THE GIBBS FREE ENERGY, G When dealing with an enclosed biological system, one would like to have a simple way of predicting whether a given reaction will or will not occur spontaneously in the system. We have seen that the crucial question is whether the entropy change for the universe is positive or negative when that reaction occurs. In our idealized system, the cell in a box, there are two separate components to the entropy change of the universe—the entropy change for the system enclosed in the box and the entropy change for the surrounding “sea”—and both must be added together before any prediction can be made. For example, it is possible for a reaction to absorb heat and thereby decrease the entropy of the sea (˜Ssea < 0) and at the same time to cause such a large degree of disordering inside the box (˜Sbox > 0) that the total ˜Suniverse = ˜Ssea + ˜Sbox is greater than 0. In this case, the reaction will occur spontaneously, even though the sea gives up heat to the box during the reaction. An example of such a reaction is the dissolving of sodium chloride in a beaker containing water (the “box”), which is a spontaneous process even though the temperature of the water drops as the salt goes into solution. Chemists have found it useful to defne a number of new “composite functions” that describe combinations of physical properties of a system. The properties that can be combined include the temperature (T), pressure (P), volume (V), energy (E), and entropy (S). The enthalpy (H) is one such composite function. But by far the most useful composite function for biologists is the Gibbs free energy, G. It serves as an accounting device that allows one to deduce the entropy change of the universe resulting from a chemical reaction in the box, while avoiding any separate consideration of the entropy change in the sea. The defnition of G is where, for a box of volume V, H is the enthalpy described above (E + PV), T is the absolute temperature, and S is the entropy. Each of these quantities applies to the inside of the box only. The change in free energy during a reaction in the box (the G of the products minus the G of the starting materials) is denoted as ˜G and, as we shall now demonstrate, it is a direct measure of the amount of disorder that is created in the universe when the reaction occurs. G = H _ TS At constant temperature the change in free energy (˜G) during a reaction equals ˜H _ T˜S. Remembering that ˜H = _h, the heat absorbed from the sea, we have _˜G = _˜H + T˜S _˜G = h + T˜S, so _˜G/T = h/T + ˜S But h/T is equal to the entropy change of the sea (˜Ssea), and the ˜S in the above equation is ˜Sbox. Therefore _˜G/T = ˜Ssea + ˜Sbox = ˜Suniverse We conclude that the free-energy change is a direct measure of the entropy change of the universe. A reaction will proceed in the direction that causes the change in the free energy (˜G) to be less than zero, because in this case there will be a positive entropy change in the universe when the reaction occurs. For a complex set of coupled reactions involving many different molecules, the total free-energy change can be com-puted simply by adding up the free energies of all the different molecular species after the reaction and comparing this value with the sum of free energies before the reaction; for common substances the required free-energy values can be found from published tables. In this way, one can predict the direction of a reaction and thereby readily check the feasibility of any proposed mechanism. Thus, for example, from the observed values for the magnitude of the electrochemical proton gradient across the inner mitochondrial membrane and the ˜G for ATP hydrolysis inside the mitochondrion, one can be certain that ATP synthase requires the passage of more than one proton for each molecule of ATP that it synthesizes. The value of ˜G for a reaction is a direct measure of how far the reaction is from equilibrium. The large negative value for ATP hydrolysis in a cell merely refects the fact that cells keep the ATP hydrolysis reaction as much as 10 orders of magnitude away from equilibrium. If a reaction reaches equilibrium, ˜G = 0, the reaction then proceeds at precisely equal rates in the forward and backward direction. For ATP hydrolysis, equilibrium is reached when the vast majority of the ATP has been hydrolyzed, as occurs in a dead cell.