from which the molecules of all protein substances are built. Amino acids are derivatives of fatty or aromatic acids, containing both an amino group (-NH 2) and a carboxyl group (-COOH). Most natural A. has a general formula
There are about 200 A. in nature, but only 20, as well as two amides, asparagine and glutamine, are involved in the construction of B. The remaining A. are called free.
In B. only left-handed amino acids are present.
From the chemical properties of A. we note them amphotericity. Due to the amphoteric nature of A. in aqueous solutions, depending on the pH of the solution, the dissociation of –COOH or –NH 2 groups is suppressed and A. exhibits the properties of an acid or alkali.
(-) alkaline environment acidic environment charge “+”
H 2 O +R-CH-COO - ← OH- +R-CH-COO- + H+ →R-CH-COOH
H 2 NH 3 N + H 3 N +
The reaction of a solution of A., in which equality of “+” and “-” charges is observed, is called the isoelectric point (IEP). In IET, the A molecule is electrically neutral and does not move in an electric field.
B.'s composition includes 20 A. and two amides—asparagine and glutamine. Of the 20 A., 8 are essential, since they cannot be synthesized in the body of humans and animals, but are synthesized by plants and microorganisms. Essential amino acids include: valine; lysine; methionine; threonine; leucine; isoleucine; tryptophan; phenylalanine.
Representatives A.
Alanine CH 3 -CH-COOH (6.02)
Cysteine CH 2 -CH-COOH (5.02)
Aspartic COOH-CH 2 -CH-COOH (2.97)
acid |
Glutamic COOH-CH 2 -CH 2 -CH-COOH (3.22)
acid |
Lysine CH 2 -CH 2 -CH 2 -CH 2 -CH-COOH (9.74)
2.2.2. Composition and general properties of proteins.
The elemental composition of B. is quite constant and almost all of them contain 50-60% C, 20-24% O, 6-7% H, 15-19% N, and the amount of sulfur is from 0 to 3%. In complex bacteria, phosphorus, iron, zinc, copper are present in small quantities.....
Properties of proteins.
Amphoteric. B. contain free NH 2 and COOH groups and can dissociate as acids and bases (see example A.). They have IET. When a solution reaction is equal to or close to the IET, proteins are characterized by extreme instability and easily precipitate from solutions under the weakest external influences. This is used to isolate proteins.
Denaturation. This is the loss of protein’s biological properties under the influence of various external influences - high temperature, the action of acids, heavy metal salts, alcohol, acetone, etc. (see colloid coagulation factors). As a result of exposure, a change in the structure of polypeptide chains occurs in the protein molecule, the spatial structure is disrupted, but decomposition into amino acids does not occur. For example, when heating a chicken egg, the white coagulates. This is irreversible denaturation; or completely dried seeds.
Biological nutritional value of proteins (BNV). It is determined by the content of essential A. in B. For this, the B. studied is compared with standard B., approved by the FAO (International Food and Agricultural Organization). The amino acid score of each essential amino acid is calculated and expressed as % content of essential A. in the protein under study (mg) x 100%
Those A., whose amino acid score is less than 100%, are called limiting. In many proteins there are no individual essential proteins at all. For example, tryptophan is absent in apple proteins; in many plant bacteria, the limiting ones are most often the four essential amino acids - lysine, tryptophan, methionine and threonine. B. that do not contain some essential A. are called defective. Plant B. are considered inferior, and animal B. are considered inferior. full-fledged. To create 1 kg of animal food, 8-12 kg of vegetable food is consumed. Based on the BOC of protein, one can estimate: 100% - milk and egg proteins; other animals B – 90-95%; B. legumes – 75-85%; B. grain crops - 60-70%.
2.2.3. The structure of proteins.
According to the polypeptide theory of the structure of B. (Danilevsky, Fischer), amino acids interact with each other to form a peptide bond - CO-NH-. Di-, tri-, pento- and polypeptides are formed.
The B. molecule is constructed from one or more interconnected polypeptide chains consisting of amino acid residues.
CH 3 CH 2 CH CH 3 CH 2 CH
H 2 N-CH-COOH + H 2 N-CH-COOH →H 2 N-CH-CO-NH-CH-COOH + H 2 O
Alanine cysteine alanylcysteine
(dipeptide)
Structure B.
There are different levels of organization of a protein molecule and each molecule has its own spatial structure. The loss or disruption of this structure causes a disruption in the function performed (denaturation).
There are different levels of organization of a protein molecule.
Primary structure. Determined by the number and sequence of amino acids in the B molecule. The primary structure is fixed genetically. With this structure, the B. molecule has a thread-like shape. …….
The primary structure of homologous proteins is used, in particular, as a criterion for establishing the relationship between individual species of plants, animals and humans.
Secondary structure. It is a helical configuration of polypeptide chains. The decisive role in its education belongs to hydrogenconnections...... However, disulfide bonds (-S-S-) can also appear between individual points of the helix, which disrupt the typical helical structure.
Tertiary structure. This is an even higher level of organization B. It characterizes the spatial configuration of the molecule. It is due to the fact that free carboxyl, amine, hydroxyl and other groups of side radicals of amino acid molecules in polypeptide chains interact with each other to form amide, ester and salt bonds. Due to this, the polypeptide chain, which has a certain secondary structure, is further folded and packed and acquires a specific spatial configuration. Hydrogen and disulfide bonds also play a significant role in its formation. A globular (spherical) form of proteins is formed.
Quaternary structure. It is formed by the combination of several proteins with a tertiary structure. It should be noted that the functional activity of a particular protein is determined by all four levels of its organization.
2.2.4. Protein classification.
Based on their structure, proteins are divided into proteins, or simple proteins, built only from amino acid residues, and proteids, or complex proteins, consisting of a simple protein and some other non-protein compound tightly bound to it. Depending on the nature of the non-protein part, proteids are divided into subgroups.
Phosphoproteins - proteins are combined with phosphoric acid.
Lipoproteins - proteins are combined with phospholipids and other lipids, for example, in membranes.
Glycoproteins - protein is combined with carbohydrates and their derivatives. For example, in the composition of plant mucilages.
Metalloproteins – contain metals, g.o. trace elements: Fe, Cu, Zn….. These are mainly metal-containing enzymes: catalase, cytochromes, etc.
Nucleoproteins are one of the most important subgroups. Here the protein combines with nucleic acids.
The classification of proteins according to solubility in various solvents is of great practical importance. The following are distinguished: faction B. by solubility:
Albumins are water soluble. A typical representative is chicken egg albumin, many proteins are enzymes.
Globulins are proteins that are soluble in weak solutions of neutral salts (4 or 10% NaCl or KCl).
Prolamins - dissolve in 70% ethyl alcohol. For example, gliadins of wheat and rye.
Glutelins - dissolve in weak alkali solutions (0.2-2%).
Histones are low-molecular alkaline bacteria contained in the nuclei of cells.
Fractions of B. differ in amino acid composition and biological nutritional value (BNC). According to BPC, the fractions are arranged in the sequence: albumins › globulins ≈ glutelins › prolamins. The content of fractions depends on the type of plant; it is not the same in different parts of the grain. (see private biochemistry of agricultural crops).
Lipids (L).
Lipids are fats (F) and fat-like substances (lipoids) that are similar in their physicochemical properties, but differ in their biological role in the body.
Lipids are generally divided into two groups: fats and lipoids. Typically, fat-soluble vitamins are also classified as lipids.
Studying the connection between the properties of substances and their structure is one of the main tasks of chemistry. A great contribution to its solution was made by the structural theory of organic compounds, whose creators included the great Russian chemist Alexander Mikhailovich Butlerov (1828-1886). It was he who first established that the properties of a substance depend not only on its composition (molecular formula), but also on the order in which the atoms in the molecule are connected to each other. This order was called "chemical structure". Butlerov predicted that composition C 4 H 10 may correspond to two substances having different structures - butane and isobutane, and confirmed this by synthesizing the latter substance.
The idea that the order in which atoms are connected is key to the properties of matter has proven to be very fruitful. It is based on the representation of molecules using graphs, in which atoms play the role of vertices, and chemical bonds between them act as edges connecting the vertices. In the graphical representation, the lengths of the bonds and the angles between them are ignored. The C molecules described above 4 H 10 are represented by the following graphs:
Hydrogen atoms are not indicated in such graphs, since their location can be unambiguously determined by the structure of the carbon skeleton. Recall that carbon in organic compounds is tetravalent, so in the corresponding graphs no more than four edges can extend from each vertex.
Graphs are mathematical objects, so they can be characterized using numbers. This is where the idea came from to express the structure of molecules with numbers that are related to the structure of molecular graphs. These numbers are called “topological indices” in chemistry. By calculating any topological index for a large number of molecules, it is possible to establish a connection between its values and the properties of substances, and then use this connection to predict the properties of new, not yet synthesized substances. To date, chemists and mathematicians have proposed hundreds of different indices that characterize certain properties of molecules.
Methods for calculating topological indices
Methods for calculating topological indices can be very diverse, but all of them must satisfy quite natural requirements:
1) each molecule has its own individual index;
2) molecules with similar properties have similar indices.
Let's see how this idea is implemented using the example of saturated hydrocarbons - alkanes. The key concept for constructing many indices is the concept of “distance matrix” D. This is the name of a matrix whose elements show the number of edges separating the corresponding vertices of the molecular graph. Let's construct this matrix for three isomeric hydrocarbons of composition C 5 H 12 . To do this, let’s draw their molecular graphs and renumber the vertices (in random order):
The diagonal elements of the distance matrix for hydrocarbons are equal to 0. In the first graph, vertex 1 is connected to vertex 2 by one edge, so the matrix element d 12 = 1. Similarly, d 13 = 2, d 14 = 3, d 15 = 4. The first row in the distance matrix of normal pentane has the form: (0 1 2 3 4). Complete distance matrices for three graphs:
molecule chemistry topological index
The distance between vertices does not depend on the order in which they are listed, so the distance matrices are symmetrical with respect to the diagonal.
The first topological index reflecting the structure of a molecular graph (G) was proposed in 1947 by Wiener. It is defined as the sum of the diagonal elements of the distance matrix plus half the sum of its non-diagonal elements:
(1)
For the above graphs corresponding to pentanes C 5 H 12 , the Wiener index takes values 20, 18 and 16. It can be assumed that it describes the degree of branching of the hydrocarbon: the highest values correspond to the least branched hydrocarbons. As the length of the carbon skeleton increases, the Wiener index increases, as there are more elements in the distance matrix. Statistical analysis using the example of several hundred hydrocarbons showed that the Wiener index correlates with some physical properties of alkanes: boiling points, heats of evaporation, molar volume.
Another type of index is based not on the distances between vertices, but on the number of nearest neighbors for each vertex. As an example, let's calculate the Randić index, which is defined as follows:
(2)
where vi– degree of the i-th vertex, that is, the number of edges extending from it. For the above graphs, the Randić index is equal to:
(3)
(4)
(5)
This index also decreases with increasing degree of branching of the carbon skeleton and can be used to describe the physical properties of alkanes.
Alkanes are the most boring type of organic molecules from a chemical point of view, since they do not contain any “features” - double and triple bonds or atoms of elements other than hydrogen and carbon (such elements are called heteroatoms). The introduction of heteroatoms into a molecule can radically change the properties of a substance. Thus, the addition of just one oxygen atom converts the rather inert gaseous ethane C 2 H 6 into liquid ethanol C 2 H 5 OH, exhibiting fairly high chemical and biological activity.
Consequently, in the topological indices of molecules more complex than alkanes, it is necessary to take into account the presence of multiple bonds and heteroatoms. This is done by assigning certain numerical coefficients - “weights” - to the vertices and edges of the graphs. For example, in a distance matrix, the diagonal elements can be defined in terms of the nuclear charge Zi(remember that for carbon Z = 6):
(6)
Off-diagonal elements are determined by summing over edges, with each edge connecting atoms with charges Ziand Zj, weight is assigned
(7)
where b is equal to the bond order between the atoms (1 for a single bond, 2 for a double bond, 3 for a triple bond). For ordinary carbon-carbon single bonds, k = 1. Let us compare the Wiener indices of propane C 3 H 8 and three oxygen-containing substances similar in composition: propyl alcohol C 3 H 8 O, its isomeric isopropyl alcohol C 3 H 8 O and acetone C 3 H 6 O.
To do this, we calculate the distance matrix according to the specified rules. In molecular graphs we indicate all atoms except hydrogen atoms.1) Propane
2) In the propyl alcohol molecule, oxygen is bonded to the outermost carbon atom:
For a single C–O bond, the weighting coefficient is 36/(68) = 0.75. Diagonal matrix element corresponding to oxygen:
d 44 = 1 – 6/8 = 0.25.
For molecules containing heteroatoms, the Wiener index ceases to be integer. 3) In the isopropyl alcohol molecule, oxygen is bonded to the middle carbon atom:
4) In acetone, the order of connection of atoms is the same as in isopropyl alcohol, but the bond between carbon and oxygen is double:
For the C=O double bond the weighting factor is 36/(268) = 0.375
As can be seen, the addition of a heteroatom to the structure of alkanes leads to an increase in the Wiener index due to an increase in the size of the distance matrix. Adding multiple bonds and increasing the degree of branching of the molecule reduces this index. These rules also apply to more complex molecules. Initially, topological indices were developed only for the purpose of predicting the physicochemical properties of substances. However, later they began to be used to solve other problems. Let's look at some of them. One application of topological indices is related to the classification of organic compounds and the creation of organic databases. The task is to find an index that one-to-one characterizes the chemical structure and from which this structure can be reconstructed. The required index must have good discriminatory ability, that is, it must distinguish between even molecules that are similar in structure. This task is enormous, since more than 20 million organic structures are already known. Its solution will apparently be found through the use of composite topological indices.
Abstract on the subject higher mathematics on the topic:
Application of graph theory in chemistry
Performed by a student from group NH-202
Moscow 2011
Graphs are the field of finite mathematics that studies discrete structures; used to solve various theoretical and applied problems.
Some basic concepts. A graph is a collection of points (vertices) and a collection of pairs of these points (not necessarily all) connected by lines (Fig. 1, a). If the lines in a graph are oriented (that is, the arrows indicate the direction of connection of the vertices), they are called arcs, or branches; if unoriented, - edges. Accordingly, a graph containing only arcs is called a directed graph, or a digraph; only edge-unoriented; arcs and ribs - mixed. A graph having multiple edges is called a multigraph; a graph containing only edges belonging to two of its disjoint subsets (parts) is bipartite; arcs (edges) and (or) vertices that correspond to certain weights or numerical values of any parameters are weighted. A path in a graph is an alternating sequence of vertices and arcs in which none of the vertices is repeated (for example, a, b in Fig. 1,a); contour - a closed path in which the first and last vertices coincide (for example, f, h); loop - an arc (edge) that begins and ends at the same vertex. A graph path is a sequence of edges in which none of the vertices are repeated (for example, c, d, e); cycle - a closed chain in which its initial and final vertices coincide. A graph is called connected if any pair of its vertices is connected by a chain or path; otherwise, the graph is called disconnected.
A tree is a connected undirected graph that does not contain cycles or contours (Fig. 1, b). The spanning subgraph of a graph is a subset of it that contains all the vertices and only certain edges. The spanning tree of a graph is its spanning subgraph, which is a tree. Graphs are called isomorphic if there is a one-to-one correspondence between the sets of their vertices and edges (arcs).
To solve problems of graph theory and its applications, graphs are represented using matrices (adjacency, incidence, two-row, etc.), as well as special ones. numerical characteristics. For example, in the adjacency matrix (Fig. 1c), the rows and columns correspond to the numbers of the vertices of the graph, and its elements take the values 0 and 1 (respectively, the absence and presence of an arc between a given pair of vertices); in the incidence matrix (Fig. 1d), the rows correspond to the numbers of the vertices, the columns correspond to the numbers of the arcs, and the elements take the values 0, + 1 and - 1 (respectively, the absence, presence of an arc entering and leaving the vertex). The most common numerical characteristics: the number of vertices (m), the number of arcs or edges (n), the cyclomatic number, or the rank of the graph (n - m + k, where k is the number of connected subgraphs in a disconnected graph; for example, for the graph in Fig. 1 ,b rank will be: 10-6+ 1 =5).
The application of graph theory is based on the construction and analysis of various classes of chemical and chemical-technological graphs, which are also called topological models, i.e. models that take into account only the nature of the connections between the vertices. The arcs (edges) and vertices of these graphs display chemical and chemical-technological concepts, phenomena, processes or objects and, accordingly, qualitative and quantitative relationships or certain relationships between them.
Rice. 1. Illustration of some basic concepts: a-mixed graph; b-spanning tree (solid arcs a, h, d, f, h) and a certain subgraph (dashed arcs c, e, g, k, l) of the digraph; c, r-matrices resp. adjacency and incidence of a digraph.
Theoretical problems. Chemical graphs make it possible to predict chemical transformations, explain the essence and systematize some basic concepts of chemistry: structure, configuration, conformations, quantum mechanical and statistical-mechanical interactions of molecules, isomerism, etc. Chemical graphs include molecular, bipartite and signal graphs of kinetic reaction equations.
Molecular graphs, used in stereochemistry and structural topology, chemistry of clusters, polymers, etc., are undirected graphs that display the structure of molecules (Fig. 2). The vertices and edges of these graphs correspond, respectively, to atoms and chemical bonds between them.
Rice. 2. Molecular graphs and trees: a, b - multigraphs, respectively. ethylene and formaldehyde; they say pentane isomers (trees 4, 5 are isomorphic to tree 2).
In the stereochemistry of organic substances, molecular trees are most often used - spanning trees of molecular graphs, which contain only all vertices corresponding to C atoms (Fig. 2, a and b). Compiling sets of molecular trees and establishing their isomorphism makes it possible to determine molecular structures and find the total number of isomers of alkanes, alkenes and alkynes (Fig. 2, c).
Molecular graphs make it possible to reduce problems related to coding, nomenclature and structural features (branching, cyclicity, etc.) of molecules of various compounds to the analysis and comparison of purely mathematical features and properties of molecular graphs and their trees, as well as their corresponding matrices. To identify quantitative correlations between the structure of molecules and the physicochemical (including pharmacological) properties of compounds, more than 20 thousand names of topological indices of molecules (Wiener, Balaban, Hosoya, Plat, Randic, etc.) have been developed, which are determined using matrices and numerical characteristics of molecular trees. For example, the Wiener index W = (m 3 + m)/6, where m is the number of vertices corresponding to C atoms, correlates with molecular volumes and refractions, enthalpies of formation, viscosity, surface tension, chromatographic constants of compounds, octane numbers of hydrocarbons and even physiological activity of drugs.
Important parameters of molecular graphs used to determine the tautomeric forms of a given substance and their reactivity, as well as in the classification of amino acids, nucleic acids, carbohydrates and other complex natural compounds, are the average and total (H) information capacities. The parameter is calculated using the Shannon information entropy formula: , where p t is the probability that the vertices m of the graph belong to the i-th type, or equivalence class, k; i = , Parameter. The study of molecular structures such as inorganic clusters or Möbius strips comes down to establishing the isomorphism of the corresponding molecular graphs by placing them (embedding) in complex polyhedra (for example, polyhedra in the case of clusters) or special ones. multidimensional surfaces (for example, Riemann surfaces). Analysis of molecular graphs of polymers, the vertices of which correspond to monomer units, and the edges to chemical bonds between them, makes it possible to explain, for example, the effects of excluded volume, leading to qualitative changes in the predicted properties of polymers.
Rice. 3. Reaction graphs: a-bipartite; b-signal level of kinetics; r 1, g 2 -r-tion; a 1 -a 6 -reagents; k-rate constants p-tsny; s-complex Laplace transform variable.
Using graph theory and principles of artificial intelligence, software has been developed for information retrieval systems in chemistry, as well as automated systems for identifying molecular structures and rational planning of organic synthesis. For the practical implementation on a computer of operations for selecting rational paths of chemical transformations based on the retrosynthetic and syntonic principles, multi-level branched search graphs for solution options are used, the vertices of which correspond to the molecular graphs of reagents and products, and the arcs depict the transformations of substances.
Rice. 4. Single-circuit chemical-technological system and corresponding graphs: a-structural diagram; b, c-material flow graphs, respectively. by total mass flow rates and component A flow rate; r - thermal flow graph; d-fragment of the system of equations (f 1 - f 6) of the material balance, obtained from the analysis of the graphs in Fig. 4, b and c; e-bipartite information digraph; g-information graph, I-mixer; II-reactor; III-distillation column; IV-refrigerator; I 1 -I 8 -technol. streams; q-mass flow; H is the enthalpy of the flow; i. s and i*, s* - resp. real and fictitious sources and sinks of material and heat flows; c-concentration of the reagent; V is the volume of the reactor.
Matrix representations of molecular graphs of various compounds are equivalent (after transforming the corresponding matrix elements) to matrix methods of quantum chemistry. Therefore, graph theory is used when performing complex quantum chemical calculations: to determine the number, properties and energies of molecular orbitals, predicting the reactivity of conjugated alternant and non-alternant polyenes, identifying aromatic and anti-aromatic properties of substances, etc.
To study disturbances in systems consisting of a large number of particles in chemical physics, so-called Feynman diagrams are used - graphs whose vertices correspond to the elementary interactions of physical particles, the edges to their paths after collisions. In particular, these graphs make it possible to study the mechanisms of oscillatory reactions and determine the stability of reaction systems.
To select rational paths for the transformation of reagent molecules for a given set of known interactions, bipartite reaction graphs are used (the vertices correspond to molecules and these reactions, the arcs correspond to the interactions of molecules in the reaction; Fig. 3,a). Such graphs make it possible to develop interactive algorithms for selecting optimal paths of chemical transformations that require the smallest number of intermediate reactions, the minimum number of reagents from the list of acceptable ones, or achieve the highest yield of products.
Signal graphs of reaction kinetics equations display systems of kinetic equations presented in algebraic-operator form (Fig. 3b). The vertices of the graphs correspond to the so-called information variables, or signals, in the form of concentrations of reagents, arcs - to the relationships of signals, and the weights of the arcs are determined by kinetic constants. Such graphs are used in studying the mechanisms and kinetics of complex catalytic reactions, complex phase equilibria in the formation of complex compounds, as well as for calculating the parameters of the additive properties of solutions.
Applied problems. To solve multidimensional problems of analysis and optimization of chemical-technological systems (CTS), the following chemical-technological graphs are used (Fig. 4): flow, information-flow, signal and reliability graphs. Flow graphs, which are weighted digraphs, include parametric, material in terms of the total mass flow rates of physical flows and the mass flow rates of some chemical components or elements, as well as thermal graphs. The listed graphs correspond to the physical and chemical transformations of substances and energy in a given chemical system.
Parametric flow graphs display the transformation of parameters (mass flow rates, etc.) of physical flows by CTS elements; the vertices of the graphs correspond to the mathematical models of the devices, as well as the sources and sinks of the specified flows, and the arcs correspond to the flows themselves, and the weights of the arcs are equal to the number of parameters of the corresponding flow. Parametric graphs are used to develop algorithms for analyzing technological modes of multi-circuit chemical systems. Such algorithms establish the sequence of calculating systems of equations of mathematical models of individual devices of any system to determine the parameters of its output flows with known values of variable input flows.
Material flow graphs display changes in the consumption of substances in chemical substances. The vertices of the graphs correspond to devices in which the total mass flow rates of physical flows and the mass flow rates of some chemical components or elements are transformed, as well as sources and sinks of substances of flows or these components; Accordingly, the arcs of the graphs correspond to physical flows or physical and fictitious (chemical transformations of substances in apparatuses) sources and sinks of any components, and the weights of the arcs are equal to the mass flow rates of both types. Thermal flow graphs display heat balances in CTS; the vertices of the graphs correspond to devices in which the heat consumption of physical flows changes, and, in addition, to the sources and sinks of thermal energy of the system; arcs correspond to physical and fictitious (physical-chemical energy conversion in devices) heat flows, and the weights of the arcs are equal to the enthalpies of the flows. Material and thermal graphs are used to compile programs for the automated development of algorithms for solving systems of equations for material and heat balances of complex chemical systems.
Information-stock graphs display the logical-information structure of systems of equations of mathematical models of CTS; are used to develop optimal algorithms for calculating these systems. A bipartite information graph (Fig. 4, e) is an undirected or oriented graph, the vertices of which correspond, respectively, to the equations f l - f 6 and the variables q 1 - V, and the branches reflect their relationship. Information graph (Fig. 4, g) - a digraph depicting the order of solving equations; the vertices of the graph correspond to these equations, sources and receivers of XTS information, and the branches correspond to information variables.
Signal graphs correspond to linear systems of equations of mathematical models of chemical technological processes and systems. The vertices of the graphs correspond to signals (for example, temperature), and the branches correspond to connections between them. Such graphs are used to analyze the static and dynamic modes of multiparameter processes and chemical systems, as well as indicators of a number of their most important properties (stability, sensitivity, controllability).
Reliability graphs are used to calculate various indicators of the reliability of chemical equipment. Among the numerous groups of these graphs (for example, parametric, logical-functional), the so-called fault trees are especially important. Each such tree is a weighted digraph that displays the interrelationship of many simple failures of individual processes and CTS devices, which lead to many secondary failures and the resulting failure of the system as a whole.
To create complexes of programs for automated synthesis of optimal highly reliable production (including resource-saving), along with the principles of artificial intelligence, oriented semantic, or semantic, graphs of CTS solution options are used. These graphs, which in a particular case are trees, depict procedures for generating a set of rational alternative CTS schemes (for example, 14 possible when separating a five-component mixture of target products by rectification) and procedures for the ordered selection among them of a scheme that is optimal according to some criterion of system efficiency.
etc.................