Determining the Energetics of Small ß-Sheet Peptides using Adaptive Steered Molecular Dynamics.

Mechanically driven unfolding is a useful computational tool for extracting the energetics and stretching pathway of peptides. In this work, two representative ß-hairpin peptides, chignolin (PDB: 1UAO ) and trpzip1 (PDB: 1LE0 ), were investigated using an adaptive variant of the original steered molecular dynamics method called adaptive steered molecular dynamics (ASMD). The ASMD method makes it possible to perform energetic calculations on increasingly complex biological systems. Although the two peptides are similar in length and have similar secondary structures, their unfolding energetics are quite different. The hydrogen bonding profile and specific residue pair interaction energies provide insight into the differing stabilities of these peptides and reveal which of the pairs provides the most significant stabilization.

Constrained Unfolding of a Helical Peptide: Implicit versus Explicit Solvents.

Steered Molecular Dynamics (SMD) has been seen to provide the potential of mean force (PMF) along a peptide unfolding pathway effectively but at significant computational cost, particularly in all-atom solvents. Adaptive steered molecular dynamics (ASMD) has been seen to provide a significant computational advantage by limiting the spread of the trajectories in a staged approach. The contraction of the trajectories at the end of each stage can be performed by taking a structure whose nonequilibrium work is closest to the Jarzynski average (in naive ASMD) or by relaxing the trajectories under a no-work condition (in full-relaxation ASMD--namely, FR-ASMD). Both approaches have been used to determine the energetics and hydrogen-bonding structure along the pathway for unfolding of a benchmark peptide initially constrained as an α-helix in a water environment. The energetics are quite different to those in vacuum, but are found to be similar between implicit and explicit solvents. Surprisingly, the hydrogen-bonding pathways are also similar in the implicit and explicit solvents despite the fact that the solvent contact plays an important role in opening the helix.

RiboVision suite for visualization and analysis of ribosomes.

RiboVision is a visualization and analysis tool for the simultaneous display of multiple layers of diverse information on primary (1D), secondary (2D), and three-dimensional (3D) structures of ribosomes. The ribosome is a macromolecular complex containing ribosomal RNA and ribosomal proteins and is a key component of life responsible for the synthesis of proteins in all living organisms. RiboVision is intended for rapid retrieval, analysis, filtering, and display of a variety of ribosomal data. Preloaded information includes 1D, 2D, and 3D structures augmented by base-pairing, base-stacking, and other molecular interactions. RiboVision is preloaded with rRNA secondary structures, rRNA domains and helical structures, phylogeny, crystallographic thermal factors, etc. RiboVision contains structures of ribosomal proteins and a database of their molecular interactions with rRNA. RiboVision contains preloaded structures and data for two bacterial ribosomes (Thermus thermophilus and Escherichia coli), one archaeal ribosome (Haloarcula marismortui), and three eukaryotic ribosomes (Saccharomyces cerevisiae, Drosophila melanogaster, and Homo sapiens). RiboVision revealed several major discrepancies between the 2D and 3D structures of the rRNAs of the small and large subunits (SSU and LSU). Revised structures mapped with a variety of data are available in RiboVision as well as in a public gallery (). RiboVision is designed to allow users to distill complex data quickly and to easily generate publication-quality images of data mapped onto secondary structures. Users can readily import and analyze their own data in the context of other work. This package allows users to import and map data from CSV files directly onto 1D, 2D, and 3D levels of structure. RiboVision has features in rough analogy with web-based map services capable of seamlessly switching the type of data displayed and the resolution or magnification of the display. RiboVision is available at .

Secondary structures of rRNAs from all three domains of life.

Accurate secondary structures are important for understanding ribosomes, which are extremely large and highly complex. Using 3D structures of ribosomes as input, we have revised and corrected traditional secondary (2°) structures of rRNAs. We identify helices by specific geometric and molecular interaction criteria, not by co-variation. The structural approach allows us to incorporate non-canonical base pairs on parity with Watson-Crick base pairs. The resulting rRNA 2° structures are up-to-date and consistent with three-dimensional structures, and are information-rich. These 2° structures are relatively simple to understand and are amenable to reproduction and modification by end-users. The 2° structures made available here broadly sample the phylogenetic tree and are mapped with a variety of data related to molecular interactions and geometry, phylogeny and evolution. We have generated 2° structures for both large subunit (LSU) 23S/28S and small subunit (SSU) 16S/18S rRNAs of Escherichia coli, Thermus thermophilus, Haloarcula marismortui (LSU rRNA only), Saccharomyces cerevisiae, Drosophila melanogaster, and Homo sapiens. We provide high-resolution editable versions of the 2° structures in several file formats. For the SSU rRNA, the 2° structures use an intuitive representation of the central pseudoknot where base triples are presented as pairs of base pairs. Both LSU and SSU secondary maps are available (http://apollo.chemistry.gatech.edu/RibosomeGallery). Mapping of data onto 2° structures was performed on the RiboVision server (http://apollo.chemistry.gatech.edu/RiboVision).

Secondary structure and domain architecture of the 23S and 5S rRNAs.

We present a de novo re-determination of the secondary (2°) structure and domain architecture of the 23S and 5S rRNAs, using 3D structures, determined by X-ray diffraction, as input. In the traditional 2° structure, the center of the 23S rRNA is an extended single strand, which in 3D is seen to be compact and double helical. Accurately assigning nucleotides to helices compels a revision of the 23S rRNA 2° structure. Unlike the traditional 2° structure, the revised 2° structure of the 23S rRNA shows architectural similarity with the 16S rRNA. The revised 2° structure also reveals a clear relationship with the 3D structure and is generalizable to rRNAs of other species from all three domains of life. The 2° structure revision required us to reconsider the domain architecture. We partitioned the 23S rRNA into domains through analysis of molecular interactions, calculations of 2D folding propensities and compactness. The best domain model for the 23S rRNA contains seven domains, not six as previously ascribed. Domain 0 forms the core of the 23S rRNA, to which the other six domains are rooted. Editable 2° structures mapped with various data are provided (http://apollo.chemistry.gatech.edu/RibosomeGallery).

Nonparametric clustering for studying RNA conformations.

The local conformation of RNA molecules is an important factor in determining their catalytic and binding properties. The analysis of such conformations is particularly difficult due to the large number of degrees of freedom, such as the measured torsion angles per residue and the interatomic distances among interacting residues. In this work, we use a nearest-neighbor search method based on the statistical mechanical Potts model to find clusters in the RNA conformational space. The proposed technique is mostly automatic and may be applied to problems, where there is no prior knowledge on the structure of the data space in contrast to many other clustering techniques. Results are reported for both single residue conformations, where the parameter set of the data space includes four to seven torsional angles, and base pair geometries, where the data space is reduced to two dimensions. Moreover, new results are reported for base stacking geometries. For the first two cases, i.e., single residue conformations and base pair geometries, we get a very good match between the results of the proposed clustering method and the known classifications with only few exceptions. For the case of base stacking geometries, we validate our classification with respect to geometrical constraints and describe the content, and the geometry of the new clusters.

Adsorption of poly(methyl methacrylate) on concave Al2O3 surfaces in nanoporous membranes.

The objective of this study was to determine the influence of polymer molecular weight and surface curvature on the adsorption of polymers onto concave surfaces. Poly(methyl methacrylate) (PMMA) of various molecular weights was adsorbed onto porous aluminum oxide membranes having various pore sizes, ranging from 32 to 220 nm. The surface coverage, expressed as repeat units per unit surface area, was observed to vary linearly with molecular weight for molecular weights below approximately 120,000 g/mol. The coverage was independent of molecular weight above this critical molar mass, as was previously reported for the adsorption of PMMA on convex surfaces. Furthermore, the coverage varied linearly with pore size. A theoretical model was developed to describe curvature-dependent adsorption by considering the density gradient that exists between the surface and the edge of the adsorption layer. According to this model, the density gradient of the adsorbed polymer segments scales inversely with particle size, while the total coverage scales linearly with particle size, in good agreement with experiment. These results show that the details of the adsorption of polymers onto concave surfaces with cylindrical geometries can be used to calculate molecular weight (below a critical molecular weight) if pore size is known. Conversely, pore size can also be determined with similar adsorption experiments. Most significantly, for polymers above a critical molecular weight, the precise molecular weight need not be known in order to determine pore size. Moreover, the adsorption developed and validated in this work can be used to predict coverage also onto surfaces with different geometries.

Scaling aspects of block co-polymer adsorption on curved surfaces from nonselective solvents.

In this paper, we have developed a geometric-based scaling model that describes the adsorption of diblock copolymer chains from good solvents and theta-solvents onto reactive surfaces of varying curvatures. To evaluate the impact of particle size on the adsorption process, we probed the adsorption of poly(styrene-b-methymethacrylate) (PS-PMMA) diblock copolymers from solvents with different degrees of selectivity on aluminum oxide (Al(2)O(3)) surfaces belonging to particles of different sizes. When the adsorbed PMMA layer is dense enough (in the case of a theta-solvent for the PMMA block), our results show good correlation between the theory and experimental results, pointing to the formation of a PMMA adsorption layer and a brushlike PS layer. Conversely, when adsorption occurs from a nonpreferential solvent, particularly on particles with high curvature, the PMMA adsorption layer at the surface becomes less dense and the grafted PS moiety exhibits a transitional morphology consisting of several layers of increasingly sparsely spaced blobs.

RNA backbone: consensus all-angle conformers and modular string nomenclature (an RNA Ontology Consortium contribution).

A consensus classification and nomenclature are defined for RNA backbone structure using all of the backbone torsion angles. By a consensus of several independent analysis methods, 46 discrete conformers are identified as suitably clustered in a quality-filtered, multidimensional dihedral angle distribution. Most of these conformers represent identifiable features or roles within RNA structures. The conformers are given two-character names that reflect the seven-angle delta epsilon zeta alpha beta gamma delta combinations empirically found favorable for the sugar-to-sugar "suite" unit within which the angle correlations are strongest (e.g., 1a for A-form, 5z for the start of S-motifs). Since the half-nucleotides are specified by a number for delta epsilon zeta and a lowercase letter for alpha beta gamma delta, this modular system can also be parsed to describe traditional nucleotide units (e.g., a1) or the dinucleotides (e.g., a1a1) that are especially useful at the level of crystallographic map fitting. This nomenclature can also be written as a string with two-character suite names between the uppercase letters of the base sequence (N1aG1gN1aR1aA1cN1a for a GNRA tetraloop), facilitating bioinformatic comparisons. Cluster means, standard deviations, coordinates, and examples are made available, as well as the Suitename software that assigns suite conformer names and conformer match quality (suiteness) from atomic coordinates. The RNA Ontology Consortium will combine this new backbone system with others that define base pairs, base-stacking, and hydrogen-bond relationships to provide a full description of RNA structural motifs.

Adsorption of Block Copolymers from Selective Solvents on Curved Surfaces.

We have investigated the adsorption of asymmetric poly(styrene-b-methyl methacrylate) block copolymers (PS-PMMA) from a selective solvent onto alumina (Al(2)O(3)) particles having variable and controllable radii. The solvent used was a bad solvent for the PS block (block A) and a good solvent for the PMMA block (block B), which has a higher affinity of the surface. Such a case represents a new class of adsorption, where both blocks compete for the adsorption sites of the metallic surface. Two theoretical models, the modified drops model and the perforated film model, have been evaluated as appropriate representation of such an adsorption scenario. The experimental results indicated that the adsorption of the PS-PMMA block copolymer generated a patterned surface comprised of a homogeneous melt layer of the PS block perforated with holes having a variable PMMA structure, depending on the distance from the bottom of the hole (alumina surface) and the distance from walls of the hole. The density gradient of the PMMA moiety in the hole reverted to the classical brush morphology at a critical distance from the surface of the hole.

Polymer Adsorption on Curved Surfaces: A Geometric Approach.

In this article, we have developed a simple model that describes the adsorption of polymer chains from a solution having a good solvent onto a reactive surface of varying curvatures. In order to evaluate the impact of particle size on the adsorption process, we have probed the adsorption of poly(methyl methacrylate) (PMMA) on aluminum oxide (Al2O3) surfaces belonging to particles of different sizes. The basic approach assumed that the details of the chemisorption mechanism of PMMA on aluminum oxide surfaces are independent of surface curvature. The combination of the experimental results with the theoretical approach that we have developed show the existence of three different regimes of adsorption of polymer chains onto the surfaces of metal nanoparticles.

Chemical reaction dynamics within anisotropic solvents in time-dependent fields.

The dynamics of low-dimensional Brownian particles coupled to time-dependent driven anisotropic heavy particles (mesogens) in a uniform bath (solvent) have been described through the use of a variant of the stochastic Langevin equation. The rotational motion of the mesogens is assumed to follow the motion of an external driving field in the linear response limit. Reaction dynamics have also been probed using a two-state model for the Brownian particles. Analytical expressions for diffusion and reaction rates have been developed and are found to be in good agreement with numerical calculations. When the external field driving the mesogens is held at constant rotational frequency, the model for reaction dynamics predicts that the applied field frequency can be used to control the product composition.