核酸单链柔性中的离子效应
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摘要
核酸(包括DNA和RNA)是生命体中最重要的分子之一,有着非常重要的生物功能,其功能与其结构以及结构变化紧密相关。核酸带有高密度的负电荷,溶液中的金属离子会凝聚在核酸附近并降低折叠静电排斥能,从而有利于核酸紧凑结构的形成。因此溶液中的离子对核酸结构和功能起着很关键的作用。
核酸单链是核酸结构的基本结构和功能单元,在与其他大分子如蛋白质相互作用时,其结构柔性起着重要的作用并强烈依赖于离子条件。因此,定量研究核酸单链柔性中的离子效应,包括离子的价数、浓度和尺寸,有助于理解核酸的结构和功能。由于核酸单链具有强烈的结构涨落且高价离子间的强关联作用,迄今为止,对离子溶液中核酸单链的结构柔性仍然缺乏系统定量的研究,特别是其中的高价离子效应和链长度效应。
核酸折叠一般是以逐级的方式进行的,首先是无序单链,再就是二级结构的形成,然后是二级结构的结构塌缩,最后是结构塌缩态经过位型搜索和三级相互作用形成,三级折叠完成,离子在其中尤其在三级折叠中起着至关重要的作用。对于复杂三级结构,不同种类离子的竞争非常复杂,因此全面系统的研究混合离子的凝聚竞争效应对理解RNA的折叠尤为重要。
针对上述核酸单链柔性中的的离子效应以及混合离子对RNA三级结构的凝聚竞争效应,本文通过Monte Carlo方法展开了系统深入的研究,主要研究内容如下：
(1)核酸单链的结构塌缩
通过简化的粗粒化模型构建核酸单链结构,采用显含离子的Monte Carlo方法,系统研究了核酸单链在不同的离子(Na+,Mg2+, Co3+)条件下的结构性质,分别从离子价数、离子尺寸和离子浓度多个方面分析了对单链结构的影响。(i)Na+可减弱核酸单链的静电排斥作用,从而有利于核酸单链的结构塌缩。随着Na+浓度的升高,核酸单链从扩展态向随机驰豫态转变；(ii)相比于Na+,高价离子(如Mg2+、Co3+)对结构塌缩更为有效；(iii)小尺寸离子更有利于单链的结构塌缩。三价离子和小尺寸二价离子皆可导致比随机弛豫态更紧凑的结构；(iv)高离子浓度下都会出现电荷反转现象。随着离子价数的增加,电荷反转的机制由离子体积关联占主导转变为离子间静电关联占主导。
(2)核酸单链的持久长度(persistence length)
持久长度是表征核酸单链柔韧性的一个量度,是核酸结构的一个重要宏观参数。核酸持久长度来自于其本征刚性和静电作用两方面的贡献,其大小也反映了核酸单链所处的离子环境。基于核酸单链在不同离子条件下的平衡态性质,我们计算了有限长核酸单链的持久长度,结果与相关实验数据一致,并进一步通过系统计算得到了持久长度随Na+/Mg2+离子浓度以及链长度变化的经验公式。这为进一步系统研究混合离子溶液中核酸单链的柔性,奠定了方法基础。
(3)高效准确地得到RNA混合离子溶液所期望的离子体浓度
RNA一般处于单价(K+、Na+)和高价(Mg2+)离子的混合溶液中,由于单价/高价离子的凝聚竞争效应和IRNA的具体静电性质相关,在模拟中通过一个普适方法分配单价和双价离子补偿进而高效准确地得到所期望的离子体浓度足至今尚未解决的问题。根据紧束缚离子模得得到的单价和双价离子对核酸凝聚等效性的纤验公式,我们得到用于补偿RNA负电荷的单价和双价离子相对比例,进而在MonteCarlo模拟中对单价和双价补偿离子进行分配。对多种RNA(包括核酸单链、双螺旋结构和多种RNA三级结构)的广泛模拟显示,此分配方法均可以高效准确地得到所期望的单价和双价离子体浓度。这为进一步的工作,系统研究混合离子溶液中RNA的离子凝聚兑竞争效应以及核酸单链的柔性,提供了重要的方法基础。
(4)不同RNA结构的离子凝聚竞争效应
RNA结构的稳定性是与核酸周围离子的微观分布紧密相关的,而不同的RNA空间结构也会对离子微观分布和凝聚竞争效应产生生要影响。由于游离离了的多自由度和高价离子间的强关联,无论是实验还是理论,对RNA复杂结构周围离子微观分布和凝聚竞争效应的研究仍然具有挑战性,特别是对于较大的RNA分r和较为宽泛的混合离子浓度范围。我们采用Monte Carlo方法,针对多种全原子结构RNA分子以及不同的混合离子浓度,系统地研究了离子的微观分布和凝聚竞争效应,并与广泛的实验进行了对比。有如下重要结论：(i)单价与双价离子在RNA附近的凝聚具有反协同性,Mg2+凝聚能力远强于Na+。所计算的核酸双螺旋结构和多种RNA三级结构的Na+/Mg2+凝聚数目与相关实验数据一致；(ii)对于同长度的B-DNA与A-RNA双螺旋结构,RNA分子周围的Mg2+凝聚数目比DNA分子稍多,这是RNA的高电荷密度和其窄而深的可容纳离子的大沟共同作用的结果；(iii)RNA三级结构越紧凑、核苷酸数目越多,Mg2+相对于Na+的凝聚能力越强。
Nucleic acid (DNA and RNA) is one of the important biological molecules, and its functions are strongly coupled to the structures and the proper structure changes. Due to the polyanionic nature of nucleic acid backbone, the folding from an extend state into compact native structure always involves strong Coulombic repulsions, thus requires metal ions in solutions to neutralize the negative backbone charges and stabilize the folded structures. Therefore, metal ions play essential roles in nucleic acid structures and functions.
Single-stranded (ss) chain is an elementary structural and functional segment of nucleic acids. The flexibility of ss chain, which may be sensitive to ionic environment, plays a significant role in its interactions with other macromolecules, e.g., proteins. Therefore, quantitative understanding how ionic condition, including ion concentration, ion valence and ion size, determines the flexibility of ss nucleic acids, is an important step toward understanding nucleic acid structures and functions. However, due to the strong dynamic conformational fluctuation of ss nucleic acids and strong correlations between multivalent ions, to quantitatively characterize the ion effects on the flexibility of ss nucleic acid chain is still a challenge, especially for long chains in multivalent ion solutions.
RNA folding is a hierarchical process. The secondary structure, signified by base-pairing and stacking interactions between the paired bases, is formed first. Subsequently, the compact tertiary structures are formed through tertiary interactions contacts and tertiary motifs. During the whole folding process, ions play important roles, especially in RNA tertiary folding. The competition between different species of ions is complicated for RNA tertiary structures. Thus, a detailed understanding of the counterion environment and the competition between different cations is essential for comprehensive understanding on RNA folding.
We have employed Monte Carlo simulations to systematically study the ion effect on the flexibility of ss nucleic acid chain and the competition between different ions binding to RNA tertiary structures. The main contents of the research are in the following:
(1) Structural Collapse of Single-stranded Nucleic Acid
In this work, we have employed the coarse-grained Monte Carlo simulations to systematically study the structural behavior of ss nucleic acid chain of finite length in monovalent. divalent, and trivalent salt solutions. The study covers the effects of ion concentration, ion valence and ion size:(ⅰ) The addition of Na+would induce ss chain to collapse from an extend state at low [Na+] to a near-random relaxation state at high [Na+](～1M);(ⅱ) Multivalent ions are more effective than Na+in inducing the structural collapse of ss chain;(ⅲ) Trivalent/small divalent ions can cause more compact state than the random relaxation state;(ⅳ) At high ion concentration, ss nucleic acids can be overcharged by Na+, Mg2+, and Co3+. The overcharging in Na+and in Co3+solutions is dominated by the ionexclusion-volume effect and ion-ion Coulomb correlations, respectively.
(2) Persistence Length of Single-stranded Nucleic Acid
Persistence length quantitatively characterizes the flexibility of a ss chain and is an important quantity for the structure flexibility of nucleic acid. The persistence length of nucleic acid can come from two contributions:an intrinsic contribution which results from the intrinsic rigidity of ss chain, and an electrostatic contribution which is dependent strongly on the ion environment. Based on the conformational ensemble of single-stranded chain in equilibrium, we calculated the ion-dependent persistence length of ss nucleic acids of different lengths. The predicted persistence lengths of ss nucleic acids agree well with the available experimental data, and we have derived the empirical formulas for the persistence length as a function of [Na+] and [Mg2+], and the chain length. The present work forms an important step toward the future work on the flexibility of single-stranded nucleic acid in mixed solutions.
(3) Efficient and Accurate Method for Obtaining the Targeted Ion Bulk Concentrations in RNA-mixed Ion Solutions.
RNA is most frequently found in the realistic solutions with different mixtures of monovalent (e.g., K+/Na+) and divalent ions (Mg2+). The competition between the monovalent and divalent binding ions is sensitive to the electrostatic properties of RNAs. A universal method to assign counterions in order to efficiently and accurately obtain the targeted ion bulk concentrations remains a challenge. Based on the empirical equivalence formula between the ion concentrations of Na+and Mg2+obtained by tightly bond ion model, we calculated the fraction for partition species of counterions added to neutralize the negative backbone charges of RNAs. Through the extentive tests for different RNAs, including single-stranded nucleic acid, RNA/DNA duplex, and complex RNA tertiary structures, the method can efficiently and accurately give the targeted ion bulk concentrations of monovalent and divalent solutions.
(4) Na+versus Mg2+binding to RNAs
A detailed spatial distribution of the counterion environment is essential to the structural stability of nucleic acids solutions, and in another way, the massive buildup of negative charges in the nucleotide backbone leads a significant effect on the counterions binding around RNA. However, due to mobile nature of counterion cloud and strong correlations between multivalent ions, the comprehensive description of ion spatial distribution and ion competition around RNA remains a challenge for most experimental and theoretical approaches, in particular for large RNA tertiary structures and over broad ranges of ion conditions. We have employed Monte Carlo simulations to quantitatively study the ionic atmosphere and the competition behavior between counterions binding to different nucleic acid structures, including duplexes and tertiary folds in mixed Na+/Mg2+solutions. The major conclutions are the following:(ⅰ) Ion-binding of the different (monovalent and divalent) ions shows anti-cooperativity and multivalent ions (Mg2+) are much more efficient than monovalent ions in binding to RNAs, and the predicted numbers of bound ions around RNAs are in good agreement with the available experimental data;(ⅱ) For the same length of RNA and DNA duplexes, the Mg2+binding to RNA is stronger than to DNA, and such difference might come from the higher backbone charge density and the deep major groove for an A-form helix than a B-form helix;(iii) Mg2+binding becomes more efficient than Na+for higher charged and larger RNA tertiary structures.
核酸单链是核酸结构的基本结构和功能单元,在与其他大分子如蛋白质相互作用时,其结构柔性起着重要的作用并强烈依赖于离子条件。因此,定量研究核酸单链柔性中的离子效应,包括离子的价数、浓度和尺寸,有助于理解核酸的结构和功能。由于核酸单链具有强烈的结构涨落且高价离子间的强关联作用,迄今为止,对离子溶液中核酸单链的结构柔性仍然缺乏系统定量的研究,特别是其中的高价离子效应和链长度效应。
核酸折叠一般是以逐级的方式进行的,首先是无序单链,再就是二级结构的形成,然后是二级结构的结构塌缩,最后是结构塌缩态经过位型搜索和三级相互作用形成,三级折叠完成,离子在其中尤其在三级折叠中起着至关重要的作用。对于复杂三级结构,不同种类离子的竞争非常复杂,因此全面系统的研究混合离子的凝聚竞争效应对理解RNA的折叠尤为重要。
针对上述核酸单链柔性中的的离子效应以及混合离子对RNA三级结构的凝聚竞争效应,本文通过Monte Carlo方法展开了系统深入的研究,主要研究内容如下：
(1)核酸单链的结构塌缩
通过简化的粗粒化模型构建核酸单链结构,采用显含离子的Monte Carlo方法,系统研究了核酸单链在不同的离子(Na+,Mg2+, Co3+)条件下的结构性质,分别从离子价数、离子尺寸和离子浓度多个方面分析了对单链结构的影响。(i)Na+可减弱核酸单链的静电排斥作用,从而有利于核酸单链的结构塌缩。随着Na+浓度的升高,核酸单链从扩展态向随机驰豫态转变；(ii)相比于Na+,高价离子(如Mg2+、Co3+)对结构塌缩更为有效；(iii)小尺寸离子更有利于单链的结构塌缩。三价离子和小尺寸二价离子皆可导致比随机弛豫态更紧凑的结构；(iv)高离子浓度下都会出现电荷反转现象。随着离子价数的增加,电荷反转的机制由离子体积关联占主导转变为离子间静电关联占主导。
(2)核酸单链的持久长度(persistence length)
持久长度是表征核酸单链柔韧性的一个量度,是核酸结构的一个重要宏观参数。核酸持久长度来自于其本征刚性和静电作用两方面的贡献,其大小也反映了核酸单链所处的离子环境。基于核酸单链在不同离子条件下的平衡态性质,我们计算了有限长核酸单链的持久长度,结果与相关实验数据一致,并进一步通过系统计算得到了持久长度随Na+/Mg2+离子浓度以及链长度变化的经验公式。这为进一步系统研究混合离子溶液中核酸单链的柔性,奠定了方法基础。
(3)高效准确地得到RNA混合离子溶液所期望的离子体浓度
RNA一般处于单价(K+、Na+)和高价(Mg2+)离子的混合溶液中,由于单价/高价离子的凝聚竞争效应和IRNA的具体静电性质相关,在模拟中通过一个普适方法分配单价和双价离子补偿进而高效准确地得到所期望的离子体浓度足至今尚未解决的问题。根据紧束缚离子模得得到的单价和双价离子对核酸凝聚等效性的纤验公式,我们得到用于补偿RNA负电荷的单价和双价离子相对比例,进而在MonteCarlo模拟中对单价和双价补偿离子进行分配。对多种RNA(包括核酸单链、双螺旋结构和多种RNA三级结构)的广泛模拟显示,此分配方法均可以高效准确地得到所期望的单价和双价离子体浓度。这为进一步的工作,系统研究混合离子溶液中RNA的离子凝聚兑竞争效应以及核酸单链的柔性,提供了重要的方法基础。
(4)不同RNA结构的离子凝聚竞争效应
RNA结构的稳定性是与核酸周围离子的微观分布紧密相关的,而不同的RNA空间结构也会对离子微观分布和凝聚竞争效应产生生要影响。由于游离离了的多自由度和高价离子间的强关联,无论是实验还是理论,对RNA复杂结构周围离子微观分布和凝聚竞争效应的研究仍然具有挑战性,特别是对于较大的RNA分r和较为宽泛的混合离子浓度范围。我们采用Monte Carlo方法,针对多种全原子结构RNA分子以及不同的混合离子浓度,系统地研究了离子的微观分布和凝聚竞争效应,并与广泛的实验进行了对比。有如下重要结论：(i)单价与双价离子在RNA附近的凝聚具有反协同性,Mg2+凝聚能力远强于Na+。所计算的核酸双螺旋结构和多种RNA三级结构的Na+/Mg2+凝聚数目与相关实验数据一致；(ii)对于同长度的B-DNA与A-RNA双螺旋结构,RNA分子周围的Mg2+凝聚数目比DNA分子稍多,这是RNA的高电荷密度和其窄而深的可容纳离子的大沟共同作用的结果；(iii)RNA三级结构越紧凑、核苷酸数目越多,Mg2+相对于Na+的凝聚能力越强。
Nucleic acid (DNA and RNA) is one of the important biological molecules, and its functions are strongly coupled to the structures and the proper structure changes. Due to the polyanionic nature of nucleic acid backbone, the folding from an extend state into compact native structure always involves strong Coulombic repulsions, thus requires metal ions in solutions to neutralize the negative backbone charges and stabilize the folded structures. Therefore, metal ions play essential roles in nucleic acid structures and functions.
Single-stranded (ss) chain is an elementary structural and functional segment of nucleic acids. The flexibility of ss chain, which may be sensitive to ionic environment, plays a significant role in its interactions with other macromolecules, e.g., proteins. Therefore, quantitative understanding how ionic condition, including ion concentration, ion valence and ion size, determines the flexibility of ss nucleic acids, is an important step toward understanding nucleic acid structures and functions. However, due to the strong dynamic conformational fluctuation of ss nucleic acids and strong correlations between multivalent ions, to quantitatively characterize the ion effects on the flexibility of ss nucleic acid chain is still a challenge, especially for long chains in multivalent ion solutions.
RNA folding is a hierarchical process. The secondary structure, signified by base-pairing and stacking interactions between the paired bases, is formed first. Subsequently, the compact tertiary structures are formed through tertiary interactions contacts and tertiary motifs. During the whole folding process, ions play important roles, especially in RNA tertiary folding. The competition between different species of ions is complicated for RNA tertiary structures. Thus, a detailed understanding of the counterion environment and the competition between different cations is essential for comprehensive understanding on RNA folding.
We have employed Monte Carlo simulations to systematically study the ion effect on the flexibility of ss nucleic acid chain and the competition between different ions binding to RNA tertiary structures. The main contents of the research are in the following:
(1) Structural Collapse of Single-stranded Nucleic Acid
In this work, we have employed the coarse-grained Monte Carlo simulations to systematically study the structural behavior of ss nucleic acid chain of finite length in monovalent. divalent, and trivalent salt solutions. The study covers the effects of ion concentration, ion valence and ion size:(ⅰ) The addition of Na+would induce ss chain to collapse from an extend state at low [Na+] to a near-random relaxation state at high [Na+](～1M);(ⅱ) Multivalent ions are more effective than Na+in inducing the structural collapse of ss chain;(ⅲ) Trivalent/small divalent ions can cause more compact state than the random relaxation state;(ⅳ) At high ion concentration, ss nucleic acids can be overcharged by Na+, Mg2+, and Co3+. The overcharging in Na+and in Co3+solutions is dominated by the ionexclusion-volume effect and ion-ion Coulomb correlations, respectively.
(2) Persistence Length of Single-stranded Nucleic Acid
Persistence length quantitatively characterizes the flexibility of a ss chain and is an important quantity for the structure flexibility of nucleic acid. The persistence length of nucleic acid can come from two contributions:an intrinsic contribution which results from the intrinsic rigidity of ss chain, and an electrostatic contribution which is dependent strongly on the ion environment. Based on the conformational ensemble of single-stranded chain in equilibrium, we calculated the ion-dependent persistence length of ss nucleic acids of different lengths. The predicted persistence lengths of ss nucleic acids agree well with the available experimental data, and we have derived the empirical formulas for the persistence length as a function of [Na+] and [Mg2+], and the chain length. The present work forms an important step toward the future work on the flexibility of single-stranded nucleic acid in mixed solutions.
(3) Efficient and Accurate Method for Obtaining the Targeted Ion Bulk Concentrations in RNA-mixed Ion Solutions.
RNA is most frequently found in the realistic solutions with different mixtures of monovalent (e.g., K+/Na+) and divalent ions (Mg2+). The competition between the monovalent and divalent binding ions is sensitive to the electrostatic properties of RNAs. A universal method to assign counterions in order to efficiently and accurately obtain the targeted ion bulk concentrations remains a challenge. Based on the empirical equivalence formula between the ion concentrations of Na+and Mg2+obtained by tightly bond ion model, we calculated the fraction for partition species of counterions added to neutralize the negative backbone charges of RNAs. Through the extentive tests for different RNAs, including single-stranded nucleic acid, RNA/DNA duplex, and complex RNA tertiary structures, the method can efficiently and accurately give the targeted ion bulk concentrations of monovalent and divalent solutions.
(4) Na+versus Mg2+binding to RNAs
A detailed spatial distribution of the counterion environment is essential to the structural stability of nucleic acids solutions, and in another way, the massive buildup of negative charges in the nucleotide backbone leads a significant effect on the counterions binding around RNA. However, due to mobile nature of counterion cloud and strong correlations between multivalent ions, the comprehensive description of ion spatial distribution and ion competition around RNA remains a challenge for most experimental and theoretical approaches, in particular for large RNA tertiary structures and over broad ranges of ion conditions. We have employed Monte Carlo simulations to quantitatively study the ionic atmosphere and the competition behavior between counterions binding to different nucleic acid structures, including duplexes and tertiary folds in mixed Na+/Mg2+solutions. The major conclutions are the following:(ⅰ) Ion-binding of the different (monovalent and divalent) ions shows anti-cooperativity and multivalent ions (Mg2+) are much more efficient than monovalent ions in binding to RNAs, and the predicted numbers of bound ions around RNAs are in good agreement with the available experimental data;(ⅱ) For the same length of RNA and DNA duplexes, the Mg2+binding to RNA is stronger than to DNA, and such difference might come from the higher backbone charge density and the deep major groove for an A-form helix than a B-form helix;(iii) Mg2+binding becomes more efficient than Na+for higher charged and larger RNA tertiary structures.
引文
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