Ribbon Model Research Articles

Protein folding invariants

This article discusses the topological invariants associated with an augmented ribbon model of single domain protein. The model is a triple (S, G, J) in S3 where S is a 2-manifold with boundary, G is a circle-with-chords, and J is an arc. The surfaces satisfy an embedding condition called laundry. The invariants are necessary and sufficient conditions for two triples to be equivalent by ambient isotopy. The model describes the native state, the unfolded state, and a unique folding pathway as a single mathematical entity. This may help illuminate some of the remarkable properties of protein. Twist transitions are introduced that allow the surface to pass through itself. A new arithmetic involving the complex numbers is used to represent variable linking numbers.

Video Condensation by Ribbon Carving

Efficient browsing of long video sequences is a key tool in visual surveillance, e.g., for postevent video forensics, but can also be used for fast review of motion pictures and home videos. While frame skipping (fixed or adaptive) is straightforward to implement, its performance is quite limited. Although more efficient techniques have been developed, such as video summarization and video montage, they lose either the temporal or semantic context of events. A recently proposed method called video synopsis deals with some of these issues but involves multiple processing stages and is fairly complex. Video condensation, that we propose here, is novel in the way information is removed from the space-time video volume, is conceptually simple and relatively easy to implement. We introduce the concept of a video ribbon inspired by that of a seam recently proposed for image resizing. We recursively carve ribbons out by minimizing an activity-aware cost function using dynamic programming. The ribbon model we develop is flexible and permits an easy adjustment of the compromise between temporal condensation ratio and anachronism of events. We also propose sliding-window ribbon carving to handle streaming video and demonstrate the method's efficiency on motor and pedestrian traffic data.

3D architecture of DNA Pol α reveals the functional core of multi-subunit replicative polymerases

Eukaryotic DNA replication requires the coordinated activity of the multi-subunit DNA polymerases: Pol α, Pol δ and Pol ɛ. The conserved catalytic and regulatory B subunits associate in a constitutive heterodimer that represents the functional core of all three replicative polymerases. Here, we combine X-ray crystallography and electron microscopy (EM) to describe subunit interaction and 3D architecture of heterodimeric yeast Pol α. The crystal structure of the C-terminal domain (CTD) of the catalytic subunit bound to the B subunit illustrates a conserved mechanism of accessory factor recruitment by replicative polymerases. The EM reconstructions of Pol α reveal a bilobal shape with separate catalytic and regulatory modules. Docking of the B–CTD complex in the EM reconstruction shows that the B subunit is tethered to the polymerase domain through a structured but flexible linker. Our combined findings provide a structural template for the common functional architecture of the three major replicative DNA polymerases.

Signaling at the membrane interface by the DGK/SK enzyme family

The sphingosine (SK) and diacylglycerol (DGK) kinases have become the subject of considerable focus recently due to their involvement as signaling enzymes in a variety of important biological processes. These lipid signaling kinases are closely related by sequence as well as functional properties. These enzymes are soluble, yet their substrates are hydrophobic. Therefore, they must act at the membrane interface. Second, for both of these enzyme families, their substrates (diacylglycerol for DGKs, sphingosine for SKs) as well as their products (phosphatidic acid for DGK, sphingosine-1-phosphate for SK) have signaling function. To understand how the signaling processes emanating from these kinases are regulated it is critical to understand the fundamental mechanisms that control their enzymatic activity. This is particularly true for the rational design of small molecules that would be useful as therapeutic compounds. Here we summarize enzymological properties of the diacylglycerol and SKs. Further, because the three-dimensional structure of the eukaryotic members of this family has yet to be determined, we discuss what can be gleaned from the recently reported structures of related prokaryotic members of this enzyme family.

Redox-switch modulation of human SSADH by dynamic catalytic loop

Succinic semialdehyde dehydrogenase (SSADH) is involved in the final degradation step of the inhibitory neurotransmitter gamma-aminobutyric acid by converting succinic semialdehyde to succinic acid in the mitochondrial matrix. SSADH deficiency, a rare autosomal recessive disease, exhibits variable clinical phenotypes, including psychomotor retardation, language delay, behaviour disturbance and convulsions. Here, we present crystal structures of both the oxidized and reduced forms of human SSADH. Interestingly, the structures show that the catalytic loop of the enzyme undergoes large structural changes depending on the redox status of the environment, which is mediated by a reversible disulphide bond formation between a catalytic Cys340 and an adjacent Cys342 residues located on the loop. Subsequent in vivo and in vitro studies reveal that the 'dynamic catalytic loop' confers a response to reactive oxygen species and changes in redox status, indicating that the redox-switch modulation could be a physiological control mechanism of human SSADH. Structural basis for the substrate specificity of the enzyme and the impact of known missense point mutations associated with the disease pathogenesis are presented as well.

ProteinVista: A Fast Molecular Visualization System Using Microsoft Direct3D

Many tools have been developed to visualize protein and molecular structures. Most high quality protein visualization tools use the OpenGL graphics library as a 3D graphics system. Currently, the performance of recent 3D graphics hardware has rapidly improved. Recent high-performance 3D graphics hardware support Microsoft Direct3D graphics library more than OpenGL and have become very popular in personal computers (PCs). In this paper, a molecular visualization system termed ProteinVista is proposed. ProteinVista is well-designed visualization system using the Microsoft Direct3D graphics library. It provides various visualization styles such as the wireframe, stick, ball and stick, space fill, ribbon, and surface model styles, in addition to display options for 3D visualization. As ProteinVista is optimized for recent 3D graphics hardware platforms and because it uses a geometry instancing technique, its rendering speed is 2.7 times faster compared to other visualization tools.

Why Do Hair Cells Have Ribbons? Focus on “Synaptic Ribbon Enables Temporal Precision of Hair Cell Afferent Synapse by Increasing the Number of Readily Releasable Vesicles: A Modeling Study”

Hair cells, like retinal photoreceptors and bipolar cells, encode stimuli with graded changes in membrane potential and transmit that signal through ribbon synapses to drive action potentials in associated afferent neurons ([Sterling and Matthews 2005][1]). Thus one would expect transmitter release

Structure of the Claudin-binding Domain of Clostridium perfringens Enterotoxin

Clostridium perfringens enterotoxin is a common cause of food-borne and antibiotic-associated diarrhea. The toxin's receptors on intestinal epithelial cells include claudin-3 and -4, members of a large family of tight junction proteins. Toxin-induced cytolytic pore formation requires residues in the NH(2)-terminal half, whereas residues near the COOH terminus are required for binding to claudins. The claudin-binding COOH-terminal domain is not toxic and is currently under investigation as a potential drug absorption enhancer. Because claudin-4 is overexpressed on some human cancers, the toxin is also being investigated for targeting chemotherapy. Our aim was to solve the structure of the claudin-binding domain to advance its therapeutic applications. The structure of a 14-kDa fragment containing residues 194 to the native COOH terminus at position 319 was solved by x-ray diffraction to a resolution of 1.75A. The structure is a nine-strand beta sandwich with previously unappreciated similarity to the receptor-binding domains of several other toxins of spore-forming bacteria, including the collagen-binding domain of ColG from Clostridium histolyticum and the large Cry family of toxins (including Cry4Ba) of Bacillus thuringiensis. Correlations with previous studies suggest that the claudin-4 binding site is on a large surface loop between strands beta8 and beta9 or includes these strands. The sequence that was crystallized (residues 194-319) binds to purified human claudin-4 with a 1:1 stoichiometry and affinity in the submicromolar range similar to that observed for binding of native toxin to cells. Our results provide a structural framework to advance therapeutic applications of the toxin and suggest a common ancestor for several receptor-binding domains of bacterial toxins.

Fluctuating semiflexible polymer ribbon constrained to a ring

Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling in addition to twist-bend coupling. Furthermore, due to the geometric constraint the polymer's effective bending stiffness increases. A new parameter for experimental investigations of polymer bundles is proposed: the mean square diameter of a ribbonlike ring, which is determined analytically in the semiflexible limit. Monte Carlo simulations are performed which affirm the model's prediction up to high flexibility.

Novel mutations of the lipoprotein lipase gene associated with hypertriglyceridemia in members of type 2 diabetic pedigrees

Increased plasma triglyceride and free fatty acid levels are frequently associated with type 2 diabetes mellitus (T2DM). To test the hypothesis that LPL gene mutations contribute to the hypertriglyceridemia observed in members of T2DM pedigrees, we screened the LPL gene in 53 hypertriglyceridemic members of 26 families. Four known and three novel mutations were identified. All three novel mutations, Lys312insC, Thr361insA, and double mutation Lys312insC + Asn291Ser, are clinically associated with hypertriglyceridemia. In vitro mutagenesis and expression studies confirm that these variants are associated with a significant reduction in LPL activity. The modeled structures displaying the Lys312insC and Thr361insA mutations showed loss of the activity-related C-terminal domain in the LPL protein. Another novel double mutation, Lys312insC + Asn291Ser, resulted in the loss of the catalytic ability of LPL attributable to the complete loss of the C-terminal domain and alteration in the heparin association site. Thus, these novel mutations of the LPL gene contribute to the hypertriglyceridemia observed in members of type 2 diabetic pedigrees.

A Novel Roll-and-Slide Mechanism of DNA Folding in Chromatin: Implications for Nucleosome Positioning

How eukaryotic genomes encode the folding of DNA into nucleosomes and how this intrinsic organization of chromatin guides biological function are questions of wide interest. The physical basis of nucleosome positioning lies in the sequence-dependent propensity of DNA to adopt the tightly bent configuration imposed by the binding of the histone proteins. Traditionally, only DNA bending and twisting deformations are considered, while the effects of the lateral displacements of adjacent base pairs are neglected. We demonstrate, however, that these displacements have a much more important structural role than ever imagined. Specifically, the lateral Slide deformations observed at sites of local anisotropic bending of DNA define its superhelical trajectory in chromatin. Furthermore, the computed cost of deforming DNA on the nucleosome is sequence-specific: in optimally positioned sequences the most easily deformed base-pair steps (CA:TG and TA) occur at sites of large positive Slide and negative Roll (where the DNA bends into the minor groove). These conclusions rest upon a treatment of DNA that goes beyond the conventional ribbon model, incorporating all essential degrees of freedom of “real” duplexes in the estimation of DNA deformation energies. Indeed, only after lateral Slide displacements are considered are we able to account for the sequence-specific folding of DNA found in nucleosome structures. The close correspondence between the predicted and observed nucleosome locations demonstrates the potential advantage of our “structural” approach in the computer mapping of nucleosome positioning.

Atomistic Simulation Approach to a Continuum Description of Self-Assembled β-Sheet Filaments

We investigated the supramolecular structure and continuum mechanical properties of a β-sheet nanofiber comprised of a self-assembling peptide ac-[RARADADA] 2-am using computer simulations. The supramolecular structure was determined by constructing candidate filaments with dimensions compatible with those observed in atomic force microscopy and selecting the most stable ones after running molecular dynamics simulations on each of them. Four structures with different backbone hydrogen-bonding patterns were identified to be similarly stable. We then quantified the continuum mechanical properties of these identified structures by running three independent simulations: thermal motion analysis, normal mode analysis, and steered molecular dynamics. Within the range of deformations investigated, the filament showed linear elasticity in transverse directions with an estimated persistence length of 1.2–4.8 μm. Although side-chain interactions govern the propensity and energetics of filament self-assembly, we found that backbone hydrogen-bonding interactions are the primary determinant of filament elasticity, as demonstrated by its effective thickness, which is smaller than that estimated by atomic force microscopy or from the molecular geometry, as well as by the similar bending stiffness of a model filament without charged side chains. The generality of our approach suggests that it should be applicable to developing continuum elastic ribbon models of other β-sheet filaments and amyloid fibrils.

Nonequilibrium Ribbon Model of Twisted Scroll Waves

We formulate a reduced model to analyze the motion of the core of a twisted scroll wave. The model is first shown to provide a simple description of the onset and nonlinear evolution of the helical state appearing in the sproing bifurcation of scroll waves. It then serves to examine the experimentally studied case of a medium with spatially varying excitability. The model shows the role of sproing in this more complex setting and highlights the differences between the convective and absolute sproing instabilities.

Scanning tunneling microscopy and spectroscopy of the electronic local density of states of graphite surfaces near monoatomic step edges

We measured the electronic local density of states (LDOS) of graphite surfaces near monoatomic step edges, which consist of either the zigzag or armchair edge, with the scanning tunneling microscopy (STM) and spectroscopy (STS) techniques. The STM data reveal that the $(\sqrt{3} \times \sqrt{3}) R 30^{\circ}$ and honeycomb superstructures coexist over a length scale of 3-4 nm from both the edges. By comparing with density-functional derived nonorthogonal tight-binding calculations, we show that the coexistence is due to a slight admixing of the two types of edges at the graphite surfaces. In the STS measurements, a clear peak in the LDOS at negative bias voltages from -100 to -20 mV was observed near the zigzag edges, while such a peak was not observed near the armchair edges. We concluded that this peak corresponds to the graphite "edge state" theoretically predicted by Fujita \textit{et al.} [J. Phys. Soc. Jpn. {\bf 65}, 1920 (1996)] with a tight-binding model for graphene ribbons. The existence of the edge state only at the zigzag type edge was also confirmed by our first-principles calculations with different edge terminations.

A New Model for Ribbons in ℝ3

Let's start with a hands-on demonstration. We take a long, rectangular strip of ad hesive tape (or postage stamps) and wind it diagonally around a cylinder in such a way that the sticky surface of the tape is entirely in contact with the cylinder. It fol lows that the two long edges of the tape must lie along parallel helices. This is true by definition? if we start with a line in a plane and then wrap the plane around a cylinder we get a helix. What about the short edges of the tape? Well, by the same definition, they must lie along parallel helices that are orthogonal to the first two! We call the resulting, familiar object a helical band (FIGURE 1). It plays a central role in this discussion.

A New Model for Ribbons in R³

A New Model for Ribbons in R³

Nontoxic crystal protein from Bacillus thuringiensis demonstrates a remarkable structural similarity to β‐pore‐forming toxins

Nontoxic crystal protein from <i>Bacillus thuringiensis</i> demonstrates a remarkable structural similarity to β‐pore‐forming toxins

Near-edge electronic structure in NbS2

The near-edge electronic and structural properties of 2H-NbS(2) were investigated using scanning tunneling microscopy (STM) and density-functional calculations. Geometry optimization of the near-edge structure using density-functional calculations was performed on [1010]- and [1010]-terminated layer edges. Ribbon model systems also included variation of the number of bound sulfur atoms at the edges. Atomic resolution STM data exhibit a pronounced electronic density of states at the outermost edge atomic sites but are otherwise bulk-like in the near-edge region. Optimized NbS2 ribbon structures confirm the STM results indicating that minimal reconstruction occurs and that the edge electronic structure exhibits a significant increase in local density of states compared to bulk. Simulated STM images using extended Hückel tight-binding calculations based on optimized ribbon structures successfully modeled the experimental STM results. The results indicate that the [1010] "Nb" edges are preferentially observed compared to the [1010] "S" edge possibly due to differences in stability.

The regulation of mDia1 by autoinhibition and its release by Rho•GTP

Formins induce the nucleation and polymerisation of unbranched actin filaments via the formin-homology domains 1 and 2. Diaphanous-related formins (Drfs) are regulated by a RhoGTPase-binding domain situated in the amino-terminal (N-terminal) region and a carboxy-terminal Diaphanous-autoregulatory domain (DAD), whose interaction stabilises an autoinhibited inactive conformation. Binding of active Rho releases DAD and activates the catalytic activity of mDia. Here, we report on the interaction of DAD with the regulatory N-terminus of mDia1 (mDia(N)) and its release by Rho*GTP. We have defined the elements required for tight binding and solved the three-dimensional structure of a complex between an mDia(N) construct and DAD by X-ray crystallography. The core DAD region is an alpha-helical peptide, which binds in the most highly conserved region of mDia(N) using mainly hydrophobic interactions. The structure suggests a two-step mechanism for release of autoinhibition whereby Rho*GTP, although having a partially nonoverlapping binding site, displaces DAD by ionic repulsion and steric clashes. We show that Rho*GTP accelerates the dissociation of DAD from the mDia(N)*DAD complex.

BALLView: An object-oriented molecular visualization and modeling framework

We present BALLView, an extensible tool for visualizing and modeling bio-molecular structures. It provides a variety of different models for bio-molecular visualization, e.g. ball-and-stick models, molecular surfaces, or ribbon models. In contrast to most existing visualization tools, BALLView also offers rich functionality for molecular modeling and simulation, including molecular mechanics methods (AMBER and CHARMM force fields), continuum electrostatics methods employing a Finite-Difference Poisson Boltzmann solver, and secondary structure calculation. Results of these computations can be exported as publication quality images or as movies. Even unexperienced users have direct access to this functionality through an intuitive graphical user interface, which makes BALLView particularly useful for teaching. For more advanced users, BALLView is extensible in different ways. Owing to its framework design, extension on the level of C per thousand+ per thousand per thousand+ code is very convenient. In addition, an interface to the scripting language Python allows the interactive rapid prototyping of new methods. BALLView is portable and runs on all major platforms (Windows, MacOS X, Linux, most Unix flavors). It is available free of charge under the GNU Public License (GPL) from our website http://www.ballview.org.