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We propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability distribution of any network node-based property, and of the network size, after only a small fraction of network nodes has been explored. The Bayesian nature of our approach provides rigorous estimates of all parameter uncertainties. We demonstrate our framework on several standard examples, including random, scale-free, and small-world networks, and apply it to study epidemic spreading on a scale-free network. We also infer properties of the large-scale network formed by hyperlinks between Wikipedia pages.
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Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs.
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Algoritmos , Simulación por Computador , Modelos Biológicos , Modelos Químicos , Modelos EstadísticosRESUMEN
Summary: The increasing number of publicly available bacterial gene expression data sets provides an unprecedented resource for the study of gene regulation in diverse conditions, but emphasizes the need for self-supervised methods for the automated generation of new hypotheses. One approach for inferring coordinated regulation from bacterial expression data is through neural networks known as denoising autoencoders (DAEs) which encode large datasets in a reduced bottleneck layer. We have generalized this application of DAEs to include deep networks and explore the effects of network architecture on gene set inference using deep learning. We developed a DAE-based pipeline to extract gene sets from transcriptomic data in Escherichia coli, validate our method by comparing inferred gene sets with known pathways, and have used this pipeline to explore how the choice of network architecture impacts gene set recovery. We find that increasing network depth leads the DAEs to explain gene expression in terms of fewer, more concisely defined gene sets, and that adjusting the width results in a tradeoff between generalizability and biological inference. Finally, leveraging our understanding of the impact of DAE architecture, we apply our pipeline to an independent uropathogenic E.coli dataset to identify genes uniquely induced during human colonization. Availability and implementation: https://github.com/BarquistLab/DAE_architecture_exploration.
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IMPORTANCE: Bacteria react very differently to survive in acidic environments, such as the human gastrointestinal tract. Escherichia coli is one of the extremely acid-resistant bacteria and has a variety of acid-defense mechanisms. Here, we provide the first genome-wide overview of the adaptations of E. coli K-12 to mild and severe acid stress at both the transcriptional and translational levels. Using ribosome profiling and RNA sequencing, we uncover novel adaptations to different degrees of acidity, including previously hidden stress-induced small proteins and novel key transcription factors for acid defense, and report mRNAs with pH-dependent differential translation efficiency. In addition, we distinguish between acid-specific adaptations and general stress response mechanisms using denoising autoencoders. This workflow represents a powerful approach that takes advantage of next-generation sequencing techniques and machine learning to systematically analyze bacterial stress responses.
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Proteínas de Escherichia coli , Escherichia coli , Humanos , Escherichia coli/genética , Perfilado de Ribosomas , Proteínas de Escherichia coli/genética , Factores de Transcripción/genética , ARN Mensajero/genéticaRESUMEN
Speed fluctuations of individual birds in natural flocks are moderate, due to the aerodynamic and biomechanical constraints of flight. Yet the spatial correlations of such fluctuations are scale-free, namely they have a range as wide as the entire group, a property linked to the capacity of the system to collectively respond to external perturbations. Scale-free correlations and moderate fluctuations set conflicting constraints on the mechanism controlling the speed of each agent, as the factors boosting correlation amplify fluctuations, and vice versa. Here, using a statistical field theory approach, we suggest that a marginal speed confinement that ignores small deviations from the natural reference value while ferociously suppressing larger speed fluctuations, is able to reconcile scale-free correlations with biologically acceptable group's speed. We validate our theoretical predictions by comparing them with field experimental data on starling flocks with group sizes spanning an unprecedented interval of over two orders of magnitude.
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Vuelo Animal , Estorninos , Animales , Reuniones MasivasRESUMEN
Studying emerging or neglected pathogens is often challenging due to insufficient information and absence of genetic tools. Dual RNA-seq provides insights into host-pathogen interactions, and is particularly informative for intracellular organisms. Here we apply dual RNA-seq to Orientia tsutsugamushi (Ot), an obligate intracellular bacterium that causes the vector-borne human disease scrub typhus. Half the Ot genome is composed of repetitive DNA, and there is minimal collinearity in gene order between strains. Integrating RNA-seq, comparative genomics, proteomics, and machine learning to study the transcriptional architecture of Ot, we find evidence for wide-spread post-transcriptional antisense regulation. Comparing the host response to two clinical isolates, we identify distinct immune response networks for each strain, leading to predictions of relative virulence that are validated in a mouse infection model. Thus, dual RNA-seq can provide insight into the biology and host-pathogen interactions of a poorly characterized and genetically intractable organism such as Ot.