我們以理論計算探討影響在蛋白質環境下的鑭系金屬離子鍵結作用力以及專一性的因素。本研究旨在於了解以下三個問題：(一) 在蛋白質中，鑭系、鈣金屬離子最理想的配位方式是什麼？(二) 何種鈣金屬離子環境最適合鑭系金屬離子進行取代反應？(三) 羧酸根(carboxylate)官能基的單芽配位/雙芽配位是否影響鑭系金屬離子的取代反應？因此， 針對這些問題我們以量子泛函方法計算以下反應的自由能：(一) 鑭系、鈣金屬離子上的水分子與羧酸根羰基(carbonyl)的連續置換反應。(二) 在EF-hand蛋白質上鑭金屬離子與鈣金屬離子的置換反應(保持/改變原本的金屬配位方式) 。
量子泛函理論計算結果顯示三種重要的因素，有利於在EF-hand蛋白質上鑭金屬離子與鈣金屬離子的置換反應，並且提供合理的解釋：(一) 在solvent-shield的EF-hand蛋白質環境下可以加速鑭與鈣金屬離子置換反應的進行。(二) 越多的Asp、Glu在EF-hand的鈣金屬離子鍵結位置上有助於鑭金屬離子產生取代反應。(三) 當越多羧酸根上的兩個氧原子能以雙芽配位同時鍵結在鑭金屬離子上，也會使反應更易進行。

因此，經由以上的研究結果顯示，在solvent-shield環境下，當鈣金屬離子鍵結有豐富的Asp、Glu，同時加上鑭金屬離子可以鍵結至少一個雙芽配位的羧酸根，鑭金屬離子方可進行置換反應。這些計算歸納的結果與發現也與實驗證據相符。

We have performed systematic theoretical studies to elucidate the factors governing the binding affinity and specificity of lanthanide cations for protein binding sites. Specifically, we have addressed the following three questions: (1) what is the most thermodynamically preferable set of protein ligands for La3+ and Ca2+, (2) what is the most preferable Ca2+-binding site for La3+ to replace Ca2+, and (3) how would monodentate vs. bidentate carboxylate binding affect the substitution of Ca2+ for La3+ in EF-hand binding sites. To address these questions, we used density functional theory combined with continuum dielectric methods to compute the free energies for (1) successively replacing a metal-bound water molecule with a carboxylate or a carbonyl group in La3+ and Ca2+ complexes, and (2) replacing Ca2+ with La3+ in classical EF-hand binding sites with and without changing the original carboxylate-binding mode. The calculations reveal three key factors and the corresponding physical bases favoring the substitution of trivalent lanthanides for Ca2+ in EF-hand motifs. First, a solvent-shielded Ca-binding cavity facilitates lanthanides to replace Ca2+, as it enhances favorable metal-ligand interactions. Second, the more Asp/Glu there are in the Ca-binding pocket, the greater the affinity for lanthanides relative to Ca2+, as trivalent lanthanides can accept more negative charge from the carboxylates than divalent Ca2+. Third, the availability of both carboxylate oxygen atoms to bind without penalty to lanthanide cations also facilitates lanthanides to replace Ca2+, as a trivalent lanthanide cation prefers binding a carboxylate bidentately more than divalent Ca2+. Thus, we predict that La3+ can dislodge Ca2+ from carboxylate-rich Ca-binding sites in buried cavities, if it can bind at least one Asp/Glu bidentately. The findings of this work are in accord with available experimental data.

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