The evolutionary safety of mutagenic drugs should be assessed before drug approval.

Some drugs increase the mutation rate of their target pathogen, a potentially concerning mechanism as the pathogen might evolve faster toward an undesired phenotype. We suggest a four-step assessment of evolutionary safety for the approval of such treatments.

Correction: A spatial vaccination strategy to reduce the risk of vaccine-resistant variants.

[This corrects the article DOI: 10.1371/journal.pcbi.1010391.].

Evolutionary safety of lethal mutagenesis driven by antiviral treatment.

Nucleoside analogs are a major class of antiviral drugs. Some act by increasing the viral mutation rate causing lethal mutagenesis of the virus. Their mutagenic capacity, however, may lead to an evolutionary safety concern. We define evolutionary safety as a probabilistic assurance that the treatment will not generate an increased number of mutants. We develop a mathematical framework to estimate the total mutant load produced with and without mutagenic treatment. We predict rates of appearance of such virus mutants as a function of the timing of treatment and the immune competence of patients, employing realistic assumptions about the vulnerability of the viral genome and its potential to generate viable mutants. We focus on the case study of Molnupiravir, which is an FDA-approved treatment against Coronavirus Disease-2019 (COVID-19). We estimate that Molnupiravir is narrowly evolutionarily safe, subject to the current estimate of parameters. Evolutionary safety can be improved by restricting treatment with this drug to individuals with a low immunological clearance rate and, in future, by designing treatments that lead to a greater increase in mutation rate. We report a simple mathematical rule to determine the fold increase in mutation rate required to obtain evolutionary safety that is also applicable to other pathogen-treatment combinations.

Phenotype switching of the mutation rate facilitates adaptive evolution.

The mutation rate plays an important role in adaptive evolution. It can be modified by mutator and anti-mutator alleles. Recent empirical evidence hints that the mutation rate may vary among genetically identical individuals: evidence from bacteria suggests that the mutation rate can be affected by expression noise of a DNA repair protein and potentially also by translation errors in various proteins. Importantly, this non-genetic variation may be heritable via a transgenerational epigenetic mode of inheritance, giving rise to a mutator phenotype that is independent from mutator alleles. Here, we investigate mathematically how the rate of adaptive evolution is affected by the rate of mutation rate phenotype switching. We model an asexual population with two mutation rate phenotypes, non-mutator and mutator. An offspring may switch from its parental phenotype to the other phenotype. We find that switching rates that correspond to so-far empirically described non-genetic systems of inheritance of the mutation rate lead to higher rates of adaptation on both artificial and natural fitness landscapes. These switching rates can maintain within the same individuals both a mutator phenotype and intermediary mutations, a combination that facilitates adaptation. Moreover, non-genetic inheritance increases the proportion of mutators in the population, which in turn increases the probability of hitchhiking of the mutator phenotype with adaptive mutations. This in turns facilitates the acquisition of additional adaptive mutations. Our results rationalize recently observed noise in the expression of proteins that affect the mutation rate and suggest that non-genetic inheritance of this phenotype may facilitate evolutionary adaptive processes.

A spatial vaccination strategy to reduce the risk of vaccine-resistant variants.

The COVID-19 pandemic demonstrated that the process of global vaccination against a novel virus can be a prolonged one. Social distancing measures, that are initially adopted to control the pandemic, are gradually relaxed as vaccination progresses and population immunity increases. The result is a prolonged period of high disease prevalence combined with a fitness advantage for vaccine-resistant variants, which together lead to a considerably increased probability for vaccine escape. A spatial vaccination strategy is proposed that has the potential to dramatically reduce this risk. Rather than dispersing the vaccination effort evenly throughout a country, distinct geographic regions of the country are sequentially vaccinated, quickly bringing each to effective herd immunity. Regions with high vaccination rates will then have low infection rates and vice versa. Since people primarily interact within their own region, spatial vaccination reduces the number of encounters between infected individuals (the source of mutations) and vaccinated individuals (who facilitate the spread of vaccine-resistant strains). Thus, spatial vaccination may help mitigate the global risk of vaccine-resistant variants.

Evolution of resistance to COVID-19 vaccination with dynamic social distancing.

The greatest hope for a return to normalcy following the COVID-19 pandemic is worldwide vaccination. Yet, a relaxation of social distancing that allows increased transmissibility, coupled with selection pressure due to vaccination, will probably lead to the emergence of vaccine resistance. We analyse the evolutionary dynamics of COVID-19 in the presence of dynamic contact reduction and in response to vaccination. We use infection and vaccination data from six different countries. We show that under slow vaccination, resistance is very likely to appear even if social distancing is maintained. Under fast vaccination, the emergence of mutants can be prevented if social distancing is maintained during vaccination. We analyse multiple human factors that affect the evolutionary potential of the virus, including the extent of dynamic social distancing, vaccination campaigns, vaccine design, boosters and vaccine hesitancy. We provide guidelines for policies that aim to minimize the probability of emergence of vaccine-resistant variants.

A generalized Robinson-Foulds distance for labeled trees.

BACKGROUND: The Robinson-Foulds (RF) distance is a well-established measure between phylogenetic trees. Despite a lack of biological justification, it has the advantages of being a proper metric and being computable in linear time. For phylogenetic applications involving genes, however, a crucial aspect of the trees ignored by the RF metric is the type of the branching event (e.g. speciation, duplication, transfer, etc). RESULTS: We extend RF to trees with labeled internal nodes by including a node flip operation, alongside edge contractions and extensions. We explore properties of this extended RF distance in the case of a binary labeling. In particular, we show that contrary to the unlabeled case, an optimal edit path may require contracting "good" edges, i.e. edges shared between the two trees. CONCLUSIONS: We provide a 2-approximation algorithm which is shown to perform well empirically. Looking ahead, computing distances between labeled trees opens up a variety of new algorithmic directions.Implementation and simulations available at https://github.com/DessimozLab/pylabeledrf .