import numpy as np
import matplotlib.pyplot as plt

# Given data
substrate_concentration_um = np.array([8.33, 12.5, 20.0, 33.3, 50.0, 80.0, 200.0])  # in μM
velocity = np.array([13.8, 19.0, 26.7, 36.3, 44.4, 53.4, 66.7])

# Reciprocal of velocity and substrate concentration
reciprocal_velocity = 1 / velocity
reciprocal_substrate_concentration = 1 / substrate_concentration_um

# Fit a linear regression
slope, intercept = np.polyfit(reciprocal_substrate_concentration, reciprocal_velocity, 1)

# Create a range of x values for the line
x = np.linspace(min(reciprocal_substrate_concentration), max(reciprocal_substrate_concentration), 100)

# Plotting the Lineweaver-Burk plot
plt.scatter(reciprocal_substrate_concentration, reciprocal_velocity, label='Data points')
plt.plot(x, slope*x + intercept, label='Fitted line', color='red')

# Adding labels and title
plt.xlabel('1/[S] (1/μM)')
plt.ylabel('1/V (1/nmol/L/min)')
plt.title('Lineweaver-Burk Plot')
plt.legend()
plt.show()
Running this code will generate the Lineweaver-Burk plot using the provided data points. The linear fit will help you determine the slope (which is related to Km/Vmax) and the intercept (which is related to 1/Vmax) from the graph.




User
give me the data table for this graph
ChatGPT
To create a Lineweaver-Burk plot, we need to compute the reciprocal of both the initial velocity (1/V) and the substrate concentration (1/[S]). Here is the data table for the Lineweaver-Burk plot:

[S] (μM)	1/[S] (1/μM)	V (nmol/L/min)	1/V (1/nmol/L/min)
8.33	0.1200	13.8	0.0725
12.5	0.0800	19.0	0.0526
20.0	0.0500	26.7	0.0374
33.3	0.0300	36.3	0.0275
50.0	0.0200	44.4	0.0225
80.0	0.0125	53.4	0.0187
200.0	0.0050	66.7	0.0150
In this table, the reciprocal of the substrate concentration (1/[S]) is computed as 1 divided by the substrate concentration in micromolar (μM), and the reciprocal of the initial velocity (1/V) is computed as 1 divided by the initial velocity in nmol/L/min. This table will be used to create the Lineweaver-Burk plot.




User
[S] (μM)	V (nmol/L/min)
8.33	13.8
12.5	19.0
20.0	26.7
33.3	36.3
50.0	44.4
80.0	53.4
200.0	66.7 estimate km and vmax of this please
ChatGPT
To estimate Km and Vmax using the Lineweaver-Burk plot, we first need to perform the linear regression on the reciprocal values of substrate concentration and velocity. Let's create the Lineweaver-Burk plot using the provided data points and then estimate Km and Vmax from the slope and y-intercept of the line.

Let's first calculate the reciprocal of both the substrate concentration (1/[S]) and the velocity (1/V):

Reciprocal of 
[
�
]
(
μM
)
=
1
[S]
Reciprocal of [S](μM)= 
[S]
1
​
 

Reciprocal of V (nmol/L/min)
=
1
V
Reciprocal of V (nmol/L/min)= 
V
1
​
 

Then we can use these reciprocal values to perform linear regression and estimate Km and Vmax.

Here are the reciprocal values:

\hline
\text{[S] (μM)} & \frac{1}{\text{[S]}} (\text{μM}^{-1}) & \text{V (nmol/L/min)} & \frac{1}{\text{V}} (\text{L/min/nmol}) \\
\hline
8.33 & 0.120 & 13.8 & 0.0725 \\
12.5 & 0.080 & 19.0 & 0.0526 \\
20.0 & 0.050 & 26.7 & 0.0374 \\
33.3 & 0.030 & 36.3 & 0.0275 \\
50.0 & 0.020 & 44.4 & 0.0225 \\
80.0 & 0.0125 & 53.4 & 0.0187 \\
200.0 & 0.005 & 66.7 & 0.015 \\
\hline
\end{array} \]
Now, we can use linear regression on these values to estimate Km and Vmax.
Let's proceed with performing linear regression on the reciprocal values of substrate concentration and velocity to estimate Km and Vmax. We'll use the linear regression equation y = mx + b, where y is 1/V, x is 1/[S], m is the slope (Km/Vmax), and b is the y-intercept (1/Vmax).

Here are the calculations:

css
Copy code
1/[S] = [0.12, 0.08, 0.05, 0.03, 0.02, 0.0125, 0.005]
1/V = [0.0725, 0.0526, 0.0374, 0.0275, 0.0225, 0.0187, 0.015]
Performing linear regression:

python
Copy code
import numpy as np

# Reciprocal values
x = np.array([0.12, 0.08, 0.05, 0.03, 0.02, 0.0125, 0.005])
y = np.array([0.0725, 0.0526, 0.0374, 0.0275, 0.0225, 0.0187, 0.015])

# Perform linear regression
m, b = np.polyfit(x, y, 1)

# Solve for Km and Vmax
Km = 1/m
Vmax = b*Km

# Print the results
print(f"Estimated Km: {Km} μM")
print(f"Estimated Vmax: {Vmax} nmol/L/min")
The estimated Km and Vmax will be printed as the results. Execute this script in a Python environment to find the estimates of Km and Vmax based on the provided data.