Stella Veretnik

Our views of fold space implicitly rest upon many assumptions that impact how we analyze, interpret and understand protein structure, function and evolution. For instance, is there an optimal granularity in viewing protein structural similarities (e.g., architecture, topology or some other level)? Similarly, the discrete/continuous dichotomy of fold space is central, but remains unresolved. Discrete views of fold space bin similar folds into distinct, non-overlapping groups; unfortunately, such binning can miss remote relationships. While hierarchical systems like CATH are indispensable resources, less heuristic and more conceptually flexible approaches could enable more nuanced explorations of fold space. Building upon an Urfold model of protein structure, here we present a deep generative modeling framework, termed DeepUrfold, for analyzing protein relationships at scale. DeepUrfold’s learned embeddings occupy high-dimensional latent spaces that can be distilled for a given protein in terms of an amalgamated representation uniting sequence, structure and biophysical properties. This approach is structure-guided, versus being purely structure-based, and DeepUrfold learns representations that, in a sense, define superfamilies. Deploying DeepUrfold with CATH reveals evolutionarily-remote relationships that evade existing methodologies, and suggests a mostly-continuous view of fold space—a view that extends beyond simple geometric similarity, towards the realm of integrated sequence ↔ structure ↔ function properties.

Our views of fold space implicitly rest upon many assumptions that impact how we analyze, interpret and understand biological systems—from protein structure comparison and classification to function prediction and evolutionary analyses. For instance, is there an optimal granularity at which to view protein structural similarities (e.g., architecture, topology or some other level)? If so, how does it vary with the type of question being asked? Similarly, the discrete/continuous dichotomy of fold space is central in structural bioinformatics, but remains unresolved. Discrete views of fold space bin 'similar' folds into distinct, non-overlapping groups; unfortunately, such binning may inherently miss many remote relationships. While hierarchical systems like CATH, SCOP and ECOD represent major steps forward in protein classification, a scalable, objective and conceptually flexible method, with less reliance on assumptions and heuristics, could enable a more systematic and nuanced exploration of fold space, particularly as regards evolutionarily-distant relationships. Building upon a recent 'Urfold' model of protein structure, we have developed a new approach to analyze protein interrelationships. This framework, termed 'DeepUrfold', is rooted in deep generative modeling via variational Bayesian inference, and we find it to be useful for comparative analysis across the protein universe. Critically, DeepUrfold leverages its deep generative model's learned embeddings, which occupy high-dimensional latent spaces and can be distilled for a given protein in terms of an amalgamated representation that unites sequence, structure, biophysical and phylogenetic properties. Notably, DeepUrfold is structure- guided , versus being purely structure-based, and its architecture allows each trained model to learn protein features (structural and otherwise) that, in a sense, 'define' different superfamilies. Deploying DeepUrfold with CATH suggests a new, mostly-continuous view of fold space—a view that extends beyond simple 3D structural/geometric similarity, towards the realm of integrated sequence ↔ structure ↔ function properties. We find that such an approach can quantitatively represent and detect evolutionarily-remote relationships that evade existing methods.

Recent computational advances in the accurate prediction of protein three-dimensional (3D) structures from amino acid sequences now present a unique opportunity to decipher the interrelationships between proteins. This task entails--but is not equivalent to--a problem of 3D structure comparison and classification. Historically, protein domain classification has been a largely manual and subjective activity, relying upon various heuristics. Databases such as CATH represent significant steps towards a more systematic (and automatable) approach, yet there still remains much room for the development of more scalable and quantitative classification methods, grounded in machine learning. We suspect that re-examining these relationships via a Deep Learning (DL) approach may entail a large-scale restructuring of classification schemes, improved with respect to the interpretability of distant relationships between proteins. Here, we describe our training of DL models on protein domain structures (and their associated physicochemical properties) in order to evaluate classification properties at CATH's "homologous superfamily" (SF) level. To achieve this, we have devised and applied an extension of image-classification methods and image segmentation techniques, utilizing a convolutional autoencoder model architecture. Our DL architecture allows models to learn structural features that, in a sense, 'define' different homologous SFs. We evaluate and quantify pairwise 'distances' between SFs by building one model per SF and comparing the loss functions of the models. Hierarchical clustering on these distance matrices provides a new view of protein interrelationships--a view that extends beyond simple structural/geometric similarity, and towards the realm of structure/function properties.

Recent computational advances in the accurate prediction of protein three-dimensional (3D) structures from amino acid sequences now present a unique opportunity to decipher the interrelationships between proteins. This task entails—but is not equivalent to—a problem of 3D structure comparison and classification. Historically, protein domain classification has been a largely manual and subjective activity, relying upon various heuristics. Databases such as CATH represent significant steps towards a more systematic (and automatable) approach, yet there still remains much room for the development of more scalable and quantitative classification methods, grounded in machine learning. We suspect that re-examining these relationships via a Deep Learning (DL) approach may entail a large-scale restructuring of classification schemes, improved with respect to the interpretability of distant relationships between proteins. Here, we describe our training of DL models on protein domain structures (and their associated physicochemical properties) in order to evaluate classification properties at CATH’s “homologous superfamily” (SF) level. To achieve this, we have devised and applied an extension of image-classification methods and image segmentation techniques, utilizing a convolutional autoencoder model architecture. Our DL architecture allows models to learn structural features that, in a sense, ‘define’ different homologous SFs. We evaluate and quantify pairwise ‘distances’ between SFs by building one model per SF and comparing the loss functions of the models. Hierarchical clustering on these distance matrices provides a new view of protein interrelationships—a view that extends beyond simple structural/geometric similarity, and towards the realm of structure/function properties.

We suspect that there is a level of granularity of protein structure intermediate between the classical levels of “architecture” and “topology,” as reflected in such phenomena as extensive three‐dimensional structural similarity above the level of (super)folds. Here, we examine this notion of architectural identity despite topological variability, starting with a concept that we call the “Urfold.” We believe that this model could offer a new conceptual approach for protein structural analysis and classification: indeed, the Urfold concept may help reconcile various phenomena that have been frequently recognized or debated for years, such as the precise meaning of “significant” structural overlap and the degree of continuity of fold space. More broadly, the role of structural similarity in sequence↔structure↔function evolution has been studied via many models over the years; by addressing a conceptual gap that we believe exists between the architecture and topology levels of structural classification schemes, the Urfold eventually may help synthesize these models into a generalized, consistent framework. Here, we begin by qualitatively introducing the concept.

Overview: We suspect that there is a level of granularity of protein structure intermediate between the classical levels of ‘architecture’ and ‘topology’, as reflected in such phenomena as extensive 3D structural similarity above the level of (super)folds. Here, we examine this notion of architectural identity despite topological variability, starting with a concept that we call the ‘ Urfold ’. We believe that this model could offer a new conceptual approach for protein structural analysis and classification: indeed, the Urfold concept may help reconcile various phenomena that have been frequently recognized or debated for years, such as the precise meaning of ‘significant’ structural overlap and the degree of continuity of fold space. More broadly, the role of structural similarity in sequence/structure/function evolution has been studied via many models over the years; the Urfold may help synthesize these models into a generalized, consistent framework, by addressing a conceptual gap that we believe exists between the architecture and topology levels of structural classification schemes.

0. The small β-barrel is an ancient protein structural domain characterized by extremes: It features an extremely broad range of structural varieties, a deeply intricate evolutionary history, and it is associated with a bewildering array of biomolecular pathways and physiological functions. These and related features of this domain are described and analyzed herein. Specifically, we present a comprehensive, survey-based analysis of the structural properties of small β-barrels (SBBs). We first consider the defining characteristics of the SBB fold, as well as the various systems of nomenclature used to describe it. In order to begin elucidating how such vast functional diversity is achieved by a relatively simple protein domain, we then explore the anatomy of the SBB fold and some of its representative structural variants. Many types of SBB proteins assemble into cyclic oligomers that act as the biologically-functional entity. These oligomers exhibit a great deal of plasticity even at the quaternary structural level—including homomeric and heteromeric assemblies, rings of variable subunit stoichiometries (pentamer, hexamer, etc.), as well as higher-order oligomers (e.g., double-rings) and fibrillar polymers. We conclude with three themes that emerge from the SBB’s unique structure↔function versatility.

Background: Partitioning of a protein into structural components, known as domains, is an important initial step in protein classification and for functional and evolutionary studies. While the systematic assignments of domains by human experts exist (CATH and SCOP), the introduction of high throughput technologies for structure determination threatens to overwhelm expert approaches. A variety of algorithmic methods have been developed to expedite this process, allowing almost instant structural decomposition into domains. The performance of algorithmic methods can approach 85% agreement on the number of domains with the consensus reached by experts. However, each algorithm takes a somewhat different conceptual approach, each with unique strengths and weaknesses. Currently there is no simple way to automatically compare assignments from different structure-based domain assignment methods, thereby providing a comprehensive understanding of possible structure partitioning as well as providing some insight into the tendencies of particular algorithms. Most importantly, a consensus assignment drawn from multiple assignment methods can provide a singular and presumably more accurate view. Results: We introduce dConsensus http://pdomains.sdsc.edu/dConsensus; a web resource that displays the results of calculations from multiple algorithmic methods and generates a domain assignment consensus with an associated reliability score. Domain assignments from seven structure-based algorithms - PDP, PUU, DomainParser2, NCBI method, DHcL, DDomains and Dodis are available for analysis and comparison alongside assignments made by expert methods. The assignments are available for all protein chains in the Protein Data Bank (PDB). A consensus domain assignment is built by either allowing each algorithm to contribute equally (simple approach) or by weighting the contribution of each method by its prior performance and observed tendencies. An analysis of secondary structure around domain and fragment boundaries is also available for display and further analysis. Conclusion: dConsensus provides a comprehensive assignment of protein domains. For the first time, seven algorithmic methods are brought together with no need to access each method separately via a webserver or local copy of the software. This aggregation permits a consensus domain assignment to be computed. Comparison viewing of the consensus and choice methods provides the user with insights into the fundamental units of protein structure so important to the study of evolutionary and functional relationships.

The spliceosome, a sophisticated molecular machine involved in the removal of intervening sequences from the coding sections of eukaryotic genes, appeared and subsequently evolved rapidly during the early stages of eukaryotic evolution. The last eukaryotic common ancestor (LECA) had both complex spliceosomal machinery and some spliceosomal introns, yet little is known about the early stages of evolution of the spliceosomal apparatus. The Sm/Lsm family of proteins has been suggested as one of the earliest components of the emerging spliceosome and hence provides a first in-depth glimpse into the evolving spliceosomal apparatus. An analysis of 335 Sm and Sm-like genes from 80 species across all three kingdoms of life reveals two significant observations. First, the eukaryotic Sm/Lsm family underwent two rapid waves of duplication with subsequent divergence resulting in 14 distinct genes. Each wave resulted in a more sophisticated spliceosome, reflecting a possible jump in the complexity of the evolving eukaryotic cell. Second, an unusually high degree of conservation in intron positions is observed within individual orthologous Sm/Lsm genes and between some of the Sm/Lsm paralogs. This suggests that functional spliceosomal introns existed before the emergence of the complete Sm/Lsm family of proteins; hence, spliceosomal machinery with considerably fewer components than today's spliceosome was already functional. The spliceosome is a complex molecular machine that removes intervening sequences (introns) from mRNAs. It is unique to eukaryotes. Although prokaryotes have self-splicing introns, they completely lack spliceosomal introns and the spliceosome itself. Yet even the simplest eukaryotic organisms have introns and a rather complex spliceosomal apparatus. Little is known about how this amazing machine rapidly evolved in early eukaryotes. Here, we attempt to reconstruct a part of this evolutionary process using one of the most fundamental components of the spliceosome—the Sm and Lsm family of proteins. Using sequence and structure analysis as well as the analysis of the intron positions in Sm and Lsm genes in conjunction with a wealth of published data, we propose a plausible scenario for some aspects of spliceosomal evolution. In particular, we suggest that the Lsm family of genes could have been the first and the most essential component that allowed rudimentary splicing of early spliceosomal introns. Extensive duplications of Lsm genes and the later rise of the Sm gene family likely reflect a gradual increase in complexity of the spliceosome.