1. What is Catalytic Rate Constant?

Definition: The catalytic rate constant (k_cat) is the rate constant for conversion of the enzyme-substrate complex to enzyme and product.

Purpose: It measures the number of substrate molecules converted to product per enzyme molecule per second when the enzyme is saturated with substrate.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( k_{cat} \) — Catalytic rate constant (s⁻¹)
• \( V_0 \) — Initial reaction rate (mol/m³·s)
• \( K_M \) — Michaelis constant (mol/m³)
• \( [E_0] \) — Initial enzyme concentration (mol/m³)
• \( S \) — Substrate concentration (mol/m³)

Explanation: The formula calculates the turnover number of an enzyme at low substrate concentrations relative to K_M.

3. Importance of Catalytic Rate Constant

Details: k_cat is a fundamental parameter in enzyme kinetics that indicates the catalytic efficiency of an enzyme. Higher values indicate more efficient enzymes.

4. Using the Calculator

Tips: Enter the initial reaction rate, Michaelis constant, initial enzyme concentration, and substrate concentration. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What does k_cat tell us about an enzyme?
A: It indicates how many substrate molecules one enzyme molecule can convert to product per second when fully saturated.

Q2: What are typical values for k_cat?
A: Values range from 1 to 10⁷ s⁻¹, with most enzymes falling between 10² and 10⁴ s⁻¹.

Q3: How is k_cat related to enzyme efficiency?
A: The catalytic efficiency is given by k_cat/K_M, combining both catalytic power and substrate binding affinity.

Q4: When is this formula most accurate?
A: When substrate concentration is much lower than K_M, under initial rate conditions.

Q5: What units should I use for the inputs?
A: Use consistent units - mol/m³ for concentrations and mol/m³·s for reaction rate.