双语化学辞典Chem Lexicon
本科Undergraduate 酶动力学、结合与生物能学 Enzyme kinetics, binding & bioenergetics

林–贝氏双倒数作图Lineweaver–Burk plot

\[\frac{1}{v_0} = \frac{K_\mathrm{M}}{V_{\max}}\cdot\frac{1}{[\mathrm{S}]} + \frac{1}{V_{\max}}\]
伊迪–霍夫斯蒂作图Eadie–Hofstee form
\[v_0 = V_{\max} - K_\mathrm{M}\frac{v_0}{[\mathrm{S}]}\]
哈尼斯–伍尔夫作图Hanes–Woolf form
\[\frac{[\mathrm{S}]}{v_0} = \frac{[\mathrm{S}]}{V_{\max}} + \frac{K_\mathrm{M}}{V_{\max}}\]

含义Meaning

把米氏方程取倒数线性化：纵截距 \(1/V_{\max}\)，横截距 \(-1/K_\mathrm{M}\)，斜率 \(K_\mathrm{M}/V_{\max}\)。

The reciprocal of the Michaelis–Menten equation is linear: y-intercept \(1/V_{\max}\), x-intercept \(-1/K_\mathrm{M}\), slope \(K_\mathrm{M}/V_{\max}\).

符号说明Symbols

符号Symbol含义 Meaning单位 Unit
\(1/v_0\)初速率倒数reciprocal initial rateL·s·mol⁻¹
\(1/[\mathrm{S}]\)底物浓度倒数reciprocal substrate concentrationL·mol⁻¹

推导Derivation

  1. 对米氏方程两边取倒数：\(\frac{1}{v_0} = \frac{K_\mathrm{M} + [\mathrm{S}]}{V_{\max}[\mathrm{S}]}\)。

    Invert the Michaelis–Menten equation.

  2. 拆成两项即为 \(y = mx + b\) 形式，\(x = 1/[\mathrm{S}]\)，\(y = 1/v_0\)。

    Split into two terms: a straight line in \(x = 1/[\mathrm{S}]\), \(y = 1/v_0\).

  3. 令 \(y = 0\) 得横截距 \(-1/K_\mathrm{M}\)。

    Setting \(y = 0\) gives the x-intercept \(-1/K_\mathrm{M}\).

适用条件与局限Assumptions & limitations

  • 倒数变换放大低底物浓度点（速率小、误差大）的权重，参数估计偏差大；现代分析宜对原始数据做非线性拟合。

    Inversion over-weights low-[S] points with large relative errors; fit the hyperbola directly by non-linear regression.

  • 主要用途是直观判断抑制类型（直线交点位置）。

    Its main value is diagnosing inhibition type from where lines cross.