Mutual information in random Boolean models of regulatory networks

The amount of mutual information contained in time series of two elements gives a measure of how well their activities are coordinated. In a large, complex network of interacting elements, such as a genetic regulatory network within a cell, the average of the mutual information over all pairs is a global measure of how well the system can coordinate its internal dynamics. We study this average pairwise mutual information in random Boolean networks (RBNs) as a function of the distribution of Boolean rules implemented at each element, assuming that the links in the network are randomly placed. Efficient numerical methods for calculating show that as the number of network nodes N approaches infinity, the quantity N exhibits a discontinuity at parameter values corresponding to critical RBNs. For finite systems it peaks near the critical value, but slightly in the disordered regime for typical parameter variations. The source of high values of N is the indirect correlations between pairs of elements from different long chains with a common starting point. The contribution from pairs that are directly linked approaches zero for critical networks and peaks deep in the disordered regime.Comment: 11 pages, 6 figures; Minor revisions for clarity and figure format, one reference adde

Stochastic sequence-level model of coupled transcription and translation in prokaryotes

<p>Abstract</p> <p>Background</p> <p>In prokaryotes, transcription and translation are dynamically coupled, as the latter starts before the former is complete. Also, from one transcript, several translation events occur in parallel. To study how events in transcription elongation affect translation elongation and fluctuations in protein levels, we propose a delayed stochastic model of prokaryotic transcription and translation at the nucleotide and codon level that includes the promoter open complex formation and alternative pathways to elongation, namely pausing, arrests, editing, pyrophosphorolysis, RNA polymerase traffic, and premature termination. Stepwise translation can start after the ribosome binding site is formed and accounts for variable codon translation rates, ribosome traffic, back-translocation, drop-off, and trans-translation.</p> <p>Results</p> <p>First, we show that the model accurately matches measurements of sequence-dependent translation elongation dynamics. Next, we characterize the degree of coupling between fluctuations in RNA and protein levels, and its dependence on the rates of transcription and translation initiation. Finally, modeling sequence-specific transcriptional pauses, we find that these affect protein noise levels.</p> <p>Conclusions</p> <p>For parameter values within realistic intervals, transcription and translation are found to be tightly coupled in <it>Escherichia coli</it>, as the noise in protein levels is mostly determined by the underlying noise in RNA levels. Sequence-dependent events in transcription elongation, e.g. pauses, are found to cause tangible effects in the degree of fluctuations in protein levels.</p

Complexity of the COVID-19 pandemic in Maringa

While extensive literature exists on the COVID-19 pandemic at regional and national levels, understanding its dynamics and consequences at the city level remains limited. This study investigates the pandemic in Maring\'a, a medium-sized city in Brazil's South Region, using data obtained by actively monitoring the disease from March 2020 to June 2022. Despite prompt and robust interventions, COVID-19 cases increased exponentially during the early spread of COVID-19, with a reproduction number lower than that observed during the initial outbreak in Wuhan. Our research demonstrates the remarkable impact of non-pharmaceutical interventions on both mobility and pandemic indicators, particularly during the onset and the most severe phases of the emergency. However, our results suggest that the city's measures were primarily reactive rather than proactive. Maring\'a faced six waves of cases, with the third and fourth waves being the deadliest, responsible for over two-thirds of all deaths and overwhelming the local healthcare system. Excess mortality during this period exceeded deaths attributed to COVID-19, indicating that the burdened healthcare system may have contributed to increased mortality from other causes. By the end of the fourth wave, nearly three-quarters of the city's population had received two vaccine doses, significantly decreasing deaths despite the surge caused by the Omicron variant. Finally, we compare these findings with the national context and other similarly sized cities, highlighting substantial heterogeneities in the spread and impact of the disease.Comment: 20 pages, 5 figures, supplementary information; accepted for publication in Scientific Report

In vivo kinetics of transcription initiation of the lar promoter in Escherichia coli. Evidence for a sequential mechanism with two rate-limiting steps

<p>Abstract</p> <p>Background</p> <p>In <it>Escherichia coli </it>the mean and cell-to-cell diversity in RNA numbers of different genes vary widely. This is likely due to different kinetics of transcription initiation, a complex process with multiple rate-limiting steps that affect RNA production.</p> <p>Results</p> <p>We measured the <it>in vivo </it>kinetics of production of individual RNA molecules under the control of the lar promoter in <it>E. coli</it>. From the analysis of the distributions of intervals between transcription events in the regimes of weak and medium induction, we find that the process of transcription initiation of this promoter involves a sequential mechanism with two main rate-limiting steps, each lasting hundreds of seconds. Both steps become faster with increasing induction by IPTG and Arabinose.</p> <p>Conclusions</p> <p>The two rate-limiting steps in initiation are found to be important regulators of the dynamics of RNA production under the control of the lar promoter in the regimes of weak and medium induction. Variability in the intervals between consecutive RNA productions is much lower than if there was only one rate-limiting step with a duration following an exponential distribution. The methodology proposed here to analyze the <it>in vivo </it>dynamics of transcription may be applicable at a genome-wide scale and provide valuable insight into the dynamics of prokaryotic genetic networks.</p

Studying genetic regulatory networks at the molecular level: delayed reaction stochastic models

Abstract Current advances in molecular biology enable us to access the rapidly increasing body of genetic information. It is still challenging to model gene systems at the molecular level. Here, we propose two types of reaction kinetic models for constructing genetic networks. Time delays involved in transcription and translation are explicitly considered to explore the effects of delays, which may be significant in genetic networks featured with feedback loops. One type of model is based on delayed effective reactions, each reaction modeling a biochemical process like transcription without involving intermediate reactions. The other is based on delayed virtual reactions, each reaction being converted from a mathematical function to model a biochemical function like gene inhibition. The latter stochastic models are derived from the corresponding mean-field models. The former ones are composed of single gene expression modules. We thus design a model of gene expression. This model is verified by our simulations using a delayed stochastic simulation algorithm, which accurately reproduces the stochastic kinetics in a recent experimental study. Various simplified versions of the model are given and evaluated. We then use the two methods to study the genetic toggle switch and the repressilator. We define the &apos;&apos;on&apos;&apos; and &apos;&apos;off&apos;&apos; states of genes and extract a binary code from the stochastic time series. The binary code can be described by the corresponding Boolean network models in certain conditions. We discuss these conditions, suggesting a method to connect Boolean models, mean-field models, and stochastic chemical models.

Cell-to-cell diversity in protein levels of a gene driven by a tetracycline inducible promoter

<p>Abstract</p> <p>Background</p> <p>Gene expression in <it>Escherichia coli </it>is regulated by several mechanisms. We measured in single cells the expression level of a single copy gene coding for green fluorescent protein (GFP), integrated into the genome and driven by a tetracycline inducible promoter, for varying induction strengths. Also, we measured the transcriptional activity of a tetracycline inducible promoter controlling the transcription of a RNA with 96 binding sites for MS2-GFP.</p> <p>Results</p> <p>The distribution of GFP levels in single cells is found to change significantly as induction reaches high levels, causing the Fano factor of the cells' protein levels to increase with mean level, beyond what would be expected from a Poisson-like process of RNA transcription. In agreement, the Fano factor of the cells' number of RNA molecules target for MS2-GFP follows a similar trend. The results provide evidence that the dynamics of the promoter complex formation, namely, the variability in its duration from one transcription event to the next, explains the change in the distribution of expression levels in the cell population with induction strength.</p> <p>Conclusions</p> <p>The results suggest that the open complex formation of the tetracycline inducible promoter, in the regime of strong induction, affects significantly the dynamics of RNA production due to the variability of its duration from one event to the next.</p