Gibbs Free Energy in Biology - ChemPRIME

# Gibbs Free Energy in Biology

## Coupled Reactions in Biology

According to the second law of thermodynamics, entropy is increasing continuously in the universe. Have you stopped to consider the order within the universe we see on a daily basis? Birds building nests, the creation of complicated burrows - and even skyscrapers! Think of your own body: an inconceivable number of atoms arranged into complicated proteins, bones, and cells. Cells grouped into organs and organs into systems. Each system serving a concerted goal to keep your body functioning day after day. That is an amazing amount of order! Does life break the second law of thermodynamics?

The answer lies with a discussion of the Gibbs Free Energy.

The Gibbs free energy has another very useful property. When a spontaneous chemical reaction occurs, the decrease in Gibbs free energy,–ΔG corresponds to the maximum possible quantity of useful work, wmax, that can be obtained. Symbolically,

–ΔG = wmax

For a reaction that is not spontaneous ΔG is positive and wmax is negative. This means that work must be done on the system (through some outside intervention) to force the non-spontaneous reaction to occur. The minimum work that must be done is given by ΔG. This tells us that in order to create order in the universe, our bodies must somehow do work to force non-spontaneous reactions to occur. Our bodies do this by consuming fuel that, when oxidized, provides excess Gibbs free energy with which to do work. By combining the oxygen we breathe with the food we eat, we can generate excess Gibbs free energy to force otherwise non-spontaneous reactions to occur. The process of breaking food down for energy is called metabolism. Metabolism encompasses the various processes by which our bodies use food nutrients to release Gibbs free energy and, by coupling with many other reactions, to build and maintain cells and the many complicated molecules found therein. Nutrients are considered the basic molecules that are needed for the survival of a living organism.

For instance, we frequently associate sugar with a source of energy. In fact sugars, such as glucose, are a great source of Gibbs free energy when combined with oxygen:

 This option will not work correctly. Unfortunately, your browser does not support inline frames.Figure 1. A glucose molecule, also known as dextrose or blood sugar.

$\text{C}_{6}\text{H}_{12}\text{O}_{6}\text{(aq)} + 6~\text{O}_{2}\text{(g)} \rightarrow 6~\text{CO}_{2}\text{(g)} + 6~\text{H}_{2}\text{O}(l)$        ΔG°' = -2870 kJ

Because reactions occur in our bodies at $\text{pH}\approx 7.0$, it is typical to refer to Gibbs free energies in biological systems with a prime (ΔG°'), indicating that all concentrations are standard, with the exception of hydronium ion concentration ($[\text{H}_{3}\text{O}^{+}] \approx 10^{-7}\text{ mol/dm}^{3}$).

The reaction of glucose with oxygen is very product-favored, as seen by the large negative value for ΔG°'. This is means that this reaction is exergonic: it releases Gibbs free energy. This process releases the same amount of free energy whether being burned in air, or within our bodies. In the air, you would notice a large amount of heat being released into the surroundings - given that we do not catch fire after eating a sweet treat, it is safe to assume our bodies must react glucose with oxygen in a different manner. In order for this excess free energy to do work, our bodies couple this reaction to other reactions. One of the most important ways that our bodies capture this released free energy is by creation of the molecule adenosine triphosphate (ATP) from adenosine diphosphate (ADP). The structures ATP and ADP are shown in Figure 2.

Figure 2. On the left is adenosine diphosphate (ADP), which can be reacted with H2PO-4 to form adenosine triphosphate (ATP). The orange spheres represent phosphorus and are the central atom in each phosphate group (PO3-4). Note the addition of a phosphate group onto the ATP molecule. Also, note that the lewis structure depicts HPO2-4, this is just a different form of the ATP and ADP equation. The addition of the phosphate group is the key feature here.

$\text{ADP}^{3+}\text{(aq)}+\text{H}_{2}\text{PO}_{4}^{-}\text{(aq) } \rightarrow \text{ATP}^{4+}\text{(aq)}+\text{H}_{2}\text{O}(l)$

$\text{ADP}^{3+}\text{(aq)}+\text{H}_{2}\text{PO}_{4}^{-}\text{(aq) } \rightarrow \text{ATP}^{4+}\text{(aq)}+\text{H}_{2}\text{O}(l)$           ΔG°' = +30.5 kJ

As written, ATP would not be formed from ADP, as the Gibbs free energy is positive. This is an example of an endergic reaction. In order for this reaction to occur as written, it would consume Gibbs free energy. This reaction can be coupled to the oxidation of glucose through multiple steps to react 32 times for each glucose molecule metabolized (in humans). Thus, the metabolism of glucose results in 32 x 30.5 kJ = 976 kJ of stored Gibbs free energy which can be released when the body reacts water with ATP to form ADP again!

\begin{align}\text{C}_{6}\text{H}_{12}\text{O}_{6}\text{(aq)} &+ 6~\text{O}_{2}\text{(g)} + \text{ADP}^{3+}\text{(aq)}+\text{H}_{2}\text{PO}_{4}^{-}\text{(aq) } \to \\ &6~\text{CO}_{2}\text{(g)} + 6~\text{H}_{2}\text{O}(l) + \text{ATP}^{4+}\text{(aq)}+\text{H}_{2}\text{O}(l) ~ ~ ~ ~ ~ ~ ~ \Delta G^{\circ\prime} = - 1894 kJ\\ \end{align}

Since the overall reaction has a negative value for free energy, the couple reaction is exergonic and therefore is product-favored. By using the reaction of glucose with oxygen, the body is able to create the energy storage molecule, ATP!

In the context we have just described, free energy is energy that is available to do useful work, not energy that we can get for nothing. When a spontaneous process occurs and there is a free energy decrease, it is the availability of useful energy which decreases. According to the first law of thermodynamics, energy cannot be consumed in any process, but according to the second law, free (or available) energy is always consumed in a spontaneous process.

When we talk about consuming energy resources by eating nutrients, it is the availability of energy that is used up. The energy originally stored in nutrient molecules is converted to free energy and stored by conversion of ADP to ATP. Once this has happened its usefulness is captured to be used by other reactions within the body - this time with the conversion of ATP to ADP driving otherwise endergonic reactions.

The above coupled reaction is a very simplified version of the metabolic process. It should be clear that this process does not occur in a single step - after all, that would require 71 molecules to collide in a single step! Metabolism of nutrients is a complicated set of smaller reactions, usually mediated by enzymes, which result in this overall coupled reaction.

Figure 3. The three stages of Metabolism.

The three stages of the metabolic process that were first noted by Hans Krebs shown in Figure 3, and described below.

(1) Digestion - The process of breaking down large biomolecules (carbohydrates or polysaccharides, fats, and proteins) into their smaller molecules (glucose, glycerol and fatty acids, and amino acids, respectively). These smaller molecules can permeate more easily and therefore can enter the bloodstream from the digestive tract.

(2) Conversion to Acetyl CoA - These smaller molecules are reorganized into even smaller molecules, such as the acetyl group which becomes attached to coenzyme A. When attached, the entire molecule is called acetyl coenzyme A, or acetyl CoA. The structure of acetyl CoA is shown in Figure 4.

(3) Oxidation of Acetyl groups to CO2 and H2O; Production of ATP from ADP - The oxidation process occurs during the course of an eight-step cycle called the citric acid cycle. During the oxidation process, other coupled reactions form ATP from ADP, called oxidative phosphorylation.

The important thing to note about the above discussion is that the formation of ATP from ADP is endergonic, and therefore the production of ATP effectively stores available Gibbs free energy for other processess. The reverse reaction, formation of ADP from ATP, releases the 30.5 kJ for each ATP - the same amount used to create it initially. As we will see shortly, this value is ideal for running many other endergonic reactions within cells., for instance the metabolism of glucose.