Question

Protein tyrosine phosphatases (PTPases) are a general class of enzymes that are involved in a variety of disease processes including diabetes and obesity. In a study by Z.-Y. Zhang and coworkers [J. Medicinal Chemistry 43 \((2000): 146]\) computational techniques were used to identify potential competitive inhibitors of a specific PTPase known as PTP1B. The structure of one of the identified potential competitive inhibitors is shown here: The reaction rate was determined in the presence and absence of inhibitor \(I\) and revealed the following initial reaction rates as a function of substrate concentration: $$\begin{array}{ccc} & \mathbf{R}_{0}\left(\boldsymbol{\mu} \mathbf{M} \mathbf{~} \mathbf{s}^{-\mathbf{1}}\right) \\ {[\mathbf{S}](\boldsymbol{\mu} \mathbf{M})} & \mathbf{R}_{0}\left(\boldsymbol{\mu} \mathbf{M} \mathbf{~} \mathbf{s}^{-1}\right),[\boldsymbol{I}]=\mathbf{0} & {\left[\begin{array}{cc} \boldsymbol{I} & =\mathbf{2 0 0} \boldsymbol{\mu} \mathbf{M} \end{array}\right]} \\ \hline 0.299 & 0.071 & 0.018 \\ 0.500 & 0.100 & 0.030 \\ 0.820 & 0.143 & 0.042 \\ 1.22 & 0.250 & 0.070 \\ 1.75 & 0.286 & 0.105 \\ 2.85 & 0.333 & 0.159 \\ 5.00 & 0.400 & 0.200 \\ 5.88 & 0.500 & 0.250 \end{array}$$ a. Determine \(K_{m}\) and \(R_{\max }\) for PTP1B. b. Demonstrate that the inhibition is competitive, and determine \(K_{i}\)

Short answer

To analyze the enzyme kinetics for PTP1B in the presence and absence of an inhibitor, we can use the Lineweaver-Burk plot. First, calculate the reciprocal values for substrate concentration and reaction rate. Create the Lineweaver-Burk plot by graphing these reciprocal values for both datasets. Determine the slope and y-intercept of the lines, and then use the uninhibited dataset values to calculate \(K_m\) and \(R_{max}\). If the plot shows parallel lines, the inhibition is competitive. Lastly, use the inhibited dataset's slope to calculate the \(K_i\) value for competitive inhibition.

Step-by-step solution

Calculate the Reciprocal Values

Compute the reciprocal values for substrate concentration and reaction rate in the presence and absence of the inhibitor using the following formula: \(1 / [S] \, and \, 1 / R\) Step 2: Draw Lineweaver-Burk Plots

Plot the Data

Plot the computed reciprocal values of substrate concentration (1 / [S]) on the x-axis and the reciprocal values of reaction rate (1 / R) on the y-axis for both the uninhibited and inhibited reaction data. Step 3: Slope and Intercept

Find the Slope and Y-intercept

Calculate the slope and y-intercept of the plotted lines for both datasets using the straight-line equation: \(y = mx + b\) Where m is the slope, and b is the y-intercept. Step 4: Find Km and Rmax

Determine Km and Rmax

Calculate Km and Rmax for PTP1B using the following formulas from the slope and y-axis intercept values of the uninhibited dataset: \(K_m = \frac{-slope}{intercept}\) \(R_{max} = \frac{1}{intercept}\) Step 5: Check for Competitive Inhibition

Identify Inhibition Type

Competitive inhibition is demonstrated if the data in the Lineweaver-Burk plot results in a group of parallel lines. If the plot indicates parallel lines, then the inhibition is competitive. Step 6: Find Ki

Determine Ki

To calculate the inhibitor constant (Ki) for competitive inhibition, we can use the following formula: \(K_i = \frac{K_m}{slope - 1}\) Use the slope value from the inhibited dataset to find the Ki value.

Key concepts

Protein Tyrosine Phosphatases

Protein tyrosine phosphatases (PTPases) play a crucial role in cellular processes by removing phosphate groups from tyrosine amino acids in proteins. These enzymes are significant because they regulate many pathways, including those involved in disease states like diabetes and obesity. PTP1B, a specific type of PTPase, has been the subject of research for its role in metabolic diseases.
Understanding how PTPases function is essential for developing inhibitors that can modulate their activity. Researchers target these enzymes with competitive inhibitors to manage diseases related to disrupted enzyme activity. This inhibitor binds to the enzyme's active site, preventing the natural substrate from attaching and thereby slowing down the enzymatic reaction.

• PTPases are involved in phosphorylation signaling pathways.
• Dysregulation can lead to metabolic disorders.
• Inhibitors can help restore balance in enzyme activity.

Lineweaver-Burk Plot

The Lineweaver-Burk plot is a method used in enzyme kinetics to analyze complex data and determine key parameters like the Michaelis-Menten constant ( Km ) and the maximum reaction rate ( R_{max} ). This graphical representation transforms the hyperbolic relationship of enzyme activity into a straight line by plotting 1/[S] against 1/R, where [S] is the substrate concentration and R is the reaction rate.
The y-intercept of this line gives the value of 1/ R_{max} , while the slope of the line provides the value of Km/R_{max} . This straight-line transformation, known as double-reciprocal plotting, simplifies the calculations and provides a clear visual representation of how different variables affect enzyme activity.

• Useful for comparing uninhibited and inhibited reactions.
• Helps identify types of enzyme inhibition.
• Provides visual evidence of competitive inhibition.

Enzyme Kinetics

Enzyme kinetics focuses on the rates at which enzymatic reactions occur and how these rates change in response to various factors. Studying enzyme kinetics helps in the understanding of how enzymes bind to substrates and turn them into products. One essential aspect of enzyme kinetics is observing how these rates differ when inhibitors are present.
By exploring the relationship between substrate concentration and reaction rate, scientists can determine key kinetic parameters. The Michaelis constant ( K_m ), for instance, indicates the concentration of substrate needed to reach half the maximum reaction rate. R_{max} represents the reaction's maximum speed when substrates are abundant. Competitive inhibitors increase the K_m without affecting R_{max} , illustrating how inhibitors can impact enzyme action.

• Provides insight into enzyme-substrate interactions.
• Examines the effect of various inhibitors.
• Key for designing drugs targeting enzymatic pathways.

Inhibition Constant

The inhibition constant, K_i , quantifies the effectiveness of an inhibitor in reducing an enzyme's activity. A lower K_i value indicates a more potent inhibitor, meaning it effectively competes with the substrate for the enzyme's active site. In competitive inhibition, K_i is determined using data from Lineweaver-Burk plots by examining the changes in slopes between inhibited and uninhibited reactions.
To calculate K_i , you would use the formula K_i = rac{K_m}{slope - 1} . This formula shows how the presence of an inhibitor alters the apparent affinity of the enzyme for its substrate, reflected by a change in slope. Understanding K_i values is crucial for drug development, particularly in designing therapies that aim to hinder specific enzyme activities.

• Essential for understanding treatment efficacy.
• Helps in comparing different inhibitors.
• Critical for enhancing drug design.