A signaling protein with both a SH2 and a SH3 domain binds to the phosphorylated form of its target protein with a Kd of 0.23 nM. The affinity of the SH3 domain by itself is 41 uM and the phosphotyrosine contact with the SH2 domain is responsible for 22 kJ/mol. What is the Kd of the SH2 domain for non-phosphorylated target?

Question

A signaling protein with both a SH2 and a SH3 domain binds to the phosphorylated form of its target protein with a Kd of 0.23 nM. The affinity of the SH3 domain by itself is 41 uM and the phosphotyrosine contact with the SH2 domain is responsible for 22 kJ/mol. What is the Kd of the SH2 domain for non-phosphorylated target?

Answer 1

To find the Kd of the SH2 domain for the non-phosphorylated target protein, we need to use the information given and make certain calculations.

Given:
- Kd for the signaling protein with both SH2 and SH3 domains binding to phosphorylated target protein = 0.23 nM
- Affinity of the SH3 domain alone = 41 uM
- Energy associated with phosphotyrosine contact with the SH2 domain = 22 kJ/mol

The affinity of a protein-protein interaction can be roughly estimated using the equation:
ΔG = -RT ln(Kd)

Where:
ΔG = Gibbs free energy change
R = gas constant (8.314 J/(mol·K))
T = temperature in Kelvin
Kd = dissociation constant

First, we need to convert the affinity of the SH3 domain from μM to M by dividing by 10^6:
Affinity of the SH3 domain = 41 uM = 41 × 10^-6 M

Next, we can use the energy associated with the phosphotyrosine contact with the SH2 domain to find the difference in free energy between binding to phosphorylated and non-phosphorylated target proteins.

ΔG = - RT ln(Kd)

We can rearrange this equation to calculate the Kd for the non-phosphorylated target protein:

Kd_non-phos = e^(-ΔG / (RT))

Let's substitute the values into the equation:

Kd_non-phos = e^(-22,000 J/mol / (8.314 J/(mol·K) × T))

To simplify the calculation, we can convert Joules to kilojoules and use room temperature, which is approximately 298 K.

Kd_non-phos = e^(-22 kJ/mol / (0.008314 kJ/(mol·K) × 298 K))

Kd_non-phos = e^(-22)

Now, we can calculate the Kd_non-phos:

Kd_non-phos = 1 / e^22

Using the value of e (Euler's number) which is approximately 2.71828, we have:

Kd_non-phos = 1 / 2.71828^22

Kd_non-phos ≈ 1.82 × 10^-10 M

Finally, we need to convert the Kd_non-phos from M to nM by multiplying by 10^9:

Kd_non-phos ≈ 1.82 × 10^-10 × 10^9 nM

Kd_non-phos ≈ 182 nM

Therefore, the Kd of the SH2 domain for the non-phosphorylated target protein is approximately 182 nM.