Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

Hepcidin as a therapeutic tool to limit iron overload and improve anemia in β-thalassemic mice.

Excessive iron absorption is one of the main features of β-thalassemia and can lead to severe morbidity and mortality. Serial analyses of β-thalassemic mice indicate that while hemoglobin levels decrease over time, the concentration of iron in the liver, spleen, and kidneys markedly increases. Iron overload is associated with low levels of hepcidin, a peptide that regulates iron metabolism by triggering degradation of ferroportin, an iron-transport protein localized on absorptive enterocytes as well as hepatocytes and macrophages. Patients with β-thalassemia also have low hepcidin levels. These observations led us to hypothesize that more iron is absorbed in β-thalassemia than is required for erythropoiesis and that increasing the concentration of hepcidin in the body of such patients might be therapeutic, limiting iron overload. Here we demonstrate that a moderate increase in expression of hepcidin in β-thalassemic mice limits iron overload, decreases formation of insoluble membrane-bound globins and reactive oxygen species, and improves anemia. Mice with increased hepcidin expression also demonstrated an increase in the lifespan of their red cells, reversal of ineffective erythropoiesis and splenomegaly, and an increase in total hemoglobin levels. These data led us to suggest that therapeutics that could increase hepcidin levels or act as hepcidin agonists might help treat the abnormal iron absorption in individuals with β-thalassemia and related disorders.

Stochastic E2F activation and reconciliation of phenomenological cell-cycle models.

The transition of the mammalian cell from quiescence to proliferation is a highly variable process. Over the last four decades, two lines of apparently contradictory, phenomenological models have been proposed to account for such temporal variability. These include various forms of the transition probability (TP) model and the growth control (GC) model, which lack mechanistic details. The GC model was further proposed as an alternative explanation for the concept of the restriction point, which we recently demonstrated as being controlled by a bistable Rb-E2F switch. Here, through a combination of modeling and experiments, we show that these different lines of models in essence reflect different aspects of stochastic dynamics in cell cycle entry. In particular, we show that the variable activation of E2F can be described by stochastic activation of the bistable Rb-E2F switch, which in turn may account for the temporal variability in cell cycle entry. Moreover, we show that temporal dynamics of E2F activation can be recast into the frameworks of both the TP model and the GC model via parameter mapping. This mapping suggests that the two lines of phenomenological models can be reconciled through the stochastic dynamics of the Rb-E2F switch. It also suggests a potential utility of the TP or GC models in defining concise, quantitative phenotypes of cell physiology. This may have implications in classifying cell types or states.

Spike avalanches exhibit universal dynamics across the sleep-wake cycle.

BACKGROUND: Scale-invariant neuronal avalanches have been observed in cell cultures and slices as well as anesthetized and awake brains, suggesting that the brain operates near criticality, i.e. within a narrow margin between avalanche propagation and extinction. In theory, criticality provides many desirable features for the behaving brain, optimizing computational capabilities, information transmission, sensitivity to sensory stimuli and size of memory repertoires. However, a thorough characterization of neuronal avalanches in freely-behaving (FB) animals is still missing, thus raising doubts about their relevance for brain function. METHODOLOGY/PRINCIPAL FINDINGS: To address this issue, we employed chronically implanted multielectrode arrays (MEA) to record avalanches of action potentials (spikes) from the cerebral cortex and hippocampus of 14 rats, as they spontaneously traversed the wake-sleep cycle, explored novel objects or were subjected to anesthesia (AN). We then modeled spike avalanches to evaluate the impact of sparse MEA sampling on their statistics. We found that the size distribution of spike avalanches are well fit by lognormal distributions in FB animals, and by truncated power laws in the AN group. FB data surrogation markedly decreases the tail of the distribution, i.e. spike shuffling destroys the largest avalanches. The FB data are also characterized by multiple key features compatible with criticality in the temporal domain, such as 1/f spectra and long-term correlations as measured by detrended fluctuation analysis. These signatures are very stable across waking, slow-wave sleep and rapid-eye-movement sleep, but collapse during anesthesia. Likewise, waiting time distributions obey a single scaling function during all natural behavioral states, but not during anesthesia. Results are equivalent for neuronal ensembles recorded from visual and tactile areas of the cerebral cortex, as well as the hippocampus. CONCLUSIONS/SIGNIFICANCE: Altogether, the data provide a comprehensive link between behavior and brain criticality, revealing a unique scale-invariant regime of spike avalanches across all major behaviors.

MicroRNA antagonism of the picornaviral life cycle: alternative mechanisms of interference.

In addition to modulating the function and stability of cellular mRNAs, microRNAs can profoundly affect the life cycles of viruses bearing sequence complementary targets, a finding recently exploited to ameliorate toxicities of vaccines and oncolytic viruses. To elucidate the mechanisms underlying microRNA-mediated antiviral activity, we modified the 3' untranslated region (3'UTR) of Coxsackievirus A21 to incorporate targets with varying degrees of homology to endogenous microRNAs. We show that microRNAs can interrupt the picornavirus life-cycle at multiple levels, including catalytic degradation of the viral RNA genome, suppression of cap-independent mRNA translation, and interference with genome encapsidation. In addition, we have examined the extent to which endogenous microRNAs can suppress viral replication in vivo and how viruses can overcome this inhibition by microRNA saturation in mouse cancer models.

The role of tectonic uplift, climate, and vegetation in the long-term terrestrial phosphorous cycle

Phosphorus (P) is a crucial element for life and therefore for maintaining ecosystem productivity. Its local availability to the terrestrial biosphere results from the interaction between climate, tectonic uplift, atmospheric transport, and biotic cycling. Here we present a mathematical model that describes the terrestrial P-cycle in a simple but comprehensive way. The resulting dynamical system can be solved analytically for steady-state conditions, allowing us to test the sensitivity of the P-availability to the key parameters and processes. Given constant inputs, we find that humid ecosystems exhibit lower P availability due to higher runoff and losses, and that tectonic uplift is a fundamental constraint. In particular, we find that in humid ecosystems the biotic cycling seem essential to maintain long-term P-availability. The time-dependent P dynamics for the Franz Josef and Hawaii chronosequences show how tectonic uplift is an important constraint on ecosystem productivity, while hydroclimatic conditions control the P-losses and speed towards steady-state. The model also helps describe how, with limited uplift and atmospheric input, as in the case of the Amazon Basin, ecosystems must rely on mechanisms that enhance P-availability and retention. Our novel model has a limited number of parameters and can be easily integrated into global climate models to provide a representation of the response of the terrestrial biosphere to global change. © 2010 Author(s).

A novel, non-apoptotic role for Scythe/BAT3: a functional switch between the pro- and anti-proliferative roles of p21 during the cell cycle.

BACKGROUND: Scythe/BAT3 is a member of the BAG protein family whose role in apoptosis has been extensively studied. However, since the developmental defects observed in Bat3-null mouse embryos cannot be explained solely by defects in apoptosis, we investigated whether BAT3 is also involved in cell-cycle progression. METHODS/PRINCIPAL FINDINGS: Using a stable-inducible Bat3-knockdown cellular system, we demonstrated that reduced BAT3 protein level causes a delay in both G1/S transition and G2/M progression. Concurrent with these changes in cell-cycle progression, we observed a reduction in the turnover and phosphorylation of the CDK inhibitor p21, which is best known as an inhibitor of DNA replication; however, phosphorylated p21 has also been shown to promote G2/M progression. Our findings indicate that in Bat3-knockdown cells, p21 continues to be synthesized during cell-cycle phases that do not normally require p21, resulting in p21 protein accumulation and a subsequent delay in cell-cycle progression. Finally, we showed that BAT3 co-localizes with p21 during the cell cycle and is required for the translocation of p21 from the cytoplasm to the nucleus during the G1/S transition and G2/M progression. CONCLUSION: Our study reveals a novel, non-apoptotic role for BAT3 in cell-cycle regulation. By maintaining a low p21 protein level during the G1/S transition, BAT3 counteracts the inhibitory effect of p21 on DNA replication and thus enables the cells to progress from G1 to S phase. Conversely, during G2/M progression, BAT3 facilitates p21 phosphorylation by cyclin A/Cdk2, an event required for G2/M progression. BAT3 modulates these pro- and anti-proliferative roles of p21 at least in part by regulating cyclin A abundance, as well as p21 translocation between the cytoplasm and the nucleus to ensure that it functions in the appropriate intracellular compartment during each phase of the cell cycle.

Targeting Gbeta gamma signaling in arterial vascular smooth muscle proliferation: a novel strategy to limit restenosis.

Restenosis continues to be a major problem limiting the effectiveness of revascularization procedures. To date, the roles of heterotrimeric G proteins in the triggering of pathological vascular smooth muscle (VSM) cell proliferation have not been elucidated. betagamma subunits of heterotrimeric G proteins (Gbetagamma) are known to activate mitogen-activated protein (MAP) kinases after stimulation of certain G protein-coupled receptors; however, their relevance in VSM mitogenesis in vitro or in vivo is not known. Using adenoviral-mediated transfer of a transgene encoding a peptide inhibitor of Gbetagamma signaling (betaARKct), we evaluated the role of Gbetagamma in MAP kinase activation and proliferation in response to several mitogens, including serum, in cultured rat VSM cells. Our results include the striking finding that serum-induced proliferation of VSM cells in vitro is mediated largely via Gbetagamma. Furthermore, we studied the effects of in vivo adenoviral-mediated betaARKct gene transfer on VSM intimal hyperplasia in a rat carotid artery restenosis model. Our in vivo results demonstrated that the presence of the betaARKct in injured rat carotid arteries significantly reduced VSM intimal hyperplasia by 70%. Thus, Gbetagamma plays a critical role in physiological VSM proliferation, and targeted Gbetagamma inhibition represents a novel approach for the treatment of pathological conditions such as restenosis.

Evolution of networks and sequences in eukaryotic cell cycle control.

The molecular networks regulating the G1-S transition in budding yeast and mammals are strikingly similar in network structure. However, many of the individual proteins performing similar network roles appear to have unrelated amino acid sequences, suggesting either extremely rapid sequence evolution, or true polyphyly of proteins carrying out identical network roles. A yeast/mammal comparison suggests that network topology, and its associated dynamic properties, rather than regulatory proteins themselves may be the most important elements conserved through evolution. However, recent deep phylogenetic studies show that fungal and animal lineages are relatively closely related in the opisthokont branch of eukaryotes. The presence in plants of cell cycle regulators such as Rb, E2F and cyclins A and D, that appear lost in yeast, suggests cell cycle control in the last common ancestor of the eukaryotes was implemented with this set of regulatory proteins. Forward genetics in non-opisthokonts, such as plants or their green algal relatives, will provide direct information on cell cycle control in these organisms, and may elucidate the potentially more complex cell cycle control network of the last common eukaryotic ancestor.

Human-chimpanzee differences in a FZD8 enhancer alter cell-cycle dynamics in the developing neocortex.

The human neocortex differs from that of other great apes in several notable regards, including altered cell cycle, prolonged corticogenesis, and increased size [1-5]. Although these evolutionary changes most likely contributed to the origin of distinctively human cognitive faculties, their genetic basis remains almost entirely unknown. Highly conserved non-coding regions showing rapid sequence changes along the human lineage are candidate loci for the development and evolution of uniquely human traits. Several studies have identified human-accelerated enhancers [6-14], but none have linked an expression difference to a specific organismal trait. Here we report the discovery of a human-accelerated regulatory enhancer (HARE5) of FZD8, a receptor of the Wnt pathway implicated in brain development and size [15, 16]. Using transgenic mice, we demonstrate dramatic differences in human and chimpanzee HARE5 activity, with human HARE5 driving early and robust expression at the onset of corticogenesis. Similar to HARE5 activity, FZD8 is expressed in neural progenitors of the developing neocortex [17-19]. Chromosome conformation capture assays reveal that HARE5 physically and specifically contacts the core Fzd8 promoter in the mouse embryonic neocortex. To assess the phenotypic consequences of HARE5 activity, we generated transgenic mice in which Fzd8 expression is under control of orthologous enhancers (Pt-HARE5::Fzd8 and Hs-HARE5::Fzd8). In comparison to Pt-HARE5::Fzd8, Hs-HARE5::Fzd8 mice showed marked acceleration of neural progenitor cell cycle and increased brain size. Changes in HARE5 function unique to humans thus alter the cell-cycle dynamics of a critical population of stem cells during corticogenesis and may underlie some distinctive anatomical features of the human brain.

Sticky central limit theorems on open books

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fréchet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine.We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky). © Institute of Mathematical Statistics, 2013.

Human Non-neutralizing HIV-1 Envelope Monoclonal Antibodies Limit the Number of Founder Viruses during SHIV Mucosal Infection in Rhesus Macaques.

HIV-1 mucosal transmission begins with virus or virus-infected cells moving through mucus across mucosal epithelium to infect CD4+ T cells. Although broadly neutralizing antibodies (bnAbs) are the type of HIV-1 antibodies that are most likely protective, they are not induced with current vaccine candidates. In contrast, antibodies that do not neutralize primary HIV-1 strains in the TZM-bl infection assay are readily induced by current vaccine candidates and have also been implicated as secondary correlates of decreased HIV-1 risk in the RV144 vaccine efficacy trial. Here, we have studied the capacity of anti-Env monoclonal antibodies (mAbs) against either the immunodominant region of gp41 (7B2 IgG1), the first constant region of gp120 (A32 IgG1), or the third variable loop (V3) of gp120 (CH22 IgG1) to modulate in vivo rectal mucosal transmission of a high-dose simian-human immunodeficiency virus (SHIV-BaL) in rhesus macaques. 7B2 IgG1 or A32 IgG1, each containing mutations to enhance Fc function, was administered passively to rhesus macaques but afforded no protection against productive clinical infection while the positive control antibody CH22 IgG1 prevented infection in 4 of 6 animals. Enumeration of transmitted/founder (T/F) viruses revealed that passive infusion of each of the three antibodies significantly reduced the number of T/F genomes. Thus, some antibodies that bind HIV-1 Env but fail to neutralize virus in traditional neutralization assays may limit the number of T/F viruses involved in transmission without leading to enhancement of viral infection. For one of these mAbs, gp41 mAb 7B2, we provide the first co-crystal structure in complex with a common cyclical loop motif demonstrated to be critical for infection by other retroviruses.

Cell cycle Start is coupled to entry into the yeast metabolic cycle across diverse strains and growth rates.

Cells have evolved oscillators with different frequencies to coordinate periodic processes. Here we studied the interaction of two oscillators, the cell division cycle (CDC) and the yeast metabolic cycle (YMC), in budding yeast. Previous work suggested that the CDC and YMC interact to separate high oxygen consumption (HOC) from DNA replication to prevent genetic damage. To test this hypothesis, we grew diverse strains in chemostat and measured DNA replication and oxygen consumption with high temporal resolution at different growth rates. Our data showed that HOC is not strictly separated from DNA replication; rather, cell cycle Start is coupled with the initiation of HOC and catabolism of storage carbohydrates. The logic of this YMC-CDC coupling may be to ensure that DNA replication and cell division occur only when sufficient cellular energy reserves have accumulated. Our results also uncovered a quantitative relationship between CDC period and YMC period across different strains. More generally, our approach shows how studies in genetically diverse strains efficiently identify robust phenotypes and steer the experimentalist away from strain-specific idiosyncrasies.

Cell cycle start is coupled to entry into the yeast metabolic cycle across diverse strains and growth rates

© 2016 Burnetti et al. Cells have evolved oscillators with different frequencies to coordinate periodic processes. Here we studied the interaction of two oscillators, the cell division cycle (CDC) and the yeast metabolic cycle (YMC), in budding yeast. Previous work suggested that the CDC and YMC interact to separate high oxygen consumption (HOC) from DNA replication to prevent genetic damage. To test this hypothesis, we grew diverse strains in chemostat and measured DNA replication and oxygen consumption with high temporal resolution at different growth rates. Our data showed that HOC is not strictly separated from DNA replication; rather, cell cycle Start is coupled with the initiation of HOC and catabolism of storage carbohydrates. The logic of this YMC-CDC coupling may be to ensure that DNA replication and cell division occur only when sufficient cellular energy reserves have accumulated. Our results also uncovered a quantitative relationship between CDC period and YMC period across different strains. More generally, our approach shows how studies in genetically diverse strains efficiently identify robust phenotypes and steer the experimentalist away from strain-specific idiosyncrasies.