Biochemical reactions equilibrium compositions

II 6.4 Calculations of Equilibrium Compositions for Systems of Biochemical 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. 

CALCULATIONS OF EQUILIBRIUM COMPOSITIONS FOR SYSTEMS OF BIOCHEMICAL REACTIONS... 

Calculation of equilibrium compositions of a single biochemical reaction or a system of biochemical reactions at specified pH... 

Equilibrium compositions of systems of biochemical reactions can be calculated using the following two programs. The first was written by Fred Krambeck (Mobil Research and Development) and the second was written by Krambeck and Alberty. The Newton-Raphson method is used to iterate to the composition with the lowest possible Gibbs energy or transformed Gibbs energy. 

R. A. Alberty. Equilibrium compositions of solutions of biochemical species and heats of biochemical reactions. Proc. Natl. Acad. Sci. USA, 88 3268-3271, 1991. 

R. A. Alberty, Calculation of equilibrium compositions of large systems of biochemical reactions, J. Phys. Chem. 104 B 4807-4814 (2000). 

Equilibrium compositions of systems of chemical reactions or systems of enzyme-catalyzed reactions can only be calculated by iterative methods, like the Newton-Raphson method, and so computer programs are required. These computer programs involve matrix operations for going back and forth between conservation matrices and stoichiometric number matrices. A more global view of biochemical equilibria can be obtained by specifying steady-state concentrations of coenzymes. These are referred to as calculations at the third level to distinguish them from the first level (chemical thermodynamic calculations in terms of species) and the second level (biochemical thermodynamic calculations at specified pH in terms of reactants). 

An important concept in thermodynamics is the equilibrium state, which will be di,s-cussed in detail in the following. sections. Here we merely note that if a system is not subjected to a continual forced flow of mass, heat, or work, the system will eventually evolve to a time-invariant state in which there are no internal or external flows of heat or mass and no change in composition as a result of chemical or biochemical reactions. This state of the system is the equilibrium state. The precise nature of the equilibrium state depends on both the character of the system and the constraints imposetl on the system by its immediate sutrounding.s and its container (e.g., a constant-volume container fixes the system volume, and a thermostatic bath fixes the system temperature see Problem 1.1). 

Many biochemical reactions take place in steps that reach equilibrium quickly, and to understand their role we need to understand the relation between their kinetic behavior and their equilibrium composition. 

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