Cann J R
Arch Biochem Biophys. 1985 Aug 1;240(2):489-99. doi: 10.1016/0003-9861(85)90055-4.
The Gilbert-Jenkins theory predicts the asymptotic shape of moving-boundary sedimentation and electrophoretic patterns and broad zone molecular sieve chromatographic elution profiles for the class of interacting systems, A + B in equilibrium C, in which two dissimilar macromolecules react reversibly to form a complex. A particularly provocative case is the one in which the complex has a greater migration velocity than that of either reactant, each of which has a different velocity. Depending upon conditions, this case predicts, for example, that in the asymptotic limit an ascending electrophoretic pattern or a frontal gel chromatographic elution profile can show two hypersharp reaction boundaries separated by a plateau. This prediction is now confirmed by numerical solution of transport equations which retain the second-order diffusional term and extrapolation of the computed patterns to zero diffusion coefficient. For finite diffusion coefficient, however, the two hypersharp reaction boundaries are separated by a weak negative gradient. These calculations are extended to an examination of the transitions between the three types of patterns admitted by the case under consideration in order to gain physical understanding and to define criteria for recognizing the transitions. Studies of this kind not only establish confidence in the Gilbert-Jenkins theory, but, in addition, they provide new insights which make for more effective application of the theory to real systems.
吉尔伯特 - 詹金斯理论预测了移动边界沉降和电泳图谱以及宽区分子筛色谱洗脱曲线的渐近形状，适用于相互作用体系“A + B ⇌ C”这一类情况，其中两种不同的大分子可逆反应形成复合物。一个特别引人关注的情况是复合物的迁移速度比任何一种反应物都快，而每种反应物的迁移速度又不同。根据条件，这种情况预测，例如在渐近极限下，上升的电泳图谱或前沿凝胶色谱洗脱曲线可能会显示出由一个平台分隔的两个超尖锐反应边界。现在通过保留二阶扩散项的输运方程的数值解以及将计算得到的图谱外推到零扩散系数，证实了这一预测。然而，对于有限的扩散系数，两个超尖锐反应边界由一个弱负梯度分隔。这些计算扩展到对所考虑情况下允许的三种类型图谱之间转变的研究，以便获得物理理解并确定识别转变的标准。这类研究不仅建立了对吉尔伯特 - 詹金斯理论的信心，而且还提供了新的见解，有助于更有效地将该理论应用于实际系统。
