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Abstract Viruses impact microbial systems through killing hosts, horizontal gene transfer, and altering cellular metabolism, consequently impacting nutrient cycles. A virus-infected cell, a “virocell,” is distinct from its uninfected sister cell as the virus commandeers cellular machinery to produce viruses rather than replicate cells. Problematically, virocell responses to the nutrient-limited conditions that abound in nature are poorly understood. Here we used a systems biology approach to investigate virocell metabolic reprogramming under nutrient limitation. Using transcriptomics, proteomics, lipidomics, and endo- and exo-metabolomics, we assessed how low phosphate (low-P) conditions impacted virocells of a marine Pseudoalteromonas host when independently infected by two unrelated phages (HP1 and HS2). With the combined stresses of infection and nutrient limitation, a set of nested responses were observed. First, low-P imposed common cellular responses on all cells (virocells and uninfected cells), including activating the canonical P-stress response, and decreasing transcription, translation, and extracellular organic matter consumption. Second, low-P imposed infection-specific responses (for both virocells), including enhancing nitrogen assimilation and fatty acid degradation, and decreasing extracellular lipid relative abundance. Third, low-P suggested virocell-specific strategies. Specifically, HS2-virocells regulated gene expression by increasing transcription and ribosomal protein production, whereas HP1-virocells accumulated host proteins, decreased extracellular peptide relative abundance, and invested in broader energy and resource acquisition. These results suggest that although environmental conditions shape metabolism in common ways regardless of infection, virocell-specific strategies exist to support viral replication during nutrient limitation, and a framework now exists for identifying metabolic strategies of nutrient-limited virocells in nature. 

Networks and temporal point processes serve as fundamental building blocks for modeling complex dynamic relational data in various domains. We propose the latent space Hawkes (LSH) model, a novel generative model for continuous-time networks of relational events, using a latent space representation for nodes. We model relational events between nodes using mutually exciting Hawkes processes with baseline intensities dependent upon the distances between the nodes in the latent space and sender and receiver specific effects. We demonstrate that our proposed LSH model can replicate many features observed in real temporal networks including reciprocity and transitivity, while also achieving superior prediction accuracy and providing more interpretable fits than existing models. 

The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node pairs using structured multivariate Hawkes processes. We fit the model using a spectral clustering and likelihood-based local refinement procedure. We find that our proposed MULCH model is far more accurate than existing models both for predictive and generative tasks. 

In many application settings involving networks, such as messages between users of an on-line social network or transactions between traders in financial markets, the observed data consist of timestamped relational events, which form a continuous-time network. We propose the Community Hawkes Independent Pairs (CHIP) generative model for such networks. We show that applying spectral clustering to an aggregated adjacency matrix constructed from the CHIP model provides consistent community detection for a growing number of nodes and time duration. We also develop consistent and computationally efficient estimators for the model parameters. We demonstrate that our proposed CHIP model and estimation procedure scales to large networks with tens of thousands of nodes and provides superior fits than existing continuous-time network models on several real networks.