A physical origin for functional domain structure in nucleic acids as evidenced by cross-linking entropy: II.

In Part I, cross-linking entropy (CLE) was proposed as a mechanism that limits the size of functional domains of RNA. To test this hypothesis, the theory is developed into an RNA secondary structure prediction filter which is applied to nearest-neighbor secondary structure (NNSS) algorithms that utilize a free energy (FE) minimization strategy. (The NNSS strategies are also referred to as the dynamic programming algorithm in the literature.) The cross-linking entropy for RNA is derived from a generalized Gaussian polymer chain model where the entropic contributions caused by the formation of base pairs (stacking) in RNA are analysed globally. Local entropic contributions are associated with the freezing out of degrees of freedom in the links. Both global and local entropic effects are strongly influenced by the persistence length. The cross-linking entropy provides a physical origin for the size of functional domains in long nucleic acid sequences and may go further to explain as to why the majority of the domain regions in typical sequences tend to be less than 600 nucleotides in length. In addition, improvements were observed in the "best guess" predictive capacity over NNSS prediction strategies. The thermodynamic distribution is more representative of the expected structures and is strongly governed by such physical parameters as the persistence length and the excluded volume. The CLE appears to generalize the tabulated penalties used in NNSS algorithms. The principal parameter influencing this entropy is the persistence length. The model is shown to accomodate a variable persistence length and is capable of describing the folding dynamics of RNA. A two-state kinetic model based on the CLE principle is used to help elucidate the folding kinetics of functional domains in the group I introns.     

Dicer-related helicase 3 forms an obligate dimer for recognizing 22G-RNA

Dicer is a specialized nuclease that produces RNA molecules of specific lengths for use in gene silencing pathways. Dicer relies on the correct measurement of RNA target duplexes to generate products of specific lengths. It is thought that Dicer uses its multidomain architecture to calibrate RNA product length. However, this measurement model is derived from structural information from a protozoan Dicer, and does not account for the helicase domain present in higher organisms. The Caenorhabditis elegans Dicer-related helicase 3 (DRH-3) is an ortholog of the Dicer and RIG-I family of double-strand RNA activated ATPases essential for secondary siRNA production. We find that DRH-3 specifies 22 bp RNAs by dimerization of the helicase domain, a process mediated by ATPase activity and the N-terminal domain. This mechanism for RNA length discrimination by a Dicer family protein suggests an alternative model for RNA length measurement by Dicer, with implications for recognition of siRNA and miRNA targets.     

A method for finding optimal rna secondary structures using a new entropy model (vsfold)

We are developing a program to calculate optimal RNA secondary structures. The model uses di-nucleotide pairing energies as with most traditional approaches. However, for long-range entropy interactions, the approach uses an entropy-loss model based on the accumulated sum of the entropy of bonding between each base-pair weighted inversely by the correlation of the RNA sequence (the Kuhn length). Stiff RNA forms very different structures from flexible RNA. The results demonstrate that the long-range folding is largely governed by this entropy and the Kuhn length.     

Non-specific binding of Na+ and Mg2+ to RNA determined by force spectroscopy methods

RNA duplex stability depends strongly on ionic conditions, and inside cells RNAs are exposed to both monovalent and multivalent ions. Despite recent advances, we do not have general methods to quantitatively account for the effects of monovalent and multivalent ions on RNA stability, and the thermodynamic parameters for secondary structure prediction have only been derived at 1M [Na(+)]. Here, by mechanically unfolding and folding a 20 bp RNA hairpin using optical tweezers, we study the RNA thermodynamics and kinetics at different monovalent and mixed monovalent/Mg(2+) salt conditions. We measure the unfolding and folding rupture forces and apply Kramers theory to extract accurate information about the hairpin free energy landscape under tension at a wide range of ionic conditions. We obtain non-specific corrections for the free energy of formation of the RNA hairpin and measure how the distance of the transition state to the folded state changes with force and ionic strength. We experimentally validate the Tightly Bound Ion model and obtain values for the persistence length of ssRNA. Finally, we test the approximate rule by which the non-specific binding affinity of divalent cations at a given concentration is equivalent to that of monovalent cations taken at 100-fold concentration for small molecular constructs.     

A method for finding optimal RNA secondary structures using a new entropy model (vsfold)

We are developing a program to calculate optimal RNA secondary structures. The model uses di-nucleotide pairing energies as with most traditional approaches. However, for long-range entropy interactions, the approach uses an entropy-loss model based on the accumulated sum of the entropy of bonding between each base-pair weighted inversely by the correlation of the RNA sequence (the Kuhn length). Stiff RNA forms very different structures from flexible RNA. The results demonstrate that the long-range folding is largely governed by this entropy and the Kuhn length.     

A comparison of the crystal structures of eukaryotic and bacterial SSU ribosomal RNAs reveals common structural features in the hypervariable regions

While the majority of the ribosomal RNA structure is conserved in the three major domains of life--archaea, bacteria, and eukaryotes, specific regions of the rRNA structure are unique to at least one of these three primary forms of life. In particular, the comparative secondary structure for the eukaryotic SSU rRNA contains several regions that are different from the analogous regions in the bacteria. Our detailed analysis of two recently determined eukaryotic 40S ribosomal crystal structures, Tetrahymena thermophila and Saccharomyces cerevisiae, and the comparison of these results with the bacterial Thermus thermophilus 30S ribosomal crystal structure: (1) revealed that the vast majority of the comparative structure model for the eukaryotic SSU rRNA is substantiated, including the secondary structure that is similar to both bacteria and archaea as well as specific for the eukaryotes, (2) resolved the secondary structure for regions of the eukaryotic SSU rRNA that were not determined with comparative methods, (3) identified eukaryotic helices that are equivalent to the bacterial helices in several of the hypervariable regions, (4) revealed that, while the coaxially stacked compound helix in the 540 region in the central domain maintains the constant length of 10 base pairs, its two constituent helices contain 5+5 bp rather than the 6+4 bp predicted with comparative analysis of archaeal and eukaryotic SSU rRNAs.     

Entropic elasticity controls nanomechanics of single tropocollagen molecules

We report molecular modeling of stretching single molecules of tropocollagen, the building block of collagen fibrils and fibers that provide mechanical support in connective tissues. For small deformation, we observe a dominance of entropic elasticity. At larger deformation, we find a transition to energetic elasticity, which is characterized by first stretching and breaking of hydrogen bonds, followed by deformation of covalent bonds in the protein backbone, eventually leading to molecular fracture. Our force-displacement curves at small forces show excellent quantitative agreement with optical tweezer experiments. Our model predicts a persistence length xi(p) approximately 16 nm, confirming experimental results suggesting that tropocollagen molecules are very flexible elastic entities. We demonstrate that assembly of single tropocollagen molecules into fibrils significantly decreases their bending flexibility, leading to decreased contributions of entropic effects during deformation. The molecular simulation results are used to develop a simple continuum model capable of describing an entire deformation range of tropocollagen molecules. Our molecular model is capable of describing different regimes of elastic and permanent deformation, without relying on empirical parameters, including a transition from entropic to energetic elasticity.     

Entropy calculation of HIV-1 Env gp120, its receptor CD4, and their complex: an analysis of configurational entropy changes upon complexation

The HIV-1 gp120/CD4 interaction shows a large, unprecedented entropy/enthalpy compensation, with the capacity to fine-tune recognition over a broad range of affinity. The intermolecular interaction involves stable hydrophobic contacts with a unique protruding CD4-Phe43 structure surrounded by an intermolecular hydrogen-bond network that covers the hemisphere of the CD4 D1 domain. We have applied a heuristic formula based on the covariance matrix of atom-positional fluctuations to assess the configurational entropy of the gp120/CD4 complex at different levels. The system was dissected into various subsets of atoms to evaluate the entropic contributions of different functional elements. By combining the trajectories of the free and complex forms, further insight into the conformational sampling was extracted. Despite the limited sampling time of 10 ns, the theoretically derived changes in configurational entropy are in fair agreement with the experimentally determined data. The simultaneous evaluation of different interaction modes through a decomposition approach is only feasible with the knowledge of the atomic trajectory of the system. The configurational entropy analysis in terms of combined trajectories presented here shall potentially provide accurate estimations of thermodynamic properties of biomolecules given sufficient sampling of conformational space.     

Wrapping of flanking non-operator DNA in lac repressor-operator complexes: implications for DNA looping

In our studies of lac repressor tetramer (T)-lac operator (O) interactions, we observed that the presence of extended regions of non-operator DNA flanking a single lac operator sequence embedded in plasmid DNA produced large and unusual cooperative and anticooperative effects on binding constants (Kobs) and their salt concentration dependences for the formation of 1:1 (TO) and especially 1:2 (TO2) complexes. To explore the origin of this striking behavior we report and analyze binding data on 1:1 (TO) and 1:2 (TO2) complexes between repressor and a single O(sym) operator embedded in 40 bp, 101 bp, and 2514 bp DNA, over very wide ranges of [salt]. We find large interrelated effects of flanking DNA length and [salt] on binding constants (K(TO)obs, K(TO2)obs) and on their [salt]-derivatives, and quantify these effects in terms of the free energy contributions of two wrapping modes, designated local and global. Both local and global wrapping of flanking DNA occur to an increasing extent as [salt] decreases. Global wrapping of plasmid-length DNA is extraordinarily dependent on [salt]. We propose that global wrapping is driven at low salt concentration by the polyelectrolyte effect, and involves a very large number (>/similar 20) of coulombic interactions between DNA phosphates and positively charged groups on lac repressor. Coulombic interactions in the global wrap must involve both the core and the second DNA-binding domain of lac repressor, and result in a complex which is looped by DNA wrapping. The non-coulombic contribution to the free energy of global wrapping is highly unfavorable ( approximately +30-50 kcal mol(-1)), which presumably results from a significant extent of DNA distortion and/or entropic constraints. We propose a structural model for global wrapping, and consider its implications for looping of intervening non-operator DNA in forming a complex between a tetrameric repressor (LacI) and one multi-operator DNA molecule in vivo and in vitro. The existence of DNA wrapping in LacI-DNA interactions motivates the proposal that most if not all DNA binding proteins may have evolved the capability to wrap and thereby organize flanking regions of DNA.     

Effect of chain topology on the self-organization and dynamics of block copolypeptides: from diblock copolymers to stars

The effect of chain topology on (i) the peptide secondary structure, (ii) the nanophase self-assembly, and (iii) the local segmental and global peptide relaxations has been studied in a series of model diblock and 3-arm star copolypeptides of poly(epsilon-carbobenzyloxy-L-lysine) (PZLL) and poly(gamma-benzyl-L-glutamate) (PBLG) with PZLL forming the core. Diblock copolypeptides are nanophase separated with PBLG and PZLL domains comprising alpha-helices packed in a hexagonal lattice. Star copolypeptides are only weakly phase separated, comprising PBLG and PZLL alpha-helices in a pseudohexagonal lattice. Phase mixing has profound consequences on the local and global dynamics. The relaxation of the peptide secondary structure speeds up, and the helix persistence length is further reduced in the stars, signifying an increased concentration of helical defects.     

Topological Constraints and Their Conformational Entropic Penalties on RNA Folds

Functional RNAs can fold into intricate structures using a number of different secondary and tertiary structural motifs. Many factors contribute to the overall free energy of the target fold. This study aims at quantifying the entropic costs coming from the loss of conformational freedom when the sugar-phosphate backbone is subjected to constraints imposed by secondary and tertiary contacts. Motivated by insights from topology theory, we design a diagrammatic scheme to represent different types of RNA structures so that constraints associated with a folded structure may be segregated into mutually independent subsets, enabling the total conformational entropy loss to be easily calculated as a sum of independent terms. We used high-throughput Monte Carlo simulations to simulate large ensembles of single-stranded RNA sequences in solution to validate the assumptions behind our diagrammatic scheme, examining the entropic costs for hairpin initiation and formation of many multiway junctions. Our diagrammatic scheme aids in the factorization of secondary/tertiary constraints into distinct topological classes and facilitates the discovery of interrelationships among multiple constraints on RNA folds. This perspective, which to our knowledge is novel, leads to useful insights into the inner workings of some functional RNA sequences, demonstrating how they might operate by transforming their structures among different topological classes.     

Role of the apical stem in maintaining the structure and function of adenovirus virus-associated RNA.

Adenovirus virus-associated (VA) RNAI maintains efficient protein synthesis during the late phase of infection by preventing the activation of the double-stranded-RNA-dependent protein kinase, DAI. A secondary structure model for VA RNAI predicts the existence of two stems joined by a complex stem-loop structure, the central domain. The structural consequences of mutations and compensating mutations introduced into the apical stem lend support to this model. In transient expression assays for VA RNA function, foreign sequences inserted into the apical stem were fully tolerated provided that the stem remained intact. Mutants in which the base of the apical stem was disrupted retained partial activity, but truncation of the apical stem abolished the ability of the RNA to block DAI activation in vitro, suggesting that the length and position of the stem are both important for VA RNA function. These results imply that VA RNAI activity depends on secondary structure at the top of the apical stem as well as in the central domain and are consistent with a two-step mechanism involving DAI interactions with both the apical stem and the central domain.     

Sequence and secondary structure of the central domain ofDrosophila 26S rRNA: A universal model for the central domain of the large rRNA containing the region in which the central break may happen

Summary An 890-bp sequence from the central region ofDrosophila melanogaster 26S ribosomal DNA (rDNA) has been determined and used in an extensive comparative analysis of the central domain of the large subunit ribosomal RNA (lrRNA) from prokaryotes, organelles, and eukaryotes. An alignment of these different sequences has allowed us to precisely map the regions of the central domain that have highly diverged during evolution. Using this sequence comparison, we have derived a secondary structure model of the central domain ofDrosophila 26S ribosomal RNA (rRNA). We show that a large part of this model can be applied to the central domain of lrRNA from prokaryotes, eukaryotes, and organelles, therefore defining a universal common structural core. Likewise, a comparative study of the secondary structure of the divergent regions has been performed in several organisms. The results show that, despite a nearly complete divergence in their length and sequence, a common structural core is also present in divergent regions. In some organisms, one or two of the divergent regions of the central domain are removed by processing events. The sequence and structure of these regions (fragmentation spacers) have been compared to those of the corresponding divergent regions that remain part of the mature rRNA in other species.     

RnaPredict—An Evolutionary Algorithm for RNA Secondary Structure Prediction

This paper presents two in-depth studies on RnaPredict, an evolutionary algorithm for RNA secondary structure prediction. The first study is an analysis of the performance of two thermodynamic models, Individual Nearest Neighbor (INN) and Individual Nearest Neighbor Hydrogen Bond (INN-HB). The correlation between the free energy of predicted structures and the sensitivity is analyzed for 19 RNA sequences. Although some variance is shown, there is a clear trend between a lower free energy and an increase in true positive base pairs. With increasing sequence length, this correlation generally decreases. In the second experiment, the accuracy of the predicted structures for these 19 sequences are compared against the accuracy of the structures generated by the mfold dynamic programming algorithm (DPA) and also to known structures. RnaPredict is shown to outperform the minimum free energy structures produced by mfold and has comparable performance when compared to suboptimal structures produced by mfold.     

Empirical calculation of the relative free energies of peptide binding to the molecular chaperone DnaK

We describe a methodology to calculate the relative free energies of protein-peptide complex formation. The interaction energy was decomposed into nonpolar, electrostatic and entropic contributions. A free energy-surface area relationship served to calculate the nonpolar free energy term. The electrostatic free energy was calculated with the finite difference Poisson-Boltzmann method and the entropic contribution was estimated from the loss in the conformational entropy of the peptide side chains. We applied this methodology to a series of DnaK*peptide complexes. On the basis of the single known crystal structure of the peptide-binding domain of DnaK with a bound heptapeptide, we modeled ten other DnaK*heptapeptide complexes with experimentally measured K(d) values from 0.06 microM to 11 microM, using molecular dynamics to refine the structures of the complexes. Molecular dynamic trajectories, after equilibration, were used for calculating the energies with greater accuracy. The calculated relative binding free energies were compared with the experimentally determined free energies. Linear scaling of the calculated terms was applied to fit them to the experimental values. The calculated binding free energies were between -7.1 kcal/mol and - 9.4 kcal/mol with a correlation coefficient of 0.86. The calculated nonpolar contributions are mainly due to the central hydrophobic binding pocket of DnaK for three amino acid residues. Negative electrostatic fields generated by the protein increase the binding affinity for basic residues flanking the hydrophobic core of the peptide ligand. Analysis of the individual energy contributions indicated that the nonpolar contributions are predominant compared to the other energy terms even for peptides with low affinity and that inclusion of the change in conformational entropy of the peptide side chains does not improve the discriminative power of the calculation. The method seems to be useful for predicting relative binding energies of peptide ligands of DnaK and might be applicable to other protein-peptide systems, particularly if only the structure of one protein-ligand complex is available.     

Efficient algorithms for folding and comparing nucleic acid sequences.

Fast algorithms for analysing sequence data are presented. An algorithm for strict homologies finds all common subsequences of length greater than or equal to 6 in two given sequences. With it, nucleic acid pieces five thousand nucleotides long can be compared in five seconds on CDC 6600. Secondary structure algorithms generate the N most stable secondary structures of an RNA molecule, taking into account all loop contributions, and the formation of all possible base-pairs in stems, including odd pairs (G.G., C.U., etc.). They allow a typical 100-nucleotide sequence to be analysed in 10 seconds. The homology and secondary structure programs are respectively illustrated with a comparison of two phage genomes, and a discussion of Drosophila melanogaster 55 RNA folding.     

Folding is not required for bilayer insertion: replica exchange simulations of an alpha-helical peptide with an explicit lipid bilayer

We implement the replica exchange molecular dynamics algorithm to study the interactions of a model peptide (WALP-16) with an explicitly represented DPPC membrane bilayer. We observe the spontaneous, unbiased insertion of WALP-16 into the DPPC bilayer and its folding into an alpha-helix with a transbilayer orientation. The free energy surface suggests that the insertion of the peptide into the DPPC bilayer precedes secondary structure formation. Although the peptide has some propensity to form a partially helical structure in the interfacial region of the DPPC/water system, this state is not a productive intermediate but rather an off-pathway trap for WALP-16 insertion. Equilibrium simulations show that the observed insertion/folding pathway mirrors the potential of mean force (PMF). Calculation of the enthalpic and entropic contributions to this PMF show that the surface bound conformation of WALP-16 is significantly lower in energy than other conformations, and that the insertion of WALP-16 into the bilayer without regular secondary structure is enthalpically unfavorable by 5-10 kcal/mol/residue. The observed insertion/folding pathway disagrees with the dominant conceptual model, which is that a surface-bound helix is an obligatory intermediate for the insertion of alpha-helical peptides into lipid bilayers. In our simulations, the observed insertion/folding pathway is favored because of a large (>100 kcal/mol) increase in system entropy that occurs when the unstructured WALP-16 peptide enters the lipid bilayer interior. The insertion/folding pathway that is lowest in free energy depends sensitively on the near cancellation of large enthalpic and entropic terms. This suggests the possibility that intrinsic membrane peptides may have a diversity of insertion/folding behaviors depending on the exact system of peptide and lipid under consideration.