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

DNA 解链温度估算DNA melting temperature estimates

\[T_m \approx 2(\mathrm{A}+\mathrm{T}) + 4(\mathrm{G}+\mathrm{C})\ {}^\circ\mathrm{C}\quad(\text{< 14 nt,华莱士规则})\]\[T_m \approx 2(\mathrm{A}+\mathrm{T}) + 4(\mathrm{G}+\mathrm{C})\ {}^\circ\mathrm{C}\quad(\text{< 14 nt, Wallace rule})\]
较长片段的经验式empirical formula for longer duplexes
\[T_m = 81.5 + 16.6\lg[\mathrm{Na^+}] + 0.41(\%\mathrm{GC}) - \frac{675}{N}\]
两态模型(非自互补双链)two-state model (non-self-complementary)
\[T_m = \frac{\Delta H^\circ}{\Delta S^\circ + R\ln(c_T/4)}\]

含义Meaning

一半双链解离为单链时的温度。GC 对有三个氢键且堆积作用更强,含量越高 T_m 越高。

The temperature at which half the duplex has melted; GC pairs (three H-bonds, stronger stacking) raise T_m.

符号说明Symbols

符号Symbol含义 Meaning单位 Unit
\(N\)碱基对数length in base pairs1
\(c_T\)总链浓度total strand concentrationmol·L⁻¹
\(\Delta H^\circ, \Delta S^\circ\)双链形成的焓变、熵变(最近邻参数求和)duplex formation enthalpy and entropy (nearest-neighbour sums)J·mol⁻¹, J·mol⁻¹·K⁻¹

推导Derivation

  1. 两态模型:\(\mathrm{A} + \mathrm{B} \rightleftharpoons \mathrm{AB}\),\(K = [\mathrm{AB}]/([\mathrm{A}][\mathrm{B}])\)。

    Two-state model \(\mathrm{A} + \mathrm{B} \rightleftharpoons \mathrm{AB}\).

  2. T_m 时一半成双链:\([\mathrm{AB}] = c_T/4\),\([\mathrm{A}] = [\mathrm{B}] = c_T/4\),所以 \(K = 4/c_T\)。

    At T_m half is duplex, giving \(K = 4/c_T\).

  3. 由 \(-RT\ln K = \Delta H^\circ - T\Delta S^\circ\) 解出 T_m。

    Solve \(-RT\ln K = \Delta H^\circ - T\Delta S^\circ\) for T.

适用条件与局限Assumptions & limitations

  • 华莱士规则只适合短引物(约 14–20 nt 以下)且在约 0.9 mol/L Na⁺ 下;精确设计用最近邻热力学参数(SantaLucia 1998)。

    Wallace rule is for short oligos at ~0.9 M Na⁺; use nearest-neighbour parameters for accuracy.

  • 错配、Mg²⁺、甲酰胺、DMSO 都会改变 T_m。

    Mismatches, Mg²⁺, formamide and DMSO shift T_m.