On the page number of RNA secondary structures with pseudoknots

Let ${\mathcal {S}}$ denote the set of (possibly noncanonical) base pairs {i, j} of an RNA tertiary structure; i.e. ${\{i, j\} \in \mathcal {S}}$ if there is a hydrogen bond between the ith and jth nucleotide. The page number of ${\mathcal {S}}$ , denoted ${\pi(\mathcal {S})}$ , is the minimum number k such that ${\mathcal {S}}$ can be decomposed into a disjoint union of k secondary structures. Here, we show that computing the page number is NP-complete; we describe an exact computation of page number, using constraint programming, and determine the page number of a collection of RNA tertiary structures, for which the topological genus is known. We describe an approximation algorithm from which it follows that ${\omega(\mathcal {S}) \leq \pi(\mathcal {S}) \leq \omega(\mathcal {S}) \cdot \log n}$ , where the clique number of ${\mathcal {S}, \omega(\mathcal {S})}$ , denotes the maximum number of base pairs that pairwise cross each other.     

Nodal distances for rooted phylogenetic trees

Dissimilarity measures for (possibly weighted) phylogenetic trees based on the comparison of their vectors of path lengths between pairs of taxa, have been present in the systematics literature since the early seventies. For rooted phylogenetic trees, however, these vectors can only separate non-weighted binary trees, and therefore these dissimilarity measures are metrics only on this class of rooted phylogenetic trees. In this paper we overcome this problem, by splitting in a suitable way each path length between two taxa into two lengths. We prove that the resulting splitted path lengths matrices single out arbitrary rooted phylogenetic trees with nested taxa and arcs weighted in the set of positive real numbers. This allows the definition of metrics on this general class of rooted phylogenetic trees by comparing these matrices through metrics in spaces M_n(\mathbb R){\mathcal{M}_n(\mathbb {R})} of real-valued n × n matrices. We conclude this paper by establishing some basic facts about the metrics for non-weighted phylogenetic trees defined in this way using L ^p metrics on M_n(\mathbb R){\mathcal{M}_n(\mathbb {R})}, with ${p \in \mathbb {R}_{ >0 }}${p \in \mathbb {R}_{ >0 }}.     

A Within-Host Virus Model with Periodic Multidrug Therapy

This paper is devoted to the investigation of the effects of periodic drug treatment on a standard within-host virus model. We first introduce the basic reproduction ratio for the model, and then show that the infection free equilibrium is globally asymptotically stable, and the disease eventually disappears if $\mathcal{R}_{0} < 1$ , while there exists at least one positive periodic state and the disease persists when $\mathcal{R}_{0}>1$ . We also consider an optimization problem by shifting the phase of these drug efficacy functions. It turns out that shifting the phase can certainly affect the stability of the infection free steady state. A numerical study is performed to illustrate our analytic results.     

Analytic Calculation of Finite-Population Reproductive Numbers for Direct- and Vector-Transmitted Diseases with Homogeneous Mixing

The basic reproductive number, $\mathcal {R}_{0}$ , provides a foundation for evaluating how various factors affect the incidence of infectious diseases. Recently, it has been suggested that, particularly for vector-transmitted diseases, $\mathcal {R}_{0}$ should be modified to account for the effects of finite host population within a single disease transmission generation. Here, we use a transmission factor approach to calculate such “finite-population reproductive numbers,” under the assumption of homogeneous mixing, for both vector-borne and directly transmitted diseases. In the case of vector-borne diseases, we estimate finitepopulation reproductive numbers for both host-to-host and vector-to-vector generations, assuming that the vector population is effectively infinite. We find simple, interpretable formulas for all three of these quantities. In the direct case, we find that finite-population reproductive numbers diverge from $\mathcal {R}_{0}$ before $\mathcal {R}_{0}$ reaches half of the population size. In the vector-transmitted case, we find that the host-to-host number diverges at even lower values of $\mathcal {R}_{0}$ , while the vector-to-vector number diverges very little over realistic parameter ranges.     

Stability of differential susceptibility and infectivity epidemic models

We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio R₀ ￡ 1{\mathcal{R}_0 \leq 1} and the existence and uniqueness of an endemic equilibrium when ${\mathcal{R}_0 >1 }${\mathcal{R}_0 >1 } . We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when ${\mathcal{R}_0 >1 }${\mathcal{R}_0 >1 } . Our results encompass and generalize those of Hyman and Li (J Math Biol 50:626–644, 2005; Math Biosci Eng 3:89–100, 2006).     

A Bovine Babesiosis Model with Dispersion

Bovine Babesiosis (BB) is a tick borne parasitic disease with worldwide over 1.3 billion bovines at potential risk of being infected. The disease, also called tick fever, causes significant mortality from infection by the protozoa upon exposure to infected ticks. An important factor in the spread of the disease is the dispersion or migration of cattle as well as ticks. In this paper, we study the effect of this factor. We introduce a number, $\mathcal{P}$ , a “proliferation index,” which plays the same role as the basic reproduction number $\mathcal{R}_{0}$ with respect to the stability/instability of the disease-free equilibrium, and observe that $\mathcal{P}$ decreases as the dispersion coefficients increase. We prove, mathematically, that if $\mathcal{P}>1$ then the tick fever will remain endemic. We also consider the case where the birth rate of ticks undergoes seasonal oscillations. Based on data from Colombia, South Africa, and Brazil, we use the model to determine the effectiveness of several intervention schemes to control the progression of BB.     

Towards a conceptualization of ETL and physical storage of semantic data warehouses as a service

The data warehouse technology has become the incontestable tool for businesses and organizations to make strategic decisions to ensure their competitively. The construction of a data warehouse ( $\mathcal{D}\mathcal{W}$ ) passes by selecting relevant information sources, extracting relevant data and loading them into the $\mathcal{D}\mathcal{W}$ . These processes require a precise expertise from designers related to logical and physical implementations of information sources, which is not usually an easy task. The diversity and heterogeneity of information sources makes the construction process of the $\mathcal{D}\mathcal{W}$ complex and time consuming. Domain ontologies have been proposed to reduce heterogeneity between sources, platforms, services, etc. They resolve syntax and semantic conflicts. The phenomenon of adopting domain ontologies by organizations creates a new type of databases, called semantic databases ( $\mathcal{S}\mathcal{D}\mathcal{B}$ ). As a consequence, they become a candidate for building the semantic $\mathcal{D}\mathcal{W}$ ( $\mathcal{S}\mathcal{D}\mathcal{W}$ ). To handle the diversity of information sources and hide the implementations aspects of sources, proposing a generic framework for constructing $\mathcal{D}\mathcal{W}$ becomes a necessity. In this paper, we first proposed an ontology-based approach for designing $\mathcal{S}\mathcal {D}\mathcal{B}$ . Secondly, ETL phases are defined at ontological level to hide the implementation details. Thirdly, a storage service for ontologies and its associated data is given. Finally, our proposal is validated through a case study and a tool.     

Stability of a Stochastic Model of an SIR Epidemic with Vaccination

We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination. The model allows for vertical transmission. The stochastic perturbation is associated with the force of infection and is such that the total population size remains constant in time. We prove almost sure positivity of solutions. The main result concerns especially the smaller values of the diffusion parameter, and describes the stability in terms of an analogue \(\mathcal{R}_\sigma\) of the basic reproduction number \(\mathcal{R}_0\) of the underlying deterministic model, with \(\mathcal{R}_\sigma \le \mathcal{R}_0\). We prove that the disease-free equilibrium is almost sure exponentially stable if \(\mathcal{R}_\sigma <1\).     

When does pathogen evolution maximize the basic reproductive number in well-mixed host–pathogen systems?

Pathogen evolution towards the largest basic reproductive number, $\mathcal R _0$ , has been observed in many theoretical models, but this conclusion does not hold universally. Previous studies of host–pathogen systems have defined general conditions under which $\mathcal R _0$ maximization occurs in terms of $\mathcal R _0$ itself. However, it is unclear what constraints these conditions impose on the functional forms of pathogen related processes (e.g. transmission, recover, or mortality) and how those constraints relate to the characteristics of natural systems. Here we focus on well-mixed SIR-type host–pathogen systems and, via a synthesis of results from the literature, we present a set of sufficient mathematical conditions under which evolution maximizes $\mathcal R _0$ . Our conditions are in terms of the functional responses of the system and yield three general biological constraints on when $\mathcal R _0$ maximization will occur. First, there are no genotype-by-environment interactions. Second, the pathogen utilizes a single transmission pathway (i.e. either horizontal, vertical, or vector transmission). Third, when mortality is density dependent: (i) there is a single infectious class that individuals cannot recover from, (ii) mortality in the infectious class is entirely density dependent, and (iii) the rates of recovery, infection progression, and mortality in the exposed classes are independent of the pathogen trait. We discuss how this approach identifies the biological mechanisms that increase the dimension of the environmental feedback and prevent $\mathcal R _0$ maximization.     

Modeling Optimal Age-Specific Vaccination Strategies Against Pandemic Influenza

In the context of pandemic influenza, the prompt and effective implementation of control measures is of great concern for public health officials around the world. In particular, the role of vaccination should be considered as part of any pandemic preparedness plan. The timely production and efficient distribution of pandemic influenza vaccines are important factors to consider in mitigating the morbidity and mortality impact of an influenza pandemic, particularly for those individuals at highest risk of developing severe disease. In this paper, we use a mathematical model that incorporates age-structured transmission dynamics of influenza to evaluate optimal vaccination strategies in the epidemiological context of the Spring 2009 A (H1N1) pandemic in Mexico. We extend previous work on age-specific vaccination strategies to time-dependent optimal vaccination policies by solving an optimal control problem with the aim of minimizing the number of infected individuals over the course of a single pandemic wave. Optimal vaccination policies are computed and analyzed under different vaccination coverages (21%–77%) and different transmissibility levels (R₀\mathcal{R}_{0} in the range of 1.8–3). The results suggest that the optimal vaccination can be achieved by allocating most vaccines to young adults (20–39 yr) followed by school age children (6–12 yr) when the vaccination coverage does not exceed 30%. For higher R₀\mathcal{R}_{0} levels ($\mathcal{R}_{0}>=2.4$\mathcal{R}_{0}>=2.4), or a time delay in the implementation of vaccination (>90 days), a quick and substantial decrease in the pool of susceptibles would require the implementation of an intensive vaccination protocol within a shorter period of time. Our results indicate that optimal age-specific vaccination rates are significantly associated with R₀\mathcal{R}_{0}, the amount of vaccines available and the timing of vaccination.     

Coupling-induced population synchronization in an excitatory population of subthreshold Izhikevich neurons

We consider an excitatory population of subthreshold Izhikevich neurons which exhibit noise-induced firings. By varying the coupling strength J, we investigate population synchronization between the noise-induced firings which may be used for efficient cognitive processing such as sensory perception, multisensory binding, selective attention, and memory formation. As J is increased, rich types of population synchronization (e.g., spike, burst, and fast spike synchronization) are found to occur. Transitions between population synchronization and incoherence are well described in terms of an order parameter $\mathcal{O}$ . As a final step, the coupling induces oscillator death (quenching of noise-induced spikings) because each neuron is attracted to a noisy equilibrium state. The oscillator death leads to a transition from firing to non-firing states at the population level, which may be well described in terms of the time-averaged population spike rate $\overline{R}$ . In addition to the statistical-mechanical analysis using $\mathcal{O}$ and $\overline{R}$ , each population and individual state are also characterized by using the techniques of nonlinear dynamics such as the raster plot of neural spikes, the time series of the membrane potential, and the phase portrait. We note that population synchronization of noise-induced firings may lead to emergence of synchronous brain rhythms in a noisy environment, associated with diverse cognitive functions.     

A mathematical model for assessing control strategies against West Nile virus

Since its incursion into North America in 1999, West Nile virus (WNV) has spread rapidly across the continent resulting in numerous human infections and deaths. Owing to the absence of an effective diagnostic test and therapeutic treatment against WNV, public health officials have focussed on the use of preventive measures in an attempt to halt the spread of WNV in humans. The aim of this paper is to use mathematical modelling and analysis to assess two main anti-WNV preventive strategies, namely: mosquito reduction strategies and personal protection. We propose a single-season ordinary differential equation model for the transmission dynamics of WNV in a mosquito-bird-human community, with birds as reservoir hosts and culicine mosquitoes as vectors. The model exhibits two equilibria; namely the disease-free equilibrium and a unique endemic equilibrium. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if a certain threshold quantity , which depends solely on parameters associated with the mosquito-bird cycle, is less than unity. The public health implication of this is that WNV can be eradicated from the mosquito-bird cycle (and, consequently, from the human population) if the adopted mosquito reduction strategy (or strategies) can make . On the other hand, it is shown, using a novel and robust technique that is based on the theory of monotone dynamical systems coupled with a regular perturbation argument and a Liapunov function, that if , then the unique endemic equilibrium is globally stable for small WNV-induced avian mortality. Thus, in this case, WNV persists in the mosquito-bird population.     

X-ray crystal structure of a mutant assimilatory nitrite reductase that shows sulfite reductase-like activity

Assimilatory nitrite reductase (aNiR) reduces nitrite ions (NO$\rm{{_{2}^{-}}}$) to ammonium ions (NH$\rm{{_{4}^{+}}}$), whereas assimilatory sulfite reductase reduces sulfite (SO$\rm{{_{3}^{2-}}}$) to hydrogen sulfide (HS(-) ). Although aNiR can also reduce SO$\rm{{_{3}^{2-}}}$, its activity is much lower than when NO$\rm{{_{2}^{-}}}$ is reduced as the substrate. To increase the SO$\rm{{_{3}^{2-}}}$-reduction activity of aNiR, we performed a N226K mutation of Nii3, a representative aNiR. The resulting Nii3-N226K variant could bind non-native targets, SO$\rm{{_{3}^{2-}}}$, and HCO$\rm{{_{3}^{-}}}$, in addition to its native target, i.e., NO$\rm{{_{2}^{-}}}$. We have determined the high-resolution structure of Nii3-N226K in its apo-state and in complex with SO$\rm{{_{3}^{2-}}}$, NO$\rm{{_{2}^{-}}}$, and HCO$\rm{{_{3}^{-}}}$. This analysis revealed conformational changes of Lys226 and the adjacent Lys224 upon binding of SO$\rm{{_{3}^{2-}}}$, but not NO$\rm{{_{2}^{-}}}$. In contrast, HCO$\rm{{_{3}^{-}}}$ binding induced a conformational change at Arg179. After replacing Asn226 with a positively charged Lys, aNiR showed affinity for several anions. A comparison of all ligand-bound structures for Nii3-N226K revealed that structural changes in the active site depend on the size of the substrate.     

Dynamics of an epidemic model with non-local infections for diseases with latency over a patchy environment

In this paper, with the assumptions that an infectious disease in a population has a fixed latent period and the latent individuals of the population may disperse, we formulate an SIR model with a simple demographic structure for the population living in an n-patch environment (cities, towns, or countries, etc.). The model is given by a system of delay differential equations with a fixed delay accounting for the latency and a non-local term caused by the mobility of the individuals during the latent period. Assuming irreducibility of the travel matrices of the infection related classes, an expression for the basic reproduction number R₀{\mathcal{R}_0} is derived, and it is shown that the disease free equilibrium is globally asymptotically stable if R₀ < 1{\mathcal{R}_0 < 1} , and becomes unstable if ${\mathcal{R}_0 > 1}${\mathcal{R}_0 > 1} . In the latter case, there is at least one endemic equilibrium and the disease will be uniformly persistent. When n = 2, two special cases allowing reducible travel matrices are considered to illustrate joint impact of the disease latency and population mobility on the disease dynamics. In addition to the existence of the disease free equilibrium and interior endemic equilibrium, the existence of a boundary equilibrium and its stability are discussed for these two special cases.     

Investigating alcohol consumption as a risk factor for HIV transmission in heterosexual settings in sub-Saharan African communities

Alcohol consumption and abuse is widespread in sub-Saharan Africa where most HIV infections occur and has been associated with risky sexual behaviors. It may therefore be one of the most common, potentially modifiable HIV risk factors in this region. A deterministic system of ordinary differential equations incorporating heterogeneity and biased sexual preferences is formulated to assess the effects of alcohol consumption on the transmission dynamics of the disease in heterosexual settings. Extensive qualitative analysis of the model is carried out and epidemic threshold such as the alcohol-induced reproductive number $({\mathcal{R}}_{A})$ , and equilibria are derived and their stabilities examined. The disease-free equilibrium is found to be globally attracting whenever the reproductive number is less than unity. In the model, heterosexuality is the source of transmissions, and therefore, targeting a reduction of the basic reproductive number $({\mathcal{R}}_{0})$ should be primary objective for any intervention programme. We show that the preference to form partnerships amongst the heterogeneous groups influences the severity of disease and its evolution, and consequently the rate of partnership formation between females and alcohol consumers and their relative infectiousness over nondrinkers has a huge positive correlation with the alcohol-induced reproductive number and hence the epidemic. The proportion or absolute number of drinkers is shown to have minimal influence on the disease dynamics, and in a community with alcohol consumers, it is more prudent to reduce their risk sexual behavior rather than to fight the spread of alcohol consumption. Thus, intervention measures targeted at reducing heterogeneous group interactions and behavior change are the key to disease control in these settings.     

Fluid flow in the osteocyte mechanical environment: a fluid–structure interaction approach

Osteocytes are believed to be the primary sensor of mechanical stimuli in bone, which orchestrate osteoblasts and osteoclasts to adapt bone structure and composition to meet physiological loading demands. Experimental studies to quantify the mechanical environment surrounding bone cells are challenging, and as such, computational and theoretical approaches have modelled either the solid or fluid environment of osteocytes to predict how these cells are stimulated in vivo. Osteocytes are an elastic cellular structure that deforms in response to the external fluid flow imposed by mechanical loading. This represents a most challenging multi-physics problem in which fluid and solid domains interact, and as such, no previous study has accounted for this complex behaviour. The objective of this study is to employ fluid–structure interaction (FSI) modelling to investigate the complex mechanical environment of osteocytes in vivo. Fluorescent staining of osteocytes was performed in order to visualise their native environment and develop geometrically accurate models of the osteocyte in vivo. By simulating loading levels representative of vigorous physiological activity ( $3,000\,\upmu \upvarepsilon $ compression and 300 Pa pressure gradient), we predict average interstitial fluid velocities $(\sim 60.5\,\upmu \text{ m/s })$ and average maximum shear stresses $(\sim 11\, \text{ Pa })$ surrounding osteocytes in vivo. Interestingly, these values occur in the canaliculi around the osteocyte cell processes and are within the range of stimuli known to stimulate osteogenic responses by osteoblastic cells in vitro. Significantly our results suggest that the greatest mechanical stimulation of the osteocyte occurs in the cell processes, which, cell culture studies have indicated, is the most mechanosensitive area of the cell. These are the first computational FSI models to simulate the complex multi-physics mechanical environment of osteocyte in vivo and provide a deeper understanding of bone mechanobiology.     

Influence of anions on metal adsorption by Rhizopus arrhizus biomass

The presence of anions in solution was found to inhibit the uptake of La(3+), Cd(2+), Pb(2+), UO(2+) (2), and Ag(+) by Rhizopus arrhizus biomass. The effects ranged from total inhibition of Cd(2+) and Pb(2+) uptake at equimolar concentrations of EDTA to no change in uptake of La(3+) or UO(2+) (2) at 12-fold molar excesses of Cl(-) or CO(2-) (3). No anion was found to enhance metal uptake levels, and the degree of inhibition generally followed the series: \documentclass{article}\pagestyle{empty}\begin{document}$${\rm EDTA } \ge \ge {\rm SO}_{;{;{;{\rm 4} } } };{{\rm 2} - } \ge {\rm Cl}; - \ge {\rm PO}_{;{;{;{\rm 4} } } };{{\rm 3} - } \ge {\rm glutamate} \ge {\rm CO}_{;{;{\rm 3} } };{{\rm 2} - } $$\end{document} The chemical equilibrium model REDEQL2 was adapted to treat metal uptake by R. arrhizus biomass and used to predict the effects of anions in solution. Comparisons with the experimental results are made and discussed in light of the assumptions underlying the model.     

Model-consistent estimation of the basic reproduction number from the incidence of an emerging infection

We investigate the merit of deriving an estimate of the basic reproduction number early in an outbreak of an (emerging) infection from estimates of the incidence and generation interval only. We compare such estimates of with estimates incorporating additional model assumptions, and determine the circumstances under which the different estimates are consistent. We show that one has to be careful when using observed exponential growth rates to derive an estimate of , and we quantify the discrepancies that arise.