Application to biochemical reactions in metabolism

In life sciences, the view of equilibrium is quite different than in the field of chemistry or chemical engineering. Chemistry is concerned with processes that approach equilibrium, and the calculation of DGo serves to determine the equilibrium concentrations that will be observed. A living organism cannot exist at equilibrium. Equilibrium would mean death. Biochemical processes are a coupled set of reactions that are not at equilibrium, but yet our theory of the free energy always uses the standard free energy as the reference.

We can calculate the free energy quantitatively by considering the value of Q, the reaction quotient in the expression

As we have seen, the value of DG = 0 at equilibrium, but there is no law that says that the process must take place at equilibrium. The coupled series of reactions in the cell are not at equilibrium but rather they proceed under steady state conditions. The reactions are poised so that the overall of effect on a series of reactions is to produce a net spontaneous change. Typical standard free energy changes for biochemical reactions are given in Table 1. Aside from the fact that biochemical transformations can occur at non-equilibrium concentrations, they can also be coupled so that one process “drives” another. This is the function of adenosine triphosphate (ATP), which is a major intracellular chemical energy source. Hydrolysis of ATP can both lead to direct phosphorylation or can release heat that used indirectly to drive other processes that would otherwise be endothermic.

Before we proceed to consider the two effects that drive biochemical processes, it is important to understand the role of the protein catalysts that promote metabolic processes. All of the reactions in the glycolytic pathway are catalyzed by enzymes. For example, the reaction considered on the previous slide is catalyzed by hexokinase. The role of enzymes is the same as that of any catalyst. The role of the enzyme is to speed up the reaction, but the enzyme does not change thermodynamics of the process. Catalysts affect the kinetics of the reaction, but not the thermodynamics. We will consider the role of catalysts in the kinetics section.

Coupled biochemical reactions

The hydrolysis of ATP to adenosine diphosphate (ADP) and inorganic phosphate (Pi) has a standard free energy change of

ATP + H₂O à ADP + phosphate DG^o = -31.0 kJ/mol

We can study the phosphorylation of glucose as an example of the kind of behavior observed in a cell. The overall reaction has a negative

D-glucose + ATP à D-glucose-6-phosphate + ADP DG^o = -16.7

The reaction can be decomposed into two reactions. First, the “spontaneous” phosphorylation of glucose is

D-glucose + phosphate à D-glucose-6-phosphate + H₂O DG^o = +14.3

We can see from the positive value of DG^o that the phosphorylation of glucose is not spontaneous at all. In fact, the reverse process of dephosphorylation is spontaneous. However, in the presence of ATP there is a coupling of the dephosphorylation of ATP and phosphorylation of glucose. The sum of the two reactions results in an overall negative free energy change under standard conditions. In this manner the strongly spontaneous hydrolysis of ATP is coupled to the otherwise unspontaneous glucose phosphorylation. This reaction is typical of the role played by ATP in the cell.

Effect of mass action: driving processes using non-equilibrium concentrations

In addition to the coupling we must also consider the fact that the values for DG^o assume a concentration of 1 M. Clearly, the concentrations in the cell are often quite different from the standard state and this will have profound consequences for the direction of spontaneous change.

While DG^o for certain steps is positive under standard conditions, the actual concentrations can give rise to a spontaneous process. For example, the enzyme aldolase catalyzes the conversion of fructose 1,6-diphosphate (FDP) to dihydroxyactone phosphate (DHAP) and glyceraldehyde-3-phosphoate (GAP). The standard free energy change for the reaction is

FDP à DHAP + GAP DG^o = +23.8 kJ

Based on the standard free energy change we would not expect this process to be spontaneous, and in fact the reverse process should be spontaneous. However, under physiological conditions the concentrations of these species in red blood cells (erythrocytes) are [FDP] = 35 mM, [DHAP] = 130 mM and [GAP] = 15 mM. We now consider whether the conversion will occur spontaneously at these concentrations. We apply Eqn. 16.2.1 using the reaction quotient,

We conclude that DG = -1434 J/mol or -1.43 kJ/mol. The reaction will occur spontaneously under the conditions of the cell.

Treating the approach to equilibrium

Although living systems function under steady state conditions, we may have use for the calculation of the equilibrium concentrations of a chemical process. For example, if we consider the phosphate transfer reaction,

D-glucose-6-phosphate à D-fructose-6-phosphate DG^o = +1.7

Which is catalyzed by phosphoglucose isomerase. The equilibrium constant for this process is

K = exp{-DG^o/RT} = exp{-1700/8.31/310} ~ 0.5

The concentration of D-fructose-6-phosphate (F6P) at equilibrium will be less than that of D-glucose-6-phosphate (G6P). If we have a surplus of F6P at an initial time, then the reaction will take place to deplete the F6P to form G6P. For example, if initial concentrations are,

[F6P] = 1.2 x 10^-3 M

[G6P] = 5 x 10^-5 M

Then we can say that we will have the following,

[F6P]_eq = [F6P] – x = 1.2 x 10^-3 M - x

[G6P] _eq = [G6P] + x = 5 x 10^-5 M + x

The equilibrium constant is

Given the above values we can write this as

Which can be written as

Hence,

[F6P]_eq = 0.0004 and [G6P] _eq = 0.00085

Table 1. The standard free energy change of common biochemical reactions.

D-glucose + ATP à D-glucose-6-phosphate + ADP	DG^o = -16.7
D-glucose-6-phosphate à D-fructose-6-phosphate	DG^o = +1.7
D-fructose- 6-diphosphate + ATP à D-fructose-1,6-diphosphate + ADP	DG^o = -14.2
D-fructose-1,6-diphosphate à glyceraldehyde-3-phosphate + dihydroxyacetone phosphate	DG^o = +23.8
dihydroxyacetone phosphate à glyceraldehyde-3-phosphate	DG^o = + 7.5
glyceraldehyde-3-phosphate + phosphate + NAD+ à 1,3-diphosphoglycerate + NADH + H^+	DG^o = + 6.3
1,3-diphosphoglycerate + ADP à 3-phosphoglycerate + ATP	DG^o = -18.8
3-phosphoglycerate à 2-phosphoglycerate	DG^o = +4.6
2-phosphoglycerate à 2-phosphoenolpyruvate + H2O	DG^o = +1.7
2- phosphoenolpyruvate + ADP à pyruvate + ATP	DG^o = -31.4
pyruvate + NADH + H^+ à lactate + NAD^+	DG^o = -25.1
pyruvate à acetaldehyde + CO2	DG^o = -19.8
acetaldehyde + NADH + H^+ à ethanol + NAD^+	DG^o = -23.7