Biochemical reactions fundamental equation

Biochemical reactions are interesting but they are not magic . Individual chemical reactions that comprise a metabolic pathway obey, obviously, the rules of organic chemistry. All too often students make fundamental errors such as showing carbon with a valency of 3 or 5, or failing properly to balance an equation when writing reactions. Furthermore, overall chemical conversions occur in relatively small steps, that is there are usually only small structural changes or differences between consecutive compounds in a pathway. 

Fundamental Equation for a Biochemical Reaction System at Specified pH... 

When the pH is specified, we enter into a whole new world of thermodynamics because there is a complete set of new thermodynamic properties, called transformed properties, new fundamental equations, new Maxwell equations, new Gibbs-Helmholtz equations, and a new Gibbs-Duhem equation. These new equations are similar to those in chemical thermodynamics, which were discussed in the preceding chapter, but they deal with properties of reactants (sums of species) rather than species. The fundamental equations for transformed thermodynamic potentials include additional terms for hydrogen ions, and perhaps metal ions. The transformed thermodynamic properties of reactants in biochemical reactions are connected with the thermodynamic properties of species in chemical reactions by equations given here. 

The preceding paragraph applies to a system in which there are no biochemical reactions. Now we consider systems with reactions that are at equilibrium (Alberty, 1992d). For a chemical reaction system, we saw (Section 3.4) that D = C + 2 and F = C + 1 for a one-phase system. For a biochemical reaction system at equilibrium, we need the fundamental equation written in terms of apparent components to show how many natural variables there are. When the reaction conditions 2 vj//f = 0 for the biochemical reactions in the system are used to eliminate one for each independent reaction from equation 4.1-18, the following fundamental equation for G in terms of apparent components is obtained ... 

In treating systems of biochemical reactions it is convenient to use the fundamental equation for G in matrix form (Alberty, 2000b). The extent of reaction t for a chemical reaction was discussed earlier in Section 2.1. For a system of chemical reactions, the extent of reaction vector , is defined by... 

Matrix Forms of the Fundamental Equations for Biochemical Reaction Systems... 

The semigrand partition function can be written for a system of biochemical reactions at specified concentrations of coenzymes, and G" = —kT n T". The fundamental equation for G" can be used to calculate the other thermodynamic... 

The chemical master equation (CME) for a given system invokes the same rate constants as the associated deterministic kinetic model. Yet the CME is more fundamental than the deterministic kinetic view. Just as Schrodinger s equation is the fundamental equation for modeling motions of atomic and subatomic particle systems, the CME is the fundamental equation for reaction systems. Remember that Schrodinger s equation is not a model for a specific mechanical system. Rather, it is a theoretical framework upon which models for particular systems can be developed. In order to write down a model for an atomic system based on Schrodinger s equation, one needs to know how to write down the Hamiltonian a priori. Similarly, the CME is not a model for a specific biochemical reaction system it is a theoretical framework. To determine the CME model for a reaction system, one must know what are the possible elementary reactions and the associated rate constants. 

As mentioned earlier, understanding the pH equation and the regulation and control of pH is fundamentally important when considering very many life and health processes. A simple indication of the importance of environmental pH is for growth of crops (soil pH) and acid rain (water pH), which can affect the ecosystem. Indeed, optimum conditions for purification of water and sewage treatment also are pH dependent. Physiologically, pH is critical to maintain normal body functions and key to biochemical reactions in the blood and other body fluids. Buffers and buffer systems are the primary means to regulate and maintain pH, and are discussed in more detail below (with examples in Appendix 3). 

Fundamental Equation for a Single Biochemical Reaction at 298.15 K and the Calculation of Reaction Properties... 

The lesson here is of fundamental importance. In reactions with feedback, and hence non-linearities in their kinetic equations, as so frequently found in biochemical reactions, there may occur oscillations and with that the possibility of controlling the dissipation with small changes in experimental conditions. Take curve c in Fig. 16.7, for example, where we see that a change (a decrease) in A(MDT)P of about 5% can lower the dissipation by nearly 20%. Conversely, if the system is oscillatory, say curve c at A(MDT)P = 41, and the need for heat, that is an increase in dissipation, becomes more urgent than the need for ATP, then a 5% change (an increase) in A(MDT)P can achieve that increase in dissipation by 20%. 

Q.6.5 The following equation is the fundamental biochemical energy reaction in heterotrophic life ... 

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