Thermodynamic properties biochemical species

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. 

A long time ago chemists realized that the most efficient way to store thermodynamic data on chemical reactions is by making tables of standard thermodynamic properties of species. The NBS Tables of Chemical Thermodynamic Properties (4) gives AfG°, Af// and Sm° for species at 298.15 K at xero ionic strength. Since the standard molar entropy is not available for many species of biochemical interest, the standard entropies of formation Af S" are used. This property of a species is calculated by using... 

A database on the thermodynamic properties of species of biochemical interest has been developed in Mathematica (7) as a package. In this package, BasicBiochemDataS (8), small matrices for 199 reactants (sums of species) contain the data at 298.15 K and zero ionic strength. There is a row in the matrix for each species that gives Af G ,Af W°, z,. ... 

Chapters 3-5 have described the calculation of various transformed thermodynamic properties of biochemical reactants and reactions from standard thermodynamic properties of species, but they have not discussed how these species properties were determined. Of course, some species properties came directly out of the National Bureau of Standard Tables (1) and CODATA Tables (2). One way to calculate standard thermodynamic properties of species not in the tables of chemical thermodynamic properties is to express the apparent equilibrium constant K in terms of the equilibrium constant K of a reference chemical reaction, that is a reference reaction written in terms of species, and binding polynomials of reactants, as described in Chapter 2. In order to do this the piiTs of the reactants in the pH range of interest must be known, and if metal ions are bound, the dissociation constants of the metal ion complexes must also be known. For the hydrolysis of adenosine triphosphate to adenosine diphosphate, the apparent equilibrium constant is given by... 

When the standard thermodynamic properties of species are unknown for two reactants in a biochemical equation, the Af Gy (7=0) and Af 7/y (/=0) of the more basic species of this reactant can be assigned values of zero, so Af Gi for that reactant can be calculated under the experimental conditions. These assigned values become conventions of the thermodynamic table, like Af G (H ) = 0 and Af 7/ (H+) = 0 at each temperature. As described in the preceding section, this was done for adenosine in dilute aqueous solution (3) in 1992, but the determination of the thermodynamic properties of adenosine in dilute aqueous (4) made it possible to drop this convention for the ATP series. 

R. A. Alberty, Calculation of thermodynamic properties of species of biochemical reactants using the inverse Legendre transform, J. Phys. Chem. 109 B, 9132-9139 (2005). 

In 1969 Wilhoit picked up where Burton had left off and compiled the standard thermodynamic properties AfG° and A H° of species involved in biochemical reactions. He recognized the problems involved in including species... 

Statistical mechanics provides a bridge between the properties of atoms and molecules (microscopic view) and the thermodynmamic properties of bulk matter (macroscopic view). For example, the thermodynamic properties of ideal gases can be calculated from the atomic masses and vibrational frequencies, bond distances, and the like, of molecules. This is, in general, not possible for biochemical species in aqueous solution because these systems are very complicated from a molecular point of view. Nevertheless, statistical mechanmics does consider thermodynamic systems from a very broad point of view, that is, from the point of view of partition functions. A partition function contains all the thermodynamic information on a system. There is a different partition function... 

The concepts involved in this approach are simple, but the equations become rather complicated. Biochemical reactions are written in terms of reactants like ATP that are made up of sums of species, and they are referred to as biochemical reactions to differentiate them from the underlying chemical reactions that are written in terms of species. The thermodynamics of biochemical reactions is independent of the properties of the enzymes that catalyze them. However, the fact that enzymes may couple reactions that might otherwise occur separately increases the number of constraints that have to be considered in thermodynamics. 

We have chosen to use C032- as a reference species in reaction numbers 1, 4, and 5. Therefore the apparent thermodynamic properties of these reactions will be calculated in terms of the biochemical reactant XCO2. (See Section 2.6 for a discussion on the treatment of CO2 in biochemical reactions.)... 

We have seen that calculating species properties from experimental values of K and A // ° is more complicated than calculating K and Ar ° from species values. Thermodynamic calculations can be made by alternate paths, and so there is more than one way to calculate species properties from experimental properties. This chapter emphasizes the concept of the inverse Legendre transform discussed by Callen (8). Biochemical reaction systems are described by transformed thermodynamic properties, and the inverse transform given in equation 6.2-1 provides the transformation from experimental reactant properties to calculated species properties. In this ehapter we first considered calculations of species properties at 298.15 K from measurements of K and Ar ° at 298.15 K. Then we considered the more difficult problem of calculating Af G°(298.15 K) and Af //°(298.15 K) from Ar G "(313.15 K) and Ar H (313.15 K). The programs developed here make it possible to go from Ar G and Ar H (F.pH,/) to Af G (298.15 K,/=0) and Af H (298.15 K,/=0) in one step. 

The calculation of Af G° and Af H° of species from experimental data on apparent equilibrium constants and transformed enthalpies of reaction is described in R. A. Alberty, Thermodynamics of Biochemical Reactions, Wiley, Hoboken, NJ (2003) and a number of places in the literature. That is not discussed here because this package is oriented toward the derivation of mathematical functions to calculate thermodynamic properties at specified T, pH, and ionic strength. There are two types of biochemical reactants in the database ... 

Chapters 1 and 2 dealt with species properties. But in this chapter we have found that when the pH is specified, it is necessary to use a Legendre transform to define a transformed Gibbs energy G of a system and that this automatically brings in a transformed enthalpy H and transformed entropy S. In fact we have entered a whole new world of thermodynamics where attention is focussed on reactants, which are sums of species, rather than on species. This world of biochemical... 

Spectroscopy will also be vital if and when we can search the atmospheres of potentially habitable planets for the presence of molecules that indicate the existence of life, a topic discussed in Chap. 5. The discussion of intermolecular forces, especially hydrogen bonding, in Sect. 1.4 serves as an introductiOTi to Chap. 6, which is devoted to the role in biochemical systems of a molecule, water, whose universality on Earth might blind us to its remarkable properties. Quite a lot of this introductory chapter has been devoted to thermodynamics. The role and importance of thermodynamics when we consider what conditions might lead to and sustain life are particularly brought out in some of the later chapters of this book. The forces between dissolved species and their solvent and between molecules that are at the boundary of solubility and therefore can form micelles and lipid bilayers were introduced in Sect. 1.4. These species and their properties re-emerge in Chap. 9 as does the topic of enzyme catalysis introduced in Sect. 1.6. 

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