Lavrinenko Igor A, Vashanov Gennady A, Hernández Cáceres José L, Nechipurenko Yury D
Department of Human and Animal Physiology, Voronezh State University, Voronezh, 394018 Russia.
Cuban Neuroscience Center, 15202 Avenida 25, Playa, 11600 La Habana, Havana Cuba.
Biophys Rev. 2023 Aug 16;15(5):1269-1278. doi: 10.1007/s12551-023-01110-4. eCollection 2023 Oct.
Despite the fact that the investigation of the structural and functional properties of hemoglobin dates back more than 150 years, the topic has not lost its relevance today. The most important component of these studies is the development of mathematical models that formalize and generalize the mechanisms determining the cooperative binding of ligands based on data on the structural and functional state of the protein. In this work, we review the mathematical relationships describing oxygen binding by hemoglobin, ranging from the classical Hüfner, Hill, and Adair equations to the Szabo-Karplus and tertiary two-state mathematical models based on the Monod-Wyman-Changeux and Koshland-Némethy-Filmer concepts. The generality of the considered equations as mathematical functions, bearing in their basis a power dependence, is demonstrated. The problems and possible solutions related to approximation of experimental data by the oxygenation equations with correlated fitting parameters are noted. Attention is paid to empirical equations, extended versions of the Hill equation, where the coefficient of cooperation is modulated by Gauss and Lorentz distributions as functions of partial oxygen pressure.
尽管对血红蛋白结构和功能特性的研究可以追溯到150多年前，但这个话题在今天仍然具有相关性。这些研究中最重要的部分是数学模型的发展，这些模型基于蛋白质结构和功能状态的数据，对决定配体协同结合的机制进行形式化和概括。在这项工作中，我们回顾了描述血红蛋白氧结合的数学关系，从经典的许夫纳、希尔和阿代尔方程到基于莫诺德-怀曼-尚热和科什兰德-内梅蒂-菲尔默概念的萨博-卡尔普斯和三级两态数学模型。证明了所考虑方程作为数学函数的一般性，其基础是幂次依赖关系。指出了与具有相关拟合参数的氧合方程逼近实验数据相关的问题和可能的解决方案。关注经验方程，即希尔方程的扩展版本，其中协同系数由高斯和洛伦兹分布作为部分氧分压的函数进行调制。
