CCBuilder:An interactive web-based tool for building, designing and assessing coiled-coil protein assemblies

Motivation: The ability to accurately model protein structures at the atomistic level underpins efforts to understand protein folding, to engineer natural proteins predictably and to design proteins de novo . Homology-based methods are well established and produce impressive results. However, these are limited to structures presented by and resolved for natural proteins. Addressing this problem more widely and deriving truly ab initio models requires mathematical descriptions for protein folds; the means to decorate these with natural, engineered or de novo sequences; and methods to score the resulting models. Results: We present CCBuilder, a web-based application that tackles the problem for a defined but large class of protein structure, the α-helical coiled coils. CCBuilder generates coiled-coil backbones, builds side chains onto these frameworks and provides a range of metrics to measure the quality of the models. Its straightforward graphical user interface provides broad functionality that allows users to build and assess models, in which helix geometry, coiled-coil architecture and topology and protein sequence can be varied rapidly. We demonstrate the utility of CCBuilder by assembling models for 653 coiled-coil structures from the PDB, which cover >96% of the known coiled-coil types, and by generating models for rarer and de novo coiled-coil structures. Availability and implementation: CCBuilder is freely available, without registration, at http://coiledcoils.chm.bris.ac.uk/app/cc_builder

Interpretation of heart rate variability via detrended fluctuation analysis and alpha-beta filter

Detrended fluctuation analysis (DFA), suitable for the analysis of nonstationary time series, has confirmed the existence of persistent long-range correlations in healthy heart rate variability data. In this paper, we present the incorporation of the alpha-beta filter to DFA to determine patterns in the power-law behaviour that can be found in these correlations. Well-known simulated scenarios and real data involving normal and pathological circumstances were used to evaluate this process. The results presented here suggest the existence of evolving patterns, not always following a uniform power-law behaviour, that cannot be described by scaling exponents estimated using a linear procedure over two predefined ranges. Instead, the power law is observed to have a continuous variation with segment length. We also show that the study of these patterns, avoiding initial assumptions about the nature of the data, may confer advantages to DFA by revealing more clearly abnormal physiological conditions detected in congestive heart failure patients related to the existence of dominant characteristic scales.Comment: 18 pages, 14 figure

Ag on Ge(111): 2D X-ray structure analysis of the (Wurzel)3 x (Wurzel)3 superstructure

We have studied the Ag/Ge(111)(Wurzel)3 x (Wurzel)3 superstructure by grazing-incidence X-ray diffraction. In our structural analysis we find striking similarities to the geometry of Au on Si(111). The Ag atoms form trimer clusters with an Ag-Ag distance of 2.94+-0.04°A with the centers of the trimers being located at the origins of the (Wurzel)3 x (Wurzel)3 lattice. The Ag layer is incomplete and at least one substrate layer is distorted

Navigating the structural landscape of de Novo α-helical bundles

The association of amphipathic α helices in water leads to α-helical-bundle protein structures. However, the driving force for thisthe hydrophobic effectis not specific and does not define the number or the orientation of helices in the associated state. Rather, this is achieved through deeper sequence-to-structure relationships, which are increasingly being discerned. For example, for one structurally extreme but nevertheless ubiquitous class of bundlethe α-helical coiled coilsrelationships have been established that discriminate between all-parallel dimers, trimers, and tetramers. Association states above this are known, as are antiparallel and mixed arrangements of the helices. However, these alternative states are less well understood. Here, we describe a synthetic-peptide system that switches between parallel hexamers and various up–down–up–down tetramers in response to single-amino-acid changes and solution conditions. The main accessible states of each peptide variant are characterized fully in solution and, in most cases, to high resolution with X-ray crystal structures. Analysis and inspection of these structures helps rationalize the different states formed. This navigation of the structural landscape of α-helical coiled coils above the dimers and trimers that dominate in nature has allowed us to design rationally a well-defined and hyperstable antiparallel coiled-coil tetramer (apCC-Tet). This robust de novo protein provides another scaffold for further structural and functional designs in protein engineering and synthetic biology

Spectral Simplicity of Apparent Complexity, Part I: The Nondiagonalizable Metadynamics of Prediction

Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type of question---correlation, predictability, predictive cost, observer synchronization, and the like---induces a distinct generator class. Answers are then functions of the class-appropriate transition dynamic. Unfortunately, these dynamics are generically nonnormal, nondiagonalizable, singular, and so on. Tractably analyzing these dynamics relies on adapting the recently introduced meromorphic functional calculus, which specifies the spectral decomposition of functions of nondiagonalizable linear operators, even when the function poles and zeros coincide with the operator's spectrum. Along the way, we establish special properties of the projection operators that demonstrate how they capture the organization of subprocesses within a complex system. Circumventing the spurious infinities of alternative calculi, this leads in the sequel, Part II, to the first closed-form expressions for complexity measures, couched either in terms of the Drazin inverse (negative-one power of a singular operator) or the eigenvalues and projection operators of the appropriate transition dynamic.Comment: 24 pages, 3 figures, 4 tables; current version always at http://csc.ucdavis.edu/~cmg/compmech/pubs/sdscpt1.ht

Attractiveness of periodic orbits in parametrically forced systemswith time-increasing friction

We consider dissipative one-dimensional systems subject to a periodic force and study numerically how a time-varying friction affects the dynamics. As a model system, particularly suited for numerical analysis, we investigate the driven cubic oscillator in the presence of friction. We find that, if the damping coefficient increases in time up to a final constant value, then the basins of attraction of the leading resonances are larger than they would have been if the coefficient had been fixed at that value since the beginning. From a quantitative point of view, the scenario depends both on the final value and the growth rate of the damping coefficient. The relevance of the results for the spin-orbit model are discussed in some detail.Comment: 30 pages, 6 figure

Structural resolution of switchable states of a de novo peptide assembly

De novo protein design is advancing rapidly. However, most designs are for single states. Here we report a de novo designed peptide that forms multiple α-helical-bundle states that are accessible and interconvertible under the same conditions. Usually in such designs amphipathic α helices associate to form compact structures with consolidated hydrophobic cores. However, recent rational and computational designs have delivered open α-helical barrels with functionalisable cavities. By placing glycine judiciously in the helical interfaces of an α-helical barrel, we obtain both open and compact states in a single protein crystal. Molecular dynamics simulations indicate a free-energy landscape with multiple and interconverting states. Together, these findings suggest a frustrated system in which steric interactions that maintain the open barrel and the hydrophobic effect that drives complete collapse are traded-off. Indeed, addition of a hydrophobic co-solvent that can bind within the barrel affects the switch between the states both in silico and experimentally