Fundamental to biological decision-making is the ability to generate bimodal expression patterns where 2 alternate expression states simultaneously exist. Here, we use a combination of single-cell analysis and mathematical modeling to examine the sources of bimodality in the transcriptional program controlling HIV’s fate decision between active replication and viral latency. We find that the HIV transactivator of transcription (Tat) protein manipulates the intrinsic toggling of HIV’s promoter, the long terminal repeat (LTR), to generate bimodal ON-OFF expression and that transcriptional positive feedback from Tat shifts and expands the regime of LTR bimodality. This result holds for both minimal synthetic viral circuits and full-length virus. Strikingly, computational analysis indicates that the Tat circuit’s noncooperative “nonlatching” feedback architecture is optimized to slow the promoter’s toggling and generate bimodality by stochastic extinction of Tat. In contrast to the standard Poisson model, theory and experiment show that nonlatching positive feedback substantially dampens the inverse noise-mean relationship to maintain stochastic bimodality despite increasing mean expression levels. Given the rapid evolution of HIV, the presence of a circuit optimized to robustly generate bimodal expression appears consistent with the hypothesis that HIV’s decision between active replication and latency provides a viral fitness advantage. More broadly, the results suggest that positive-feedback circuits may have evolved not only for signal amplification but also for robustly generating bimodality by decoupling expression fluctuations (noise) from mean expression levels.

Summary of bimodal soil data used in the parametric study and calibration process reproduced from Zhao et al. [36].

Index and other properties of the soils used in validating the proposed equation.

Little is known about the early evolution of Venus and a potential habitable period during the first 1 billion years. In particular, it remains unclear whether or not plate tectonics and an active carbonate-silicate cycle were present. In the presence of liquid water but without plate tectonics, weathering would have been limited to freshly produced basaltic crust, with an early carbon cycle restricted to the crust and atmosphere. With the evaporation of surface water, weathering would cease. With ongoing volcanism, carbonate sediments would be buried and sink downwards. Thereby, carbonates would heat up until they become unstable and the crust would become depleted in carbonates. With urn:x-wiley:21699097:media:jgre21738:jgre21738-math-0001 supply to the atmosphere the surface temperature rises further, the depth below which decarbonation occurs decreases, causing the release of even more urn:x-wiley:21699097:media:jgre21738:jgre21738-math-0002. We assess the habitable period of an early stagnant-lid Venus by employing a coupled interior-atmosphere evolution model accounting for urn:x-wiley:21699097:media:jgre21738:jgre21738-math-0003 degassing, weathering, carbonate burial, and crustal decarbonation. We find that if initial surface conditions allow for liquid water, weathering can keep the planet habitable for up to 900 Myr, followed by evaporation of water and rapid crustal carbonate depletion. For the atmospheric urn:x-wiley:21699097:media:jgre21738:jgre21738-math-0004 of stagnant-lid exoplanets, we predict a bimodal distribution, depending on whether or not these planets experienced a runaway greenhouse in their history. Planets with high atmospheric urn:x-wiley:21699097:media:jgre21738:jgre21738-math-0005 could be associated with crustal carbonate depletion as a consequence of a runaway greenhouse, whereas planets with low atmospheric urn:x-wiley:21699097:media:jgre21738:jgre21738-math-0006 would indicate active silicate weathering and thereby a habitable climate.

Suggested values of Xa1, Xa2 and Xr according to soil dry density.

Best fitting parameters for evaluating the performance of the proposed equation.

Slope ratio and distances between curves for different soil types [20].

A single transcription factor may interact with a multitude of targets on the genome, some of which are at gene promoters, others being part of DNA repeat elements. Being sequestered at binding sites, protein molecules can be prevented from partaking in other pathways, specifically, from regulating the expression of the very gene that encodes them. Acting as decoys at the expense of the autoregulatory loop, the binding sites can have a profound impact on protein abundance—on its mean as well as on its cell-to-cell variability. In order to quantify this impact, we study in this paper a mathematical model for pulsatile expression of a transcription factor that autoregulates its expression and interacts with decoys. We determine the exact stationary distribution for protein abundance at the single-cell level, showing that in the case of non-cooperative positive autoregulation, the distribution can be bimodal, possessing a basal expression mode and a distinct, up-regulated, mode. Bimodal protein distributions are more feasible if the rate of degradation is the same irrespective of whether protein is bound or not. Contrastingly, the presence of decoy binding sites which protect the protein from degradation reduces the availability of the bimodal scenario.

Accumulating data indicate that cancer stem cells contribute to tumor chemoresistance and their persistence alters clinical outcome. Our previous study has shown that ovarian cancer may be initiated by ovarian cancer initiating cells (OCIC) characterized by surface antigen CD44 and c-KIT (CD117). It has been experimentally demonstrated that a microRNA, namely miR-193a, targets c-KIT mRNA for degradation and could play a crucial role in ovarian cancer development. How miR-193a is regulated is poorly understood and the emerging picture is complex. To unravel this complexity, we propose a mathematical model to explore how estrogen-mediated up-regulation of another target of miR-193a, namely E2F6, can attenuate the function of miR-193a in two ways, one through a competition of E2F6 and c-KIT transcripts for miR-193a, and second by binding of E2F6 protein, in association with a polycomb complex, to the promoter of miR-193a to down-regulate its transcription. Our model predicts that this bimodal control increases the expression of c-KIT and that the second mode of epigenetic regulation is required to generate a switching behavior in c-KIT and E2F6 expressions. Additional analysis of the TCGA ovarian cancer dataset demonstrates that ovarian cancer patients with low expression of EZH2, a polycomb-group family protein, show positive correlation between E2F6 and c-KIT. We conjecture that a simultaneous EZH2 inhibition and anti-estrogen therapy can constitute an effective combined therapeutic strategy against ovarian cancer.

Quorum Sensing (QS) drives coordinated phenotypic outcomes among bacterial populations. Its role in mediating infectious disease has led to the elucidation of numerous autoinducers and their corresponding QS signaling pathways. Among them, the Lsr (LuxS-regulated) QS system is conserved in scores of bacteria, and its signal molecule, autoinducer-2 (AI-2), is synthesized as a product of 1-carbon metabolism. Lsr signal transduction processes, therefore, may help organize population scale activities in numerous bacterial consortia. Conceptions of how Lsr QS organizes population scale behaviors remain limited, however. Using mathematical simulations, we examined how desynchronized Lsr QS activation, arising from cell-to-cell population heterogeneity, could lead to bimodal Lsr signaling and fractional activation. This has been previously observed experimentally. Governing these processes are an asynchronous AI-2 uptake, where positive intracellular feedback in Lsr expression is combined with negative feedback between cells. The resulting activation patterns differ from that of the more widely studied LuxIR system, the topology of which consists of only positive feedback. To elucidate differences, both QS systems were simulated in 2D, where cell populations grow and signal each other via traditional growth and diffusion equations. Our results demonstrate that the LuxIR QS system produces an ‘outward wave’ of autoinduction, and the Lsr QS system yields dispersed autoinduction from spatially-localized secretion and uptake profiles. In both cases, our simulations mirror previously demonstrated experimental results. As a whole, these models inform QS observations and synthetic biology designs.

as in Example 2 of the original paper [8]. The algorithms behave as one would expect if they are selecting for independence. For the bimodal/Gaussian-like cases, ICA-EBM and Infomax (sub) do well, and for the unimodal/maximum kurtosis/low sparsity case Infomax-super, FastICA and ICA-EBM all do extremely well. Numbers in boldface indicate when separation was good.

Reliability of the measure of relevance for the two sample-problem expressed in sensitivity and specificity indexes. Two different distributions, uniform and bimodal, were used for evaluating reliability. Like the objectivity also the reliability property of the relevance measure goes up to excellent levels (sensitivity and specificity about 100%) with increased normalized biological differences and sample sizes.aMean rates (in %) of the variables detected as relevant or significant by .bMean rates (in %) of variables detected as relevant or significant by applying appropriate nonparametric tests.

T. cruzi PCR samples distribution according to classification of high and low antibody levels for each serology test.

Electrocardiogram abnormalities distribution in groups of donors with four tests concordant serology reactivity, as high and low antibody levels.