Initial Reaction Rate at Low Substrate Concentration Calculator

Initial Reaction Rate Formula:

\[ V_0 = \frac{k_{cat} \times [E_0] \times S}{K_M} \]

Catalytic Rate Constant (k_cat):

s^-1

Initial Enzyme Concentration ([E₀]):

mol/m³

Substrate Concentration (S):

mol/m³

Michaelis Constant (K_M):

mol/m³

Initial Reaction Rate (V₀):

mol/m³·s

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1. What is Initial Reaction Rate at Low Substrate Concentration?

Definition: This calculator determines the initial reaction rate (V₀) of an enzyme-catalyzed reaction when substrate concentration is much lower than the Michaelis constant (S ≪ K_M).

Purpose: It helps biochemists and enzymologists understand reaction kinetics under conditions where the reaction rate is directly proportional to substrate concentration.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_0 = \frac{k_{cat} \times [E_0] \times S}{K_M} \]

Where:

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

Explanation: The formula represents the first-order region of Michaelis-Menten kinetics where reaction rate is linearly dependent on substrate concentration.

3. Importance of Initial Reaction Rate Calculation

Details: Calculating initial rates helps determine enzyme efficiency, compare different enzymes, and understand metabolic pathway regulation.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: When is this equation valid?
A: Only when substrate concentration is much lower than K_M (typically S < 0.1×K_M).

Q2: What does k_cat represent?
A: The turnover number - how many substrate molecules one enzyme site converts to product per second.

Q3: How do I determine K_M experimentally?
A: Through a series of initial rate measurements at different substrate concentrations and nonlinear regression.

Q4: What units should I use?
A: Consistent molar units (mol/m³ = mM) and time in seconds.

Q5: Can I use this for inhibitor studies?
A: Only for competitive inhibitors where the apparent K_M changes but k_cat remains constant.