Epidemic models on complex networks are widely used to assess how the social structure of a population affects epidemic spreading. However, their numerical simulation can be computationally heavy, especially for large networks. In this paper, we introduce NEXT-Net: a flexible implementation of the next reaction method for simulating epidemic spreading on both static and temporal weighted networks. We find that NEXT-Net is substantially faster than alternative algorithms, while being exact. It permits, in particular, to efficiently simulate epidemics on networks with millions of nodes on a standard computer. It also permits simulating a broad range of epidemic models on temporal networks, including scenarios in which the network structure changes in response to the epidemic. NEXT-Net is implemented in C++ and accessible from Python and R, thus combining speed with user friendliness. These features make our algorithm an ideal tool for a broad range of applications.

Biological cells replicate their genomes in a well-planned manner. The DNA replication program of an organism determines the timing at which different genomic regions are replicated, with fundamental consequences for cell homeostasis and genome stability. In a growing cell culture, genomic regions that are replicated early should be more abundant than regions that are replicated late. This abundance pattern can be experimentally measured using deep sequencing. However, a general quantitative theory linking this pattern to the replication program is still lacking. In this paper, we predict the abundance of DNA fragments in asynchronously growing cultures from any given stochastic model of the DNA replication program. As key examples, we present stochastic models of the DNA replication programs in budding yeast and Escherichia coli. In both cases, our model results are in excellent agreement with experimental data and permit to infer key information about the replication program. In particular, our method is able to infer the locations of known replication origins in budding yeast with high accuracy. These examples demonstrate that our method can provide insight into a broad range of organisms, from bacteria to eukaryotes.

Neural organoids model the development of the human brain and are an indispensable tool for studying neurodevelopment. Whole-organoid lineage tracing has revealed the number of progenies arising from each initial stem cell to be highly diverse, with lineage sizes ranging from one to more than 20,000 cells. This high variability exceeds what can be explained by existing stochastic models of corticogenesis and indicates the existence of an additional source of stochasticity. To explain this variability, we introduce the SAN model which distinguishes Symmetrically diving, Asymmetrically dividing, and Non-proliferating cells. In the SAN model, the additional source of stochasticity is the survival time of a lineage's pool of symmetrically dividing cells. These survival times result from neutral competition within the sub-population of all symmetrically dividing cells. We demonstrate that our model explains the experimentally observed variability of lineage sizes and derive the quantitative relationship between survival time and lineage size. We also show that our model implies the existence of a regulatory mechanism which keeps the size of the symmetrically dividing cell population constant. Our results provide quantitative insight into the clonal composition of neural organoids and how it arises. This is relevant for many applications of neural organoids, and similar processes may occur in other developing tissues both in vitro and in vivo.

Motivation: Counting molecules using next-generation sequencing (NGS) suffers from PCR amplification bias, which reduces the accuracy of many quantitative NGS-based experimental methods such as RNA-Seq. This is true even if molecules are made distinguishable using unique molecular identifiers (UMIs) before PCR amplification, and distinct UMIs are counted instead of reads: Molecules that are lost entirely during the sequencing process will still cause underestimation of the molecule count, and amplification artifacts like PCR chimeras create phantom UMIs and thus cause over-estimation. Results: We introduce the TRUmiCount algorithm to correct for both types of errors. The TRUmiCount algorithm is based on a mechanistic model of PCR amplification and sequencing, whose two parameters have an immediate physical interpretation as PCR efficiency and sequencing depth and can be estimated from experimental data without requiring calibration experiments or spike-ins. We show that our model captures the main stochastic properties of amplification and sequencing, and that it allows us to filter out phantom UMIs and to estimate the number of molecules lost during the sequencing process. Finally, we demonstrate that the phantom-filtered and loss-corrected molecule counts computed by TRUmiCount measure the true number of molecules with considerably higher accuracy than the raw number of distinct UMIs, even if most UMIs are sequenced only once as is typical for single-cell RNA-Seq. Availability and implementation: TRUmiCount is available at http://www.cibiv.at/software/trumicount and through Bioconda (http://bioconda.github.io). Supplementary information: Supplementary information is available at Bioinformatics online.