Active processes in one dimension

We consider the thermal and athermal overdamped motion of particles in 1D geometries where discrete internal degrees of freedom (spin) are coupled with the translational motion. Adding a driving velocity that depends on the time-dependent spin constitutes the simplest model of active particles (run-and-tumble processes) where the violation of the equipartition principle and of the Sutherland-Einstein relation can be studied in detail even when there is generalized reversibility. We give an example (with four spin values) where the irreversibility of the translational motion manifests itself only in higher-order (than two) time correlations. We derive a generalized telegraph equation as the Smoluchowski equation for the spatial density for an arbitrary number of spin values. We also investigate the Arrhenius exponential law for run-and-tumble particles, due to their activity the slope of the potential becomes important in contrast to the passive diffusion case and activity enhances the escape from a potential well (if that slope is high enough). Finally, in the absence of a driving velocity, the presence of internal currents such as in the chemistry of molecular motors may be transmitted to the translational motion and the internal activity is crucial for the direction of the emerging spatial current.Comment: 26 pages, 3 figure

Additional file 2: of Interlog protein network: an evolutionary benchmark of protein interaction networks for the evaluation of clustering algorithms

Network Parameters. Some network parameter are included to gain clear insight about four PPINs and IPN. Also, all calculated external clustering measures and indices are presented in this table. The ranges for Rand, Jaccard and Fowlkes-Mallows are [0, 1] which are presented in percent whereas the Minkowski rang is [0, +∞). These values are computed for all species and five clustering algorithms. (DOCX 17 kb

Three-way interaction model to trace the mechanisms involved in Alzheimer’s disease transgenic mice

<div><p>Alzheimer's disease (AD) is the most common cause for dementia in human. Currently, more than 46 million people in the world suffer from AD and it is estimated that by 2050 this number increases to more than 131 million. AD is considered as a complex disease. Therefore, understanding the mechanism of AD is a universal challenge. Nowadays, a huge number of disease-related high-throughput “omics” datasets are freely available. Such datasets contain valuable information about disease-related pathways and their corresponding gene interactions. In the present work, a three-way interaction model is used as a novel approach to understand AD-related mechanisms. This model can trace the dynamic nature of co-expression relationship between two genes by introducing their link to a third gene. Apparently, such relationships cannot be traced by the classical two-way interaction model. Liquid association method was applied to capture the statistically significant triplets which are involved in three-way interaction. Subsequently, gene set enrichment analysis (GSEA) and gene regulatory network (GRN) inference were applied to analyze the biological relevance of the statistically significant triplets. The results of this study suggest that the innate immunity processes are important in AD. Specifically, our results suggest that <i>H2-Ob</i> as the switching gene and the gene pair {<i>Csf1r</i>, <i>Milr1</i>} form a statistically significant and biologically relevant triplet, which may play an important role in AD. We propose that the homeostasis-related link between mast cells and microglia is presumably controlled with <i>H2-Ob</i> expression levels as a switching gene.</p></div

FDR vs. -log (<i>p</i>-value).

<p>The changes in FDR (BH-corrected <i>p</i>-value) versus -log (<i>p</i>-value) for the first 300000 results of fastLA [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0184697#pone.0184697.ref021" target="_blank">21</a>]. As shown FDR = 0.001 corresponds to -log (<i>p</i>- value) = 6.817.</p

Gene set enrichment analysis.

<p>Enriched terms based on (A) “biological process”; (B) “cellular component”; and (C) “KEGG pathway” for two gene groups, genes in X₃ position and all of the genes involved in the triplets. The common terms in these two groups are shown in red. The high frequency of common terms suggest that the results of liquid association method are consistent with the biological expectation from three-way interactions, that is, the presence of switching and switched genes in the same biological pathway.</p

Biologically relevant triplets.

<p>By tracing statistically significant triplets in the enriched terms, 12 triplets in which X₁ and X₂ are involved in the same biological process or pathway were determined.</p

Le Courrier

28 juin 18221822/06/28 (A0,N179)

Network visualization of the complex (loose) attractor in the present-day model.

<p>Node size and color are proportional to betweenness and closeness centrality measures respectively.</p

Boolean rules governing the state of the 4-node network of the 1965 proposed central dogma depicted in Fig 1B derived from [1, 2].

<p>The symbols “&”, “|” and “!” represent “AND”, “OR” and “NOT” operators.</p

Examples of the statistically triplets.

<p>In each case, a considerable change in the correlation of X₁ and X₂ occurs as a result of change in X₃.</p