Coherus BioSciences, 1000 Avenida Acaso, Camarillo, CA 93012, United States.
Bristol Myers Squibb, Redwood City, CA, United States.
J Pharm Sci. 2021 Jul;110(7):2585-2589. doi: 10.1016/j.xphs.2021.03.026. Epub 2021 Apr 6.
Because the authors continue to note instances in the scientific literature of failure to use the correct receptor binding site concentration for determining binding constants, herein we discuss the fundamental concepts that need to be considered to determine correct binding constants or conversely calculate accurate reactant concentrations with known equilibrium constants. We also show the derivation and analytical solutions of the cubic and quartic equations that give the exact free ligand concentration in bivalent and trivalent receptor systems at equilibrium as a function of the macroscopic equilibrium dissociation constants and the total concentrations of ligand and multivalent protein. These equations and solutions strongly reemphasize the critical dependency of deriving the correct concentrations of bound or free ligand and multivalent protein on the choice of the correct concentration basis for the multivalent protein, which is in turn dependent upon the type of equilibrium constant used. These results demonstrate the importance of choosing the proper multivalent protein concentration for the determination of either valid microscopic or valid macroscopic equilibrium dissociation constants from binding isotherms of ligand-multivalent protein complexes.
由于作者在科学文献中不断指出未能使用正确的受体结合位点浓度来确定结合常数的情况，因此在这里我们讨论了需要考虑的基本概念，以确定正确的结合常数，或者反过来根据已知的平衡常数计算准确的反应物浓度。我们还展示了推导和分析二价和三价受体系统中平衡时的精确游离配体浓度的三次和四次方程的解析解，这些方程是作为宏观平衡离解常数和配体及多价蛋白的总浓度的函数给出的。这些方程和解决方案强烈地强调了推导出正确的结合或游离配体和多价蛋白浓度的关键依赖于多价蛋白的正确浓度基础的选择，而这反过来又取决于所使用的平衡常数的类型。这些结果表明，从配体-多价蛋白复合物的结合等温线上确定有效的微观或有效的宏观平衡离解常数时，选择适当的多价蛋白浓度的重要性。
