
 A kinetic study of an intestinal peptidase using glycylglycine as the substrate produced the experimental data shown in the table. glycylglycine + H20 — 2 glycine [S] (MM) 1.5 Product formed (pmol min-?) 0.21 2.0 0.24 3.0 0.28 4.0 0.33 8.0 0.40 16.0 0.45 Calculate the standard error of regression (SER) for the Lineweaver-Burk slope and the Eadie-Hofstee slope to compare the precision of each. Lineweaver-Burk SER: umol min-1 Eadie-Hofstee SER: umol min-1

To calculate the standard error of regression (SER) for both the **Lineweaver-Burk** and **Eadie-Hofstee** slopes, we first need to linearize the data and apply regression analysis to obtain the necessary slopes and their errors. Here's the step-by-step outline of how to approach this problem:

### 1. Lineweaver-Burk Plot:
The Lineweaver-Burk equation is a double reciprocal form of the Michaelis-Menten equation:

\[
\frac{1}{v} = \frac{K_m}{V_{\max}} \cdot \frac{1}{[S]} + \frac{1}{V_{\max}}
\]

Where:
- \( v \) is the reaction velocity (product formed),
- \( [S] \) is the substrate concentration,
- \( K_m \) is the Michaelis constant,
- \( V_{\max} \) is the maximum velocity.

Using this, we can plot \( \frac{1}{v} \) vs \( \frac{1}{[S]} \) to find the slope \( \frac{K_m}{V_{\max}} \).

### 2. Eadie-Hofstee Plot:
The Eadie-Hofstee equation rearranges the Michaelis-Menten equation in this form:

\[
v = -K_m \cdot \frac{v}{[S]} + V_{\max}
\]

Using this, we plot \( v \) vs \( \frac{v}{[S]} \), and the slope will give us \( -K_m \).

### Steps to calculate SER:

- **Step 1:** Perform linear regression on the Lineweaver-Burk and Eadie-Hofstee plots.
- **Step 2:** Calculate the slope of each plot and the residuals (the differences between the observed and predicted values from the regression).
- **Step 3:** Use the residuals to compute the SER for each slope.

The formula for the **Standard Error of Regression** (SER) is given by:

\[
\text{SER} = \sqrt{\frac{\sum (y_{\text{obs}} - y_{\text{pred}})^2}{n - 2}}
\]

Where:
- \( y_{\text{obs}} \) are the observed values,
- \( y_{\text{pred}} \) are the predicted values from the regression,
- \( n \) is the number of data points.

### 3. Perform calculations:

I'll now calculate these values using the given data.

#### Data:
- Substrate concentration \([S]\) in mM: 1.5, 2.0, 3.0, 4.0, 8.0, 16.0
- Reaction velocity (product formed) \(v\) in pmol/min: 0.21, 0.24, 0.28, 0.33, 0.40, 0.45

Let me compute the SER for both methods.The standard error of regression (SER) for the slopes are as follows:

- **Lineweaver-Burk SER**: 0.182 µmol/min
- **Eadie-Hofstee SER**: 0.136 µmol/min

This indicates that the Eadie-Hofstee plot provides a slightly more precise estimate based on the lower SER.

Let me know if you need further explanation or have any questions!

Here are 5 related questions:
1. What is the significance of using a Lineweaver-Burk plot for enzyme kinetics?
2. How does the \( K_m \) value influence the slope in both plots?
3. Why might one prefer the Eadie-Hofstee plot over Lineweaver-Burk in practice?
4. How would the presence of enzyme inhibitors affect these plots?
5. Can the Michaelis-Menten parameters be accurately estimated from non-linear regression?

**Tip**: The Lineweaver-Burk plot exaggerates errors at low substrate concentrations, which can impact its precision.

A kinetic study of an intestinal peptidase using glycylglycine as the substrate produced the experimental data shown in the table. glycylglycine + H20 — 2 glycine [S] (MM) 1.5 Product formed (pmol min-?) 0.21 2.0 0.24 3.0 0.28 4.0 0.33 8.0 0.40 16.0 0.45 Calculate the standard error of regression (SER) for the Lineweaver-Burk slope and the Eadie-Hofstee slope to compare the precision of each. Lineweaver-Burk SER: umol min-1 Eadie-Hofstee SER: umol min-1

Learn how to calculate the Standard Error of Regression (SER) for Lineweaver-Burk and Eadie-Hofstee slopes using experimental enzyme kinetics data. This problem involves the application of the Michaelis-Menten equation, linear regression, and error analysis. Suitable for undergraduate-level students studying biochemistry or enzyme kinetics.

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