Problem 11 - Cell and Molecular Biology: Concepts and Experiments

Question

If the reaction \(\mathrm{XA}+\mathrm{Y} \rightleftharpoons \mathrm{XY}+\mathrm{A}\) has a \(\Delta G^{\circ \prime}\) of \(+7.3 \mathrm{kcal} / \mathrm{mol}\) could this reaction be driven in the cell by coupling it to ATP hydrolysis? Why or why not?

Step-by-Step Solution

Answer

No, coupling alone is not enough; the reaction remains at equilibrium.

Step 1: Understand the Exercise Problem

The problem involves evaluating whether a reaction, having a specified standard free energy change (\(\Delta G^{\circ \prime}\) = +7.3 kcal/mol), can be driven forward through coupling with ATP hydrolysis, which is a common cellular strategy to drive thermodynamically unfavorable reactions.

Step 2: Assess the Role of ATP Hydrolysis

ATP hydrolysis, the reaction \( \mathrm{ATP} + \mathrm{H_2O} \rightarrow \mathrm{ADP} + \mathrm{P_i} \), is known to have a \(\Delta G^{\circ \prime}\) of approximately -7.3 kcal/mol under standard conditions in cells. This negative value indicates that ATP hydrolysis releases energy, and it can be used to drive other reactions that are energetically unfavorable.

Step 3: Calculate the Net \(\Delta G^{\circ \prime}\) of the Coupled Reaction

To determine if the reaction can proceed, add the \(\Delta G^{\circ \prime}\) values of the target reaction (+7.3 kcal/mol) and ATP hydrolysis (-7.3 kcal/mol). The net \(\Delta G^{\circ \prime}\) for the coupled reactions is \((+7.3) + (-7.3) = 0 \text{ kcal/mol}\).

Step 4: Analyze the Result

A \(\Delta G^{\circ \prime}\) of 0 kcal/mol for the coupled reaction means it is at equilibrium under standard conditions, indicating the reaction is not spontaneous in either direction without external forces in a cell. For the reaction to be driven forward, more energy is needed than what ATP hydrolysis alone provides.

Key Concepts

Free Energy Change

Free energy change, denoted as \( \Delta G \), is a pivotal concept in biochemistry and thermodynamics.It represents the amount of energy available to do work in a reaction.Positive \( \Delta G \) values, like +7.3 kcal/mol in our exercise, indicate that energy must be input for the reaction to proceed.Conversely, negative \( \Delta G \) values suggest that the reaction releases energy, proceeding spontaneously.

Every reaction's tendency to occur under standard conditions is measured by its standard free energy change, \( \Delta G^{\circ \prime} \).When \( \Delta G^{\circ \prime} \) is 0, as we calculated for the coupled reaction, it indicates an equilibrium state with no net change favoring either direction.In real cellular conditions, these values help determine reaction feasibility, guiding biochemists in understanding cellular energy landscapes.

Coupled Reactions

Coupled reactions are a biological strategy to make energetically unfavorable reactions proceed by linking them with favorable ones, such as ATP hydrolysis.This is a common cellular tactic where the energy released from a spontaneous reaction drives a non-spontaneous one.

In this exercise, the reaction \( \mathrm{XA} + \mathrm{Y} \rightleftharpoons \mathrm{XY} + \mathrm{A} \) is not initially favorable, with its \( \Delta G^{\circ \prime} \) of +7.3 kcal/mol.The process of coupling involves adding the \( \Delta G^{\circ \prime} \) of ATP hydrolysis, which is \(-7.3 \text{ kcal/mol}\).The resulting net \( \Delta G^{\circ \prime} \) is 0 kcal/mol, creating an equilibrium.This technique is vital in cellular metabolism, as it allows cells to perform functions otherwise impossible by distributing energy effectively.

Thermodynamic Favorability

Thermodynamic favorability describes whether a reaction can occur spontaneously under a given set of conditions.

The value of \( \Delta G^{\circ \prime} \) is crucial here.A negative \( \Delta G^{\circ \prime} \) suggests the reaction is thermodynamically favorable and will likely proceed without additional energy.A positive \( \Delta G^{\circ \prime} \), as seen in our uncoupled reaction, indicates non-spontaneity.

However, the use of coupled reactions, such as combining a reaction with ATP hydrolysis, can shift these dynamics.By counterbalancing an unfavorable \( \Delta G^{\circ \prime} \) with a favorable one, cells achieve processes like muscle contraction and biosynthesis.Understanding this balance enables scientists to manipulate biochemical pathways, fostering innovations in biotechnology and medicine.