Ion Effects In The Flexibility Of Single-stranded Nucleic Acid Chain

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 AcidIn 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 AcidPersistence 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 RNAsA 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.