Comparison of structural networks across homologous proteins

Protein sequence determines its structure and function. The indirect relationship between protein function and structure lies deep-rooted in the structural topology that has evolved into performing optimal function. The evolution of structure and its interconnectivity has been conventionally studied by comparing the root means square deviation between protein structures at the backbone level. Two factors that are necessary for the quantitative comparison of non-covalent interactions are (a) explicit inclusion of the coordinates of side-chain atoms and (b) consideration of multiple structures from the conformational landscape to account for structural variability. We have recently addressed these fundamental issues by investigating the alteration of inter-residue interactions across an ensemble of protein structure networks through a graph spectral approach. In this study, we have developed a rigorous method to compare the structure networks of homologous proteins, with a wide range of sequence identity percentages. A range of dissimilarity measures that show the extent of change in the network across homologous structures are generated, which also includes the comparison of the protein structure variability. We discuss in detail, scenarios where the variation of structure is not accompanied by loss or gain of the overall network and its vice versa. The sequence-based phylogeny among the homologs is also compared with the lineage obtained from information from such a robust structure comparison. In summary, we can obtain a quantitative comparison score for the structure networks of homologous proteins, which also enables us to study the evolution of protein function based on the variation of their topologies.

Characterization of Japanese Plum (Prunus salicina) PsMYB10 Alleles Reveals Structural Variation and Polymorphisms Correlating With Fruit Skin Color

The red to blue hue of plant organs is caused due to anthocyanins, which are water-soluble flavonoid pigments. The accumulation of these pigments is regulated by a complex of R2R3-MYB transcription factors (TFs), basic-helix-loop-helix (bHLH), and WD-repeat (WDR) proteins (MBW complex). In Rosaceae species, R2R3-MYBs, particularly MYB10 genes, are responsible for part of the natural variation in anthocyanin colors. Japanese plum cultivars, which are hybrids of Prunus salicina, have high variability in the color hue and pattern, going from yellow-green to red and purple-blue, probably as a result of the interspecific hybridization origin of the crop. Because of such variability, Japanese plum can be considered as an excellent model to study the color determination in Rosaceae fruit tree species. Here, we cloned and characterized the alleles of the PsMYB10 genes in the linkage group LG3 region where quantitative trait loci (QTLs) for the organ color have been mapped to other Prunus species. Allele segregation in biparental populations as well as in a panel of varieties, combined with the whole-genome sequence of two varieties with contrasting fruit color, allowed the organization of the MYB10 alleles into haplotypes. With the help of this strategy, alleles were assigned to genes and at least three copies of PsMYB10.1 were identified in some varieties. In total, we observed six haplotypes, which were able to characterize 91.36% of the cultivars. In addition, two alleles of PsMYB10.1 were found to be highly associated with anthocyanin and anthocyanin-less skin. Their expression during the fruit development confirms their role in the fruit skin coloration. Here, we provide a highly efficient molecular marker for the early selection of colored or non-colored fruits in Japanese plum breeding programs.

Toward a Three-Dimensional Chromosome Shape Alphabet

The study of the three-dimensional (3D) structure of chromosomes-the largest macromolecules in biology-is one of the most challenging to date in structural biology. Here, we develop a novel representation of 3D chromosome structures, as sequences of shape letters from a finite shape alphabet, which provides a compact and efficient way to analyze ensembles of chromosome shape data, akin to the analysis of texts in a language by using letters. We construct a Chromosome Shape Alphabet from an ensemble of chromosome 3D structures inferred from Hi-C data-via SIMBA3D or other methods-by segmenting curves based on topologically associating domains (TADs) boundaries, and by clustering all TADs' 3D structures into groups of similar shapes. The median shapes of these groups, with some pruning and processing, form the Chromosome Shape Letters (CSLs) of the alphabet. We provide a proof of concept for these CSLs by reconstructing independent test curves by using only CSLs (and corresponding transformations) and comparing these reconstructions with the original curves. Finally, we demonstrate how CSLs can be used to summarize shapes in an ensemble of chromosome 3D structures by using generalized sequence logos.

Characterizing the structural variability of HIV-2 protease upon the binding of diverse ligands using a structural alphabet approach

The HIV-2 protease (PR2) is an important target for designing new drugs against the HIV-2 infection. In this study, we explored the structural backbone variability of all available PR2 structures complexed with various inhibitors using a structural alphabet approach. 77% of PR2 positions are structurally variable, meaning they exhibit different local conformations in PR2 structures. This variability was observed all along the structure, particularly in the elbow and flap regions. A part of these backbone changes observed between the 18 PR2 is induced by intrinsic flexibility, and ligand binding putatively induces others occurring in the binding pocket. These latter changes could be important for PR2 adaptation to diverse ligands and are accompanied by changes outside the binding pocket. In addition, the study of the link between structural variability of the pocket and PR2-ligand interactions allowed us to localize pocket regions important for ligand binding and catalytic function, regions important for ligand recognition that adjust their backbone in response to ligand binding and regions important for the pocket opening and closing that have large intrinsic flexibility. Finally, we suggested that differences in ligand effectiveness for PR2 could be partially explained by different backbone deformations induced by these ligands. To conclude, this study is the first characterization of the PR2 structural variability considering ligand diversity. It provides information about the recognition of PR2 to various ligands and its mechanisms to adapt its local conformation to bound ligands that could help understand the resistance of PR2 to its inhibitors, a major antiretroviral class. Communicated by Ramaswamy H. Sarma.

COVARIANCE ESTIMATION USING CONJUGATE GRADIENT FOR 3D CLASSIFICATION IN CRYO-EM

Classifying structural variability in noisy projections of biological macromolecules is a central problem in Cryo-EM. In this work, we build on a previous method for estimating the covariance matrix of the three-dimensional structure present in the molecules being imaged. Our proposed method allows for incorporation of contrast transfer function and non-uniform distribution of viewing angles, making it more suitable for real-world data. We evaluate its performance on a synthetic dataset and an experimental dataset obtained by imaging a 70S ribosome complex.

Covariance Matrix Estimation for the Cryo-EM Heterogeneity Problem

In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly oriented copies of a molecule. The problem of single particle reconstruction (SPR) from cryo-EM is to use the resulting set of noisy two-dimensional projection images taken at unknown directions to reconstruct the three-dimensional (3D) structure of the molecule. In some situations, the molecule under examination exhibits structural variability, which poses a fundamental challenge in SPR. The heterogeneity problem is the task of mapping the space of conformational states of a molecule. It has been previously suggested that the leading eigenvectors of the covariance matrix of the 3D molecules can be used to solve the heterogeneity problem. Estimating the covariance matrix is challenging, since only projections of the molecules are observed, but not the molecules themselves. In this paper, we formulate a general problem of covariance estimation from noisy projections of samples. This problem has intimate connections with matrix completion problems and high-dimensional principal component analysis. We propose an estimator and prove its consistency. When there are finitely many heterogeneity classes, the spectrum of the estimated covariance matrix reveals the number of classes. The estimator can be found as the solution to a certain linear system. In the cryo-EM case, the linear operator to be inverted, which we term the projection covariance transform, is an important object in covariance estimation for tomographic problems involving structural variation. Inverting it involves applying a filter akin to the ramp filter in tomography. We design a basis in which this linear operator is sparse and thus can be tractably inverted despite its large size. We demonstrate via numerical experiments on synthetic datasets the robustness of our algorithm to high levels of noise.