Thermodynamics Part 1: Gibbs Free Energy, PEP, and ATP Metabolism

Course Information & Administration

• Instructor: Dr. Daniel J. Slade (dslade@vt.edu)
• Office/Location: 4115
• Lecture Schedule: Monday, Wednesday, Friday from 11:15 AM - 12:05 PM
• Teaching Assistant-Led Sessions: Wednesdays from 5:30 PM - 6:20 PM
• Lecture Topic: Lecture 7 – Thermodynamics Part 1
• Date: September 5, 2025

For Today's Discussion

• Investigate the daily human requirement for ATP.
• Quiz 2 Preparation: Practice problems are available on Canvas under Files $\rightarrow$ Practice Questions and linked in a new Module titled Practice Questions. The answer key will be uploaded on Sunday, June 8.

Gibbs Free Energy ($\Delta G$)

• Spontaneous Reaction (Exergonic):
  • Defined by \Delta G < 0 .
  • Reactants have higher free energy than products.
  • The reaction proceeds without external input of energy.
  • Equation: $\Delta G = \Delta G^\circ + RT \ln Q$
• Non-Spontaneous Reaction (Endergonic):
  • Defined by \Delta G > 0 .
  • Products have higher free energy than reactants.
  • The reaction requires an input of energy to proceed.
  • Equation: $\Delta G = \Delta G^\circ + RT \ln Q$

Important Teaching Moments to Remember

1. Enzymes and Free Energy of Activation ($\Delta G^\ddagger$ or $\Delta E_a$): Enzymes decrease the Gibbs Free Energy of activation, thereby speeding up the reaction. However, they have absolutely no effect on the overall free energy of the reaction ($\Delta G$).
2. Thermodynamics vs. Kinetics: Thermodynamics \text{($\Delta G)}$ tells you nothing about the rate of a reaction. Reaction rate falls under the study of kinetics, which will be covered later.

Two-Step Reaction for Phosphoenolpyruvate (PEP)

• Overall Reaction: Hydrolysis of Phosphoenolpyruvate (PEP) to pyruvate + inorganic phosphate ($\text{P}_\text{i}$).
  • Overall standard free energy change: $\Delta G^\circ = -62.2 \text{ kJ/mol}$.
• Step 1: Hydrolysis of PEP to Pyruvate (enol form) and $\text{P}_\text{i}$:
  • $\text{H}<em>2\text{C=C-COO}^- \text{(PEP)} + \text{H}</em>2\text{O} \rightarrow \text{H}<em>2\text{C=C(OH)-COO}^- \text{(Pyruvate, unstable enol form)} + \text{P}</em>\text{i}$
  • Associated standard free energy change: $\Delta G = -28.6 \text{ kJ/mol}$.
• Step 2: Tautomerization of Enol Pyruvate to Keto Pyruvate:
  • $\text{H}<em>2\text{C=C(OH)-COO}^- \text{(Pyruvate, unstable enol)} \rightarrow \text{H}</em>3\text{C-C(=O)-COO}^- \text{(Pyruvate, stable keto form)}$
  • Associated standard free energy change: $\Delta G = -33.6 \text{ kJ/mol}$.
  • A link for reviewing ketones, aldehydes, and their naming conventions is provided as a refresher.

Enzymes in ATP and Pyruvate Production

Key Note: Pay close attention to the standard free energy changes ($\Delta G^\circ'$ and $\Delta G$) in these reactions.

• Enolase Reaction:

  • Catalyzes: 2-Phosphoglycerate $\xrightarrow{\text{Enolase, Mg}^{2+}}$ Phosphoenolpyruvate (PEP) + $\text{H}_2\text{O}$
  • Standard free energy change: $\Delta G = +1.8 \text{ kJ/mol}$
  • This is an endergonic reaction, unfavorable under standard conditions.

• Pyruvate Kinase Reaction:

  • Catalyzes: Phosphoenolpyruvate (PEP) + ADP $\xrightarrow{\text{Pyruvate Kinase, Mg}^{2+}, \text{K}^{+}}$ Pyruvate + ATP
  • Standard free energy change: \Delta G^\circ' = -31.7 \text{ kJ/mol}
  • This is a highly exergonic reaction, driving ATP synthesis.

• Comparison of Hydrolysis Free Energies (Table 3.2):

  • Phosphoenolpyruvate $\rightarrow$ pyruvate + $\text{P}_\text{i}$: \Delta G^\circ' = -62.2 \text{ kJ/mol}
  • Adenosine-5'-triphosphate $\rightarrow$ ADP + $\text{P}_\text{i}$: \Delta G^\circ' = -35.7 \text{ kJ/mol} (from figure 3.6)
  • Adenosine-5'-triphosphate $\rightarrow$ ADP + $\text{P}_\text{i}$ (with excess $\text{Mg}^{2+}$): \Delta G^\circ' = -30.5 \text{ kJ/mol} (from figure 3.6)

Daily Human ATP Usage

• Proof We Don't Store ATP:
  • An average person has only about $50 \text{ g}$ (or $0.11 \text{ lbs}$) of ATP/ADP in their body at any given time.
  • For a $100 \text{ lbs}$ individual, this is only $0.11\%$ of body weight, highlighting the constant need for regeneration.
• Calculations for Daily ATP Requirement:
  1. Typical Daily Energy Intake: Average of $2800 \text{ calories/day}$, which converts to approximately $11,700 \text{ kJ}$.
  2. Thermodynamic Efficiency: Assuming $50\%$ thermodynamic efficiency, the useful energy for cellular work is $5,850 \text{ kJ}$.
  3. ATP Yield per Hydrolysis: In a cell, ATP hydrolysis typically yields about $50 \text{ kJ/mol}$. (Note: Standard conditions are $-30.5 \text{ kJ/mol}$ to $-35.7 \text{ kJ/mol}$, but cellular conditions allow for higher yield).
  4. Moles of ATP Recycled Daily: To supply $5,850 \text{ kJ}$, approximately $5,850 \text{ kJ} / 50 \text{ kJ/mol} = 117 \text{ moles of ATP}$ are required each day.
  5. Mass of ATP Recycled Daily: This equates to roughly $65 \text{ kg}$ of ATP used/recycled per day.
  6. Recycling Frequency: Since we only have $50 \text{ g}$ of ATP/ADP in our bodies, each ATP molecule must be recycled $(65,000 \text{ g}) / (50 \text{ g}) = 1,300$ times per day.
  7. Recycling Rate: This means every ATP molecule in the body is recycled approximately every $54 \text{ seconds}$ ($(24 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute}) / 1300 \text{ recycles} \approx 66.5 \text{ seconds}$; the slide suggests $54 \text{ seconds}$, indicating slightly different precise values in calculation or average).

For Next Class (Monday)

• Topics: Protein primary, secondary, tertiary, and quaternary structure.
• Quiz 2: Will cover pH, pKa, and stereochemistry. **