A mathematical model for the within-host (re)infection dynamics of SARS-CoV-2.

Interactions between SARS-CoV-2 and the immune system during infection are complex. However, understanding the within-host SARS-CoV-2 dynamics is of enormous importance for clinical and public health outcomes. Current mathematical models focus on describing the within-host SARS-CoV-2 dynamics during the acute infection phase. Thereby they ignore important long-term post-acute infection effects. We present a mathematical model, which not only describes the SARS-CoV-2 infection dynamics during the acute infection phase, but extends current approaches by also recapitulating clinically observed long-term post-acute infection effects, such as the recovery of the number of susceptible epithelial cells to an initial pre-infection homeostatic level, a permanent and full clearance of the infection within the individual, immune waning, and the formation of long-term immune capacity levels after infection. Finally, we used our model and its description of the long-term post-acute infection dynamics to explore reinfection scenarios differentiating between distinct variant-specific properties of the reinfecting virus. Together, the model's ability to describe not only the acute but also the long-term post-acute infection dynamics provides a more realistic description of key outcomes and allows for its application in clinical and public health scenarios.

Pharmacokinetics of a single orally administered therapeutic dosage of cyclosporine A in healthy cats.

This study aimed to determine a pharmacokinetic profile for a single dosage of cyclosporine A (CsA) clinically used for immunosuppression in cats. Blood-CsA-concentrations were measured before and 1, 2, 4, 6, 8, 12 and 24 h after oral administration of 7 mg/kg body weight (BW) CsA (Atopica® oral solution) to 8 healthy adult cats using high-performance liquid chromatography coupled to mass spectrometry. Pharmacokinetic parameters were calculated using WinNonLin software based on a 1-compartment-model. The median maximum plasma-concentration of 1466 ng/ml (530-2235 ng/ml; minimum-maximum) was reached after 2.0 h (1.0-4.7 h). The area under the curve was 12,568 h x ng/ml (5732-20,820 h x ng/ml) and the apparent total clearance of the drug from plasma was 557 ml/h/kg (336-1221 ml/h/kg). Half-life of absorption into the central compartment was 0.6 h (0.4-2.6 h), half-life of elimination from the central compartment was 4.6 h (1.4-7.5 h).

Allelic correlation is a marker of trade-offs between barriers to transmission of expression variability and signal responsiveness in genetic networks.

Genetic networks should respond to signals but prevent the transmission of spontaneous fluctuations. Limited data from mammalian cells suggest that noise transmission is uncommon, but systematic claims about noise transmission have been limited by the inability to directly measure it. Here, we build a mathematical framework modeling allelic correlation and noise transmission, showing that allelic correlation and noise transmission correspond across model parameters and network architectures. Limiting noise transmission comes with the trade-off of being unresponsive to signals, and within responsive regimes, there is a further trade-off between response time and basal noise transmission. Analysis of allele-specific single-cell RNA-sequencing data revealed that genes encoding upstream factors in signaling pathways and cell-type-specific factors have higher allelic correlation than downstream factors, suggesting they are more subject to regulation. Overall, our findings suggest that some noise transmission must result from signal responsiveness, but it can be minimized by trading off for a slower response. A record of this paper's transparent peer review process is included in the supplemental information.

Altered expression response upon repeated gene repression in single yeast cells.

Cells must continuously adjust to changing environments and, thus, have evolved mechanisms allowing them to respond to repeated stimuli. While faster gene induction upon a repeated stimulus is known as reinduction memory, responses to repeated repression have been less studied so far. Here, we studied gene repression across repeated carbon source shifts in over 1,500 single Saccharomyces cerevisiae cells. By monitoring the expression of a carbon source-responsive gene, galactokinase 1 (Gal1), and fitting a mathematical model to the single-cell data, we observed a faster response upon repeated repressions at the population level. Exploiting our single-cell data and quantitative modeling approach, we discovered that the faster response is mediated by a shortened repression response delay, the estimated time between carbon source shift and Gal1 protein production termination. Interestingly, we can exclude two alternative hypotheses, i) stronger dilution because of e.g., increased proliferation, and ii) a larger fraction of repressing cells upon repeated repressions. Collectively, our study provides a quantitative description of repression kinetics in single cells and allows us to pinpoint potential mechanisms underlying a faster response upon repeated repression. The computational results of our study can serve as the starting point for experimental follow-up studies.

H4K20 Methylation Is Differently Regulated by Dilution and Demethylation in Proliferating and Cell-Cycle-Arrested Xenopus Embryos.

DNA replication during cell division leads to dilution of histone modifications and can thus affect chromatin-mediated gene regulation, raising the question of how the cell-cycle shapes the histone modification landscape, particularly during embryogenesis. We tackled this problem by manipulating the cell cycle during early Xenopus laevis embryogenesis and analyzing in vivo histone H4K20 methylation kinetics. The global distribution of un-, mono-, di-, and tri-methylated histone H4K20 was measured by mass spectrometry in normal and cell-cycle-arrested embryos over time. Using multi-start maximum likelihood optimization and quantitative model selection, we found that three specific biological methylation rate constants were required to explain the measured H4K20 methylation state kinetics. While demethylation is essential for regulating H4K20 methylation kinetics in non-cycling cells, demethylation is very likely dispensable in rapidly dividing cells of early embryos, suggesting that cell-cycle-mediated dilution of H4K20 methylation is an essential regulatory component for shaping its epigenetic landscape during early development. A record of this paper's transparent peer review process is included in the Supplemental Information.

Gene Networks with Transcriptional Bursting Recapitulate Rare Transient Coordinated High Expression States in Cancer.

Non-genetic transcriptional variability is a potential mechanism for therapy resistance in melanoma. Specifically, rare subpopulations of cells occupy a transient pre-resistant state characterized by coordinated high expression of several genes and survive therapy. How might these rare states arise and disappear within the population? It is unclear whether the canonical models of probabilistic transcriptional pulsing can explain this behavior, or if it requires special, hitherto unidentified mechanisms. We show that a minimal model of transcriptional bursting and gene interactions can give rise to rare coordinated high expression states. These states occur more frequently in networks with low connectivity and depend on three parameters. While entry into these states is initiated by a long transcriptional burst that also triggers entry of other genes, the exit occurs through independent inactivation of individual genes. Together, we demonstrate that established principles of gene regulation are sufficient to describe this behavior and argue for its more general existence. A record of this paper's transparent peer review process is included in the Supplemental Information.

Domain Model Explains Propagation Dynamics and Stability of Histone H3K27 and H3K36 Methylation Landscapes.

Chromatin states must be maintained during cell proliferation to uphold cellular identity and genome integrity. Inheritance of histone modifications is central in this process. However, the histone modification landscape is challenged by incorporation of new unmodified histones during each cell cycle, and the principles governing heritability remain unclear. We take a quantitative computational modeling approach to describe propagation of histone H3K27 and H3K36 methylation states. We measure combinatorial H3K27 and H3K36 methylation patterns by quantitative mass spectrometry on subsequent generations of histones. Using model comparison, we reject active global demethylation and invoke the existence of domains defined by distinct methylation endpoints. We find that H3K27me3 on pre-existing histones stimulates the rate of de novo H3K27me3 establishment, supporting a read-write mechanism in timely chromatin restoration. Finally, we provide a detailed quantitative picture of the mutual antagonism between H3K27 and H3K36 methylation and propose that it stabilizes epigenetic states across cell division.