Dissociation Constant For Competitive Inhibition Of Enzyme Catalysis Calculator

Formula Used:

\[ K_i = \frac{I}{\left(\frac{\left(\frac{k_2 \cdot [E_0] \cdot S}{V_0} - S\right)}{K_M} - 1\right)} \]

Inhibitor Concentration (I):

mol/m³

Final Rate Constant (k₂):

1/s

Initial Enzyme Concentration ([E₀]):

mol/m³

Substrate Concentration (S):

mol/m³

Initial Reaction Rate (V₀):

mol/m³·s

Michaelis Constant (K_M):

mol/m³

Enzyme Inhibitor Dissociation Constant (K_i):

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1. What is Enzyme Inhibitor Dissociation Constant?

The Enzyme Inhibitor Dissociation Constant (K_i) is a measure of the affinity between an enzyme and its inhibitor. It represents the concentration of inhibitor required to occupy half of the enzyme's active sites and is measured by titrating inhibitor into an enzyme solution while monitoring heat changes.

2. How Does the Calculator Work?

The calculator uses the competitive inhibition formula:

\[ K_i = \frac{I}{\left(\frac{\left(\frac{k_2 \cdot [E_0] \cdot S}{V_0} - S\right)}{K_M} - 1\right)} \]

Where:

\( K_i \) — Enzyme inhibitor dissociation constant (mol/m³)
\( I \) — Inhibitor concentration (mol/m³)
\( k_2 \) — Final rate constant (1/s)
\( [E_0] \) — Initial enzyme concentration (mol/m³)
\( S \) — Substrate concentration (mol/m³)
\( V_0 \) — Initial reaction rate (mol/m³·s)
\( K_M \) — Michaelis constant (mol/m³)

Explanation: This formula calculates the dissociation constant for competitive enzyme inhibition, which describes how tightly an inhibitor binds to an enzyme's active site.

3. Importance of Dissociation Constant Calculation

Details: Accurate determination of K_i is crucial for understanding enzyme-inhibitor interactions, drug design, and predicting the effectiveness of enzyme inhibitors in biological systems and pharmaceutical applications.

4. Using the Calculator

Tips: Enter all values in appropriate units (mol/m³ for concentrations, 1/s for rate constant, mol/m³·s for reaction rate). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What does a lower K_i value indicate?
A: A lower K_i value indicates stronger binding affinity between the enzyme and inhibitor, meaning the inhibitor is more effective at lower concentrations.

Q2: How is competitive inhibition different from other types?
A: In competitive inhibition, the inhibitor competes with the substrate for the same active site on the enzyme, increasing the apparent K_M without affecting V_max.

Q3: What are typical K_i values for effective inhibitors?
A: Effective enzyme inhibitors typically have K_i values in the nanomolar to micromolar range (10^-9 to 10^-6 mol/m³).

Q4: Can this calculator be used for non-competitive inhibition?
A: No, this specific formula is designed for competitive inhibition. Different equations are used for non-competitive and uncompetitive inhibition mechanisms.

Q5: What experimental methods measure K_i?
A: Common methods include isothermal titration calorimetry, enzyme kinetics studies, fluorescence spectroscopy, and surface plasmon resonance.