Allosteric Enzyme Reaction Velocity (v)

Maximum Reaction Velocity (V_m) (e.g., M/min) Maximum rate of reaction at saturating substrate concentration. Units determine output velocity units (e.g., M/min).

Substrate Concentration [S] (e.g., M) Current substrate concentration. Units must be consistent with K''m base units.

Cooperativity Coefficient (n) Hill coefficient representing the degree of cooperativity. n > 1 indicates positive cooperativity. Dimensionless.

Constant (K''_m) (e.g., Mⁿ) Constant related to substrate affinity. Note: Units are (Concentration)ⁿ, consistent with [S] units.

Calculation Explanation

This calculator estimates the reaction velocity (v) for allosteric enzymes exhibiting cooperative binding, using the Hill equation (Eq 3.18).

Hill Equation (Eq 3.18):
v = (V_m ⋅ [S]ⁿ) / (K''_m + [S]ⁿ)

Where:

v: Reaction velocity (units determined by V_m).
V_m: Maximum reaction velocity (e.g., M/min).
[S]: Substrate concentration (e.g., M).
n: Cooperativity coefficient (Hill coefficient, dimensionless). n > 1 indicates positive cooperativity (sigmoidal v vs [S] curve), n = 1 simplifies to Michaelis-Menten, n < 1 indicates negative cooperativity.
K''_m: Constant related to substrate affinity. It represents K_0.5ⁿ, where K_0.5 is the substrate concentration at which v = V_m/2. Units are (Concentration Units of [S])ⁿ.

Ensure consistent concentration units are used for [S] and the base unit of K''_m. For example, if [S] is in M, K''_m should be in Mⁿ.

Allosteric Enzyme Reaction Velocity (v)

Result

Calculation Explanation