Question

Draw Lineweaver-Burk plots for the behavior of an enzyme for which the following experimental data are available. $$\begin{array}{ccc}{[\mathrm{S}]} & V, \text { No Inhibitor } & V, \text { Inhibitor Present } \\\\(\mathrm{mM}) & \left(\mathrm{mmol} \mathrm{min}^{-1}\right) & \left(\mathrm{mmol} \mathrm{min}^{-1}\right) \\\3.0 & 4.58 & 3.66 \\\5.0 & 6.40 & 5.12 \\\7.0 & 7.72 & 6.18 \\ 9.0 & 8.72 & 6.98 \\\11.0 & 9.50 & 7.60 \\\\\hline\end{array}$$ What are the \(K_{\mathrm{M}}\) and \(V_{\max }\) values for the inhibited and uninhibited reactions? Is the inhibitor competitive or noncompetitive?

Short answer

Calculate the reciprocal values, plot Lineweaver-Burk plots, and use the intercepts to determine \(K_{M}\) and \(V_{max}\). Identify the type of inhibition based on the values.

Step-by-step solution

- Understand the Lineweaver-Burk Plot

A Lineweaver-Burk plot is a double reciprocal graph of the Michaelis-Menten equation, plotted as 1/V versus 1/[S].

- Calculate Reciprocal Values

Calculate the reciprocal values of the substrate concentration \([\text{S}]\text{ and } 1/[\text{S}]\) and the reaction velocities \([V] \text{ and } 1/[V] \) both in the presence and absence of the inhibitor.

- Construct the Lineweaver-Burk Plot

Plot 1/V versus 1/[S] for both the conditions (with and without inhibitor). The x-intercept will give \( -1/K_{M}\) and the y-intercept will give \(1/V_{max}\).

- Determine \(K_{M}\) and \(V_{max}\)

Use the linear equations derived from the Lineweaver-Burk plot to determine \(K_{M}\) (Michaelis constant) and \(V_{max}\) (maximum velocity) for both conditions.

- Identify the Type of Inhibition

Compare the \(K_{M}\) and \(V_{max}\) values. If \(K_{M}\) increases and \(V_{max}\) remains the same, the inhibitor is competitive. If \(V_{max}\) decreases but \(K_{M}\) remains the same, the inhibitor is noncompetitive.

Key concepts

Michaelis-Menten Equation

The Michaelis-Menten Equation is a foundational principle in enzyme kinetics. It describes how the rate of enzymatic reactions depends on the concentration of the substrate. The equation is represented as:

\[ v = \frac{V_{max} [S]}{K_M + [S]} \]

Where:

• v is the reaction velocity
• V_{max} is the maximum velocity of the reaction
• [S] is the substrate concentration
• K_M is the Michaelis constant, which indicates the substrate concentration at half-maximal velocity

This equation helps us understand how enzymes function under different substrate concentrations and the efficiency of enzyme-catalyzed reactions.

Enzyme Inhibition

Enzyme inhibition refers to the process where molecules (inhibitors) decrease enzyme activity. There are two main types of inhibition, competitive and noncompetitive:

- Competitive Inhibition: The inhibitor competes with the substrate for binding at the active site of the enzyme. It increases the K_M without affecting the V_{max}

- Noncompetitive Inhibition: The inhibitor binds to a different site on the enzyme and decreases the V_{max} without changing the K_M. This kind of inhibition affects the enzyme activity regardless of substrate concentration.

Understanding how an inhibitor operates can help in designing drugs or in studying metabolic pathways where enzyme regulation is crucial.

Kinetic Parameters

Kinetic parameters are crucial for characterizing the functionality of enzymes. The two primary kinetic parameters are:

\[- K_M: \] This is the Michaelis constant, representing the substrate concentration at which the reaction velocity is half of V_{max}. A lower K_M indicates high affinity between enzyme and substrate.

\[- V_{max}: \] This is the maximum reaction velocity when the enzyme is saturated with substrate. It reflects the catalytic efficiency of the enzyme.

In experiments, these parameters can be determined using a Lineweaver-Burk plot, which helps to linearize the Michaelis-Menten equation and allows for easier calculation and comparison of these kinetic values in both inhibited and uninhibited scenarios. Proper understanding of these parameters is vital for evaluating enzyme behavior and for potential applications in biotechnology and medicine.