F1-ATP 酶水解 ATP 的 2 位点模型与 3 位点模型:使用组合学和守恒方程的明确数学证明。

IF 1.3 4区 生物学 Q3 BIOLOGY
Theory in Biosciences Pub Date : 2024-09-01 Epub Date: 2024-07-30 DOI:10.1007/s12064-024-00421-8
Sunil Nath
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引用次数: 0

摘要

F1-ATPase 酶是已知的最小分子马达,在 ATP 的水解作用驱动下以 120° 的步长旋转。它是一种多亚基酶,包含三个催化位点。一个核心问题是,这三个位点发生的基本化学反应如何与机械旋转耦合。为了回答这个问题,人们提出了各种模型和耦合方案。它们可分为两个位点(双位点)模型和三个位点(三位点)模型,前者如 Boyer 于 50 年前首次提出的结合变化机制,后者如 Nath 于 25 年前首次提出并在 1 年前完善的扭转机制。使用不同方法整理的实验数据已确凿表明,F1-ATP 酶的稳态 ATP 水解发生在三位模式中。因此,人们不断修改旧模型,使其符合新的事实。在此,我们开发了一种基于组合学和守恒定律的纯数学方法,以检验所提出的模型是 2 位还是 3 位。基于这种新颖的组合方法,我们证明了旧模型和修改后的模型实际上是双位点模型,因为在这些模型中,F1-ATPase 的催化和旋转只发生在两个被结合核苷酸占据的催化位点上。因此,这些模型与一致的实验数据相矛盾。根据我们新颖的数学方法,最近关于 F1-ATP 酶水解 ATP 的 2023 模型已被证明是一个真正的三位点模型。这种纯数学证明是 ATP 机理的重要一步。然而,在我们看来,这种纯数学证明在解决分子生物学问题方面还没有充分发挥其巨大的科学潜力。我们相信,创造性地应用纯数学证明(另一个例子见 Nath 在 Theory Biosci 141:249-260, 2022 中的文章)有助于最终解决在分析基本生物问题时理所当然会出现的各种长期存在的分子级问题。事实证明,标准的实验、理论或计算方法很难解决这些问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

2-Site versus 3-site models of ATP hydrolysis by F<sub>1</sub>-ATPase: definitive mathematical proof using combinatorics and conservation equations.

2-Site versus 3-site models of ATP hydrolysis by F1-ATPase: definitive mathematical proof using combinatorics and conservation equations.

The F1-ATPase enzyme is the smallest-known molecular motor that rotates in 120° steps, driven by the hydrolysis of ATP. It is a multi-subunit enzyme that contains three catalytic sites. A central question is how the elementary chemical reactions that occur in the three sites are coupled to mechanical rotation. Various models and coupling schemes have been formulated in an attempt to answer this question. They can be classified as 2-site (bi-site) models, exemplified by Boyer's binding change mechanism first proposed 50 years ago, and 3-site (tri-site) models such as Nath's torsional mechanism, first postulated 25 years ago and embellished 1 year back. Experimental data collated using diverse approaches have conclusively shown that steady-state ATP hydrolysis by F1-ATPase occurs in tri-site mode. Hence older models have been continually modified to make them conform to the new facts. Here, we have developed a pure mathematical approach based on combinatorics and conservation laws to test if proposed models are 2-site or 3-site. Based on this novel combinatorial approach, we have proved that older and modified models are effectively bi‒site models in that catalysis and rotation in F1-ATPase occurs in these models with only two catalytic sites occupied by bound nucleotide. Hence these models contradict consensus experimental data. The recent 2023 model of ATP hydrolysis by F1-ATPase has been proved to be a true tri-site model based on our novel mathematical approach. Such pure mathematical proofs constitute an important step forward for ATP mechanism. However, in what must be considered an aspect with great scientific potential, the power of such mathematical proofs has not been fully exploited to solve molecular biological problems, in our opinion. We believe that the creative application of pure mathematical proofs (for another example see Nath in Theory Biosci 141:249-260, 2022) can help resolve with finality various longstanding molecular-level issues that arise as a matter of course in the analysis of fundamental biological problems. Such issues have proved extraordinarily difficult to resolve by standard experimental, theoretical, or computational approaches.

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来源期刊
Theory in Biosciences
Theory in Biosciences 生物-生物学
CiteScore
2.70
自引率
9.10%
发文量
21
审稿时长
3 months
期刊介绍: Theory in Biosciences focuses on new concepts in theoretical biology. It also includes analytical and modelling approaches as well as philosophical and historical issues. Central topics are: Artificial Life; Bioinformatics with a focus on novel methods, phenomena, and interpretations; Bioinspired Modeling; Complexity, Robustness, and Resilience; Embodied Cognition; Evolutionary Biology; Evo-Devo; Game Theoretic Modeling; Genetics; History of Biology; Language Evolution; Mathematical Biology; Origin of Life; Philosophy of Biology; Population Biology; Systems Biology; Theoretical Ecology; Theoretical Molecular Biology; Theoretical Neuroscience & Cognition.
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