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生化学

Enzyme Kinetics Simulator (Michaelis-Menten)

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

Enzyme Presets

Basic Parameters

Km (mmol/L)
mM
Vmax (μmol/min)
基質濃度 [S]
mM

Inhibitor設定

Inhibitor濃度 [I]
mM
阻害定数 Ki
mM
Reaction Rate v (at [S])
—
μmol/min
Apparent Km
— mmol/L
Apparent Vmax
— μmol/min
v / Vmax比
— %
触媒効率 kcat/Km
—
Mm
Theory & Key Formulas
$v = \dfrac{V_{max}[S]}{K_m + [S]}$

競合阻害：$K_m^{app} = K_m(1 + [I]/K_i)$
非競合阻害：$V_{max}^{app} = V_{max}/(1 + [I]/K_i)$
反競合阻害：$K_m^{app} = K_m/(1 + [I]/K_i)$, $V_{max}^{app}$↓

🎓 Learn Enzyme Kinetics Through Conversation

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酵素 反応Velocityって、基質を増やしてもどこかで頭打ちになよね。なんでLinearに速くなり続けないんか？
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酵素分子 数が有限だfrom 。基質[S]が少ないとき、Velocityは[S]にほぼ比例して増える（酵素が暇している状態）。でも[S]を増やしていくと、全て 酵素分子が「フル回転」してしまい、それ以上速くならない。こ 上限がVmax = kcat × [E_total]だ。kcat（触媒定数）は酵素1分子が1秒間に処理できる基質分子数 こと。
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競合Inhibitorって薬で例えるとどんなも か？基質を増やせば克服できるって不思議な感じがし。
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スタチン（コレステロール低下薬）が典型例。HMG-CoA還元酵素 活性部位にHMG-CoAに似た構造で結合して邪魔をする。基質（HMG-CoA）を増やすと競合Inhibitorを追い出せるfrom 、「競合」阻害と言う。ただし体内では基質濃度を勝手に上げられない で、臨床的には高用量 Inhibitorを使う。Vmaxは変わらず曲線 立ち上がりが右にシフトするんだ。
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非競合阻害は基質を増やしても克服できないと ことで…なんで活性部位と違う場所に結合するだけでそんなに影響があるんか？
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酵素はProteinで、ある部位が変形すると全体 形が変わる（アロステリック効果）。アロステリック部位にInhibitorが結合すると酵素全体 形が変わり、活性部位 形も歪んで触媒効率が落ちる。Vmaxが低下する一方、Kmは変わらない（基質親和性は保たれる） で、LineウィーBar-Barクプロットではy切片が変化してx切片が変わらないPatternになる。
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CAEや工学分野で 酵素反応モデRingってどんな場面で出てきか？
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バイオリアクター設計（発酵槽 最適化、医薬品製造）で酵素動力学Modelが直接使われる。CFDで流体混合と組み合わせた「反応流体Simulation」でミカエリス-メンテンVelocity式がSource項として入る。また燃料電池 白金触媒 表面反応も形式的にはRunグミュア-ヒンShellウッドModel（酵素反応 工学版）で記述する。代謝Flux解析（MFA）でも同じ数学的枠組みが使われる。

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.

What is Enzyme Kinetics Simulator?

Enzyme Kinetics Simulator is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.

By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.

Physical Model & Key Equations

The simulator is based on the governing equations behind Enzyme Kinetics Simulator (Michaelis-Menten). Understanding these equations is key to interpreting the results correctly.

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Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.

Real-World Applications

Engineering Design: The concepts behind Enzyme Kinetics Simulator (Michaelis-Menten) are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.

Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.

CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.

Common Misconceptions and Points of Caution

Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.

Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.

Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.