A superposition free method for protein conformational ensemble analyses and local clustering based on a differential geometry representation of backbone

Here a differential geometry (DG) representation of protein backbone is explored on the analyses of protein conformational ensembles. The protein backbone is described by curvature, κ, and torsion, τ, values per residue and we propose 1) a new dissimilarity and protein flexibility measurement and 2) a local conformational clustering method. The methods were applied to Ubiquitin and c-Myb-KIX protein conformational ensembles and results show that κ\τ metric space allows to properly judge protein flexibility by avoiding the superposition problem. The d_max measurement presents equally good or superior results when compared to RMSF, especially for the intrinsically unstructured protein. The clustering method is unique as it relates protein global to local dynamics by providing a global clustering solutions per residue. The methods proposed can be especially useful to the analyses of highly flexible proteins. The software written for the analyses presented here is available at https://github.com/AMarinhoSN/FleXgeo for academic usage only.     

The influence of habitat and adults on the spatial distribution of juvenile corals

Population distributions are affected by a variety of spatial processes, including dispersal, intraspecific dynamics and habitat selection. Within reef‐building coral communities, these processes are especially important during the earliest life stages when reproduction provides mobility among sessile organisms and populations experience the greatest mortality bottlenecks both before and immediately after settlement. Here, we used large‐area imaging to create photomosaics that allowed us to identify and map the location of 4681 juvenile (1–5 cm diameter) and 25 902 adult (>5 cm diameter) coral colonies from eight 100‐m² plots across the forereef of Palmyra Atoll. Using metrics of density, percent cover and the relative location of each colony within each plot, we examined abundance and spatial relationships between juvenile and adult coral taxa. Within coral taxa, juvenile density was generally positively related to the numerical density and percent cover of adults. Nearest neighbor analyses showed aggregation of juveniles near adults of the same taxon for two of the focal taxa (Pocillopora and Fungiids), while all other taxa showed random spatial patterning relative to adults. Three taxa had clustered distributions of juveniles overall. Additionally, we found that on a colony level, juveniles for five of nine focal taxa (accounting for >98% of all identified juveniles) associated with a specific habitat type, with four of those five taxa favoring unconsolidated (e.g. rubble) over consolidated substrata. The general lack of clustering in juvenile corals contrasts with consistent clustering patterns seen in adult corals, suggesting that adult spatial patterns are largely driven by processes occurring after maturity such as partial colony mortality, including fission and fragmentation. The association of many taxa with unconsolidated habitat also suggests that corals may play an important role in colonizing natural rubble patches that could contribute to reef stabilization over time.     

Classifying behavior from short‐interval biologging data: An example with GPS tracking of birds

1. Recent advances in digital data collection have spurred accumulation of immense quantities of data that have potential to lead to remarkable ecological insight, but that also present analytic challenges. In the case of biologging data from birds, common analytical approaches to classifying movement behaviors are largely inappropriate for these massive data sets.
2. We apply a framework for using K‐means clustering to classify bird behavior using points from short time interval GPS tracks. K‐means clustering is a well‐known and computationally efficient statistical tool that has been used in animal movement studies primarily for clustering segments of consecutive points. To illustrate the utility of our approach, we apply K‐means clustering to six focal variables derived from GPS data collected at 1–11 s intervals from free‐flying bald eagles (Haliaeetus leucocephalus) throughout the state of Iowa, USA. We illustrate how these data can be used to identify behaviors and life‐stage‐ and age‐related variation in behavior.
3. After filtering for data quality, the K‐means algorithm identified four clusters in >2 million GPS telemetry data points. These four clusters corresponded to three movement states: ascending, flapping, and gliding flight; and one non‐moving state: perching. Mapping these states illustrated how they corresponded tightly to expectations derived from natural history observations; for example, long periods of ascending flight were often followed by long gliding descents, birds alternated between flapping and gliding flight.
4. The K‐means clustering approach we applied is both an efficient and effective mechanism to classify and interpret short‐interval biologging data to understand movement behaviors. Furthermore, because it can apply to an abundance of very short, irregular, and high‐dimensional movement data, it provides insight into small‐scale variation in behavior that would not be possible with many other analytical approaches.

     

Isolation by distance and sharp discontinuities in gene frequencies: implications for the phylogeography of an alpine insect species, Carabus solieri

Analysis of genetic isolation by distance (IBD) is of prime importance for the study of processes responsible for spatial population genetic structure and is thus frequently used in case studies. However, the identification of a significant IBD pattern does not necessarily imply the absence of sharp discontinuities in gene frequencies. Therefore, identifying barriers to gene flow and/or secondary contact between differentiated entities remains a major challenge in population biology. Geographical genetic structure of 41 populations (1080 individuals) of an alpine insect species, Carabus solieri, was studied using 10 microsatellite loci. All populations were significantly differentiated and spatially structured according to IBD over the entire range. However, clustering analyses clearly identified three main clusters of populations, which correspond to geographical entities. Whereas IBD also occurs within each cluster, population structure was different according to which group of populations was considered. The southernmost cluster corresponds to the most fragmented part of the range. Consistently, it was characterized by relatively high levels of differentiation associated with low genetic diversity, and the slope of the regression of genetic differentiation against geographical distances was threefold those of the two other clusters. Comparisons of within-cluster and between-cluster IBD patterns revealed barriers to gene flow. A comparison of the two approaches, IBD and clustering analyses, provided us with valuable information with which to infer the phylogeography of the species, and in particular to propose postglacial colonization routes from two potential refugia located in Italy and in southeastern France. Our study highlights strongly the possible confounding contribution of barriers to gene flow to IBD pattern and emphasizes the utility of the model-based clustering analysis to identify such barriers.     

Protein fragment clustering and canonical local shapes

A novel clustering method is used to cluster protein fragments by shape. The centroids (mean fragments from each cluster) form a basis set of structural motifs. A database of 156,643 seven-residue fragments is used, and eight different basis sets with varying levels of resolution are generated. Coarse basis sets contain tens of centroids and provide meaningful local shapes, which are more detailed than the traditional secondary structure categories. High-resolution basis sets contain thousands of centroids and can be used to model tertiary structure of longer segments. The basis sets generated fit nontraining set proteins with the expected accuracy.     

Higher-order interhelical spatial interactions in membrane proteins

Higher-order interactions are important for protein folding and assembly. We introduce the concept of interhelical three-body interactions as derived from Delaunay triangulation and alpha shapes of protein structures. In addition to glycophorin A, where triplets are strongly correlated with protein stability, we found that tight interhelical triplet interactions exist extensively in other membrane proteins, where many types of triplets occur far more frequently than in soluble proteins. We developed a probabilistic model for estimating the value of membrane helical interaction triplet (MHIT) propensity. Because the number of known structures of membrane proteins is limited, we developed a bootstrap method for determining the 95% confidence intervals of estimated MHIT values. We identified triplets that have high propensity for interhelical interactions and are unique to membrane proteins, e.g. AGF, AGG, GLL, GFF and others. A significant fraction (32%) of triplet types contains triplets that may be involved in interhelical hydrogen bond interactions, suggesting the prevalent and important roles of H-bond in the assembly of TM helices. There are several well-defined spatial conformations for triplet interactions on helices with similar parallel or antiparallel orientations and with similar right-handed or left-handed crossing angles. Often, they contain small residues and correspond to the regions of the closest contact between helices. Sequence motifs such as GG4 and AG4 can be part of the three-body interactions that have similar conformations, which in turn can be part of a higher-order cooperative four residue spatial motif observed in helical pairs from different proteins. In many cases, spatial motifs such as serine zipper and polar clamp are part of triplet interactions. On the basis of the analysis of the archaeal rhodopsin family of proteins, tightly packed triplet interactions can be achieved with several different choices of amino acid residues.     

Parameterization and classification of the protein universe via geometric techniques

We present a scheme for the classification of 3487 non-redundant protein structures into 1207 non-hierarchical clusters by using recurring structural patterns of three to six amino acids as keys of classification. This results in several signature patterns, which seem to decide membership of a protein in a functional category. The patterns provide clues to the key residues involved in functional sites as well as in protein-protein interaction. The discovered patterns include a "glutamate double bridge" of superoxide dismutase, the functional interface of the serine protease and inhibitor, interface of homo/hetero dimers, and functional sites of several enzyme families. We use geometric invariants to decide superimposability of structural patterns. This allows the parameterization of patterns and discovery of recurring patterns via clustering. The geometric invariant-based approach eliminates the computationally explosive step of pair-wise comparison of structures. The results provide a vast resource for the biologists for experimental validation of the proposed functional sites, and for the design of synthetic enzymes, inhibitors and drugs.     

Combining inference from evolution and geometric probability in protein structure evaluation

Starting from the hypothesis that evolutionarily important residues form a spatially limited cluster in a protein's native fold, we discuss the possibility of detecting a non-native structure based on the absence of such clustering. The relevant residues are determined using the Evolutionary Trace method. We propose a quantity to measure clustering of the selected residues on the structure and show that the exact values for its average and variance over several ensembles of interest can be found. This enables us to study the behavior of the associated z-scores. Since our approach rests on an analytic result, it proves to be general, customizable, and computationally fast. We find that clustering is indeed detectable in a large representative protein set. Furthermore, we show that non-native structures tend to achieve lower residue-clustering z-scores than those attained by the native folds. The most important conclusion that we draw from this work is that consistency between structural and evolutionary information, manifested in clustering of key residues, imposes powerful constraints on the conformational space of a protein.     

Anthrax toxin triggers endocytosis of its receptor via a lipid raft-mediated clathrin-dependent process

The protective antigen (PA) of the anthrax toxin binds to a cell surface receptor and thereby allows lethal factor (LF) to be taken up and exert its toxic effect in the cytoplasm. Here, we report that clustering of the anthrax toxin receptor (ATR) with heptameric PA or with an antibody sandwich causes its association to specialized cholesterol and glycosphingolipid-rich microdomains of the plasma membrane (lipid rafts). We find that although endocytosis of ATR is slow, clustering it into rafts either via PA heptamerization or using an antibody sandwich is necessary and sufficient to trigger efficient internalization and allow delivery of LF to the cytoplasm. Importantly, altering raft integrity using drugs prevented LF delivery and cleavage of cytosolic MAPK kinases, suggesting that lipid rafts could be therapeutic targets for drugs against anthrax. Moreover, we show that internalization of PA is dynamin and Eps15 dependent, indicating that the clathrin-dependent pathway is the major route of anthrax toxin entry into the cell. The present work illustrates that although the physiological role of the ATR is unknown, its trafficking properties, i.e., slow endocytosis as a monomer and rapid clathrin-mediated uptake on clustering, make it an ideal anthrax toxin receptor.