66.667
μmol/(L·min)
5
μmol/L
100
μmol/(L·min)
10,000
min^-1
2.0000e+3
L/(μmol·min)
66.667
μmol/(L·min)
0
%
66.67
%
66.667
μmol/(L·min)
5
μmol/L
100
μmol/(L·min)
10,000
min^-1
2.0000e+3
L/(μmol·min)
66.667
μmol/(L·min)
0
%
66.67
%
The Enzyme Kinetics Calculator is a comprehensive tool for analyzing enzyme-catalyzed reactions with support for all major types of reversible inhibition. It computes reaction velocity, apparent kinetic parameters, turnover number, and catalytic efficiency in a single interface. Enzyme inhibition is central to pharmacology (most drugs are enzyme inhibitors), toxicology (understanding poisoning mechanisms), metabolic regulation (feedback inhibition), and biotechnology (enzyme engineering). This calculator handles competitive, uncompetitive, and noncompetitive (mixed) inhibition, allowing you to see how an inhibitor changes the effective Km and Vmax, and quantify the degree of inhibition at any substrate and inhibitor concentration.
The general equation for enzyme kinetics with inhibition uses the alpha (α) notation:
$$v = \frac{V_{max} [S]}{\alpha K_m + \alpha' [S]}$$
where α and α' depend on the inhibition type:
No inhibitor: α = 1, α' = 1 → standard Michaelis-Menten
Competitive inhibition: α = 1 + [I]/Ki, α' = 1
$$v = \frac{V_{max} [S]}{K_m(1 + [I]/K_i) + [S]}$$
Apparent Km increases; Vmax unchanged.
Uncompetitive inhibition: α = 1, α' = 1 + [I]/Ki
$$v = \frac{V_{max} [S]/(1 + [I]/K_i)}{K_m/(1 + [I]/K_i) + [S]}$$
Both apparent Km and Vmax decrease by the same factor.
Noncompetitive (mixed) inhibition: α = α' = 1 + [I]/Ki (pure noncompetitive)
$$v = \frac{V_{max} [S]/(1 + [I]/K_i)}{K_m + [S]}$$
Vmax decreases; Km unchanged (pure noncompetitive).
The turnover number and catalytic efficiency are:
$$k_{cat} = \frac{V_{max}}{[E]_t}, \quad \text{Efficiency} = \frac{k_{cat}}{K_m}$$
The reaction velocity shows the actual rate under the given conditions. Compare apparent Km and apparent Vmax with the uninhibited values to understand the inhibitor's effect. The fraction inhibited quantifies the degree of inhibition as a percentage — useful for determining drug efficacy at a given dose. kcat tells you how many substrate molecules each enzyme converts per minute. Catalytic efficiency (kcat/Km) is the best single measure of enzyme performance; values near 10⁸-10⁹ M⁻¹s⁻¹ indicate diffusion-limited catalysis (kinetically perfect enzyme).
Inputs
Results
With competitive inhibitor at [I] = Ki: α = 1 + 10/10 = 2. Apparent Km = 5 × 2 = 10 μmol/L. Vmax stays 100. v = 100×10/(10+10) = 50 μmol/(L·min). Without inhibitor, v = 66.67, so inhibition = (66.67−50)/66.67 = 25%.
Inputs
Results
Noncompetitive with [I]=5, Ki=10: α = α' = 1.5. Apparent Vmax = 100/1.5 = 66.67. Km unchanged at 5. v = 66.67×10/(5+10) = 44.44. Inhibition = (66.67−44.44)/66.67 = 33.3%.
A competitive inhibitor resembles the substrate and binds to the enzyme's active site, preventing substrate binding. It increases the apparent Km (lower apparent affinity) but does not affect Vmax because at high enough substrate concentrations, the substrate outcompetes the inhibitor. Many drugs, such as statins (HMG-CoA reductase inhibitors), work this way.
An uncompetitive inhibitor binds only to the enzyme-substrate complex (ES), not to the free enzyme. It decreases both apparent Vmax and apparent Km by the same factor. On a Lineweaver-Burk plot, it produces parallel lines. It is most common in multi-substrate reactions.
A noncompetitive (or mixed) inhibitor binds to both the free enzyme and the ES complex, but at a site different from the active site. In pure noncompetitive inhibition (Ki = Ki'), Vmax decreases while Km is unchanged. In mixed inhibition, both parameters change.
Ki is the inhibition constant — the dissociation constant of the enzyme-inhibitor complex. A smaller Ki means tighter binding and more potent inhibition. It is determined by measuring enzyme kinetics at multiple inhibitor concentrations and fitting the data to the appropriate inhibition model.
Compare kinetic data with and without inhibitor. Competitive: increased Km, same Vmax. Uncompetitive: both decrease proportionally. Noncompetitive: decreased Vmax, same Km (pure) or both change (mixed). Lineweaver-Burk plots show characteristic line patterns for each type.
An enzyme whose catalytic efficiency (kcat/Km) approaches the rate of substrate diffusion (~10⁸-10⁹ M⁻¹s⁻¹). Examples include triosephosphate isomerase, carbonic anhydrase, and acetylcholinesterase. These are sometimes called kinetically perfect enzymes because they catalyze reactions as fast as substrates can arrive.
Initially, increasing temperature increases the rate (Arrhenius behavior). But above the optimal temperature, the enzyme begins to denature, causing rapid loss of activity. The Michaelis-Menten parameters Vmax and Km both change with temperature, and thermal denaturation adds an inactivation term.
Allosteric inhibitors bind to a site other than the active site and induce conformational changes that reduce catalytic activity. Unlike simple competitive/noncompetitive models, allosteric enzymes often show sigmoidal (cooperative) kinetics described by the Hill equation rather than Michaelis-Menten.
Drug candidates are characterized by their Ki, mechanism of inhibition (competitive, noncompetitive, irreversible), and selectivity for the target enzyme over related enzymes. IC₅₀ (concentration for 50% inhibition) is the most common screening metric, related to Ki by the Cheng-Prusoff equation.
It relates IC₅₀ to Ki depending on the inhibition type. For competitive inhibitors: Ki = IC₅₀/(1 + [S]/Km). For uncompetitive: Ki = IC₅₀(1 + [S]/Km)/([S]/Km). This correction is essential because IC₅₀ depends on substrate concentration while Ki does not.
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The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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