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 pairs | 1 |
| \(c_T\) | 总链浓度total strand concentration | mol·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
两态模型:\(\mathrm{A} + \mathrm{B} \rightleftharpoons \mathrm{AB}\),\(K = [\mathrm{AB}]/([\mathrm{A}][\mathrm{B}])\)。
Two-state model \(\mathrm{A} + \mathrm{B} \rightleftharpoons \mathrm{AB}\).
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 \(K = 4/c_T\).
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.