Haber R S, Loeb J N
J Gen Physiol. 1983 Jan;81(1):1-28. doi: 10.1085/jgp.81.1.1.
A mathematical model is presented which describes the theoretical relationship between ligand concentration and physiological response for systems in which the response is dependent upon simultaneous occupancy of two receptor ligand-binding sites. The treatment considers both the possibility of intrinsic differences between the binding sites with regard to ligand affinity, as well as the possibility of mutually induced changes in affinity resulting from allosteric interactions. Unlike the Monod-Wyman-Changeux formulation for allosteric enzymes, the general model put forward here makes double occupancy an absolute requirement for enzymatic function. It is shown that such a model leads to the prediction of a curvilinear Hill plot from which one can obtain an explicit estimate of the degree of allosteric interaction between the two ligand binding sites as well as the Gibbs standard free energy change for the overall binding reaction. It is then shown that, in the specific instance of Na, K-ATPase-mediated K+ transport by the turkey erythrocyte, the configuration of the Hill curve describing the rate of ouabain-sensitive K+ transport as a function of external K+ concentration conforms closely to that predicted by the model described above. The results are of particular interest because they indicate a strongly cooperative interaction between the two K+ binding sites on the transport protein such that occupancy of one site results in an enhancement of the affinity of the other site for K+ by a minimum of 15- to 20-fold. Finally, we consider in detail a model of the Monod-Wyman-Changeux type in which, by contrast, both singly and doubly occupied forms of the enzyme are assumed to be catalytically active, and which we analogously extend to allow for the possibility of asymmetry between the two ligand binding sites. Although it is shown that the two models can not be differentiated from each other in the present experimental system, they yield virtually identical estimates for the degree of positive cooperativity between the two K+ binding sites.
本文提出了一个数学模型，该模型描述了在响应取决于两个受体配体结合位点同时被占据的系统中，配体浓度与生理反应之间的理论关系。该处理方法既考虑了结合位点在配体亲和力方面存在内在差异的可能性，也考虑了变构相互作用导致亲和力相互诱导变化的可能性。与变构酶的莫诺德 - 怀曼 - 尚热公式不同，这里提出的通用模型使双重占据成为酶功能的绝对要求。结果表明，这样的模型会导致预测出一条曲线型的希尔图，从中可以明确估计两个配体结合位点之间的变构相互作用程度以及整个结合反应的吉布斯标准自由能变化。然后表明，在火鸡红细胞中由钠钾 - ATP酶介导的钾离子转运的特定情况下，描述哇巴因敏感的钾离子转运速率作为外部钾离子浓度函数的希尔曲线构型与上述模型预测的构型非常吻合。这些结果特别令人感兴趣，因为它们表明转运蛋白上的两个钾离子结合位点之间存在强烈的协同相互作用，使得一个位点被占据会导致另一个位点对钾离子的亲和力至少增强15至20倍。最后，我们详细考虑了一个莫诺德 - 怀曼 - 尚热类型的模型，相比之下，该模型假设酶的单占据和双占据形式都具有催化活性，并且我们类似地进行扩展以考虑两个配体结合位点之间不对称的可能性。虽然结果表明在当前实验系统中这两个模型无法相互区分，但它们对两个钾离子结合位点之间的正协同作用程度给出了几乎相同的估计。
