Viruses have established symbiotic relationships with almost every other living organism on Earth and at all levels of biological organisation, from other viruses up to entire ecosystems. In most cases, peacefully coexisting with their hosts, but in most relevant cases, parasitising them and inducing diseases. Viruses are playing an essential role in shaping the eco-evolutionary dynamics of their hosts, and have been also involved in some of the major evolutionary innovations either by working as vectors of genetic information or by being themselves coopted by the host into their genomes. Viruses can be studied at different levels of biological organisation, from the molecular mechanisms of genome replication, gene expression and encapsidation, to global pandemics. All these levels are different and yet connected through the presence of threshold conditions allowing for the formation of a capsid, the loss of genetic information or epidemic spreading. These thresholds, as it occurs with temperatures separating phases in a liquid, define sharp qualitative types of behaviour. These {\em phase transitions} are very well known in Physics. They have been studied by means of simple, but powerful models able to capture their essential properties, allowing to understand them. Can the physics of phase transitions be an inspiration for our understanding of viral dynamics at different scales? Here we review well-known examples of transition phenomena in virology and their simplest mathematical modelling approaches. We suggest that the advantages of abstract, simplified pictures used in Physics are also the key to properly understand the origins and evolution of complexity in viruses. By means of several examples, we explore this multilevel landscape and how minimal models provide deep insights into a diverse array of problems. The relevance of these transitions in connecting dynamical patterns across levels and their evolutionary and clinical implications are outlined.

Complex systems exhibit critical thresholds at which they transition among alternative phases. Complex systems theory has been applied to analyze disease progression, distinguishing three stages along progression: (i) a normal non-infected state, (ii) a pre-disease state in which the host is infected and responds; therapeutic interventions could still be effective, (iii) an irreversible state, where the system is seriously threatened. The Dynamical Network Biomarker (DNB) theory sought for early-warnings of the transition from health to disease. Such DNBs might range from individual genes to complex structures in transcriptional regulatory or protein-protein interaction networks. Here we revisit transcriptomic data obtained during infection of tobacco plants with tobacco etch potyvirus to identify DNBs signaling the transition from mild/reversible to severe/irreversible disease. We identified genes showing a sudden transition in expression along disease. Some of these genes cluster in modules that show the properties of DNBs. These modules contain both genes known to be involved in response to pathogens (e.g., ADH2, CYP19, ERF1, KAB1, LAP1, MBF1C, PR1, or TPS5) and other genes not previously related to biotic stress responses (e.g., ABCI6, BBX21, NAP1, OSM34, or ZPN1).

The generation of different types of defective viral genomes (DVG) is an unavoidable consequence of the error-prone replication of RNA viruses. In recent years, a particular class of DVGs, those containing long deletions or genome rearrangements, has gain interest due to their potential therapeutic and biotechnological applications. Identifying such DVGs in high-throughput sequencing data has become an interesting computational problem. Up to nowadays, several algorithms have been proposed, though all incur in false positives, a problem of practical interest if such DVGs have to be synthetized and tested in the laboratory. Here we develop a novel software, DVGfinder, that wraps the two most commonly used algorithms into a pipeline that predicts DVGs. Using a gradient boosting classifier machine learning algorithm, we evaluate the performance of DVGfinder compared to previous algorithms and found that it outcompetes their precision and sensitivity in simulated datasets. DVGfinder generates user-friendly output files in HTML format that can assist users to identify DVGs based on their associated probability of being true positives.