Enzyme Kinetics (Michaelis-Menten) Calculator

ANA›Life Services Authority›National Calculator Authority›Enzyme Kinetics (Michaelis-Menten) Calculator

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Enzyme Kinetics (Michaelis-Menten) Calculator

Calculate enzyme reaction velocity (V), Michaelis constant (Km), maximum velocity (Vmax), turnover number (kcat), and catalytic efficiency using the Michaelis-Menten model.

Solve For

Reaction Velocity (V) Michaelis Constant (Km) Maximum Velocity (Vmax) Substrate Concentration ([S]) Turnover Number (kcat) Catalytic Efficiency (kcat/Km)

Maximum Velocity, Vmax (µmol/min)

Michaelis Constant, Km (µM)

Substrate Concentration, [S] (µM)

Observed Velocity, V (µmol/min)

Total Enzyme Concentration, [E]t (µM)

Calculate

function enzToggleInputs() { var mode = document.getElementById("enz-solve-for").value;

// All groups var groups = { vmax: document.getElementById("enz-group-vmax"), km: document.getElementById("enz-group-km"), substrate: document.getElementById("enz-group-substrate"), velocity: document.getElementById("enz-group-velocity"), enzyme: document.getElementById("enz-group-enzyme") };

// Reset all visible Object.values(groups).forEach(function(g){ g.style.display = "none"; });

if (mode === "velocity") { groups.vmax.style.display = ""; groups.km.style.display = ""; groups.substrate.style.display = ""; } else if (mode === "km") { groups.vmax.style.display = ""; groups.substrate.style.display = ""; groups.velocity.style.display = ""; } else if (mode === "vmax") { groups.km.style.display = ""; groups.substrate.style.display = ""; groups.velocity.style.display = ""; } else if (mode === "substrate") { groups.vmax.style.display = ""; groups.km.style.display = ""; groups.velocity.style.display = ""; } else if (mode === "kcat") { groups.vmax.style.display = ""; groups.enzyme.style.display = ""; } else if (mode === "efficiency") { groups.vmax.style.display = ""; groups.km.style.display = ""; groups.enzyme.style.display = ""; } }

function enzFmt(val, decimals) { decimals = decimals || 4; if (Math.abs(val) >= 1e6 || (Math.abs(val) " + "Reaction Velocity (V)" + enzFmt(V) + " µmol/min" + "Enzyme Saturation" + enzFmt(saturation, 2) + "%" + "V / Vmax Ratio" + enzFmt(V / Vmax, 4) + "" + "[S] / Km Ratio" + enzFmt(S / Km, 4) + "" + "At Half-Saturation ([S] = Km)?" + (Math.abs(S - Km) " + ""; }

} else if (mode === "km") { var Vmax = getVal("enz-vmax"); var S = getVal("enz-substrate"); var V = getVal("enz-velocity");

if (Vmax === null || Vmax = Vmax) errors.push("V must be less than Vmax (V " + "Michaelis Constant (Km)" + enzFmt(Km) + " µM" + "V / Vmax Ratio" + enzFmt(V / Vmax, 4) + "" + "Enzyme Saturation" + enzFmt((V / Vmax) * 100, 2) + "%" + ""; } }

} else if (mode === "vmax") { var Km = getVal("enz-km"); var S = getVal("enz-substrate"); var V = getVal("enz-velocity");

if (Km === null || Km " + "Maximum Velocity (Vmax)" + enzFmt(Vmax) + " µmol/min" + "V / Vmax Ratio" + enzFmt(V / Vmax, 4) + "" + "Enzyme Saturation" + enzFmt((V / Vmax) * 100, 2) + "%" + ""; }

} else if (mode === "substrate") { var Vmax = getVal("enz-vmax"); var Km = getVal("enz-km"); var V = getVal("enz-velocity");

if (Vmax === null || Vmax = Vmax) errors.push("V must be less than Vmax (V " + "Substrate Concentration ([S])" + enzFmt(S) + " µM" + "[S] / Km Ratio" + enzFmt(S / Km, 4) + "" + "Enzyme Saturation" + enzFmt((V / Vmax) * 100, 2) + "%" + ""; }

} else if (mode === "kcat") { var Vmax = getVal("enz-vmax"); var Et = getVal("enz-enzyme");

if (Vmax === null || Vmax " + "Turnover Number (kcat)" + enzFmt(kcat_sec) + " s⁻¹" + "Turnover Number (kcat)" + enzFmt(kcat_min) + " min⁻¹" + "Vmax / [E]t" + enzFmt(kcat_min, 4) + " min⁻¹" + ""; }

} else if (mode === "efficiency") { var Vmax = getVal("enz-vmax"); var Km = getVal("enz-km"); var Et = getVal("enz-enzyme");

if (Vmax === null || Vmax " + "Turnover Number (kcat)" + enzFmt(kcat_sec) + " s⁻¹" + "Michaelis Constant (Km)" + enzFmt(Km) + " µM" + "Catalytic Efficiency (kcat/Km)" + enzFmt(efficiency) + " M⁻¹s⁻¹" + "Catalytic Efficiency (kcat/Km)" + enzFmt(efficiency / 1e6) + " µM⁻¹s⁻¹" + "% of Diffusion Limit (~10⁸ M⁻¹s⁻¹)" + enzFmt(pct_diffusion, 4) + "%" + ""; } }

if (errors.length > 0) { resultDiv.innerHTML = "Input Error:" + errors.map(function(e){ return ""; }).join("") + ""; } else { resultDiv.innerHTML = html; } }

// Initialize visible inputs on load enzToggleInputs();

#### Formulas Used

Michaelis-Menten Equation:

V = (Vmax · [S]) / (Km + [S])

Rearrangements:

Km = [S] · (Vmax − V) / V
Vmax = V · (Km + [S]) / [S]
[S] = Km · V / (Vmax − V)
kcat = Vmax / [E]t
Catalytic Efficiency = kcat / Km (M⁻¹s⁻¹)

Where:

Vmax = maximum reaction velocity (µmol/min)
Km = Michaelis constant — [S] at V = Vmax/2 (µM)
kcat = turnover number (s⁻¹)
[E]t = total enzyme concentration (µM)

#### Assumptions & References

[S] ≫ [E]t: substrate concentration greatly exceeds enzyme concentration so [S] is not depleted.
Diffusion-limited enzymes (catalytically perfect) have kcat/Km ≈ 10⁸–10⁹ M⁻¹s⁻¹.
References: Michaelis L & Menten ML (1913). Biochem Z 49:333–369. | Berg JM et al. Biochemistry, 9th ed. W.H. Freeman.

Enzyme Kinetics (Michaelis-Menten) Calculator

Enzyme Kinetics (Michaelis-Menten) Calculator

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Enzyme Kinetics (Michaelis-Menten) Calculator

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