To increase situational awareness and support evidence-based policymaking, we formulated a mathematical model for coronavirus disease transmission within a regional population. This compartmental model accounts for quarantine, self-isolation, social distancing, a nonexponentially distributed incubation period, asymptomatic persons, and mild and severe forms of symptomatic disease. We used Bayesian inference to calibrate region-specific models for consistency with daily reports of confirmed cases in the 15 most populous metropolitan statistical areas in the United States. We also quantified uncertainty in parameter estimates and forecasts. This online learning approach enables early identification of new trends despite considerable variability in case reporting.

SUMMARY Neuronal activity-inducible gene transcription correlates with rapid and transient increases in histone acetylation at promoters and enhancers of activity-regulated genes. Exactly how histone acetylation modulates transcription of these genes has remained unknown. We used single-cell in situ transcriptional analysis to show that Fos and Npas4 are transcribed in stochastic bursts in mouse neurons and that membrane depolarization increases mRNA expression by increasing burst frequency. We then expressed dCas9-p300 or dCas9-HDAC8 fusion proteins to mimic or block activity-induced histone acetylation locally at enhancers. Adding histone acetylation increased Fos transcription by prolonging burst duration and resulted in higher Fos protein levels and an elevation of resting membrane potential. Inhibiting histone acetylation reduced Fos transcription by reducing burst frequency and impaired experience-dependent Fos protein induction in the hippocampus in vivo. Thus, activity-inducible histone acetylation tunes the transcriptional dynamics of experience-regulated genes to affect selective changes in neuronal gene expression and cellular function.

The dynamics of short-lived mRNA results in bursts of protein production in gene regulatory networks. We investigate the propagation of bursting noise between different levels of mathematical modelling and demonstrate that conventional approaches based on diffusion approximations can fail to capture bursting noise. An alternative coarse-grained model, the so-called piecewise deterministic Markov process (PDMP), is seen to outperform the diffusion approximation in biologically relevant parameter regimes. We provide a systematic embedding of the PDMP model into the landscape of existing approaches, and we present analytical methods to calculate its stationary distribution and switching frequencies.

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Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. In addition to slow chromatin and/or DNA looping dynamics, one source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e. the non-adiabatic binding regime. Here, we introduce a simple analytical framework, known as a piecewise deterministic Markov process (PDMP), that accurately describes the stochastic dynamics of gene expression in the non-adiabatic regime. We illustrate the utility of the PDMP on a non-trivial dynamical system by analysing the properties of a titration-based oscillator in the non-adiabatic limit. We first show how to transform the underlying chemical master equation into a PDMP where the slow transitions between promoter states are stochastic, but whose rates depend upon the faster deterministic dynamics of the transcription factors regulated by these promoters. We show that the PDMP accurately describes the observed periods of stochastic cycles in activator and repressor-based titration oscillators. We then generalize our PDMP analysis to more complicated versions of titration-based oscillators to explain how multiple binding sites lengthen the period and improve coherence. Last, we show how noise-induced oscillation previously observed in a titration-based oscillator arises from non-adiabatic and discrete binding events at the promoter site.