Transit times and mean ages for nonautonomous and autonomous compartmental systems

We develop a theory for transit times and mean ages for nonautonomous compartmental systems. Using the McKendrick-von F\"orster equation, we show that the mean ages of mass in a compartmental system satisfy a linear nonautonomous ordinary differential equation that is exponentially stable. We then define a nonautonomous version of transit time as the mean age of mass leaving the compartmental system at a particular time and show that our nonautonomous theory generalises the autonomous case. We apply these results to study a nine-dimensional nonautonomous compartmental system modeling the terrestrial carbon cycle, which is a modification of the Carnegie-Ames-Stanford approach (CASA) model, and we demonstrate that the nonautonomous versions of transit time and mean age differ significantly from the autonomous quantities when calculated for that model

Phage inducible islands in the gram-positive cocci

The SaPIs are a cohesive subfamily of extremely common phage-inducible chromosomal islands (PICIs) that reside quiescently at specific att sites in the staphylococcal chromosome and are induced by helper phages to excise and replicate. They are usually packaged in small capsids composed of phage virion proteins, giving rise to very high transfer frequencies, which they enhance by interfering with helper phage reproduction. As the SaPIs represent a highly successful biological strategy, with many natural Staphylococcus aureus strains containing two or more, we assumed that similar elements would be widespread in the Gram-positive cocci. On the basis of resemblance to the paradigmatic SaPI genome, we have readily identified large cohesive families of similar elements in the lactococci and pneumococci/streptococci plus a few such elements in Enterococcus faecalis. Based on extensive ortholog analyses, we found that the PICI elements in the four different genera all represent distinct but parallel lineages, suggesting that they represent convergent evolution towards a highly successful lifestyle. We have characterized in depth the enterococcal element, EfCIV583, and have shown that it very closely resembles the SaPIs in functionality as well as in genome organization, setting the stage for expansion of the study of elements of this type. In summary, our findings greatly broaden the PICI family to include elements from at least three genera of cocci

Mathematical Modeling for Studying the Sustainability of Plants Subject to the Stress of Two Distinct Herbivores

Viability of plants, especially endangered species, are usually affected by multiple stressors, including insects, herbivores, environmental factors and other plant species. We present new mathematical models, based on systems of ordinary differential equations, of two distinct herbivore species feeding (two stressors) on the same plant species. The new feature is the explicit functional form modeling the simultaneous feedback interactions (synergistic or additive or antagonistic) between the three species in the ecosystem. The goal is to investigate whether the coexistence of the plant and both herbivore species is possible (a sustainable system) and under which conditions sustainability is feasible. Our theoretical analysis of the novel model without including competitions among the two herbivores reveals that the number of equilibrium states and their local stability depends on the type of interaction between the stressors: synergistic or additive or antagonistic. Our numerical results, based on value of parameters available, suggest that a sustainable system requires significant herbivore inter- or intra-species competition or both types. Additionally, our numerical findings indicate that competition and interaction of additive type promotes coexistence equilibrium states with the highest plant biomass. Furthermore, the system can exhibit periodic behavior and show the potential for multi-stability

Recombination rate and selection strength in HIV intra-patient evolution

The evolutionary dynamics of HIV during the chronic phase of infection is driven by the host immune response and by selective pressures exerted through drug treatment. To understand and model the evolution of HIV quantitatively, the parameters governing genetic diversification and the strength of selection need to be known. While mutation rates can be measured in single replication cycles, the relevant effective recombination rate depends on the probability of coinfection of a cell with more than one virus and can only be inferred from population data. However, most population genetic estimators for recombination rates assume absence of selection and are hence of limited applicability to HIV, since positive and purifying selection are important in HIV evolution. Here, we estimate the rate of recombination and the distribution of selection coefficients from time-resolved sequence data tracking the evolution of HIV within single patients. By examining temporal changes in the genetic composition of the population, we estimate the effective recombination to be r=1.4e-5 recombinations per site and generation. Furthermore, we provide evidence that selection coefficients of at least 15% of the observed non-synonymous polymorphisms exceed 0.8% per generation. These results provide a basis for a more detailed understanding of the evolution of HIV. A particularly interesting case is evolution in response to drug treatment, where recombination can facilitate the rapid acquisition of multiple resistance mutations. With the methods developed here, more precise and more detailed studies will be possible, as soon as data with higher time resolution and greater sample sizes is available.Comment: to appear in PLoS Computational Biolog

Horizontal DNA transfer mechanisms of bacteria as weapons of intragenomic conflict

Horizontal DNA transfer (HDT) is a pervasive mechanism of diversification in many microbial species, but its primary evolutionary role remains controversial. Much recent research has emphasised the adaptive benefit of acquiring novel DNA, but here we argue instead that intragenomic conflict provides a coherent framework for understanding the evolutionary origins of HDT. To test this hypothesis, we developed a mathematical model of a clonally descended bacterial population undergoing HDT through transmission of mobile genetic elements (MGEs) and genetic transformation. Including the known bias of transformation toward the acquisition of shorter alleles into the model suggested it could be an effective means of counteracting the spread of MGEs. Both constitutive and transient competence for transformation were found to provide an effective defence against parasitic MGEs; transient competence could also be effective at permitting the selective spread of MGEs conferring a benefit on their host bacterium. The coordination of transient competence with cell-cell killing, observed in multiple species, was found to result in synergistic blocking of MGE transmission through releasing genomic DNA for homologous recombination while simultaneously reducing horizontal MGE spread by lowering the local cell density. To evaluate the feasibility of the functions suggested by the modelling analysis, we analysed genomic data from longitudinal sampling of individuals carrying Streptococcus pneumoniae. This revealed the frequent within-host coexistence of clonally descended cells that differed in their MGE infection status, a necessary condition for the proposed mechanism to operate. Additionally, we found multiple examples of MGEs inhibiting transformation through integrative disruption of genes encoding the competence machinery across many species, providing evidence of an ongoing "arms race." Reduced rates of transformation have also been observed in cells infected by MGEs that reduce the concentration of extracellular DNA through secretion of DNases. Simulations predicted that either mechanism of limiting transformation would benefit individual MGEs, but also that this tactic's effectiveness was limited by competition with other MGEs coinfecting the same cell. A further observed behaviour we hypothesised to reduce elimination by transformation was MGE activation when cells become competent. Our model predicted that this response was effective at counteracting transformation independently of competing MGEs. Therefore, this framework is able to explain both common properties of MGEs, and the seemingly paradoxical bacterial behaviours of transformation and cell-cell killing within clonally related populations, as the consequences of intragenomic conflict between self-replicating chromosomes and parasitic MGEs. The antagonistic nature of the different mechanisms of HDT over short timescales means their contribution to bacterial evolution is likely to be substantially greater than previously appreciated

Differential branching fraction and angular analysis of Λb0→Λμ+μ−\Lambda^{0}_{b} \rightarrow \Lambda \mu^+\mu^- decays

The differential branching fraction of the rare decay $\Lambda^{0}_{b} \rightarrow \Lambda \mu^+\mu^-$ is measured as a function of $q^{2}$, the square of the dimuon invariant mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of 3.0 \mbox{ fb}^{-1}, collected by the LHCb experiment. Evidence of signal is observed in the $q^2$ region below the square of the $J/\psi$ mass. Integrating over 15 < q^{2} < 20 \mbox{ GeV}^2/c^4 the branching fraction is measured as d\mathcal{B}(\Lambda^{0}_{b} \rightarrow \Lambda \mu^+\mu^-)/dq^2 = (1.18 ^{+ 0.09} _{-0.08} \pm 0.03 \pm 0.27) \times 10^{-7} ( \mbox{GeV}^{2}/c^{4})^{-1}, where the uncertainties are statistical, systematic and due to the normalisation mode, $\Lambda^{0}_{b} \rightarrow J/\psi \Lambda$, respectively. In the $q^2$ intervals where the signal is observed, angular distributions are studied and the forward-backward asymmetries in the dimuon ($A^{l}_{\rm FB}$) and hadron ($A^{h}_{\rm FB}$) systems are measured for the first time. In the range 15 < q^2 < 20 \mbox{ GeV}^2/c^4 they are found to be A^{l}_{\rm FB} = -0.05 \pm 0.09 \mbox{ (stat)} \pm 0.03 \mbox{ (syst)} and A^{h}_{\rm FB} = -0.29 \pm 0.07 \mbox{ (stat)} \pm 0.03 \mbox{ (syst)}.Comment: 27 pages, 10 figures, Erratum adde

Study of B−→DK−π+π−B^{-}\to DK^-\pi^+\pi^- and B−→Dπ−π+π−B^-\to D\pi^-\pi^+\pi^- decays and determination of the CKM angle γ\gamma

We report a study of the suppressed $B^-\to DK^-\pi^+\pi^-$ and favored $B^-\to D\pi^-\pi^+\pi^-$ decays, where the neutral $D$ meson is detected through its decays to the $K^{\mp}\pi^{\pm}$ and CP-even $K^+K^-$ and $\pi^+\pi^-$ final states. The measurement is carried out using a proton-proton collision data sample collected by the LHCb experiment, corresponding to an integrated luminosity of 3.0~fb$^{-1}$. We observe the first significant signals in the CP-even final states of the $D$ meson for both the suppressed $B^-\to DK^-\pi^+\pi^-$ and favored $B^-\to D\pi^-\pi^+\pi^-$ modes, as well as in the doubly Cabibbo-suppressed $D\to K^+\pi^-$ final state of the $B^-\to D\pi^-\pi^+\pi^-$ decay. Evidence for the ADS suppressed decay $B^{-}\to DK^-\pi^+\pi^-$, with $D\to K^+\pi^-$, is also presented. From the observed yields in the $B^-\to DK^-\pi^+\pi^-$, $B^-\to D\pi^-\pi^+\pi^-$ and their charge conjugate decay modes, we measure the value of the weak phase to be $\gamma=(74^{+20}_{-19})^{\rm o}$. This is one of the most precise single-measurement determinations of $\gamma$ to date.Comment: 22 pages, 9 figures; All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-020.htm

Measurement of the mass and lifetime of the Ωb−\Omega_b^- baryon

A proton-proton collision data sample, corresponding to an integrated luminosity of 3 fb$^{-1}$ collected by LHCb at $\sqrt{s}=7$ and 8 TeV, is used to reconstruct $63\pm9$ $\Omega_b^-\to\Omega_c^0\pi^-$, $\Omega_c^0\to pK^-K^-\pi^+$ decays. Using the $\Xi_b^-\to\Xi_c^0\pi^-$, $\Xi_c^0\to pK^-K^-\pi^+$ decay mode for calibration, the lifetime ratio and absolute lifetime of the $\Omega_b^-$ baryon are measured to be \begin{align*} \frac{\tau_{\Omega_b^-}}{\tau_{\Xi_b^-}} &= 1.11\pm0.16\pm0.03, \\ \tau_{\Omega_b^-} &= 1.78\pm0.26\pm0.05\pm0.06~{\rm ps}, \end{align*} where the uncertainties are statistical, systematic and from the calibration mode (for $\tau_{\Omega_b^-}$ only). A measurement is also made of the mass difference, $m_{\Omega_b^-}-m_{\Xi_b^-}$, and the corresponding $\Omega_b^-$ mass, which yields \begin{align*} m_{\Omega_b^-}-m_{\Xi_b^-} &= 247.4\pm3.2\pm0.5~{\rm MeV}/c^2, \\ m_{\Omega_b^-} &= 6045.1\pm3.2\pm 0.5\pm0.6~{\rm MeV}/c^2. \end{align*} These results are consistent with previous measurements.Comment: 11 pages, 5 figures, All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2016-008.htm

Measurements of the branching fractions of B+→ppK+ decays

The branching fractions of the decay B+ → pp̄K+ for different intermediate states are measured using data, corresponding to an integrated luminosity of 1.0 fb-1, collected by the LHCb experiment. The total branching fraction, its charmless component Mpp̄ < 2.85 GeV/c2 and the branching fractions via the resonant cc̄ states η c(1S) and ψ(2S) relative to the decay via a J/ψ intermediate state are [Equation not available: see fulltext.] Upper limits on the B + branching fractions into the η c(2S) meson and into the charmonium-like states X(3872) and X(3915) are also obtained