You are working at a major pharmaceutical company, and you have purified an engineered enzyme, and you need to determine the protein stability (kJ/mol). Accordingly, you have collected equilibrium unfolding data using the chemical denaturant urea at 20°C, pH 7.5 and I atmosphere using fluorescence spectroscopy. a) Determine the protein stability (AG [kJ/mol]) via nonlinear least squares (using the available data). b) Write the partial differential equation (i.e., general functional form, variable, constants). c) Describe what would happen to the isotherm if the temperature was increased to 25 °C. Urea [M] FL 340nm 0 0.25 0.5 0.75 1 1.25 1.5 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 316 315.5 315 314.5 314 315 300 275 225 125 75 60 55 54 53 52.5 52.25 52 51.75 51.5 dG = Vdp - SdT + μA dnд + μB dng dGTP = μA dna + μg dng A = Folded State B= Unfolded State
![You are working at a major pharmaceutical company, and you have purified an engineered enzyme, and you need to determine the
protein stability (kJ/mol). Accordingly, you have collected equilibrium unfolding data using the chemical denaturant urea at 20°C,
pH 7.5 and I atmosphere using fluorescence spectroscopy.
a) Determine the protein stability (AG [kJ/mol]) via nonlinear least squares (using the available data).
b) Write the partial differential equation (i.e., general functional form, variable, constants).
c) Describe what would happen to the isotherm if the temperature was increased to 25 °C.
Urea [M]
0
0.25
0.5
0.75
1
1.25
1.5
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
FL 340nm
316
315.5
315
314.5
314
315
300
275
225
125
75
60
55
54
53
52.5
52.25
52
51.75
51.5
dG = Vdp-SdT+μA dnд + μB dng
dGp = μA dnA+ μg dng
A = Folded State
B = Unfolded State](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fd33ee2-f5e3-49b7-93e4-7501009ecd7d%2Fee22c4dc-90da-4b4f-9e42-d5e761f82884%2Fq81ave_processed.jpeg&w=3840&q=75)
To determine the protein stability (ΔG in kJ/mol) using the provided equilibrium unfolding data, you can perform a linear fit to the data using the linear extrapolation method. The linear extrapolation method assumes that the free energy change (ΔG) of unfolding is proportional to the concentration of the denaturant (urea in this case). The equation for this linear relationship is as follows:
ΔG = m * [denaturant] + b
Where:
- ΔG is the free energy change in kJ/mol.
- [denaturant] is the concentration of the denaturant (urea) in M.
- m is the slope of the line.
- b is the y-intercept of the line.
Here's how you can calculate ΔG:
Select two data points from the linear region of the unfolding curve. In this case, you can use the points where the urea concentration is 0 M (the native state) and 2 M (the unfolded state) because they seem to be in the linear region:
Point 1: [denaturant] = 0 M, FL 340 nm = 314 Point 2: [denaturant] = 2 M, FL 340 nm = 275
Calculate the slope (m) using these two points:
m = (FL 340 nm at Point 2 - FL 340 nm at Point 1) / ([denaturant] at Point 2 - [denaturant] at Point 1) m = (275 - 314) / (2 - 0) = -39 / 2 = -19.5 kJ/mol per M
Use the slope and one of the points to calculate the y-intercept (b):
ΔG = m * [denaturant] + b ΔG = -19.5 * 0 + b ΔG = b
Since ΔG = 0 kJ/mol when [denaturant] = 0 M (native state), b = 0 kJ/mol.
Now you have the equation to calculate ΔG for any denaturant concentration:
ΔG = -19.5 * [denaturant]
Step by step
Solved in 4 steps
