Conformational Entropy of the RNA Phosphate Backbone and Its Contribution to the Folding Free Energy

While major contributors to the free energy of RNA tertiary structures such as basepairing, base-stacking, and charge and counterion interactions have been studied extensively, little is known about the intrinsic free energy of the backbone. To assess the magnitude of the entropic strains along the phosphate backbone and their impact on the folding free energy, we have formulated a mathematical treatment for computing the volume of the main-chain torsion-angle conformation space between every pair of nucleobases along any sequence to compute the corresponding backbone entropy. To validate this method, we have compared the computed conformational entropies against a statistical free energy analysis of structures in the crystallographic database from several-thousand backbone conformations between nearest-neighbor nucleobases as well as against extensive computer simulations. Using this calculation, we analyzed the backbone entropy of several ribozymes and riboswitches and found that their entropic strains are highly localized along their sequences. The total entropic penalty due to steric congestions in the backbone for the native fold can be as high as 2.4 cal/K/mol per nucleotide for these medium and large RNAs, producing a contribution to the overall free energy of up to 0.72 kcal/mol per nucleotide. For these RNAs, we found that low-entropy high-strain residues are predominantly located at loops with tight turns and at tertiary interaction platforms with unusual structural motifs.     

Free Energy Landscape and Multiple Folding Pathways of an H-Type RNA Pseudoknot

How RNA sequences fold to specific tertiary structures is one of the key problems for understanding their dynamics and functions. Here, we study the folding process of an H-type RNA pseudoknot by performing a large-scale all-atom MD simulation and bias-exchange metadynamics. The folding free energy landscapes are obtained and several folding intermediates are identified. It is suggested that the folding occurs via multiple mechanisms, including a step-wise mechanism starting either from the first helix or the second, and a cooperative mechanism with both helices forming simultaneously. Despite of the multiple mechanism nature, the ensemble folding kinetics estimated from a Markov state model is single-exponential. It is also found that the correlation between folding and binding of metal ions is significant, and the bound ions mediate long-range interactions in the intermediate structures. Non-native interactions are found to be dominant in the unfolded state and also present in some intermediates, possibly hinder the folding process of the RNA.     

A Test and Refinement of Folding Free Energy Nearest Neighbor Parameters for RNA Including N6-Methyladenosine

RNA folding free energy change parameters are widely used to predict RNA secondary structure and to design RNA sequences. These parameters include terms for the folding free energies of helices and loops. Although the full set of parameters has only been traditionally available for the four common bases and backbone, it is well known that covalent modifications of nucleotides are widespread in natural RNAs. Covalent modifications are also widely used in engineered sequences. We recently derived a full set of nearest neighbor terms for RNA that includes N⁶-methyladenosine (m⁶A). In this work, we test the model using 98 optical melting experiments, matching duplexes with or without N⁶-methylation of A. Most experiments place RRACH, the consensus site of N⁶-methylation, in a variety of contexts, including helices, bulge loops, internal loops, dangling ends, and terminal mismatches. For matched sets of experiments that include either A or m⁶A in the same context, we find that the parameters for m⁶A are as accurate as those for A. Across all experiments, the root mean squared deviation between estimated and experimental free energy changes is 0.67 kcal/mol. We used the new experimental data to refine the set of nearest neighbor parameter terms for m⁶A. These parameters enable prediction of RNA secondary structures including m⁶A, which can be used to model how N⁶-methylation of A affects RNA structure.     

Salt-Dependent Folding Energy Landscape of RNA Three-Way Junction

RNAs are highly negatively charged chain molecules. Metal ions play a crucial role in RNA folding stability and conformational changes. In this work, we employ the recently developed tightly bound ion (TBI) model, which accounts for the correlation between ions and the fluctuation of ion distributions, to investigate the ion-dependent free energy landscape for the three-way RNA junction in a 16S rRNA domain. The predicted electrostatic free energy landscape suggests that 1), ion-mediated electrostatic interactions cause an ensemble of unfolded conformations narrowly populated around the maximally extended structure; and 2), Mg²⁺ ion-induced correlation effects help bring the helices to the folded state. Nonelectrostatic interactions, such as noncanonical interactions within the junctions and between junctions and helix stems, might further limit the conformational diversity of the unfolded state, resulting in a more ordered unfolded state than the one predicted from the electrostatic effect. Moreover, the folded state is predominantly stabilized by the coaxial stacking force. The TBI-predicted folding stability agrees well with the experimental measurements for the different Na⁺ and Mg²⁺ ion concentrations. For Mg²⁺ solutions, the TBI model, which accounts for the Mg²⁺ ion correlation effect, gives more improved predictions than the Poisson-Boltzmann theory, which tends to underestimate the role of Mg²⁺ in stabilizing the folded structure. Detailed control tests indicate that the dominant ion correlation effect comes from the charge-charge Coulombic correlation rather than the size (excluded volume) correlation between the ions. Furthermore, the model gives quantitative predictions for the ion size effect in the folding energy landscape and folding cooperativity.     

Contribution of Peptide Backbone to Anti-Citrullinated Peptide Antibody Reactivity

Rheumatoid arthritis (RA) is one of the most common autoimmune diseases, affecting approximately 1–2% of the world population. One of the characteristic features of RA is the presence of autoantibodies. Especially the highly specific anti-citrullinated peptide antibodies (ACPAs), which have been found in up to 70% of RA patients’ sera, have received much attention. Several citrullinated proteins are associated with RA, suggesting that ACPAs may react with different sequence patterns, separating them from traditional antibodies, whose reactivity usually is specific towards a single target. As ACPAs have been suggested to be involved in the development of RA, knowledge about these antibodies may be crucial. In this study, we examined the influence of peptide backbone for ACPA reactivity in immunoassays. The antibodies were found to be reactive with a central Cit-Gly motif being essential for ACPA reactivity and to be cross-reactive between the selected citrullinated peptides. The remaining amino acids within the citrullinated peptides were found to be of less importance for antibody reactivity. Moreover, these findings indicated that the Cit-Gly motif in combination with peptide backbone is essential for antibody reactivity. Based on these findings it was speculated that any amino acid sequence, which brings the peptide into a properly folded structure for antibody recognition is sufficient for antibody reactivity. These findings are in accordance with the current hypothesis that structural homology rather than sequence homology are favored between citrullinated epitopes. These findings are important in relation to clarifying the etiology of RA and to determine the nature of ACPAs, e.g. why some Cit-Gly-containing sequences are not targeted by ACPAs.     

RNA二级结构的最小自由能算法

RNA(即tRNA,rRNA,mRNA和SnRNA)有两大主要功能：一是某些病毒的遗传物质;二是参与蛋白质的合成,这些与细胞分化、代谢、记忆的储存等有重要关系,这些功能与RNA二级结构的稳定性。自由能密切相关．常用的计算自由能的方法有热力学微扰法及热力学微积分法等．本文以寻找最小自由能二级结构为目的,给出了RNA二级结构的最小自由能算法,该算法的时间复杂性不超过O(n^4)。     

Free Energy Landscape for the Entire Transport Cycle of Triose-Phosphate/Phosphate Translocator

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磷酸丙糖异构酶的折叠及稳定性研究

从鸡胸肌中纯化出磷酸丙糖异构酶(triosephosphateisomerase,TIM),通过蛋白质内源荧光,圆二色性,紫外吸收二阶导数光谱等多种研究溶液构象的方法,对TIM被盐酸胍和热变性过程进行了详细的研究.结果表明,用不同测量方法得到TIM的变性过程均高度协同,没有观察到折叠中间态,应用单分子二态去折叠模型计算了TIM去折叠的热力学参数.通过圆二色光谱在222nm处的变化监测的TIM热变性过程也是高度协同的二态过程,天然态TIM的表观Tm为64.6℃.在低浓度盐酸胍存在下,TIM的热稳定性降低.讨论了二体蛋白质的可能去折叠机制,证明在使用的实验条件下磷酸丙糖异构酶去折叠过程中二级结构与三级结构的变化是同时发生的,其去折叠遵循观察不到二体解离的表观二态过程.     

The Effect of Tensile Stress on the Conformational Free Energy Landscape of Disulfide Bonds

Disulfide bridges are no longer considered to merely stabilize protein structure, but are increasingly recognized to play a functional role in many regulatory biomolecular processes. Recent studies have uncovered that the redox activity of native disulfides depends on their C–C–S–S dihedrals, and . Moreover, the interplay of chemical reactivity and mechanical stress of disulfide switches has been recently elucidated using force–clamp spectroscopy and computer simulation. The and angles have been found to change from conformations that are open to nucleophilic attack to sterically hindered, so–called closed states upon exerting tensile stress. In view of the growing evidence of the importance of C–C–S–S dihedrals in tuning the reactivity of disulfides, here we present a systematic study of the conformational diversity of disulfides as a function of tensile stress. With the help of force-clamp metadynamics simulations, we show that tensile stress brings about a large stabilization of the closed conformers, thereby giving rise to drastic changes in the conformational free energy landscape of disulfides. Statistical analysis shows that native TDi, DO and interchain Ig protein disulfides prefer open conformations, whereas the intrachain disulfide bridges in Ig proteins favor closed conformations. Correlating mechanical stress with the distance between the two –carbons of the disulfide moiety reveals that the strain of intrachain Ig protein disulfides corresponds to a mechanical activation of about 100 pN. Such mechanical activation leads to a severalfold increase of the rate of the elementary redox reaction step. All these findings constitute a step forward towards achieving a full understanding of functional disulfides.     

Contribution of Mutation and RNA Recombination to the Evolution of a Plant Pathogenic RNA

The nucleotide sequence of 17 variants of the satellite RNA of cucumber mosaic virus (CMV-satRNA) isolated from field-infected tomato plants in the springs of 1989, 1990, and 1991 was determined. The sequence of each of the 17 satRNAs was unique and was between 334 and 340 nucleotides in length; 57 positions were polymorphic. There was much genetic divergence, ranging from 0.006 to 0.141 nucleotide substitutions per site for pairwise comparisons, and averaging 0.074 for any pair. When the polymorphic positions were analyzed relative to a secondary structure model proposed for CMV-satRNAs, it was found that there were significantly different numbers of changes in base-paired and non–base-paired positions, and that mutations that did not disrupt base pairing were preferred at the putatively paired sites. This supports the concept that the need to maintain a functional structure may limit genetic divergence of CMV-satRNA. Phylogenetic analyses showed that the 17 CMV-satRNA variants clustered into two subgroups, I and II, and evolutionary lines proceeding by the sequential accumulation of mutations were apparent. Three satRNA variants were outliers for these two phylogenetic groups. They were shown to be recombinants of subgroup I and II satRNAs by calculating phylogenies for different molecular regions and by using Sawyer's test for gene conversion. At least two recombination events were required to produce these three recombinant satRNAs. Thus, recombinants were found to be frequent (∼17%) in natural populations of CMV-satRNA, and recombination may make an important contribution to the generation of new variants. To our knowledge this is the first report of data allowing the frequency of recombinant isolates in natural populations of an RNA replicon to be estimated. Received: 14 May 1996 / Accepted: 17 July 1996     

The Osmolyte TMAO Stabilizes Native RNA Tertiary Structures in the Absence of Mg: Evidence for a Large Barrier to Folding from Phosphate Dehydration

The stabilization of RNA tertiary structures by ions is well known, but the neutral osmolyte trimethylamine oxide (TMAO) can also effectively stabilize RNA tertiary structure. To begin to understand the physical basis for the effects of TMAO on RNA, we have quantitated the TMAO-induced stabilization of five RNAs with known structures. So-called m values, the increment in unfolding free energy per molal of osmolyte at constant KCl activity, are ∼ 0 for a hairpin secondary structure and between 0.70 and 1.85 kcal mol^− 1m^− 1 for four RNA tertiary structures (30-86 nt). Further analysis of two RNAs by small-angle X-ray scattering and hydroxyl radical probing shows that TMAO reduces the radius of gyration of the unfolded ensemble to the same endpoint as seen in titration with Mg²⁺ and that the structures stabilized by TMAO and Mg²⁺ are indistinguishable. Remarkably, TMAO induces the native conformation of a Mg²⁺ ion chelation site formed in part by a buried phosphate, even though Mg²⁺ is absent. TMAO interacts weakly, if at all, with KCl, ruling out the possibility that TMAO stabilizes RNA indirectly by increasing salt activity. TMAO is, however, strongly excluded from the vicinity of dimethylphosphate (unfavorable interaction free energy, + 211 cal mol^− 1m^− 1 for the potassium salt), an ion that mimics the RNA backbone phosphate. We suggest that formation of RNA tertiary structure is accompanied by substantial phosphate dehydration (loss of 66-173 water molecules in the RNA structures studied) and that TMAO works principally by reducing the energetic penalty associated with this dehydration. The strong parallels we find between the effects of TMAO and Mg²⁺ suggest that RNA sequence is more important than specific ion interactions in specifying the native structure.     

Fast Folding of an RNA Tetraloop on a Rugged Energy Landscape Detected by a Stacking-Sensitive Probe

We investigate the microsecond-timescale kinetics of the RNA hairpin ga^∗cUUCGguc. The fluorescent nucleotide 2-aminopurine (a^∗) reports mainly on base stacking. Ten kinetic traces and the temperature denaturation curve are globally fitted to four-state models of the free-energy surface. In the best-fitting sequential model, the hairpin unfolds over successively larger barriers in at least three stages: stem fraying and increased base-stacking fluctuations; concerted loss of hydrogen bonding and partial unstacking; and additional unstacking of single strands at the highest temperatures. Parallel and trap models also provide adequate fits: such pathways probably also play a role in the complete free-energy surface of the hairpin. To interpret the model states structurally, 200 ns of molecular dynamics, including six temperature-jump simulations, were run. Although the sampling is by no means comprehensive, five different states were identified using hydrogen bonding and base stacking as reaction coordinates. The four to five states required to explain the experiments or simulations set a lower limit on the complexity of this small RNA hairpin's energy landscape.     

Correlation of RNA Secondary Structure Statistics with Thermodynamic Stability and Applications to Folding

The accurate prediction of the secondary and tertiary structure of an RNA with different folding algorithms is dependent on several factors, including the energy functions. However, an RNA higher-order structure cannot be predicted accurately from its sequence based on a limited set of energy parameters. The inter- and intramolecular forces between this RNA and other small molecules and macromolecules, in addition to other factors in the cell such as pH, ionic strength, and temperature, influence the complex dynamics associated with transition of a single stranded RNA to its secondary and tertiary structure. Since all of the factors that affect the formation of an RNAs 3D structure cannot be determined experimentally, statistically derived potential energy has been used in the prediction of protein structure. In the current work, we evaluate the statistical free energy of various secondary structure motifs, including base-pair stacks, hairpin loops, and internal loops, using their statistical frequency obtained from the comparative analysis of more than 50,000 RNA sequences stored in the RNA Comparative Analysis Database (rCAD) at the Comparative RNA Web (CRW) Site. Statistical energy was computed from the structural statistics for several datasets. While the statistical energy for a base-pair stack correlates with experimentally derived free energy values, suggesting a Boltzmann-like distribution, variation is observed between different molecules and their location on the phylogenetic tree of life. Our statistical energy values calculated for several structural elements were utilized in the Mfold RNA-folding algorithm. The combined statistical energy values for base-pair stacks, hairpins and internal loop flanks result in a significant improvement in the accuracy of secondary structure prediction; the hairpin flanks contribute the most.