Stoichiometric numbers glycolysis reactions

Systems of biochemical reactions like glycolysis, the citric acid cycle, and larger and smaller sequential and cyclic sets of enzyme-catalyzed reactions present challenges to make calculations and to obtain an overview. The calculations of equilibrium compositions for these systems of reactions are different from equilibrium calculations on chemical reactions because additional constraints, which arise from the enzyme mechanisms, must be taken into account. These additional constraints are taken into account when the stoichiometric number matrix is used in the equilibrium calculation via the program equcalcrx, but they must be explicitly written out when the conservation matrix is used with the program equcalcc. The stoichiometric number matrix for a system of reactions can also be used to calculate net reactions and pathways. 

This net reaction is obtained by multiplying the first five reactions of glycolysis by 1, the second five reactions by 2, and adding. This causes the intermediates to cancel. Alternatively, this net reaction can be calculated by multiplying the stoichiometric number matrix v for the 10 reactions of glycolysis by the pathway matrix s, where (,v )r = 1,1,1,1,1,2,2,2,2,2, according to equation 6.1-3. 

Problem 6.2 illustrates the use of equation 6.2-1 by applying it to four net reactions that represent the oxidation of glucose to carbon dioxide and water (1) the net reaction for glycolysis, (2) the net reaction catalyzed by the pyruvate dehydrogenase complex, (3) the net reaction for the citric acid cycle, and (4) the net reaction for oxidative phosphorylation. The v in equation 6.2-1 is the apparent stoichiometric number matrix for these four reactions. The net reaction is... 

Glycolysis involves 10 biochemical reactions and 16 reactants. Water is not counted as a reactant in writing the stoichiometric number matrix or the conservation matrix for reasons described in Section 6.3. Thus there are six components because C = N — R = 16 — 10 = 6. From a chemical standpoint this is a surprise because the reactants involve only C, H, O, N, and P. Since H and O are not conserved at specified pH in dilute aqueous solution, there are only three conservation equations based on elements. Thus three additional conservation relations arise from the mechanisms of the enzyme-catalyzed reactions in glycolysis. Some of these conservation relations are discussed in Alberty (1992a). At specified pH in dilute aqueous solutions the reactions in glycolysis are... 

Figure 6.1 Apparent stoichiometric number matrix v for the 10 reactions of glycolysis at specified pH in dilute aqueous solutions, (see Problem 6.3) [With permission from R. A. Alberty, J. Phys. Chem. B 104, 4807-4814 (2000). Copyright 2000 American Chemical Society.]...

In writing the stoichiometric number matrix for glycolysis, there is a choice as to the order of the reactants. To make Glc, ATP, ADP, NAD0X, NADred, and P components, they are put first in the rows for reactants in the apparent stoichiometric number matrix, followed by the rest of the reactants ending with Pyr. The stoichiometric number matrix for glycolysis is shown in Fig. 6.1. To check that these 10 reactions are indeed independent, a row reduction of the transposed stoichiometric number matrix can be used. Another way to test the correctness of this matrix is to calculate the net reaction using equation 6.1-3. 

---