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Dictionary learning (DL), implemented via matrix factorization (MF), is commonly used in computational biology to tackle ubiquitous clustering problems. The method is favored due to its conceptual simplicity and relatively low computational complexity. However, DL algorithms produce results that lack interpretability in terms of real biological data. Additionally, they are not optimized for graph-structured data and hence often fail to handle them in a scalable manner. In order to address these limitations, we propose a novel DL algorithm called online convex network dictionary learning (online cvxNDL). Unlike classical DL algorithms, online cvxNDL is implemented via MF and designed to handle extremely large datasets by virtue of its online nature. Importantly, it enables the interpretation of dictionary elements, which serve as cluster representatives, through convex combinations of real measurements. Moreover, the algorithm can be applied to data with a network structure by incorporating specialized subnetwork sampling techniques. To demonstrate the utility of our approach, we apply cvxNDL on 3D-genome RNAPII ChIA-Drop data with the goal of identifying important long-range interaction patterns (long-range dictionary elements). ChIA-Drop probes higher-order interactions, and produces data in the form of hypergraphs whose nodes represent genomic fragments. The hyperedges represent observed physical contacts. Our hypergraph model analysis has the objective of creating an interpretable dictionary of long-range interaction patterns that accurately represent global chromatin physical contact maps. Through the use of dictionary information, one can also associate the contact maps with RNA transcripts and infer cellular functions. To accomplish the task at hand, we focus on RNAPII-enriched ChIA-Drop data from Drosophila Melanogaster S2 cell lines. Our results offer two key insights. First, we demonstrate that online cvxNDL retains the accuracy of classical DL (MF) methods while simultaneously ensuring unique interpretability and scalability. Second, we identify distinct collections of proximal and distal interaction patterns involving chromatin elements shared by related processes across different chromosomes, as well as patterns unique to specific chromosomes. To associate the dictionary elements with biological properties of the corresponding chromatin regions, we employ Gene Ontology (GO) enrichment analysis and perform multiple RNA coexpression studies. Author summary: We introduce a novel method for dictionary learning termed online convex Network Dictionary Learning (online cvxNDL). The method operates in an online manner and utilizes representative subnetworks of a network dataset as dictionary elements. A key feature of online cvxNDL is its ability to work with graph-structured data and generate dictionary elements that represent convex combinations of real data points, thus ensuring interpretability. Online cvxNDL is used to investigate long-range chromatin interactions in S2 cell lines of Drosophila Melanogaster obtained through RNAPII ChIA-Drop measurements represented as hypergraphs. The results show that dictionary elements can accurately and efficiently reconstruct the original interactions present in the data, even when subjected to convexity constraints. To shed light on the biological relevance of the identified dictionaries, we perform Gene Ontology enrichment and RNA-seq coexpression analyses. These studies uncover multiple long-range interaction patterns that are chromosome-specific. Furthermore, the findings affirm the significance of convex dictionaries in representing TADs cross-validated by imaging methods (such as 3-color FISH (fluorescence in situ hybridization)). [ABSTRACT FROM AUTHOR]

Post-translational modifications (PTMs) of proteins play a vital role in their function and stability. These modifications influence protein folding, signaling, protein-protein interactions, enzyme activity, binding affinity, aggregation, degradation, and much more. To date, over 400 types of PTMs have been described, representing chemical diversity well beyond the genetically encoded amino acids. Such modifications pose a challenge to the successful design of proteins, but also represent a major opportunity to diversify the protein engineering toolbox. To this end, we first trained artificial neural networks (ANNs) to predict eighteen of the most abundant PTMs, including protein glycosylation, phosphorylation, methylation, and deamidation. In a second step, these models were implemented inside the computational protein modeling suite Rosetta, which allows flexible combination with existing protocols to model the modified sites and understand their impact on protein stability as well as function. Lastly, we developed a new design protocol that either maximizes or minimizes the predicted probability of a particular site being modified. We find that this combination of ANN prediction and structure-based design can enable the modification of existing, as well as the introduction of novel, PTMs. The potential applications of our work include, but are not limited to, glycan masking of epitopes, strengthening protein-protein interactions through phosphorylation, as well as protecting proteins from deamidation liabilities. These applications are especially important for the design of new protein therapeutics where PTMs can drastically change the therapeutic properties of a protein. Our work adds novel tools to Rosetta's protein engineering toolbox that allow for the rational design of PTMs. Author summary: Machine learning (ML) is changing the world of protein design, from structure prediction methods like AlphaFold to fixed-backbone design methods like ProteinMPNN. ML methods have made much progress in various aspects of protein computational biology, both complementing and, in some cases, surpassing traditional macromolecular modeling methods such as those combined in libraries like the Rosetta software suite. However, a lack of compatibility and flexibility can hinder interoperability with existing methods, preventing the full potential of these new solutions from being realized. Here, we first present a new machine learning tool for predicting post-translational modifications (PTMs), which play an important role in the stability and function of proteins, and then highlight how the implementation of this tool in the existing Rosetta toolbox can facilitate new applications. To this end, we combine PTM prediction with protein design, maximizing or minimizing the predicted probability of a post-translational modification occurring at a specific site. As one example, we predict the N-linked glycosylation of influenza hemagglutinin, which has applications in both understanding the evolution of viral strains over time, and engineering additional glycosylation sites to mask unwanted epitopes of vaccine candidates. [ABSTRACT FROM AUTHOR]

Generalist microbes have adapted to a multitude of environmental stresses through their integrated stress response system. Individual stress responses have been quantified by E. coli metabolism and expression (ME) models under thermal, oxidative and acid stress, respectively. However, the systematic quantification of cross-stress & cross-talk among these stress responses remains lacking. Here, we present StressME: the unified stress response model of E. coli combining thermal (FoldME), oxidative (OxidizeME) and acid (AcidifyME) stress responses. StressME is the most up to date ME model for E. coli and it reproduces all published single-stress ME models. Additionally, it includes refined rate constants to improve prediction accuracy for wild-type and stress-evolved strains. StressME revealed certain optimal proteome allocation strategies associated with cross-stress and cross-talk responses. These stress-optimal proteomes were shaped by trade-offs between protective vs. metabolic enzymes; cytoplasmic vs. periplasmic chaperones; and expression of stress-specific proteins. As StressME is tuned to compute metabolic and gene expression responses under mild acid, oxidative, and thermal stresses, it is useful for engineering and health applications. The modular design of our open-source package also facilitates model expansion (e.g., to new stress mechanisms) by the computational biology community. Author summary: A fundamental understanding of multi-stress adaptation in E.coli has potential industrial relevance. While individual stress responses have been quantified through the protein regulatory network in E.coli, the systematic quantification of the cross-stress & cross-talk among stress responses remains lacking. Here, we develop a new modeling pipeline by which thermal, oxidative and acid stress response can be coupled to each other, and the metabolic activities, protein and metabolic flux redistribution due to cross-stress & cross-talk can be quantified. We optimize the effective rate constants in the integrated model. We then confirm the model robustness by validating against the published data under single stress. Finally, we use the model to characterize the cross-adaptation between protective and catalytic proteins as well as between chaperones present in different cellular compartments. We find effective cross-protection against cross stress by adapting the E.coli cells to the thermal stress first. We also indicate the presence of cross-talk through trade-offs by which the cell may refuse to give up more protein allocation away from one stress response to the other, because doing so would decrease stress tolerance further. The single stress plug-in design makes the model build-up pipeline flexible and expandable, allowing incorporation of more stressors into the model architecture for industrial applications. [ABSTRACT FROM AUTHOR]