How are enzyme inhibitors used in medicine?

Common examples include statins that inhibit HMG-CoA reductase, ACE inhibitors for hypertension, sildenafil as a PDE5 inhibitor, aspirin as an irreversible COX inhibitor, and HIV protease inhibitors.

What is a Lineweaver-Burk plot?

It is a double-reciprocal plot of 1/v versus 1/[S]. The y-intercept is 1/Vmax and the x-intercept is -1/Km, so changes in the line help identify inhibitor type.

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Biochemistry

Enzyme Kinetics Simulator (Michaelis-Menten)

Q: What is the Michaelis constant Km?

Km is the substrate concentration at which the enzyme reaches half its maximum rate (Vmax/2). A lower Km indicates higher substrate affinity, so the enzyme works efficiently even at low substrate concentration.

Q: What is the difference between competitive and noncompetitive inhibition?

Competitive inhibitors compete with the substrate for the active site, increasing apparent Km while Vmax remains unchanged. Noncompetitive inhibitors bind at an allosteric site and lower apparent Vmax while apparent Km remains unchanged.

Vary Km, Vmax, and inhibitor type/concentration to draw Michaelis-Menten curves in real time. Compare competitive, non-competitive, and mixed inhibition using Lineweaver-Burk and Eadie-Hofstee plots.

Enzyme Presets

Basic Parameters

Km (mmol/L)

Vmax (μmol/min)

Substrate concentration [S]

Inhibitor Settings

Inhibitor concentration [I]

Inhibition constant Ki

Reaction rate v (at [S])

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μmol/min

0.0

Reaction rate v [μmol/min]

% of Vmax (saturation)

Fraction of bound enzyme

0.00

[S] / Km

Adjust [S], Vmax, Km, and the inhibitor with the sliders to see active-site saturation and the reaction rate plateau.

Enzyme (Active Site) Substrate S ES Complex Product P

Compare

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Apparent Km (μmol/L)

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Apparent Vmax (μmol/min)

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v / Vmax ratio (%)

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Catalytic efficiency Vmax/Km

Theory & Key Formulas

Lineweaver–Burk plot

Compare

Theory & Key Formulas

$v = \dfrac{V_{max}[S]}{K_m + [S]}$

Competitive inhibition: $K_m^{app} = K_m(1 + [I]/K_i)$
Noncompetitive inhibition: $V_{max}^{app} = V_{max}/(1 + [I]/K_i)$
Uncompetitive inhibition: $K_m^{app} = K_m/(1 + [I]/K_i)$, $V_{max}^{app}$↓

🎓 Learn Enzyme Kinetics Through Conversation

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Enzyme reaction rates level off even when substrate keeps increasing. Why don't they keep rising linearly?

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Because the number of enzyme molecules is finite. At low [S], the rate is almost proportional to substrate concentration because many enzymes are idle. As [S] increases, essentially every enzyme becomes occupied and turns over as fast as it can, so the rate approaches the upper limit Vmax = kcat × [E_total]. The catalytic constant kcat is the number of substrate molecules one enzyme molecule can process per second.

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What is a real drug example of a competitive inhibitor? It feels odd that increasing substrate can overcome it.

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Statins, used to lower cholesterol, are a classic example. They resemble HMG-CoA and bind to the active site of HMG-CoA reductase, blocking the true substrate. Raising the substrate concentration can outcompete the inhibitor, which is why this is called competitive inhibition. In the body, substrate concentration is not freely adjustable, so dosage matters clinically. Vmax stays the same while the curve shifts to the right.

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Noncompetitive inhibition cannot be overcome by adding substrate. How can binding somewhere other than the active site have such a large effect?

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Enzymes are proteins, so changing one region can reshape the whole molecule through an allosteric effect. When an inhibitor binds at an allosteric site, the active site geometry or catalytic motion can be impaired. Vmax decreases while Km is unchanged in ideal noncompetitive inhibition, so the Lineweaver-Burk plot changes its y-intercept while the x-intercept stays fixed.

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Where does enzyme reaction modeling appear in CAE or engineering?

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It appears directly in bioreactor design, such as fermentation optimization and pharmaceutical manufacturing. In CFD, Michaelis-Menten rate expressions can be used as source terms in reactive-flow simulations that combine reaction kinetics with fluid mixing. Similar kinetic ideas also appear in catalytic surface reactions, such as Langmuir-Hinshelwood models for fuel-cell catalysts, and in metabolic flux analysis.

Frequently Asked Questions

What is the Michaelis constant Km?

It is the substrate concentration at which the reaction rate is half of Vmax (Vmax/2). A smaller Km indicates higher substrate affinity for the enzyme, meaning the reaction proceeds rapidly even at low substrate concentrations. For example, hexokinase has a Km for glucose of about 0.15 mmol/L, and at blood glucose levels (around 5 mmol/L), it exhibits over 90% activity.

What is the difference between competitive and non-competitive inhibition?

Competitive inhibitors bind competitively to the same active site as the substrate. The apparent KmApp = Km(1+[I]/Ki) increases, while Vmax remains unchanged. Inhibition can be overcome by adding a large amount of substrate. Non-competitive inhibitors bind to a site other than the active site (allosteric site), reducing VmaxApp but leaving KmApp unchanged. A key feature is that inhibition cannot be overcome by increasing substrate concentration.

How do I read a Lineweaver-Burk plot?

It is a double-reciprocal plot with 1/v on the vertical axis and 1/[S] on the horizontal axis. The y-intercept is 1/Vmax, and the x-intercept is -1/Km. The pattern of line changes differs by inhibitor type: competitive inhibition shows the same y-intercept with increased slope (lines intersect at the same y-intercept), non-competitive inhibition shows the same slope with increased y-intercept (lines intersect on the x-axis), and mixed inhibition changes both.

What is uncompetitive inhibition?

This inhibitor binds only to the enzyme-substrate complex (ES) formed after the substrate binds to the enzyme. Both KmApp and VmaxApp decrease, and the Lineweaver-Burk plot yields lines parallel to the original line. It is distinct from competitive and non-competitive inhibition, though most pharmaceuticals are competitive or mixed inhibitors.

How is the enzyme reaction model used in bioreactor design?

In the design of continuous stirred-tank reactors (CSTR) and plug-flow reactors (PFR), the Michaelis-Menten rate equation $v = V_{max}[S]/(K_m + [S])$ is directly used as the source term in material balance equations. In CFD simulations, it is combined with fluid mixing behavior (flow velocity, diffusion) as a "reaction flow analysis," and temperature dependence (Arrhenius-type kcat) can also be incorporated. This mathematical framework is essential for bioprocess optimization in pharmaceuticals, food, and environmental engineering.

How to Use

Set Vmax (maximum velocity in μmol/min) using the slider or numeric input—typical range 0.1–10 for assay conditions.
Adjust Km (Michaelis constant in mM) to reflect substrate affinity; lower Km indicates tighter binding.
Enter substrate concentration [S] in mM and inhibitor concentration [I] to observe curve shifts under competitive, non-competitive, or uncompetitive inhibition.
The simulator plots v = Vmax[S]/(Km + [S]) in real time, with inhibitor effects applied to Km or Vmax accordingly.

Worked Example

For horseradish peroxidase (HRP) oxidizing H₂O₂: Vmax = 5.2 μmol/min, Km = 2.8 mM. At [S] = 10 mM, velocity = 5.2 × 10/(2.8 + 10) = 3.8 μmol/min. Adding competitive inhibitor (e.g., phenolic substrate analog at 1.5 mM with Ki = 0.9 mM) increases apparent Km to 5.4 mM, reducing v to 2.9 μmol/min while Vmax remains unchanged.

Practical Notes

Competitive inhibitors (e.g., statins vs. HMG-CoA reductase) increase Km linearly; double-reciprocal (Lineweaver-Burk) plots show y-intercept invariance—critical for drug screening.
Non-competitive inhibitors lower Vmax without changing Km; use this mode to simulate allosteric modulators or irreversible inhibitors in serum assays.
For clinical enzymology (glucose oxidase, lactate dehydrogenase), ensure [S] spans 0.1–10× Km to visualize the transition between zero-order and first-order kinetics.