Problem 34 - Chemistry and Chemical Reactivity

Question

The first step of the metabolic process known as glycolysis is the conversion of glucose to glucose6-phosphate. This process has a positive value for \(\Delta_{\mathrm{r}} G^{\circ \prime}\). Glucose \(+P_{i} \rightarrow\) Glucose-6-phosphate \(+\mathrm{H}_{2} \mathrm{O}\) \(\Delta_{\mathrm{r}} G^{\circ \prime}=+13.8 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn}\) This reaction is coupled to the hydrolysis of ATP \(\mathrm{ATP}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{ADP}+\mathrm{P}_{\mathrm{i}} \quad \Delta_{\mathrm{r}} G^{\circ \prime}=-30.5 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn}\) What is the sum of these two equations and the value of \(\Delta_{\mathrm{r}} G^{\circ}\) ' for the coupled reaction? Is the coupled reaction product-favored at equilibrium?

Step-by-Step Solution

Answer

The coupled reaction \(\Delta_{\mathrm{r}} G^{\circ'}\) is -16.7 kJ/mol, so it is product-favored.

Step 1: Understand the Reaction Coupling

In biochemical processes, reactions with a positive \( \Delta_{\mathrm{r}} G^{\circ'} \) are often unfavorable and do not happen spontaneously. However, these reactions can be driven forward by coupling them with a second reaction that has a more negative \( \Delta_{\mathrm{r}} G^{\circ'} \). Here, the unfavorable process (conversion of glucose to glucose-6-phosphate) is being coupled with a favorable process (hydrolysis of ATP).

Step 2: Write the Coupled Reaction

To couple the reactions, simply add the two reactions together. This involves adding the left sides of both equations and the right sides of both equations:Glucose + \( P_{i} \) + ATP + \( H_{2}O \) \( \rightarrow \) Glucose-6-phosphate + \( H_{2}O \) + ADP + \( P_{i} \).Notice that \( P_{i} \) and \( H_{2}O \) are present on both sides. We can cancel out each \( P_{i} \) and \( H_{2}O \) molecule from both sides of the equation.

Step 3: Simplify the Coupled Reaction

After canceling the common terms, the net equation for the coupled reaction is:Glucose + ATP \( \rightarrow \) Glucose-6-phosphate + ADP.

Step 4: Calculate the Net \( \Delta_{\mathrm{r}} G^{\circ'} \) for the Coupled Reaction

The net \( \Delta_{\mathrm{r}} G^{\circ'} \) for a coupled reaction is the sum of the \( \Delta_{\mathrm{r}} G^{\circ'} \) values of the individual reactions:\[ \Delta_{\mathrm{r}} G^{\circ'}_{\text{net}} = +13.8 \text{ kJ/mol} + (-30.5 \text{ kJ/mol}) = -16.7 \text{ kJ/mol} \]

Step 5: Determine if the Coupled Reaction is Product-Favored

A reaction is product-favored at equilibrium if \( \Delta_{\mathrm{r}} G^{\circ'} \) is negative. In this coupled reaction, \( \Delta_{\mathrm{r}} G^{\circ'} \) is -16.7 kJ/mol, which is negative. Therefore, the reaction is product-favored at equilibrium.

Key Concepts

Biochemical Reactions

Biochemical reactions are the foundation of life, driving processes that convert substances essential for cellular functions. They involve the transformation of molecules through breaking and forming chemical bonds. These reactions are orchestrated by enzymes, which act as highly selective catalysts. An important factor in biochemical reactions is the change in Gibbs free energy, represented by \( \Delta_{\mathrm{r}} G^{ \circ '} \). This value helps determine whether a reaction will occur spontaneously. A negative \( \Delta_{\mathrm{r}} G^{ \circ '} \) indicates a spontaneous reaction, while a positive value suggests the reaction needs additional energy to proceed. In glycolysis, the first step is an example of a biochemical reaction where glucose is converted into glucose-6-phosphate. Although beneficial for cellular metabolism, this reaction has a \( \Delta_{\mathrm{r}} G^{ \circ '} \) value of +13.8 kJ/mol, rendering it unfavorable on its own. It’s intriguing how the indomitable cellular machinery overcomes this by linking reactions strategically: a hallmark of complex and efficient biological systems.

ATP Hydrolysis

ATP hydrolysis is a biochemical reaction of great importance, serving as a key energy source in cells. ATP, or adenosine triphosphate, contains high-energy phosphate bonds. When ATP undergoes hydrolysis, it releases a phosphate group, forming ADP (adenosine diphosphate) and inorganic phosphate \(( P_{i} \). This reaction involves:

• The breakdown of ATP by the addition of a water molecule (thus classified as hydrolysis).
• The release of energy, with a \( \Delta_{\mathrm{r}} G^{ \circ '} \) of -30.5 kJ/mol, making it highly favorable.

The significance of ATP hydrolysis lies in its role as a universal energy currency in living organisms. The energy released is harnessed to drive otherwise unfavorable processes, enabling vital functions like muscle contraction, nerve impulse propagation, and biosynthetic reactions. The efficiency and universality of ATP as an energy carrier highlight the elegance of biological systems in adapting and optimizing energy use for a myriad of functions.

Reaction Coupling

Reaction coupling is an ingenious mechanism in cellular metabolism. It allows cells to perform unfavorable reactions by pairing them with favorable ones. In the context of energy, reaction coupling often involves the hydrolysis of ATP, which releases considerable energy. Here’s what happens in a coupled reaction:

• The energetically unfavorable process (e.g., conversion of glucose to glucose-6-phosphate) receives the boost it needs by being "coupled" with ATP hydrolysis.
• The reactions are mathematically combined, summing their \( \Delta_{\mathrm{r}} G^{ \circ '} \) values, effectively lowering the energy required for the overall process.

In our glycolysis example, the coupling of glucose phosphorylation with ATP hydrolysis results in a net \( \Delta_{\mathrm{r}} G^{ \circ '} \) of -16.7 kJ/mol. This negative value signifies that the coupled reaction is indeed favorable and product-favored at equilibrium. By utilizing reaction coupling, cells can efficiently channel energy where needed, illustrating the dynamic nature of biochemical pathways in sustaining life.