含义Meaning
描述协同结合：\(n_\mathrm{H} > 1\) 为正协同（S 形曲线，如血红蛋白结合 O₂，\(n_\mathrm{H} \approx 2.8\)），\(n_\mathrm{H} = 1\) 退化为双曲线。
Describes cooperative binding: \(n_\mathrm{H} > 1\) is positive cooperativity (sigmoidal, haemoglobin–O₂ \(n_\mathrm{H} \approx 2.8\)); \(n_\mathrm{H} = 1\) is hyperbolic.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\theta\) | 结合位点饱和分数fractional saturation | 1 |
| \([\mathrm{L}]\) | 配体浓度（或分压）ligand concentration (or pressure) | mol·L⁻¹ |
| \(n_\mathrm{H}\) | 希尔系数Hill coefficient | 1 |
| \(K_{0.5}\) | 半饱和配体浓度half-saturation concentration | mol·L⁻¹ |
推导Derivation
设想极端协同：n 个配体同时结合 \(\mathrm{P} + n\mathrm{L} \rightleftharpoons \mathrm{PL}_n\)，\(K_d = [\mathrm{P}][\mathrm{L}]^n/[\mathrm{PL}_n]\)。
Assume all-or-none binding \(\mathrm{P} + n\mathrm{L} \rightleftharpoons \mathrm{PL}_n\).
饱和分数 \(\theta = [\mathrm{PL}_n]/([\mathrm{P}] + [\mathrm{PL}_n]) = [\mathrm{L}]^n/(K_d + [\mathrm{L}]^n)\)，令 \(K_d = K_{0.5}^n\)。
Then \(\theta = [\mathrm{L}]^n/(K_d + [\mathrm{L}]^n)\) with \(K_d = K_{0.5}^n\).
实际协同不是全或无，所以用经验参数 \(n_\mathrm{H}\)（≤ 位点数）代替 n。
Real cooperativity is not all-or-none, so the empirical \(n_\mathrm{H}\) (≤ number of sites) replaces n.
取对数得希尔作图，中点斜率为 \(n_\mathrm{H}\)。
Taking logs gives the Hill plot with slope \(n_\mathrm{H}\) at midpoint.
适用条件与局限Assumptions & limitations
唯象方程，不给出机理；MWC（协同）和 KNF（序贯）模型才有机理意义。
Phenomenological; MWC and KNF models give mechanism.
希尔作图在两端趋向斜率 1，\(n_\mathrm{H}\) 只取中段。
The Hill plot tends to slope 1 at the extremes; read \(n_\mathrm{H}\) at the midpoint.