Question

Thermodynamics of Citrate Synthase Reaction in Cells Citrate is formed by the condensation of acetyl-CoA with oxaloacetate, catalyzed by citrate synthase: Oxaloacetate \(+\) acetyl-CoA \(+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\) citrate \(+\mathrm{CoA}+\mathrm{H}^{+}\) In rat heart mitochondria at \(\mathrm{pH} 7.0\) and \(25^{\circ} \mathrm{C}\), the concentrations of reactants and products are oxaloacetate, \(1 \mu \mathrm{M}\); acetyl-CoA, \(1 \mu \mathrm{M}\); citrate, \(220 \mu \mathrm{m}\); and CoA, \(65 \mu \mathrm{M}\). The standard free-energy change for the citrate synthase reaction is \(-32.2 \mathrm{~kJ} / \mathrm{mol}\). What is the direction of metabolite flow through the citrate synthase reaction in rat heart cells? Explain.

Short answer

The direction is towards reactants, as \( \Delta G \) is positive.

Step-by-step solution

Write Down the Reaction Equation

The reaction we are considering is: \[ \text{Oxaloacetate} + \text{acetyl-CoA} + \text{H}_2\text{O} \rightleftharpoons \text{citrate} + \text{CoA} + \text{H}^+ \] We have the concentrations of oxaloacetate as \(1 \mu \mathrm{M}\), acetyl-CoA as \(1 \mu \mathrm{M}\), citrate as \(220 \mu \mathrm{M}\), and CoA as \(65 \mu \mathrm{M}\).

Use the Reaction Quotient Formula

The reaction quotient \( Q \) for the reaction can be calculated using the formula: \[ Q = \frac{[\text{citrate}][\text{CoA}]}{[\text{oxaloacetate}][\text{acetyl-CoA}]} \] Substituting the given concentrations: \[ Q = \frac{(220 \times 10^{-6})(65 \times 10^{-6})}{(1 \times 10^{-6})(1 \times 10^{-6})} \] Simplifying yields: \[ Q = \frac{220 \times 65}{1} = 14,300 \]

Calculate Actual Free Energy Change

Use the formula for Gibbs free energy change: \[ \Delta G = \Delta G^\circ + RT \ln Q \] Given \( \Delta G^\circ = -32.2 \text{ kJ/mol} \), and using \( R = 8.314 \times 10^{-3} \text{ kJ/mol·K} \) and \( T = 298 \text{ K} \) (since \( 25^\circ\text{C} = 298\text{ K} \)), we find: \[ \Delta G = -32.2 + 8.314 \times 10^{-3} \times 298 \times \ln(14300) \] Calculate \( \ln(14300) \approx 9.568 \), and substitute into the equation to find \( \Delta G \).

Evaluate the Sign of \( \Delta G \)

Compute the numerical value for \( \Delta G \) using the values from Step 3: \[ \Delta G = -32.2 + (8.314 \times 10^{-3} \times 298 \times 9.568) \] Solve to find \( \Delta G \approx 32.4 \text{ kJ/mol} \). Since \( \Delta G \) is positive, the reaction is non-spontaneous under the given conditions.

Determine the Direction of Metabolite Flow

Since \( \Delta G \) is positive, the spontaneous direction of the reaction is towards the reactants under these specific concentrations, which means the flow of metabolites would be preferred in the reverse direction, from citrate and CoA back to oxaloacetate and acetyl-CoA.

Key concepts

Thermodynamics

Thermodynamics is a fundamental concept in understanding how reactions occur and how energy is transferred in biological systems. It focuses on the study of energy changes, particularly heat and work. In the context of biochemical reactions like the citrate synthase reaction, thermodynamics helps us understand the flow of energy in the cell and how this affects the directionality and rate of reactions.

For the citrate synthase reaction, thermodynamics provides us with the tools to calculate the energy change associated with the conversion of substrates to products. This involves considering the energy supplied by the reactants and the energy required to form the products. It can also help deduce whether a reaction can proceed spontaneously based on energy considerations, which is crucial in metabolic pathways. The study of thermodynamics allows scientists to predict how changes in temperature, pressure, or concentration might shift the balance of these reactions.

Gibbs Free Energy

Gibbs free energy, denoted as \( abla G \), plays a critical role in determining the spontaneity of a reaction in biochemistry. It combines enthalpy (total energy) and entropy (degree of disorder) to decide whether a process will occur without outside intervention.

In the case of citrate synthase, the reaction is assessed under cellular conditions, adjusting for concentration differences which affect the free energy. The standard change in Gibbs free energy (\( abla G^{\circ} \)) is typically provided for reactions. However, to find actual free energy changes, we use the formula: \[ abla G = abla G^{\circ} + RT \ln Q \] where \( R \) is the universal gas constant (8.314 J/mol×K) and \( T \) is the temperature in Kelvin. Here, \( Q \) is the reaction quotient, which reflects the ratio of product concentrations to reactant concentrations under non-standard conditions.

In our example, the calculated \( abla G \) of approximately 32.4 kJ/mol shows a positive value, indicating a non-spontaneous reaction under the studied conditions. This means energy input is needed for the reaction to proceed in the forward direction.

Metabolite Flow

Metabolite flow refers to the movement of substances within a cell's metabolic pathways. It encompasses the conversion of metabolites through enzymatic reactions, which are typically organized in a sequential manner in metabolic pathways.

In the citrate synthase reaction, the direction of metabolite flow is crucial for maintaining cellular function. Reactions proceed in the direction where the flow favors product formation. When \( abla G \) is positive, as in our citrate synthase example, the reaction naturally flows towards the formation of reactants under the given conditions. This can seem counterintuitive, as one might expect product formation. However, the laws of thermodynamics determine that the reaction naturally shifts in the direction that is energetically more favorable, or requires less energy input.

Understanding metabolite flow helps biochemists predict and manipulate pathways for desired outcomes. It highlights the importance of controlling conditions such as concentrations to influence reaction courses.

Cellular Conditions

Cellular conditions refer to the specific environment within the cell where reactions occur, impacting both the reactant concentrations and the actual extent of reaction processes. Biological systems are inherently dynamic, and factors such as temperature, pH, and cellular compartmentalization vastly influence metabolic reactions.

The citrate synthase reaction occurs in the mitochondrial matrix, where conditions such as a pH of 7.0 and a temperature of 25°C influence the reaction dynamics. Reactant and product concentrations within these compartments further affect the reaction quotient \( Q \), changing the calculated \( abla G \) and determining the likely direction of spontaneous flow.

By adapting these cellular conditions, cells regulate the efficiency and directionality of biochemical pathways, ensuring they respond appropriately to the organism's metabolic demands. These mechanisms allow cells to fine-tune energy production, manage resources, and adapt to changes in their environment effectively. Understanding these principles is key in fields like metabolic engineering and drug development, where altering these parameters can shift metabolic pathways to achieve desired outcomes.