Question

The turnover number for an enzyme obeying MichaelisMenten kinetics is: a. \(k_{2}\). b. \(k_{\text {cat }} / K_{\mathrm{M}}\). c. \(k_{1} / k_{-1}\). d. \(\left(k_{1}+k_{2}\right)\). e. \(\Delta G^{*}\).

Short answer

The turnover number is \( k_{2} \), so the answer is (a).

Step-by-step solution

Understanding Turnover Number

The turnover number, also represented as \( k_{cat} \), is the maximum number of substrate molecules converted to product per enzyme molecule per unit time when the enzyme is fully saturated with substrate.

Identifying the Correct Term

Turnover number is also known as the catalytic rate constant \( k_{cat} \). In Michaelis-Menten kinetics, it is specifically represented by \( k_{2} \). The defining characteristic is that it depends only on the chemistry that converts the enzyme-substrate complex to product and free enzyme.

Matching with Options

Review the options provided: a. \( k_{2} \)b. \( \frac{k_{cat}}{K_M} \)c. \( \frac{k_{1}}{k_{-1}} \)d. \( k_{1} + k_{2} \)e. \( \Delta G^{*} \)Accordingly, the correct answer for the turnover number is option a, which matches \( k_{2} \).

Key concepts

enzyme kinetics

Enzyme kinetics is the study of the rates at which enzyme-catalyzed reactions proceed. It is crucial in understanding how enzymes facilitate biological processes. One primary model describing enzyme kinetics is the Michaelis-Menten model. This model explains how substrates bind to enzymes and are converted to products over time.
Enzymes are protein molecules that act as catalysts. They increase the reaction rates by lowering the energy barriers to the chemical transformations.
Key elements of enzyme kinetics include:

• **Substrate concentration**: As the concentration of substrate increases, the reaction rate increases until a maximum rate ( V_{max} ) is reached.
• **Michaelis constant ( K_{M} )**: This is the substrate concentration at which the reaction rate is half of V_{max} . It provides insights into the affinity between an enzyme and its substrate.
• **Enzyme saturation**: At a certain level, every enzyme molecule will be occupied by a substrate molecule, leading to a maximal rate of reaction.

Understanding these concepts helps in determining how changes in conditions can affect enzymatic reaction rates and is fundamental to fields like biochemistry and pharmacology.

turnover number

The turnover number in enzyme kinetics is also known as the catalytic constant, symbolized as (k_{cat}) . It is a vital parameter that indicates how efficient an enzyme is.
Simply put, the turnover number measures the number of substrate molecules a single enzyme molecule can convert into product per unit of time when the enzyme is at full activity with a saturation of substrate.
Here are some crucial aspects:

• **Saturation point**: The enzyme is fully saturated with substrate, meaning all enzyme sites are occupied.
• **Maximum rate**: (k_{cat}) represents the upper limit of the enzyme's catalytic speed.
• **Relation to (k_{2}) **: In contexts following the Michaelis-Menten kinetics, (k_{cat}) is the same as (k_{2}) , the rate constant for the conversion of the enzyme-substrate complex into the product.

The turnover number is valuable for researchers to compare the efficiencies of different enzymes, providing insights into enzyme activity and potential enhancements or inhibitors that might affect this process.

catalytic rate constant

The catalytic rate constant ( (k_{cat}) ) is an essential concept in enzyme kinetics closely tied to enzyme efficiency and performance. It represents the speed at which an enzyme-catalyzed reaction occurs, acting as a pivotal indicator of how fast an enzyme can process substrate into product once it is bound to the enzyme.
Several points about (k_{cat}) include:

• **Definition**: (k_{cat}) is defined as the rate constant of the conversion of the enzyme-substrate complex to enzyme and product, particularly near the maximum rate conditions.
• **Measurement**: It is expressed in units of per second and is calculated as the maximum rate of reaction ( V_{max}) divided by the molar concentration of enzyme sites ( [E]_{total}) .
• **Quantitative essence**: (k_{cat}) provides a measurable rate constant useful for understanding the capabilities of different enzymes under full substrate saturation.

In Michaelis-Menten kinetics, knowing the catalytic rate constant allows the comparison of enzyme capabilities, particularly how they function under optimal conditions, and is critical for applications in biochemistry and biotechnology.