Against the COVID-19 pandemic, non-pharmaceutical interventions have been widely applied and vaccinations have taken off. The upcoming question is how the interplay between vaccinations and social measures will shape infections and hospitalizations. Hence, we extend the Susceptible-Exposed-Infectious-Removed (SEIR) model including these elements. We calibrate it to data of Luxembourg, Austria and Sweden until 15 December 2020. Sweden results having the highest fraction of undetected, Luxembourg of infected and all three being far from herd immunity in December. We quantify the level of social interaction, showing that a level around 1/3 of before the pandemic was still required in December to keep the effective reproduction number $R_{\mathit{eff}}\left(t\right)$ below 1, for all three countries. Aiming to vaccinate the whole population within 1 year at constant rate would require on average 1,700 fully vaccinated people/day in Luxembourg, 24,000 in Austria and 28,000 in Sweden, and could lead to herd immunity only by mid summer. Herd immunity might not be reached in 2021 if too slow vaccines rollout speeds are employed. The model thus estimates which vaccination rates are too low to allow reaching herd immunity in 2021, depending on social interactions. Vaccination will considerably, but not immediately, help to curb the infection; thus limiting social interactions remains crucial for the months to come.

Monitoring SARS-CoV-2 in wastewater has shown to be an effective tool for epidemiological surveillance. More specifically, RNA levels determined with RT-qPCR have been shown to track with the infection dynamics within the population. However, the surveillance of individual lineages circulating in the population based on genomic sequencing of wastewater samples is challenging, as the genetic material constitutes a mixture of different viral haplotypes. Here, we identify specific signature mutations from individual SARS-CoV-2 lineages in wastewater samples to estimate lineages circulating in Luxembourg. We compare circulating lineages and mutations to those detected in clinical samples amongst infected individuals. We show that especially for dominant lineages, the allele frequencies of signature mutations correspond to the occurrence of particular lineages in the population. In addition, we provide evidence that regional clusters can also be discerned. We focused on the time period between November 2020 and March 2021 in which several variants of concern emerged and specifically traced the lineage B.1.1.7, which became dominant in Luxembourg during that time. During the subsequent time points, we were able to reconstruct short haplotypes, highlighting the co-occurrence of several signature mutations. Our results highlight the potential of genomic surveillance in wastewater samples based on amplicon short-read data. By extension, our work provides the basis for the early detection of novel SARS-CoV-2 variants.

The observations of phenotypic plasticity have stimulated the revival of ‘epigenetics’. Over the past 70 years the term has come in many colors and flavors, depending on the biological discipline and time period. The meanings span from Waddington’s “epigenotype” and “epigenetic landscape” to the molecular biologists’ “epigenetic marks” embodied by DNA methylation and histone modifications. Here we seek to quell the ambiguity of the name. First we place “epigenetics” in the various historical contexts. Then, by presenting the formal concepts of dynamical systems theory we show that the “epigenetic landscape” is more than a metaphor: it has specific mathematical foundations. The latter explains how gene regulatory networks produce multiple attractor states, the self-stabilizing patterns of gene activation across the genome that account for “epigenetic memory”. This network dynamics approach replaces the reductionist correspondence of molecular epigenetic modifications with concept of the epigenetic landscape, by providing a concrete and crisp correspondence.

Digital PCR (dPCR) exploits limiting dilution of a template into an array of PCR reactions. From this array the number of reactions that contain at least one (as opposed to zero) initial template is determined, allowing inferring the original template concentration. Here we present a novel protocol to efficiently infer the concentration of a sample and its optimal dilution for dPCR from few targeted qPCR assays. By taking advantage of the real-time amplification feature of qPCR as opposed to relying on endpoint PCR assessment as in standard dPCR prior knowledge of template concentration is not necessary. This eliminates the need for serial dilutions in a separate titration and reduces the number of necessary reactions. We describe the theory underlying our approach and discuss experimental moments that contribute to uncertainty. We present data from a controlled experiment where the initial template concentration is known as proof of principle and apply our method on directly monitoring transcript level change during cell differentiation as well as gauging amplicon numbers in cDNA samples after pre-amplification.