Consider the folding of a globular protein at 35°C. You perform a protein folding
experiment and determine that ΔG’= -3.3 kJ/mol. You find that at the end of the
experiment, 1 𝝁M is in the folded state and 4 𝝁M of the protein is in the unfolded
state. Calculate ΔG°’

To calculate \( \Delta G^\circ' \), we use the relationship between \( \Delta G' \) and \( \Delta G^\circ' \):

\[
\Delta G' = \Delta G^\circ' + RT \ln(Q)
\]

where:
- \( \Delta G' \) is the free energy change under experimental conditions, which is given as \( -3.3 \, \text{kJ/mol} \).
- \( \Delta G^\circ' \) is the standard free energy change we want to find.
- \( R \) is the universal gas constant, \( 8.314 \times 10^{-3} \, \text{kJ/(mol·K)} \).
- \( T \) is the temperature in Kelvin (35°C = 308 K).
- \( Q \) is the reaction quotient, which is the ratio of the concentrations of the unfolded and folded states.

### Step 1: Calculate the reaction quotient \( Q \).
The reaction quotient \( Q \) is given by:

\[
Q = \frac{[\text{unfolded}]}{[\text{folded}]}
\]

In this experiment:
- \( [\text{folded}] = 1 \, \mu M \)
- \( [\text{unfolded}] = 4 \, \mu M \)

So:

\[
Q = \frac{4 \, \mu M}{1 \, \mu M} = 4
\]

### Step 2: Substitute values into the equation.
\[
-3.3 \, \text{kJ/mol} = \Delta G^\circ' + (8.314 \times 10^{-3} \, \text{kJ/(mol·K)})(308 \, \text{K}) \ln(4)
\]

Calculate \( RT \ln(4) \):
- \( \ln(4) \approx 1.386 \)
- \( RT \ln(4) = (8.314 \times 10^{-3})(308)(1.386) \)

\[
RT \ln(4) \approx (2.561 \, \text{kJ/mol})
\]

### Step 3: Solve for \( \Delta G^\circ' \).

\[
-3.3 \, \text{kJ/mol} = \Delta G^\circ' + 2.561 \, \text{kJ/mol}
\]

\[
\Delta G^\circ' = -3.3 \, \text{kJ/mol} - 2.561 \, \text{kJ/mol}
\]

\[
\Delta G^\circ' \approx -5.861 \, \text{kJ/mol}
\]

So, the standard free energy change \( \Delta G^\circ' \) is approximately \( -5.86 \, \text{kJ/mol} \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How does temperature affect the folding of a protein and its \( \Delta G^\circ' \)?
2. What does a negative \( \Delta G^\circ' \) indicate about a protein's folding stability?
3. How would the calculation change if the concentration of the folded and unfolded states were reversed?
4. What is the significance of the reaction quotient \( Q \) in determining \( \Delta G' \)?
5. How do different values of \( \Delta G^\circ' \) relate to the equilibrium constant \( K \) for protein folding?

**Tip:** Always check the units in thermodynamic calculations to ensure consistency, especially when working with temperatures and gas constants.

Consider the folding of a globular protein at 35°C. You perform a protein folding experiment and determine that ΔG’= -3.3 kJ/mol. You find that at the end of the experiment, 1 μM is in the folded state and 4 μM of the protein is in the unfolded state. Calculate ΔG°’.

Explore how to calculate the standard free energy change (ΔG°’) for a protein folding experiment at 35°C. Using ΔG' = -3.3 kJ/mol and concentrations of folded (1 μM) and unfolded (4 μM) states, learn step-by-step how to determine ΔG°’ with thermodynamic principles. Suitable for undergraduate-level students.

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